Data.SBV

(The sbv library is hosted at http://github.com/LeventErkok/sbv. Comments, bug reports, and patches are always welcome.)

SBV: SMT Based Verification

Express properties about Haskell programs and automatically prove them using SMT solvers.

>>> prove $ \x -> x `shiftL` 2 .== 4 * (x :: SWord8)
Q.E.D.

>>> prove $ \x -> x `shiftL` 2 .== 2 * (x :: SWord8)
Falsifiable. Counter-example:
  s0 = 32 :: Word8

The function prove has the following type:

    prove :: Provable a => a -> IO ThmResult

The class Provable comes with instances for n-ary predicates, for arbitrary n. The predicates are just regular Haskell functions over symbolic types listed below. Functions for checking satisfiability (sat and allSat) are also provided.

The sbv library introduces the following symbolic types:

• SBool: Symbolic Booleans (bits).
• SWord8, SWord16, SWord32, SWord64: Symbolic Words (unsigned).
• SInt8, SInt16, SInt32, SInt64: Symbolic Ints (signed).
• SInteger: Unbounded signed integers.
• SReal: Algebraic-real numbers
• SFloat: IEEE-754 single-precision floating point values
• SDouble: IEEE-754 double-precision floating point values
• SChar, SString, RegExp: Characters, strings and regular expressions
• SList: Symbolic lists (which can be nested)
• STuple, STuple2, STuple3, .., STuple8 : Symbolic tuples (upto 8-tuples, can be nested)
• SEither: Symbolic sums
• SMaybe: Symbolic optional values
• SSet: Symbolic sets
• SArray, SFunArray: Flat arrays of symbolic values.
• Symbolic polynomials over GF(2^n), polynomial arithmetic, and CRCs.
• Uninterpreted constants and functions over symbolic values, with user defined SMT-Lib axioms.
• Uninterpreted sorts, and proofs over such sorts, potentially with axioms.
• Model validation: SBV can validate models returned by solvers, which allows for protection against bugs in SMT solvers and SBV itself. (See the validateModel parameter.)

The user can construct ordinary Haskell programs using these types, which behave very similar to their concrete counterparts. In particular these types belong to the standard classes Num, Bits, custom versions of Eq (EqSymbolic) and Ord (OrdSymbolic), along with several other custom classes for simplifying programming with symbolic values. The framework takes full advantage of Haskell's type inference to avoid many common mistakes.

Furthermore, predicates (i.e., functions that return SBool) built out of these types can also be:

• proven correct via an external SMT solver (the prove function)
• checked for satisfiability (the sat, allSat functions)
• used in synthesis (the sat function with existentials)
• quick-checked

If a predicate is not valid, prove will return a counterexample: An assignment to inputs such that the predicate fails. The sat function will return a satisfying assignment, if there is one. The allSat function returns all satisfying assignments.

The sbv library uses third-party SMT solvers via the standard SMT-Lib interface: http://smtlib.cs.uiowa.edu/

The SBV library is designed to work with any SMT-Lib compliant SMT-solver. Currently, we support the following SMT-Solvers out-of-the box:

• ABC from University of Berkeley: http://www.eecs.berkeley.edu/~alanmi/abc/
• CVC4 from Stanford: http://cvc4.cs.stanford.edu/web/
• Boolector from Johannes Kepler University: http://fmv.jku.at/boolector/
• MathSAT from Fondazione Bruno Kessler and DISI-University of Trento: http://mathsat.fbk.eu/
• Yices from SRI: http://yices.csl.sri.com/
• Z3 from Microsoft: http://github.com/Z3Prover/z3/wiki

SBV requires recent versions of these solvers; please see the file SMTSolverVersions.md in the source distribution for specifics.

SBV also allows calling these solvers in parallel, either getting results from multiple solvers or returning the fastest one. (See proveWithAll, proveWithAny, etc.)

Support for other compliant solvers can be added relatively easily, please get in touch if there is a solver you'd like to see included.

Documentation

The SBV library is really two things:

• A framework for writing symbolic programs in Haskell, i.e., programs operating on symbolic values along with the usual concrete counterparts.
• A framework for proving properties of such programs using SMT solvers.

The programming goal of SBV is to provide a seamless experience, i.e., let people program in the usual Haskell style without distractions of symbolic coding. While Haskell helps in some aspects (the Num and Bits classes simplify coding), it makes life harder in others. For instance, if-then-else only takes Bool as a test in Haskell, and comparisons (> etc.) only return Bools. Clearly we would like these values to be symbolic (i.e., SBool), thus stopping us from using some native Haskell constructs. When symbolic versions of operators are needed, they are typically obtained by prepending a dot, for instance == becomes .==. Care has been taken to make the transition painless. In particular, any Haskell program you build out of symbolic components is fully concretely executable within Haskell, without the need for any custom interpreters. (They are truly Haskell programs, not AST's built out of pieces of syntax.) This provides for an integrated feel of the system, one of the original design goals for SBV.

Incremental query mode: SBV provides a wide variety of ways to utilize SMT-solvers, without requiring the user to deal with the solvers themselves. While this mode is convenient, advanced users might need access to the underlying solver at a lower level. For such use cases, SBV allows users to have an interactive session: The user can issue commands to the solver, inspect the values/results, and formulate new constraints. This advanced feature is available through the Data.SBV.Control module, where most SMTLib features are made available via a typed-API.

Symbolic types

Booleans

type SBool = SBV Bool

A symbolic boolean/bit

Boolean values and functions

sTrue :: SBool

Symbolic True

sFalse :: SBool

Symbolic False

sNot :: SBool -> SBool

Symbolic boolean negation

(.&&) :: SBool -> SBool -> SBool infixr 3

Symbolic conjunction

(.||) :: SBool -> SBool -> SBool infixr 2

Symbolic disjunction

(.<+>) :: SBool -> SBool -> SBool infixl 6

Symbolic logical xor

(.~&) :: SBool -> SBool -> SBool infixr 3

Symbolic nand

(.~|) :: SBool -> SBool -> SBool infixr 2

Symbolic nor

(.=>) :: SBool -> SBool -> SBool infixr 1

Symbolic implication

(.<=>) :: SBool -> SBool -> SBool infixr 1

Symbolic boolean equivalence

fromBool :: Bool -> SBool

Conversion from Bool to SBool

oneIf :: (Ord a, Num a, SymVal a) => SBool -> SBV a

Returns 1 if the boolean is sTrue, otherwise 0.

Logical aggregations

sAnd :: [SBool] -> SBool

Generalization of and

sOr :: [SBool] -> SBool

Generalization of or

sAny :: (a -> SBool) -> [a] -> SBool

Generalization of any

sAll :: (a -> SBool) -> [a] -> SBool

Generalization of all

Bit-vectors

Unsigned bit-vectors

type SWord8 = SBV Word8

8-bit unsigned symbolic value

type SWord16 = SBV Word16

16-bit unsigned symbolic value

type SWord32 = SBV Word32

32-bit unsigned symbolic value

type SWord64 = SBV Word64

64-bit unsigned symbolic value

Signed bit-vectors

type SInt8 = SBV Int8

8-bit signed symbolic value, 2's complement representation

type SInt16 = SBV Int16

16-bit signed symbolic value, 2's complement representation

type SInt32 = SBV Int32

32-bit signed symbolic value, 2's complement representation

type SInt64 = SBV Int64

64-bit signed symbolic value, 2's complement representation

Unbounded integers

The SBV library supports unbounded signed integers with the type SInteger, which are not subject to overflow/underflow as it is the case with the bounded types, such as SWord8, SInt16, etc. However, some bit-vector based operations are not supported for the SInteger type while in the verification mode. That is, you can use these operations on SInteger values during normal programming/simulation. but the SMT translation will not support these operations since there corresponding operations are not supported in SMT-Lib. Note that this should rarely be a problem in practice, as these operations are mostly meaningful on fixed-size bit-vectors. The operations that are restricted to bounded word/int sizes are:

• Rotations and shifts: rotateL, rotateR, shiftL, shiftR
• Bitwise logical ops: .&., .|., xor, complement
• Extraction and concatenation: split, #, and extend (see the Splittable class)

Usual arithmetic (+, -, *, sQuotRem, sQuot, sRem, sDivMod, sDiv, sMod) and logical operations (.<, .<=, .>, .>=, .==, ./=) operations are supported for SInteger fully, both in programming and verification modes.

type SInteger = SBV Integer

Infinite precision signed symbolic value

Floating point numbers

Floating point numbers are defined by the IEEE-754 standard; and correspond to Haskell's Float and Double types. For SMT support with floating-point numbers, see the paper by Rummer and Wahl: http://www.philipp.ruemmer.org/publications/smt-fpa.pdf.

type SFloat = SBV Float

IEEE-754 single-precision floating point numbers

type SDouble = SBV Double

IEEE-754 double-precision floating point numbers

Algebraic reals

Algebraic reals are roots of single-variable polynomials with rational coefficients. (See http://en.wikipedia.org/wiki/Algebraic_number.) Note that algebraic reals are infinite precision numbers, but they do not cover all real numbers. (In particular, they cannot represent transcendentals.) Some irrational numbers are algebraic (such as sqrt 2), while others are not (such as pi and e).

SBV can deal with real numbers just fine, since the theory of reals is decidable. (See http://smtlib.cs.uiowa.edu/theories-Reals.shtml.) In addition, by leveraging backend solver capabilities, SBV can also represent and solve non-linear equations involving real-variables. (For instance, the Z3 SMT solver, supports polynomial constraints on reals starting with v4.0.)

type SReal = SBV AlgReal

Infinite precision symbolic algebraic real value

data AlgReal

Algebraic reals. Note that the representation is left abstract. We represent rational results explicitly, while the roots-of-polynomials are represented implicitly by their defining equation

Instances

Eq AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

(==) :: AlgReal -> AlgReal -> Bool

(/=) :: AlgReal -> AlgReal -> Bool

Fractional AlgReal

NB: Following the other types we have, we require `a/0` to be `0` for all a.

Defined in Data.SBV.Core.AlgReals

Methods

(/) :: AlgReal -> AlgReal -> AlgReal

recip :: AlgReal -> AlgReal

fromRational :: Rational -> AlgReal

Num AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

(+) :: AlgReal -> AlgReal -> AlgReal

(-) :: AlgReal -> AlgReal -> AlgReal

(*) :: AlgReal -> AlgReal -> AlgReal

negate :: AlgReal -> AlgReal

abs :: AlgReal -> AlgReal

signum :: AlgReal -> AlgReal

fromInteger :: Integer -> AlgReal

Ord AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

compare :: AlgReal -> AlgReal -> Ordering

(<) :: AlgReal -> AlgReal -> Bool

(<=) :: AlgReal -> AlgReal -> Bool

(>) :: AlgReal -> AlgReal -> Bool

(>=) :: AlgReal -> AlgReal -> Bool

max :: AlgReal -> AlgReal -> AlgReal

min :: AlgReal -> AlgReal -> AlgReal

Real AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

toRational :: AlgReal -> Rational

Show AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

showsPrec :: Int -> AlgReal -> ShowS

show :: AlgReal -> String

showList :: [AlgReal] -> ShowS

Arbitrary AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

arbitrary :: Gen AlgReal

shrink :: AlgReal -> [AlgReal]

Random AlgReal

Defined in Data.SBV.Core.AlgReals

Methods

randomR :: RandomGen g => (AlgReal, AlgReal) -> g -> (AlgReal, g)

random :: RandomGen g => g -> (AlgReal, g)

randomRs :: RandomGen g => (AlgReal, AlgReal) -> g -> [AlgReal]

randoms :: RandomGen g => g -> [AlgReal]

randomRIO :: (AlgReal, AlgReal) -> IO AlgReal

randomIO :: IO AlgReal

HasKind AlgReal

Defined in Data.SBV.Core.Kind

Methods

kindOf :: AlgReal -> Kind

hasSign :: AlgReal -> Bool

intSizeOf :: AlgReal -> Int

isBoolean :: AlgReal -> Bool

isBounded :: AlgReal -> Bool

isReal :: AlgReal -> Bool

isFloat :: AlgReal -> Bool

isDouble :: AlgReal -> Bool

isUnbounded :: AlgReal -> Bool

isUninterpreted :: AlgReal -> Bool

isChar :: AlgReal -> Bool

isString :: AlgReal -> Bool

isList :: AlgReal -> Bool

isSet :: AlgReal -> Bool

isTuple :: AlgReal -> Bool

isMaybe :: AlgReal -> Bool

isEither :: AlgReal -> Bool

showType :: AlgReal -> String

SymVal AlgReal

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV AlgReal)

literal :: AlgReal -> SBV AlgReal

fromCV :: CV -> AlgReal

isConcretely :: SBV AlgReal -> (AlgReal -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV AlgReal)

forall_ :: MonadSymbolic m => m (SBV AlgReal)

mkForallVars :: MonadSymbolic m => Int -> m [SBV AlgReal]

exists :: MonadSymbolic m => String -> m (SBV AlgReal)

exists_ :: MonadSymbolic m => m (SBV AlgReal)

mkExistVars :: MonadSymbolic m => Int -> m [SBV AlgReal]

free :: MonadSymbolic m => String -> m (SBV AlgReal)

free_ :: MonadSymbolic m => m (SBV AlgReal)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV AlgReal]

symbolic :: MonadSymbolic m => String -> m (SBV AlgReal)

symbolics :: MonadSymbolic m => [String] -> m [SBV AlgReal]

unliteral :: SBV AlgReal -> Maybe AlgReal

isConcrete :: SBV AlgReal -> Bool

isSymbolic :: SBV AlgReal -> Bool

SatModel AlgReal

AlgReal as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (AlgReal, [CV])

cvtModel :: (AlgReal -> Maybe b) -> Maybe (AlgReal, [CV]) -> Maybe (b, [CV])

SMTValue AlgReal

Defined in Data.SBV.Control.Utils

Methods

sexprToVal :: SExpr -> Maybe AlgReal

Metric AlgReal

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace AlgReal :: Type

Methods

toMetricSpace :: SBV AlgReal -> SBV (MetricSpace AlgReal)

fromMetricSpace :: SBV (MetricSpace AlgReal) -> SBV AlgReal

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV AlgReal -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV AlgReal -> m ()

IEEEFloatConvertible AlgReal

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV AlgReal

toSFloat :: SRoundingMode -> SBV AlgReal -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV AlgReal

toSDouble :: SRoundingMode -> SBV AlgReal -> SDouble

type MetricSpace AlgReal

Defined in Data.SBV.Core.Model

type MetricSpace AlgReal = AlgReal

sRealToSInteger :: SReal -> SInteger

Convert an SReal to an SInteger. That is, it computes the largest integer n that satisfies sIntegerToSReal n <= r essentially giving us the floor.

For instance, 1.3 will be 1, but -1.3 will be -2.

Characters, Strings and Regular Expressions

Support for characters, strings, and regular expressions (intial version contributed by Joel Burget) adds support for QF_S logic, described here: http://smtlib.cs.uiowa.edu/theories-UnicodeStrings.shtml and here: http://rise4fun.com/z3/tutorialcontent/sequences. Note that this logic is still not part of official SMTLib (as of March 2018), so it should be considered experimental.

See Data.SBV.Char, Data.SBV.String, Data.SBV.RegExp for related functions.

type SChar = SBV Char

A symbolic character. Note that, as far as SBV's symbolic strings are concerned, a character is currently an 8-bit unsigned value, corresponding to the ISO-8859-1 (Latin-1) character set: http://en.wikipedia.org/wiki/ISO/IEC_8859-1. A Haskell Char, on the other hand, is based on unicode. Therefore, there isn't a 1-1 correspondence between a Haskell character and an SBV character for the time being. This limitation is due to the SMT-solvers only supporting this particular subset. However, there is a pending proposal to add support for unicode, and SBV will track these changes to have full unicode support as solvers become available. For details, see: http://smtlib.cs.uiowa.edu/theories-UnicodeStrings.shtml

type SString = SBV String

A symbolic string. Note that a symbolic string is not a list of symbolic characters, that is, it is not the case that SString = [SChar], unlike what one might expect following Haskell strings. An SString is a symbolic value of its own, of possibly arbitrary but finite length, and internally processed as one unit as opposed to a fixed-length list of characters.

Symbolic lists

Support for symbolic lists (intial version contributed by Joel Burget) adds support for sequence support, described here: http://rise4fun.com/z3/tutorialcontent/sequences. Note that this logic is still not part of official SMTLib (as of March 2018), so it should be considered experimental.

See Data.SBV.List for related functions.

type SList a = SBV [a]

A symbolic list of items. Note that a symbolic list is not a list of symbolic items, that is, it is not the case that SList a = [a], unlike what one might expect following haskell lists/sequences. An SList is a symbolic value of its own, of possibly arbitrary but finite length, and internally processed as one unit as opposed to a fixed-length list of items. Note that lists can be nested, i.e., we do allow lists of lists of ... items.

Tuples

Tuples can be used as symbolic values. This is useful in combination with lists, for example SBV [(Integer, String)] is a valid type. These types can be arbitrarily nested, eg SBV [(Integer, [(Char, (Integer, String))])]. Instances of upto 8-tuples are provided.

type STuple a b = SBV (a, b)

Symbolic 2-tuple. NB. STuple and STuple2 are equivalent.

type STuple2 a b = SBV (a, b)

Symbolic 2-tuple. NB. STuple and STuple2 are equivalent.

type STuple3 a b c = SBV (a, b, c)

Symbolic 3-tuple.

type STuple4 a b c d = SBV (a, b, c, d)

Symbolic 4-tuple.

type STuple5 a b c d e = SBV (a, b, c, d, e)

Symbolic 5-tuple.

type STuple6 a b c d e f = SBV (a, b, c, d, e, f)

Symbolic 6-tuple.

type STuple7 a b c d e f g = SBV (a, b, c, d, e, f, g)

Symbolic 7-tuple.

type STuple8 a b c d e f g h = SBV (a, b, c, d, e, f, g, h)

Symbolic 8-tuple.

Sum types

type SMaybe a = SBV (Maybe a)

Symbolic Maybe

type SEither a b = SBV (Either a b)

Symbolic Either

Sets

data RCSet a

A RCSet is either a regular set or a set given by its complement from the corresponding universal set.

Constructors

RegularSet (Set a)

ComplementSet (Set a)

Instances

Show a => Show (RCSet a)

Show instance. Regular sets are shown as usual. Complements are shown "U -" notation.

Defined in Data.SBV.Core.Concrete

Methods

showsPrec :: Int -> RCSet a -> ShowS

show :: RCSet a -> String

showList :: [RCSet a] -> ShowS

HasKind a => HasKind (RCSet a)

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: RCSet a -> Kind

hasSign :: RCSet a -> Bool

intSizeOf :: RCSet a -> Int

isBoolean :: RCSet a -> Bool

isBounded :: RCSet a -> Bool

isReal :: RCSet a -> Bool

isFloat :: RCSet a -> Bool

isDouble :: RCSet a -> Bool

isUnbounded :: RCSet a -> Bool

isUninterpreted :: RCSet a -> Bool

isChar :: RCSet a -> Bool

isString :: RCSet a -> Bool

isList :: RCSet a -> Bool

isSet :: RCSet a -> Bool

isTuple :: RCSet a -> Bool

isMaybe :: RCSet a -> Bool

isEither :: RCSet a -> Bool

showType :: RCSet a -> String

(Ord a, SymVal a) => SymVal (RCSet a)

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (RCSet a))

literal :: RCSet a -> SBV (RCSet a)

fromCV :: CV -> RCSet a

isConcretely :: SBV (RCSet a) -> (RCSet a -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (RCSet a))

forall_ :: MonadSymbolic m => m (SBV (RCSet a))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (RCSet a)]

exists :: MonadSymbolic m => String -> m (SBV (RCSet a))

exists_ :: MonadSymbolic m => m (SBV (RCSet a))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (RCSet a)]

free :: MonadSymbolic m => String -> m (SBV (RCSet a))

free_ :: MonadSymbolic m => m (SBV (RCSet a))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (RCSet a)]

symbolic :: MonadSymbolic m => String -> m (SBV (RCSet a))

symbolics :: MonadSymbolic m => [String] -> m [SBV (RCSet a)]

unliteral :: SBV (RCSet a) -> Maybe (RCSet a)

isConcrete :: SBV (RCSet a) -> Bool

isSymbolic :: SBV (RCSet a) -> Bool

(Ord a, SymVal a) => SMTValue (RCSet a)

Defined in Data.SBV.Control.Utils

Methods

sexprToVal :: SExpr -> Maybe (RCSet a)

type SSet a = SBV (RCSet a)

Symbolic Set. Note that we use RCSet, which supports both regular sets and complements, i.e., those obtained from the universal set (of the right type) by removing elements.

Arrays of symbolic values

class SymArray array where

Flat arrays of symbolic values An array a b is an array indexed by the type SBV a, with elements of type SBV b.

If a default value is supplied, then all the array elements will be initialized to this value. Otherwise, they will be left unspecified, i.e., a read from an unwritten location will produce an uninterpreted constant.

While it's certainly possible for user to create instances of SymArray, the SArray and SFunArray instances already provided should cover most use cases in practice. Note that there are a few differences between these two models in terms of use models:

• SArray produces SMTLib arrays, and requires a solver that understands the array theory. SFunArray is internally handled, and thus can be used with any solver. (Note that all solvers except abc support arrays, so this isn't a big decision factor.)
• For both arrays, if a default value is supplied, then reading from uninitialized cell will return that value. If the default is not given, then reading from uninitialized cells is still OK for both arrays, and will produce an uninterpreted constant in both cases.
• Only SArray supports checking equality of arrays. (That is, checking if an entire array is equivalent to another.) SFunArrays cannot be checked for equality. In general, checking wholesale equality of arrays is a difficult decision problem and should be avoided if possible.
• Only SFunArray supports compilation to C. Programs using SArray will not be accepted by the C-code generator.
• You cannot use quickcheck on programs that contain these arrays. (Neither SArray nor SFunArray.)
• With SArray, SBV transfers all array-processing to the SMT-solver. So, it can generate programs more quickly, but they might end up being too hard for the solver to handle. With SFunArray, SBV only generates code for individual elements and the array itself never shows up in the resulting SMTLib program. This puts more onus on the SBV side and might have some performance impacts, but it might generate problems that are easier for the SMT solvers to handle.

As a rule of thumb, try SArray first. These should generate compact code. However, if the backend solver has hard time solving the generated problems, switch to SFunArray. If you still have issues, please report so we can see what the problem might be!

Methods

readArray :: array a b -> SBV a -> SBV b

Read the array element at a

writeArray :: SymVal b => array a b -> SBV a -> SBV b -> array a b

Update the element at a to be b

mergeArrays :: SymVal b => SBV Bool -> array a b -> array a b -> array a b

Merge two given arrays on the symbolic condition Intuitively: mergeArrays cond a b = if cond then a else b. Merging pushes the if-then-else choice down on to elements

Instances

SymArray SFunArray

Defined in Data.SBV.Core.Data

Methods

newArray_ :: (MonadSymbolic m, HasKind a, HasKind b) => Maybe (SBV b) -> m (SFunArray a b)

newArray :: (MonadSymbolic m, HasKind a, HasKind b) => String -> Maybe (SBV b) -> m (SFunArray a b)

readArray :: SFunArray a b -> SBV a -> SBV b

writeArray :: SymVal b => SFunArray a b -> SBV a -> SBV b -> SFunArray a b

mergeArrays :: SymVal b => SBV Bool -> SFunArray a b -> SFunArray a b -> SFunArray a b

newArrayInState :: (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (SFunArray a b)

SymArray SArray

Defined in Data.SBV.Core.Data

Methods

newArray_ :: (MonadSymbolic m, HasKind a, HasKind b) => Maybe (SBV b) -> m (SArray a b)

newArray :: (MonadSymbolic m, HasKind a, HasKind b) => String -> Maybe (SBV b) -> m (SArray a b)

readArray :: SArray a b -> SBV a -> SBV b

writeArray :: SymVal b => SArray a b -> SBV a -> SBV b -> SArray a b

mergeArrays :: SymVal b => SBV Bool -> SArray a b -> SArray a b -> SArray a b

newArrayInState :: (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (SArray a b)

newArray_ :: (SymArray array, HasKind a, HasKind b) => Maybe (SBV b) -> Symbolic (array a b)

Create a new anonymous array, possibly with a default initial value.

NB. For a version which generalizes over the underlying monad, see newArray_

newArray :: (SymArray array, HasKind a, HasKind b) => String -> Maybe (SBV b) -> Symbolic (array a b)

Create a named new array, possibly with a default initial value.

NB. For a version which generalizes over the underlying monad, see newArray

data SArray a b

Arrays implemented in terms of SMT-arrays: http://smtlib.cs.uiowa.edu/theories-ArraysEx.shtml

• Maps directly to SMT-lib arrays
• Reading from an unintialized value is OK. If the default value is given in newArray, it will be the result. Otherwise, the read yields an uninterpreted constant.
• Can check for equality of these arrays
• Cannot be used in code-generation (i.e., compilation to C)
• Cannot quick-check theorems using SArray values
• Typically slower as it heavily relies on SMT-solving for the array theory

Instances

SymArray SArray

Defined in Data.SBV.Core.Data

Methods

newArray_ :: (MonadSymbolic m, HasKind a, HasKind b) => Maybe (SBV b) -> m (SArray a b)

newArray :: (MonadSymbolic m, HasKind a, HasKind b) => String -> Maybe (SBV b) -> m (SArray a b)

readArray :: SArray a b -> SBV a -> SBV b

writeArray :: SymVal b => SArray a b -> SBV a -> SBV b -> SArray a b

mergeArrays :: SymVal b => SBV Bool -> SArray a b -> SArray a b -> SArray a b

newArrayInState :: (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (SArray a b)

(HasKind a, HasKind b, MProvable m p) => MProvable m (SArray a b -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: (SArray a b -> p) -> SymbolicT m SBool

forAll :: [String] -> (SArray a b -> p) -> SymbolicT m SBool

forSome_ :: (SArray a b -> p) -> SymbolicT m SBool

forSome :: [String] -> (SArray a b -> p) -> SymbolicT m SBool

prove :: (SArray a b -> p) -> m ThmResult

proveWith :: SMTConfig -> (SArray a b -> p) -> m ThmResult

sat :: (SArray a b -> p) -> m SatResult

satWith :: SMTConfig -> (SArray a b -> p) -> m SatResult

allSat :: (SArray a b -> p) -> m AllSatResult

allSatWith :: SMTConfig -> (SArray a b -> p) -> m AllSatResult

optimize :: OptimizeStyle -> (SArray a b -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> (SArray a b -> p) -> m OptimizeResult

isVacuous :: (SArray a b -> p) -> m Bool

isVacuousWith :: SMTConfig -> (SArray a b -> p) -> m Bool

isTheorem :: (SArray a b -> p) -> m Bool

isTheoremWith :: SMTConfig -> (SArray a b -> p) -> m Bool

isSatisfiable :: (SArray a b -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> (SArray a b -> p) -> m Bool

validate :: Bool -> SMTConfig -> (SArray a b -> p) -> SMTResult -> m SMTResult

(HasKind a, HasKind b) => Show (SArray a b)

Defined in Data.SBV.Core.Data

Methods

showsPrec :: Int -> SArray a b -> ShowS

show :: SArray a b -> String

showList :: [SArray a b] -> ShowS

SymVal b => Mergeable (SArray a b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> SArray a b -> SArray a b -> SArray a b

select :: (Ord b0, SymVal b0, Num b0) => [SArray a b] -> SArray a b -> SBV b0 -> SArray a b

EqSymbolic (SArray a b)

Defined in Data.SBV.Core.Model

Methods

(.==) :: SArray a b -> SArray a b -> SBool

(./=) :: SArray a b -> SArray a b -> SBool

(.===) :: SArray a b -> SArray a b -> SBool

(./==) :: SArray a b -> SArray a b -> SBool

distinct :: [SArray a b] -> SBool

allEqual :: [SArray a b] -> SBool

sElem :: SArray a b -> [SArray a b] -> SBool

data SFunArray a b

Arrays implemented internally, without translating to SMT-Lib functions:

• Internally handled by the library and not mapped to SMT-Lib, hence can be used with solvers that don't support arrays. (Such as abc.)
• Reading from an unintialized value is OK. If the default value is given in newArray, it will be the result. Otherwise, the read yields an uninterpreted constant.
• Cannot check for equality of arrays.
• Can be used in code-generation (i.e., compilation to C).
• Can not quick-check theorems using SFunArray values
• Typically faster as it gets compiled away during translation.

Instances

SymArray SFunArray

Defined in Data.SBV.Core.Data

Methods

newArray_ :: (MonadSymbolic m, HasKind a, HasKind b) => Maybe (SBV b) -> m (SFunArray a b)

newArray :: (MonadSymbolic m, HasKind a, HasKind b) => String -> Maybe (SBV b) -> m (SFunArray a b)

readArray :: SFunArray a b -> SBV a -> SBV b

writeArray :: SymVal b => SFunArray a b -> SBV a -> SBV b -> SFunArray a b

mergeArrays :: SymVal b => SBV Bool -> SFunArray a b -> SFunArray a b -> SFunArray a b

newArrayInState :: (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (SFunArray a b)

(HasKind a, HasKind b, MProvable m p) => MProvable m (SFunArray a b -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: (SFunArray a b -> p) -> SymbolicT m SBool

forAll :: [String] -> (SFunArray a b -> p) -> SymbolicT m SBool

forSome_ :: (SFunArray a b -> p) -> SymbolicT m SBool

forSome :: [String] -> (SFunArray a b -> p) -> SymbolicT m SBool

prove :: (SFunArray a b -> p) -> m ThmResult

proveWith :: SMTConfig -> (SFunArray a b -> p) -> m ThmResult

sat :: (SFunArray a b -> p) -> m SatResult

satWith :: SMTConfig -> (SFunArray a b -> p) -> m SatResult

allSat :: (SFunArray a b -> p) -> m AllSatResult

allSatWith :: SMTConfig -> (SFunArray a b -> p) -> m AllSatResult

optimize :: OptimizeStyle -> (SFunArray a b -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> (SFunArray a b -> p) -> m OptimizeResult

isVacuous :: (SFunArray a b -> p) -> m Bool

isVacuousWith :: SMTConfig -> (SFunArray a b -> p) -> m Bool

isTheorem :: (SFunArray a b -> p) -> m Bool

isTheoremWith :: SMTConfig -> (SFunArray a b -> p) -> m Bool

isSatisfiable :: (SFunArray a b -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> (SFunArray a b -> p) -> m Bool

validate :: Bool -> SMTConfig -> (SFunArray a b -> p) -> SMTResult -> m SMTResult

(HasKind a, HasKind b) => Show (SFunArray a b)

Defined in Data.SBV.Core.Data

Methods

showsPrec :: Int -> SFunArray a b -> ShowS

show :: SFunArray a b -> String

showList :: [SFunArray a b] -> ShowS

SymVal b => Mergeable (SFunArray a b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> SFunArray a b -> SFunArray a b -> SFunArray a b

select :: (Ord b0, SymVal b0, Num b0) => [SFunArray a b] -> SFunArray a b -> SBV b0 -> SFunArray a b

Creating symbolic values

Single value

These functions simplify declaring symbolic variables of various types. Strictly speaking, they are just synonyms for free (specialized at the given type), but they might be easier to use. We provide both the named and anonymous versions, latter with the underscore suffix.

sBool :: String -> Symbolic SBool

Declare a named SBool

NB. For a version which generalizes over the underlying monad, see sBool

sBool_ :: Symbolic SBool

Declare an unnamed SBool

NB. For a version which generalizes over the underlying monad, see sBool_

sWord8 :: String -> Symbolic SWord8

Declare a named SWord8

NB. For a version which generalizes over the underlying monad, see sWord8

sWord8_ :: Symbolic SWord8

Declare an unnamed SWord8

NB. For a version which generalizes over the underlying monad, see sWord8_

sWord16 :: String -> Symbolic SWord16

Declare a named SWord16

NB. For a version which generalizes over the underlying monad, see sWord16

sWord16_ :: Symbolic SWord16

Declare an unnamed SWord16

NB. For a version which generalizes over the underlying monad, see sWord16_

sWord32 :: String -> Symbolic SWord32

Declare a named SWord32

NB. For a version which generalizes over the underlying monad, see sWord32

sWord32_ :: Symbolic SWord32

Declare an unamed SWord32

NB. For a version which generalizes over the underlying monad, see sWord32_

sWord64 :: String -> Symbolic SWord64

Declare a named SWord64

NB. For a version which generalizes over the underlying monad, see sWord64

sWord64_ :: Symbolic SWord64

Declare an unnamed SWord64

NB. For a version which generalizes over the underlying monad, see sWord64_

sInt8 :: String -> Symbolic SInt8

Declare a named SInt8

NB. For a version which generalizes over the underlying monad, see sInt8

sInt8_ :: Symbolic SInt8

Declare an unnamed SInt8

NB. For a version which generalizes over the underlying monad, see sInt8_

sInt16 :: String -> Symbolic SInt16

Declare a named SInt16

NB. For a version which generalizes over the underlying monad, see sInt16

sInt16_ :: Symbolic SInt16

Declare an unnamed SInt16

NB. For a version which generalizes over the underlying monad, see sInt16_

sInt32 :: String -> Symbolic SInt32

Declare a named SInt32

NB. For a version which generalizes over the underlying monad, see sInt32

sInt32_ :: Symbolic SInt32

Declare an unnamed SInt32

NB. For a version which generalizes over the underlying monad, see sInt32_

sInt64 :: String -> Symbolic SInt64

Declare a named SInt64

NB. For a version which generalizes over the underlying monad, see sInt64

sInt64_ :: Symbolic SInt64

Declare an unnamed SInt64

NB. For a version which generalizes over the underlying monad, see sInt64_

sInteger :: String -> Symbolic SInteger

Declare a named SInteger

NB. For a version which generalizes over the underlying monad, see sInteger

sInteger_ :: Symbolic SInteger

Declare an unnamed SInteger

NB. For a version which generalizes over the underlying monad, see sInteger_

sReal :: String -> Symbolic SReal

Declare a named SReal

NB. For a version which generalizes over the underlying monad, see sReal

sReal_ :: Symbolic SReal

Declare an unnamed SReal

NB. For a version which generalizes over the underlying monad, see sReal_

sFloat :: String -> Symbolic SFloat

Declare a named SFloat

NB. For a version which generalizes over the underlying monad, see sFloat

sFloat_ :: Symbolic SFloat

Declare an unnamed SFloat

NB. For a version which generalizes over the underlying monad, see sFloat_

sDouble :: String -> Symbolic SDouble

Declare a named SDouble

NB. For a version which generalizes over the underlying monad, see sDouble

sDouble_ :: Symbolic SDouble

Declare an unnamed SDouble

NB. For a version which generalizes over the underlying monad, see sDouble_

sChar :: String -> Symbolic SChar

Declare a named SChar

NB. For a version which generalizes over the underlying monad, see sChar

sChar_ :: Symbolic SChar

Declare an unnamed SChar

NB. For a version which generalizes over the underlying monad, see sChar_

sString :: String -> Symbolic SString

Declare a named SString

NB. For a version which generalizes over the underlying monad, see sString

sString_ :: Symbolic SString

Declare an unnamed SString

NB. For a version which generalizes over the underlying monad, see sString_

sList :: SymVal a => String -> Symbolic (SList a)

Declare a named SList

NB. For a version which generalizes over the underlying monad, see sList

sList_ :: SymVal a => Symbolic (SList a)

Declare an unnamed SList

NB. For a version which generalizes over the underlying monad, see sList_

sTuple :: SymVal tup => String -> Symbolic (SBV tup)

Declare a named tuple.

NB. For a version which generalizes over the underlying monad, see sTuple

sTuple_ :: SymVal tup => Symbolic (SBV tup)

Declare an unnamed tuple.

NB. For a version which generalizes over the underlying monad, see sTuple_

sEither :: (SymVal a, SymVal b) => String -> Symbolic (SEither a b)

Declare a named SEither.

NB. For a version which generalizes over the underlying monad, see sEither

sEither_ :: (SymVal a, SymVal b) => Symbolic (SEither a b)

Declare an unnamed SEither.

NB. For a version which generalizes over the underlying monad, see sEither_

sMaybe :: SymVal a => String -> Symbolic (SMaybe a)

Declare a named SMaybe.

NB. For a version which generalizes over the underlying monad, see sMaybe

sMaybe_ :: SymVal a => Symbolic (SMaybe a)

Declare an unnamed SMaybe.

NB. For a version which generalizes over the underlying monad, see sMaybe_

sSet :: (Ord a, SymVal a) => String -> Symbolic (SSet a)

Declare a named SSet.

NB. For a version which generalizes over the underlying monad, see sSet

sSet_ :: (Ord a, SymVal a) => Symbolic (SSet a)

Declare an unnamed SSet.

NB. For a version which generalizes over the underlying monad, see sSet_

List of values

These functions simplify declaring a sequence symbolic variables of various types. Strictly speaking, they are just synonyms for mapM free (specialized at the given type), but they might be easier to use.

sBools :: [String] -> Symbolic [SBool]

Declare a list of SBools

NB. For a version which generalizes over the underlying monad, see sBools

sWord8s :: [String] -> Symbolic [SWord8]

Declare a list of SWord8s

NB. For a version which generalizes over the underlying monad, see sWord8s

sWord16s :: [String] -> Symbolic [SWord16]

Declare a list of SWord16s

NB. For a version which generalizes over the underlying monad, see sWord16s

sWord32s :: [String] -> Symbolic [SWord32]

Declare a list of SWord32s

NB. For a version which generalizes over the underlying monad, see sWord32s

sWord64s :: [String] -> Symbolic [SWord64]

Declare a list of SWord64s

NB. For a version which generalizes over the underlying monad, see sWord64s

sInt8s :: [String] -> Symbolic [SInt8]

Declare a list of SInt8s

NB. For a version which generalizes over the underlying monad, see sInt8s

sInt16s :: [String] -> Symbolic [SInt16]

Declare a list of SInt16s

NB. For a version which generalizes over the underlying monad, see sInt16s

sInt32s :: [String] -> Symbolic [SInt32]

Declare a list of SInt32s

NB. For a version which generalizes over the underlying monad, see sInt32s

sInt64s :: [String] -> Symbolic [SInt64]

Declare a list of SInt64s

NB. For a version which generalizes over the underlying monad, see sInt64s

sIntegers :: [String] -> Symbolic [SInteger]

Declare a list of SIntegers

NB. For a version which generalizes over the underlying monad, see sIntegers

sReals :: [String] -> Symbolic [SReal]

Declare a list of SReals

NB. For a version which generalizes over the underlying monad, see sReals

sFloats :: [String] -> Symbolic [SFloat]

Declare a list of SFloats

NB. For a version which generalizes over the underlying monad, see sFloats

sDoubles :: [String] -> Symbolic [SDouble]

Declare a list of SDoubles

NB. For a version which generalizes over the underlying monad, see sDoubles

sChars :: [String] -> Symbolic [SChar]

Declare a list of SChars

NB. For a version which generalizes over the underlying monad, see sChars

sStrings :: [String] -> Symbolic [SString]

Declare a list of SStrings

NB. For a version which generalizes over the underlying monad, see sStrings

sLists :: SymVal a => [String] -> Symbolic [SList a]

Declare a list of SLists

NB. For a version which generalizes over the underlying monad, see sLists

sTuples :: SymVal tup => [String] -> Symbolic [SBV tup]

Declare a list of tuples.

NB. For a version which generalizes over the underlying monad, see sTuples

sEithers :: (SymVal a, SymVal b) => [String] -> Symbolic [SEither a b]

Declare a list of SEither values.

NB. For a version which generalizes over the underlying monad, see sEithers

sMaybes :: SymVal a => [String] -> Symbolic [SMaybe a]

Declare a list of SMaybe values.

NB. For a version which generalizes over the underlying monad, see sMaybes

sSets :: (Ord a, SymVal a) => [String] -> Symbolic [SSet a]

Declare a list of SSet values.

NB. For a version which generalizes over the underlying monad, see sSets

Symbolic Equality and Comparisons

class EqSymbolic a where

Symbolic Equality. Note that we can't use Haskell's Eq class since Haskell insists on returning Bool Comparing symbolic values will necessarily return a symbolic value.

Minimal complete definition

(.==)

Methods

(.==) :: a -> a -> SBool infix 4

Symbolic equality.

(./=) :: a -> a -> SBool infix 4

Symbolic inequality.

(.===) :: a -> a -> SBool infix 4

Strong equality. On floats ('SFloat'/'SDouble'), strong equality is object equality; that is NaN == NaN holds, but +0 == -0 doesn't. On other types, (.===) is simply (.==). Note that (.==) is the right notion of equality for floats per IEEE754 specs, since by definition +0 == -0 and NaN equals no other value including itself. But occasionally we want to be stronger and state NaN equals NaN and +0 and -0 are different from each other. In a context where your type is concrete, simply use fpIsEqualObject. But in a polymorphic context, use the strong equality instead.

NB. If you do not care about or work with floats, simply use (.==) and (./=).

(./==) :: a -> a -> SBool infix 4

Negation of strong equality. Equaivalent to negation of (.===) on all types.

distinct :: [a] -> SBool

Returns (symbolic) sTrue if all the elements of the given list are different.

allEqual :: [a] -> SBool

Returns (symbolic) sTrue if all the elements of the given list are the same.

sElem :: a -> [a] -> SBool

Symbolic membership test.

Instances

EqSymbolic Bool

Defined in Data.SBV.Core.Model

Methods

(.==) :: Bool -> Bool -> SBool

(./=) :: Bool -> Bool -> SBool

(.===) :: Bool -> Bool -> SBool

(./==) :: Bool -> Bool -> SBool

distinct :: [Bool] -> SBool

allEqual :: [Bool] -> SBool

sElem :: Bool -> [Bool] -> SBool

EqSymbolic a => EqSymbolic [a]

Defined in Data.SBV.Core.Model

Methods

(.==) :: [a] -> [a] -> SBool

(./=) :: [a] -> [a] -> SBool

(.===) :: [a] -> [a] -> SBool

(./==) :: [a] -> [a] -> SBool

distinct :: [[a]] -> SBool

allEqual :: [[a]] -> SBool

sElem :: [a] -> [[a]] -> SBool

EqSymbolic a => EqSymbolic (Maybe a)

Defined in Data.SBV.Core.Model

Methods

(.==) :: Maybe a -> Maybe a -> SBool

(./=) :: Maybe a -> Maybe a -> SBool

(.===) :: Maybe a -> Maybe a -> SBool

(./==) :: Maybe a -> Maybe a -> SBool

distinct :: [Maybe a] -> SBool

allEqual :: [Maybe a] -> SBool

sElem :: Maybe a -> [Maybe a] -> SBool

EqSymbolic (SBV a)

Defined in Data.SBV.Core.Model

Methods

(.==) :: SBV a -> SBV a -> SBool

(./=) :: SBV a -> SBV a -> SBool

(.===) :: SBV a -> SBV a -> SBool

(./==) :: SBV a -> SBV a -> SBool

distinct :: [SBV a] -> SBool

allEqual :: [SBV a] -> SBool

sElem :: SBV a -> [SBV a] -> SBool

EqSymbolic a => EqSymbolic (S a)

Symbolic equality for S.

Defined in Documentation.SBV.Examples.ProofTools.BMC

Methods

(.==) :: S a -> S a -> SBool

(./=) :: S a -> S a -> SBool

(.===) :: S a -> S a -> SBool

(./==) :: S a -> S a -> SBool

distinct :: [S a] -> SBool

allEqual :: [S a] -> SBool

sElem :: S a -> [S a] -> SBool

(EqSymbolic a, EqSymbolic b) => EqSymbolic (Either a b)

Defined in Data.SBV.Core.Model

Methods

(.==) :: Either a b -> Either a b -> SBool

(./=) :: Either a b -> Either a b -> SBool

(.===) :: Either a b -> Either a b -> SBool

(./==) :: Either a b -> Either a b -> SBool

distinct :: [Either a b] -> SBool

allEqual :: [Either a b] -> SBool

sElem :: Either a b -> [Either a b] -> SBool

(EqSymbolic a, EqSymbolic b) => EqSymbolic (a, b)

Defined in Data.SBV.Core.Model

Methods

(.==) :: (a, b) -> (a, b) -> SBool

(./=) :: (a, b) -> (a, b) -> SBool

(.===) :: (a, b) -> (a, b) -> SBool

(./==) :: (a, b) -> (a, b) -> SBool

distinct :: [(a, b)] -> SBool

allEqual :: [(a, b)] -> SBool

sElem :: (a, b) -> [(a, b)] -> SBool

EqSymbolic (SArray a b)

Defined in Data.SBV.Core.Model

Methods

(.==) :: SArray a b -> SArray a b -> SBool

(./=) :: SArray a b -> SArray a b -> SBool

(.===) :: SArray a b -> SArray a b -> SBool

(./==) :: SArray a b -> SArray a b -> SBool

distinct :: [SArray a b] -> SBool

allEqual :: [SArray a b] -> SBool

sElem :: SArray a b -> [SArray a b] -> SBool

(EqSymbolic a, EqSymbolic b, EqSymbolic c) => EqSymbolic (a, b, c)

Defined in Data.SBV.Core.Model

Methods

(.==) :: (a, b, c) -> (a, b, c) -> SBool

(./=) :: (a, b, c) -> (a, b, c) -> SBool

(.===) :: (a, b, c) -> (a, b, c) -> SBool

(./==) :: (a, b, c) -> (a, b, c) -> SBool

distinct :: [(a, b, c)] -> SBool

allEqual :: [(a, b, c)] -> SBool

sElem :: (a, b, c) -> [(a, b, c)] -> SBool

(EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d) => EqSymbolic (a, b, c, d)

Defined in Data.SBV.Core.Model

Methods

(.==) :: (a, b, c, d) -> (a, b, c, d) -> SBool

(./=) :: (a, b, c, d) -> (a, b, c, d) -> SBool

(.===) :: (a, b, c, d) -> (a, b, c, d) -> SBool

(./==) :: (a, b, c, d) -> (a, b, c, d) -> SBool

distinct :: [(a, b, c, d)] -> SBool

allEqual :: [(a, b, c, d)] -> SBool

sElem :: (a, b, c, d) -> [(a, b, c, d)] -> SBool

(EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d, EqSymbolic e) => EqSymbolic (a, b, c, d, e)

Defined in Data.SBV.Core.Model

Methods

(.==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

(./=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

(.===) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

(./==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

distinct :: [(a, b, c, d, e)] -> SBool

allEqual :: [(a, b, c, d, e)] -> SBool

sElem :: (a, b, c, d, e) -> [(a, b, c, d, e)] -> SBool

(EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d, EqSymbolic e, EqSymbolic f) => EqSymbolic (a, b, c, d, e, f)

Defined in Data.SBV.Core.Model

Methods

(.==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

(./=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

(.===) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

(./==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

distinct :: [(a, b, c, d, e, f)] -> SBool

allEqual :: [(a, b, c, d, e, f)] -> SBool

sElem :: (a, b, c, d, e, f) -> [(a, b, c, d, e, f)] -> SBool

(EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d, EqSymbolic e, EqSymbolic f, EqSymbolic g) => EqSymbolic (a, b, c, d, e, f, g)

Defined in Data.SBV.Core.Model

Methods

(.==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

(./=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

(.===) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

(./==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

distinct :: [(a, b, c, d, e, f, g)] -> SBool

allEqual :: [(a, b, c, d, e, f, g)] -> SBool

sElem :: (a, b, c, d, e, f, g) -> [(a, b, c, d, e, f, g)] -> SBool

class (Mergeable a, EqSymbolic a) => OrdSymbolic a where

Symbolic Comparisons. Similar to Eq, we cannot implement Haskell's Ord class since there is no way to return an Ordering value from a symbolic comparison. Furthermore, OrdSymbolic requires Mergeable to implement if-then-else, for the benefit of implementing symbolic versions of max and min functions.

Minimal complete definition

(.<)

Methods

(.<) :: a -> a -> SBool infix 4

Symbolic less than.

(.<=) :: a -> a -> SBool infix 4

Symbolic less than or equal to.

(.>) :: a -> a -> SBool infix 4

Symbolic greater than.

(.>=) :: a -> a -> SBool infix 4

Symbolic greater than or equal to.

smin :: a -> a -> a

Symbolic minimum.

smax :: a -> a -> a

Symbolic maximum.

inRange :: a -> (a, a) -> SBool

Is the value withing the allowed inclusive range?

Instances

OrdSymbolic a => OrdSymbolic [a]

Defined in Data.SBV.Core.Model

Methods

(.<) :: [a] -> [a] -> SBool

(.<=) :: [a] -> [a] -> SBool

(.>) :: [a] -> [a] -> SBool

(.>=) :: [a] -> [a] -> SBool

smin :: [a] -> [a] -> [a]

smax :: [a] -> [a] -> [a]

inRange :: [a] -> ([a], [a]) -> SBool

OrdSymbolic a => OrdSymbolic (Maybe a)

Defined in Data.SBV.Core.Model

Methods

(.<) :: Maybe a -> Maybe a -> SBool

(.<=) :: Maybe a -> Maybe a -> SBool

(.>) :: Maybe a -> Maybe a -> SBool

(.>=) :: Maybe a -> Maybe a -> SBool

smin :: Maybe a -> Maybe a -> Maybe a

smax :: Maybe a -> Maybe a -> Maybe a

inRange :: Maybe a -> (Maybe a, Maybe a) -> SBool

(Ord a, SymVal a) => OrdSymbolic (SBV a)

Defined in Data.SBV.Core.Model

Methods

(.<) :: SBV a -> SBV a -> SBool

(.<=) :: SBV a -> SBV a -> SBool

(.>) :: SBV a -> SBV a -> SBool

(.>=) :: SBV a -> SBV a -> SBool

smin :: SBV a -> SBV a -> SBV a

smax :: SBV a -> SBV a -> SBV a

inRange :: SBV a -> (SBV a, SBV a) -> SBool

(OrdSymbolic a, OrdSymbolic b) => OrdSymbolic (Either a b)

Defined in Data.SBV.Core.Model

Methods

(.<) :: Either a b -> Either a b -> SBool

(.<=) :: Either a b -> Either a b -> SBool

(.>) :: Either a b -> Either a b -> SBool

(.>=) :: Either a b -> Either a b -> SBool

smin :: Either a b -> Either a b -> Either a b

smax :: Either a b -> Either a b -> Either a b

inRange :: Either a b -> (Either a b, Either a b) -> SBool

(OrdSymbolic a, OrdSymbolic b) => OrdSymbolic (a, b)

Defined in Data.SBV.Core.Model

Methods

(.<) :: (a, b) -> (a, b) -> SBool

(.<=) :: (a, b) -> (a, b) -> SBool

(.>) :: (a, b) -> (a, b) -> SBool

(.>=) :: (a, b) -> (a, b) -> SBool

smin :: (a, b) -> (a, b) -> (a, b)

smax :: (a, b) -> (a, b) -> (a, b)

inRange :: (a, b) -> ((a, b), (a, b)) -> SBool

(OrdSymbolic a, OrdSymbolic b, OrdSymbolic c) => OrdSymbolic (a, b, c)

Defined in Data.SBV.Core.Model

Methods

(.<) :: (a, b, c) -> (a, b, c) -> SBool

(.<=) :: (a, b, c) -> (a, b, c) -> SBool

(.>) :: (a, b, c) -> (a, b, c) -> SBool

(.>=) :: (a, b, c) -> (a, b, c) -> SBool

smin :: (a, b, c) -> (a, b, c) -> (a, b, c)

smax :: (a, b, c) -> (a, b, c) -> (a, b, c)

inRange :: (a, b, c) -> ((a, b, c), (a, b, c)) -> SBool

(OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d) => OrdSymbolic (a, b, c, d)

Defined in Data.SBV.Core.Model

Methods

(.<) :: (a, b, c, d) -> (a, b, c, d) -> SBool

(.<=) :: (a, b, c, d) -> (a, b, c, d) -> SBool

(.>) :: (a, b, c, d) -> (a, b, c, d) -> SBool

(.>=) :: (a, b, c, d) -> (a, b, c, d) -> SBool

smin :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

smax :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

inRange :: (a, b, c, d) -> ((a, b, c, d), (a, b, c, d)) -> SBool

(OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d, OrdSymbolic e) => OrdSymbolic (a, b, c, d, e)

Defined in Data.SBV.Core.Model

Methods

(.<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

(.<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

(.>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

(.>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> SBool

smin :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

smax :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

inRange :: (a, b, c, d, e) -> ((a, b, c, d, e), (a, b, c, d, e)) -> SBool

(OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d, OrdSymbolic e, OrdSymbolic f) => OrdSymbolic (a, b, c, d, e, f)

Defined in Data.SBV.Core.Model

Methods

(.<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

(.<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

(.>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

(.>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> SBool

smin :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)

smax :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)

inRange :: (a, b, c, d, e, f) -> ((a, b, c, d, e, f), (a, b, c, d, e, f)) -> SBool

(OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d, OrdSymbolic e, OrdSymbolic f, OrdSymbolic g) => OrdSymbolic (a, b, c, d, e, f, g)

Defined in Data.SBV.Core.Model

Methods

(.<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

(.<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

(.>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

(.>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> SBool

smin :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)

smax :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)

inRange :: (a, b, c, d, e, f, g) -> ((a, b, c, d, e, f, g), (a, b, c, d, e, f, g)) -> SBool

class Equality a where

Equality as a proof method. Allows for very concise construction of equivalence proofs, which is very typical in bit-precise proofs.

Methods

(===) :: a -> a -> IO ThmResult infix 4

Instances

(SymVal a, SymVal b, EqSymbolic z) => Equality ((SBV a, SBV b) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b) -> z) -> ((SBV a, SBV b) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c) -> z) -> ((SBV a, SBV b, SBV c) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d) -> z) -> ((SBV a, SBV b, SBV c, SBV d) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d, SBV e) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> z) -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> z) -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> z) -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> SBV g -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> SBV g -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> SBV g -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> z) -> (SBV a -> SBV b -> SBV c -> z) -> IO ThmResult

(SymVal a, SymVal b, EqSymbolic z) => Equality (SBV a -> SBV b -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> z) -> (SBV a -> SBV b -> z) -> IO ThmResult

(SymVal a, EqSymbolic z) => Equality (SBV a -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> z) -> (SBV a -> z) -> IO ThmResult

Conditionals: Mergeable values

class Mergeable a where

Symbolic conditionals are modeled by the Mergeable class, describing how to merge the results of an if-then-else call with a symbolic test. SBV provides all basic types as instances of this class, so users only need to declare instances for custom data-types of their programs as needed.

A Mergeable instance may be automatically derived for a custom data-type with a single constructor where the type of each field is an instance of Mergeable, such as a record of symbolic values. Users only need to add Generic and Mergeable to the deriving clause for the data-type. See Status for an example and an illustration of what the instance would look like if written by hand.

The function select is a total-indexing function out of a list of choices with a default value, simulating array/list indexing. It's an n-way generalization of the ite function.

Minimal complete definition: None, if the type is instance of Generic. Otherwise symbolicMerge. Note that most types subject to merging are likely to be trivial instances of Generic.

Minimal complete definition

Nothing

Methods

symbolicMerge :: Bool -> SBool -> a -> a -> a

Merge two values based on the condition. The first argument states whether we force the then-and-else branches before the merging, at the word level. This is an efficiency concern; one that we'd rather not make but unfortunately necessary for getting symbolic simulation working efficiently.

select :: (Ord b, SymVal b, Num b) => [a] -> a -> SBV b -> a

Total indexing operation. select xs default index is intuitively the same as xs !! index, except it evaluates to default if index underflows/overflows.

symbolicMerge :: (Generic a, GMergeable (Rep a)) => Bool -> SBool -> a -> a -> a

Merge two values based on the condition. The first argument states whether we force the then-and-else branches before the merging, at the word level. This is an efficiency concern; one that we'd rather not make but unfortunately necessary for getting symbolic simulation working efficiently.

Instances

Mergeable ()

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> () -> () -> ()

select :: (Ord b, SymVal b, Num b) => [()] -> () -> SBV b -> ()

Mergeable Mostek

Defined in Documentation.SBV.Examples.BitPrecise.Legato

Methods

symbolicMerge :: Bool -> SBool -> Mostek -> Mostek -> Mostek

select :: (Ord b, SymVal b, Num b) => [Mostek] -> Mostek -> SBV b -> Mostek

Mergeable Status

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

symbolicMerge :: Bool -> SBool -> Status -> Status -> Status

select :: (Ord b, SymVal b, Num b) => [Status] -> Status -> SBV b -> Status

Mergeable a => Mergeable [a]

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> [a] -> [a] -> [a]

select :: (Ord b, SymVal b, Num b) => [[a]] -> [a] -> SBV b -> [a]

Mergeable a => Mergeable (Maybe a)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> Maybe a -> Maybe a -> Maybe a

select :: (Ord b, SymVal b, Num b) => [Maybe a] -> Maybe a -> SBV b -> Maybe a

Mergeable a => Mergeable (ZipList a)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> ZipList a -> ZipList a -> ZipList a

select :: (Ord b, SymVal b, Num b) => [ZipList a] -> ZipList a -> SBV b -> ZipList a

SymVal a => Mergeable (SBV a)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> SBV a -> SBV a -> SBV a

select :: (Ord b, SymVal b, Num b) => [SBV a] -> SBV a -> SBV b -> SBV a

Mergeable a => Mergeable (S a)

Defined in Documentation.SBV.Examples.ProofTools.Fibonacci

Methods

symbolicMerge :: Bool -> SBool -> S a -> S a -> S a

select :: (Ord b, SymVal b, Num b) => [S a] -> S a -> SBV b -> S a

Mergeable a => Mergeable (S a)

Defined in Documentation.SBV.Examples.ProofTools.Sum

Methods

symbolicMerge :: Bool -> SBool -> S a -> S a -> S a

select :: (Ord b, SymVal b, Num b) => [S a] -> S a -> SBV b -> S a

Mergeable a => Mergeable (Move a)

Mergeable instance for Move simply pushes the merging the data after run of each branch starting from the same state.

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

symbolicMerge :: Bool -> SBool -> Move a -> Move a -> Move a

select :: (Ord b, SymVal b, Num b) => [Move a] -> Move a -> SBV b -> Move a

SymVal a => Mergeable (AppS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.Append

Methods

symbolicMerge :: Bool -> SBool -> AppS a -> AppS a -> AppS a

select :: (Ord b, SymVal b, Num b) => [AppS a] -> AppS a -> SBV b -> AppS a

Mergeable a => Mergeable (FibS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.Fib

Methods

symbolicMerge :: Bool -> SBool -> FibS a -> FibS a -> FibS a

select :: (Ord b, SymVal b, Num b) => [FibS a] -> FibS a -> SBV b -> FibS a

Mergeable a => Mergeable (GCDS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.GCD

Methods

symbolicMerge :: Bool -> SBool -> GCDS a -> GCDS a -> GCDS a

select :: (Ord b, SymVal b, Num b) => [GCDS a] -> GCDS a -> SBV b -> GCDS a

Mergeable a => Mergeable (DivS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.IntDiv

Methods

symbolicMerge :: Bool -> SBool -> DivS a -> DivS a -> DivS a

select :: (Ord b, SymVal b, Num b) => [DivS a] -> DivS a -> SBV b -> DivS a

Mergeable a => Mergeable (SqrtS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.IntSqrt

Methods

symbolicMerge :: Bool -> SBool -> SqrtS a -> SqrtS a -> SqrtS a

select :: (Ord b, SymVal b, Num b) => [SqrtS a] -> SqrtS a -> SBV b -> SqrtS a

SymVal a => Mergeable (LenS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.Length

Methods

symbolicMerge :: Bool -> SBool -> LenS a -> LenS a -> LenS a

select :: (Ord b, SymVal b, Num b) => [LenS a] -> LenS a -> SBV b -> LenS a

Mergeable a => Mergeable (SumS a)

Defined in Documentation.SBV.Examples.WeakestPreconditions.Sum

Methods

symbolicMerge :: Bool -> SBool -> SumS a -> SumS a -> SumS a

select :: (Ord b, SymVal b, Num b) => [SumS a] -> SumS a -> SBV b -> SumS a

Mergeable b => Mergeable (a -> b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a -> b) -> (a -> b) -> a -> b

select :: (Ord b0, SymVal b0, Num b0) => [a -> b] -> (a -> b) -> SBV b0 -> a -> b

(Mergeable a, Mergeable b) => Mergeable (Either a b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> Either a b -> Either a b -> Either a b

select :: (Ord b0, SymVal b0, Num b0) => [Either a b] -> Either a b -> SBV b0 -> Either a b

(Mergeable a, Mergeable b) => Mergeable (a, b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a, b) -> (a, b) -> (a, b)

select :: (Ord b0, SymVal b0, Num b0) => [(a, b)] -> (a, b) -> SBV b0 -> (a, b)

(Ix a, Mergeable b) => Mergeable (Array a b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> Array a b -> Array a b -> Array a b

select :: (Ord b0, SymVal b0, Num b0) => [Array a b] -> Array a b -> SBV b0 -> Array a b

SymVal b => Mergeable (SFunArray a b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> SFunArray a b -> SFunArray a b -> SFunArray a b

select :: (Ord b0, SymVal b0, Num b0) => [SFunArray a b] -> SFunArray a b -> SBV b0 -> SFunArray a b

SymVal b => Mergeable (SArray a b)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> SArray a b -> SArray a b -> SArray a b

select :: (Ord b0, SymVal b0, Num b0) => [SArray a b] -> SArray a b -> SBV b0 -> SArray a b

SymVal e => Mergeable (STree i e)

Defined in Data.SBV.Tools.STree

Methods

symbolicMerge :: Bool -> SBool -> STree i e -> STree i e -> STree i e

select :: (Ord b, SymVal b, Num b) => [STree i e] -> STree i e -> SBV b -> STree i e

(Mergeable a, Mergeable b, Mergeable c) => Mergeable (a, b, c)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a, b, c) -> (a, b, c) -> (a, b, c)

select :: (Ord b0, SymVal b0, Num b0) => [(a, b, c)] -> (a, b, c) -> SBV b0 -> (a, b, c)

(Mergeable a, Mergeable b, Mergeable c, Mergeable d) => Mergeable (a, b, c, d)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

select :: (Ord b0, SymVal b0, Num b0) => [(a, b, c, d)] -> (a, b, c, d) -> SBV b0 -> (a, b, c, d)

(Mergeable a, Mergeable b, Mergeable c, Mergeable d, Mergeable e) => Mergeable (a, b, c, d, e)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

select :: (Ord b0, SymVal b0, Num b0) => [(a, b, c, d, e)] -> (a, b, c, d, e) -> SBV b0 -> (a, b, c, d, e)

(Mergeable a, Mergeable b, Mergeable c, Mergeable d, Mergeable e, Mergeable f) => Mergeable (a, b, c, d, e, f)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f)

select :: (Ord b0, SymVal b0, Num b0) => [(a, b, c, d, e, f)] -> (a, b, c, d, e, f) -> SBV b0 -> (a, b, c, d, e, f)

(Mergeable a, Mergeable b, Mergeable c, Mergeable d, Mergeable e, Mergeable f, Mergeable g) => Mergeable (a, b, c, d, e, f, g)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g)

select :: (Ord b0, SymVal b0, Num b0) => [(a, b, c, d, e, f, g)] -> (a, b, c, d, e, f, g) -> SBV b0 -> (a, b, c, d, e, f, g)

ite :: Mergeable a => SBool -> a -> a -> a

If-then-else. This is by definition symbolicMerge with both branches forced. This is typically the desired behavior, but also see iteLazy should you need more laziness.

iteLazy :: Mergeable a => SBool -> a -> a -> a

A Lazy version of ite, which does not force its arguments. This might cause issues for symbolic simulation with large thunks around, so use with care.

Symbolic integral numbers

class (SymVal a, Num a, Bits a, Integral a) => SIntegral a

Symbolic Numbers. This is a simple class that simply incorporates all number like base types together, simplifying writing polymorphic type-signatures that work for all symbolic numbers, such as SWord8, SInt8 etc. For instance, we can write a generic list-minimum function as follows:

   mm :: SIntegral a => [SBV a] -> SBV a
   mm = foldr1 (a b -> ite (a .<= b) a b)

It is similar to the standard Integral class, except ranging over symbolic instances.

Instances

SIntegral Int8

Defined in Data.SBV.Core.Model

SIntegral Int16

Defined in Data.SBV.Core.Model

SIntegral Int32

Defined in Data.SBV.Core.Model

SIntegral Int64

Defined in Data.SBV.Core.Model

SIntegral Integer

Defined in Data.SBV.Core.Model

SIntegral Word8

Defined in Data.SBV.Core.Model

SIntegral Word16

Defined in Data.SBV.Core.Model

SIntegral Word32

Defined in Data.SBV.Core.Model

SIntegral Word64

Defined in Data.SBV.Core.Model

SIntegral Word4

SIntegral instance, using default methods

Defined in Documentation.SBV.Examples.Misc.Word4

Division and Modulus

class SDivisible a where

The SDivisible class captures the essence of division. Unfortunately we cannot use Haskell's Integral class since the Real and Enum superclasses are not implementable for symbolic bit-vectors. However, quotRem and divMod both make perfect sense, and the SDivisible class captures this operation. One issue is how division by 0 behaves. The verification technology requires total functions, and there are several design choices here. We follow Isabelle/HOL approach of assigning the value 0 for division by 0. Therefore, we impose the following pair of laws:

     x sQuotRem 0 = (0, x)
     x sDivMod  0 = (0, x)

Note that our instances implement this law even when x is 0 itself.

NB. quot truncates toward zero, while div truncates toward negative infinity.

Minimal complete definition

sQuotRem, sDivMod

Methods

sQuotRem :: a -> a -> (a, a)

sDivMod :: a -> a -> (a, a)

sQuot :: a -> a -> a

sRem :: a -> a -> a

sDiv :: a -> a -> a

sMod :: a -> a -> a

Instances

SDivisible Int8

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Int8 -> Int8 -> (Int8, Int8)

sDivMod :: Int8 -> Int8 -> (Int8, Int8)

sQuot :: Int8 -> Int8 -> Int8

sRem :: Int8 -> Int8 -> Int8

sDiv :: Int8 -> Int8 -> Int8

sMod :: Int8 -> Int8 -> Int8

SDivisible Int16

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Int16 -> Int16 -> (Int16, Int16)

sDivMod :: Int16 -> Int16 -> (Int16, Int16)

sQuot :: Int16 -> Int16 -> Int16

sRem :: Int16 -> Int16 -> Int16

sDiv :: Int16 -> Int16 -> Int16

sMod :: Int16 -> Int16 -> Int16

SDivisible Int32

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Int32 -> Int32 -> (Int32, Int32)

sDivMod :: Int32 -> Int32 -> (Int32, Int32)

sQuot :: Int32 -> Int32 -> Int32

sRem :: Int32 -> Int32 -> Int32

sDiv :: Int32 -> Int32 -> Int32

sMod :: Int32 -> Int32 -> Int32

SDivisible Int64

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Int64 -> Int64 -> (Int64, Int64)

sDivMod :: Int64 -> Int64 -> (Int64, Int64)

sQuot :: Int64 -> Int64 -> Int64

sRem :: Int64 -> Int64 -> Int64

sDiv :: Int64 -> Int64 -> Int64

sMod :: Int64 -> Int64 -> Int64

SDivisible Integer

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Integer -> Integer -> (Integer, Integer)

sDivMod :: Integer -> Integer -> (Integer, Integer)

sQuot :: Integer -> Integer -> Integer

sRem :: Integer -> Integer -> Integer

sDiv :: Integer -> Integer -> Integer

sMod :: Integer -> Integer -> Integer

SDivisible Word8

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Word8 -> Word8 -> (Word8, Word8)

sDivMod :: Word8 -> Word8 -> (Word8, Word8)

sQuot :: Word8 -> Word8 -> Word8

sRem :: Word8 -> Word8 -> Word8

sDiv :: Word8 -> Word8 -> Word8

sMod :: Word8 -> Word8 -> Word8

SDivisible Word16

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Word16 -> Word16 -> (Word16, Word16)

sDivMod :: Word16 -> Word16 -> (Word16, Word16)

sQuot :: Word16 -> Word16 -> Word16

sRem :: Word16 -> Word16 -> Word16

sDiv :: Word16 -> Word16 -> Word16

sMod :: Word16 -> Word16 -> Word16

SDivisible Word32

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Word32 -> Word32 -> (Word32, Word32)

sDivMod :: Word32 -> Word32 -> (Word32, Word32)

sQuot :: Word32 -> Word32 -> Word32

sRem :: Word32 -> Word32 -> Word32

sDiv :: Word32 -> Word32 -> Word32

sMod :: Word32 -> Word32 -> Word32

SDivisible Word64

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: Word64 -> Word64 -> (Word64, Word64)

sDivMod :: Word64 -> Word64 -> (Word64, Word64)

sQuot :: Word64 -> Word64 -> Word64

sRem :: Word64 -> Word64 -> Word64

sDiv :: Word64 -> Word64 -> Word64

sMod :: Word64 -> Word64 -> Word64

SDivisible CV

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: CV -> CV -> (CV, CV)

sDivMod :: CV -> CV -> (CV, CV)

sQuot :: CV -> CV -> CV

sRem :: CV -> CV -> CV

sDiv :: CV -> CV -> CV

sMod :: CV -> CV -> CV

SDivisible SInteger

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInteger -> SInteger -> (SInteger, SInteger)

sDivMod :: SInteger -> SInteger -> (SInteger, SInteger)

sQuot :: SInteger -> SInteger -> SInteger

sRem :: SInteger -> SInteger -> SInteger

sDiv :: SInteger -> SInteger -> SInteger

sMod :: SInteger -> SInteger -> SInteger

SDivisible SInt64

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt64 -> SInt64 -> (SInt64, SInt64)

sDivMod :: SInt64 -> SInt64 -> (SInt64, SInt64)

sQuot :: SInt64 -> SInt64 -> SInt64

sRem :: SInt64 -> SInt64 -> SInt64

sDiv :: SInt64 -> SInt64 -> SInt64

sMod :: SInt64 -> SInt64 -> SInt64

SDivisible SInt32

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt32 -> SInt32 -> (SInt32, SInt32)

sDivMod :: SInt32 -> SInt32 -> (SInt32, SInt32)

sQuot :: SInt32 -> SInt32 -> SInt32

sRem :: SInt32 -> SInt32 -> SInt32

sDiv :: SInt32 -> SInt32 -> SInt32

sMod :: SInt32 -> SInt32 -> SInt32

SDivisible SInt16

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt16 -> SInt16 -> (SInt16, SInt16)

sDivMod :: SInt16 -> SInt16 -> (SInt16, SInt16)

sQuot :: SInt16 -> SInt16 -> SInt16

sRem :: SInt16 -> SInt16 -> SInt16

sDiv :: SInt16 -> SInt16 -> SInt16

sMod :: SInt16 -> SInt16 -> SInt16

SDivisible SInt8

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt8 -> SInt8 -> (SInt8, SInt8)

sDivMod :: SInt8 -> SInt8 -> (SInt8, SInt8)

sQuot :: SInt8 -> SInt8 -> SInt8

sRem :: SInt8 -> SInt8 -> SInt8

sDiv :: SInt8 -> SInt8 -> SInt8

sMod :: SInt8 -> SInt8 -> SInt8

SDivisible SWord64

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord64 -> SWord64 -> (SWord64, SWord64)

sDivMod :: SWord64 -> SWord64 -> (SWord64, SWord64)

sQuot :: SWord64 -> SWord64 -> SWord64

sRem :: SWord64 -> SWord64 -> SWord64

sDiv :: SWord64 -> SWord64 -> SWord64

sMod :: SWord64 -> SWord64 -> SWord64

SDivisible SWord32

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord32 -> SWord32 -> (SWord32, SWord32)

sDivMod :: SWord32 -> SWord32 -> (SWord32, SWord32)

sQuot :: SWord32 -> SWord32 -> SWord32

sRem :: SWord32 -> SWord32 -> SWord32

sDiv :: SWord32 -> SWord32 -> SWord32

sMod :: SWord32 -> SWord32 -> SWord32

SDivisible SWord16

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord16 -> SWord16 -> (SWord16, SWord16)

sDivMod :: SWord16 -> SWord16 -> (SWord16, SWord16)

sQuot :: SWord16 -> SWord16 -> SWord16

sRem :: SWord16 -> SWord16 -> SWord16

sDiv :: SWord16 -> SWord16 -> SWord16

sMod :: SWord16 -> SWord16 -> SWord16

SDivisible SWord8

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord8 -> SWord8 -> (SWord8, SWord8)

sDivMod :: SWord8 -> SWord8 -> (SWord8, SWord8)

sQuot :: SWord8 -> SWord8 -> SWord8

sRem :: SWord8 -> SWord8 -> SWord8

sDiv :: SWord8 -> SWord8 -> SWord8

sMod :: SWord8 -> SWord8 -> SWord8

SDivisible SWord4

SDvisible instance, using default methods

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

sQuotRem :: SWord4 -> SWord4 -> (SWord4, SWord4)

sDivMod :: SWord4 -> SWord4 -> (SWord4, SWord4)

sQuot :: SWord4 -> SWord4 -> SWord4

sRem :: SWord4 -> SWord4 -> SWord4

sDiv :: SWord4 -> SWord4 -> SWord4

sMod :: SWord4 -> SWord4 -> SWord4

SDivisible Word4

SDvisible instance, using 0-extension

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

sQuotRem :: Word4 -> Word4 -> (Word4, Word4)

sDivMod :: Word4 -> Word4 -> (Word4, Word4)

sQuot :: Word4 -> Word4 -> Word4

sRem :: Word4 -> Word4 -> Word4

sDiv :: Word4 -> Word4 -> Word4

sMod :: Word4 -> Word4 -> Word4

Bit-vector operations

Conversions

sFromIntegral :: forall a b. (Integral a, HasKind a, Num a, SymVal a, HasKind b, Num b, SymVal b) => SBV a -> SBV b

Conversion between integral-symbolic values, akin to Haskell's fromIntegral

Shifts and rotates

Symbolic words (both signed and unsigned) are an instance of Haskell's Bits class, so regular bitwise operations are automatically available for them. Shifts and rotates, however, require specialized type-signatures since Haskell insists on an Int second argument for them.

sShiftLeft :: (SIntegral a, SIntegral b) => SBV a -> SBV b -> SBV a

Generalization of shiftL, when the shift-amount is symbolic. Since Haskell's shiftL only takes an Int as the shift amount, it cannot be used when we have a symbolic amount to shift with.

sShiftRight :: (SIntegral a, SIntegral b) => SBV a -> SBV b -> SBV a

Generalization of shiftR, when the shift-amount is symbolic. Since Haskell's shiftR only takes an Int as the shift amount, it cannot be used when we have a symbolic amount to shift with.

NB. If the shiftee is signed, then this is an arithmetic shift; otherwise it's logical, following the usual Haskell convention. See sSignedShiftArithRight for a variant that explicitly uses the msb as the sign bit, even for unsigned underlying types.

sRotateLeft :: (SIntegral a, SIntegral b) => SBV a -> SBV b -> SBV a

Generalization of rotateL, when the shift-amount is symbolic. Since Haskell's rotateL only takes an Int as the shift amount, it cannot be used when we have a symbolic amount to shift with. The first argument should be a bounded quantity.

sBarrelRotateLeft :: (SFiniteBits a, SFiniteBits b) => SBV a -> SBV b -> SBV a

An implementation of rotate-left, using a barrel shifter like design. Only works when both arguments are finite bitvectors, and furthermore when the second argument is unsigned. The first condition is enforced by the type, but the second is dynamically checked. We provide this implementation as an alternative to sRotateLeft since SMTLib logic does not support variable argument rotates (as opposed to shifts), and thus this implementation can produce better code for verification compared to sRotateLeft.

>>> prove $ \x y -> (x `sBarrelRotateLeft`  y) `sBarrelRotateRight` (y :: SWord32) .== (x :: SWord64)
Q.E.D.

sRotateRight :: (SIntegral a, SIntegral b) => SBV a -> SBV b -> SBV a

Generalization of rotateR, when the shift-amount is symbolic. Since Haskell's rotateR only takes an Int as the shift amount, it cannot be used when we have a symbolic amount to shift with. The first argument should be a bounded quantity.

sBarrelRotateRight :: (SFiniteBits a, SFiniteBits b) => SBV a -> SBV b -> SBV a

An implementation of rotate-right, using a barrel shifter like design. See comments for sBarrelRotateLeft for details.

>>> prove $ \x y -> (x `sBarrelRotateRight` y) `sBarrelRotateLeft`  (y :: SWord32) .== (x :: SWord64)
Q.E.D.

sSignedShiftArithRight :: (SFiniteBits a, SIntegral b) => SBV a -> SBV b -> SBV a

Arithmetic shift-right with a symbolic unsigned shift amount. This is equivalent to sShiftRight when the argument is signed. However, if the argument is unsigned, then it explicitly treats its msb as a sign-bit, and uses it as the bit that gets shifted in. Useful when using the underlying unsigned bit representation to implement custom signed operations. Note that there is no direct Haskell analogue of this function.

Finite bit-vector operations

class (Ord a, SymVal a, Num a, Bits a) => SFiniteBits a where

Finite bit-length symbolic values. Essentially the same as SIntegral, but further leaves out Integer. Loosely based on Haskell's FiniteBits class, but with more methods defined and structured differently to fit into the symbolic world view. Minimal complete definition: sFiniteBitSize.

Minimal complete definition

sFiniteBitSize

Methods

sFiniteBitSize :: SBV a -> Int

Bit size.

lsb :: SBV a -> SBool

Least significant bit of a word, always stored at index 0.

msb :: SBV a -> SBool

Most significant bit of a word, always stored at the last position.

blastBE :: SBV a -> [SBool]

Big-endian blasting of a word into its bits.

blastLE :: SBV a -> [SBool]

Little-endian blasting of a word into its bits.

fromBitsBE :: [SBool] -> SBV a

Reconstruct from given bits, given in little-endian.

fromBitsLE :: [SBool] -> SBV a

Reconstruct from given bits, given in little-endian.

sTestBit :: SBV a -> Int -> SBool

Replacement for testBit, returning SBool instead of Bool.

sExtractBits :: SBV a -> [Int] -> [SBool]

Variant of sTestBit, where we want to extract multiple bit positions.

sPopCount :: SBV a -> SWord8

Variant of popCount, returning a symbolic value.

setBitTo :: SBV a -> Int -> SBool -> SBV a

A combo of setBit and clearBit, when the bit to be set is symbolic.

fullAdder :: SBV a -> SBV a -> (SBool, SBV a)

Full adder, returns carry-out from the addition. Only for unsigned quantities.

fullMultiplier :: SBV a -> SBV a -> (SBV a, SBV a)

Full multipler, returns both high and low-order bits. Only for unsigned quantities.

sCountLeadingZeros :: SBV a -> SWord8

Count leading zeros in a word, big-endian interpretation.

sCountTrailingZeros :: SBV a -> SWord8

Count trailing zeros in a word, big-endian interpretation.

Instances

SFiniteBits Int8

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Int8 -> Int

lsb :: SBV Int8 -> SBool

msb :: SBV Int8 -> SBool

blastBE :: SBV Int8 -> [SBool]

blastLE :: SBV Int8 -> [SBool]

fromBitsBE :: [SBool] -> SBV Int8

fromBitsLE :: [SBool] -> SBV Int8

sTestBit :: SBV Int8 -> Int -> SBool

sExtractBits :: SBV Int8 -> [Int] -> [SBool]

sPopCount :: SBV Int8 -> SWord8

setBitTo :: SBV Int8 -> Int -> SBool -> SBV Int8

fullAdder :: SBV Int8 -> SBV Int8 -> (SBool, SBV Int8)

fullMultiplier :: SBV Int8 -> SBV Int8 -> (SBV Int8, SBV Int8)

sCountLeadingZeros :: SBV Int8 -> SWord8

sCountTrailingZeros :: SBV Int8 -> SWord8

SFiniteBits Int16

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Int16 -> Int

lsb :: SBV Int16 -> SBool

msb :: SBV Int16 -> SBool

blastBE :: SBV Int16 -> [SBool]

blastLE :: SBV Int16 -> [SBool]

fromBitsBE :: [SBool] -> SBV Int16

fromBitsLE :: [SBool] -> SBV Int16

sTestBit :: SBV Int16 -> Int -> SBool

sExtractBits :: SBV Int16 -> [Int] -> [SBool]

sPopCount :: SBV Int16 -> SWord8

setBitTo :: SBV Int16 -> Int -> SBool -> SBV Int16

fullAdder :: SBV Int16 -> SBV Int16 -> (SBool, SBV Int16)

fullMultiplier :: SBV Int16 -> SBV Int16 -> (SBV Int16, SBV Int16)

sCountLeadingZeros :: SBV Int16 -> SWord8

sCountTrailingZeros :: SBV Int16 -> SWord8

SFiniteBits Int32

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Int32 -> Int

lsb :: SBV Int32 -> SBool

msb :: SBV Int32 -> SBool

blastBE :: SBV Int32 -> [SBool]

blastLE :: SBV Int32 -> [SBool]

fromBitsBE :: [SBool] -> SBV Int32

fromBitsLE :: [SBool] -> SBV Int32

sTestBit :: SBV Int32 -> Int -> SBool

sExtractBits :: SBV Int32 -> [Int] -> [SBool]

sPopCount :: SBV Int32 -> SWord8

setBitTo :: SBV Int32 -> Int -> SBool -> SBV Int32

fullAdder :: SBV Int32 -> SBV Int32 -> (SBool, SBV Int32)

fullMultiplier :: SBV Int32 -> SBV Int32 -> (SBV Int32, SBV Int32)

sCountLeadingZeros :: SBV Int32 -> SWord8

sCountTrailingZeros :: SBV Int32 -> SWord8

SFiniteBits Int64

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Int64 -> Int

lsb :: SBV Int64 -> SBool

msb :: SBV Int64 -> SBool

blastBE :: SBV Int64 -> [SBool]

blastLE :: SBV Int64 -> [SBool]

fromBitsBE :: [SBool] -> SBV Int64

fromBitsLE :: [SBool] -> SBV Int64

sTestBit :: SBV Int64 -> Int -> SBool

sExtractBits :: SBV Int64 -> [Int] -> [SBool]

sPopCount :: SBV Int64 -> SWord8

setBitTo :: SBV Int64 -> Int -> SBool -> SBV Int64

fullAdder :: SBV Int64 -> SBV Int64 -> (SBool, SBV Int64)

fullMultiplier :: SBV Int64 -> SBV Int64 -> (SBV Int64, SBV Int64)

sCountLeadingZeros :: SBV Int64 -> SWord8

sCountTrailingZeros :: SBV Int64 -> SWord8

SFiniteBits Word8

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Word8 -> Int

lsb :: SBV Word8 -> SBool

msb :: SBV Word8 -> SBool

blastBE :: SBV Word8 -> [SBool]

blastLE :: SBV Word8 -> [SBool]

fromBitsBE :: [SBool] -> SBV Word8

fromBitsLE :: [SBool] -> SBV Word8

sTestBit :: SBV Word8 -> Int -> SBool

sExtractBits :: SBV Word8 -> [Int] -> [SBool]

sPopCount :: SBV Word8 -> SWord8

setBitTo :: SBV Word8 -> Int -> SBool -> SBV Word8

fullAdder :: SBV Word8 -> SBV Word8 -> (SBool, SBV Word8)

fullMultiplier :: SBV Word8 -> SBV Word8 -> (SBV Word8, SBV Word8)

sCountLeadingZeros :: SBV Word8 -> SWord8

sCountTrailingZeros :: SBV Word8 -> SWord8

SFiniteBits Word16

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Word16 -> Int

lsb :: SBV Word16 -> SBool

msb :: SBV Word16 -> SBool

blastBE :: SBV Word16 -> [SBool]

blastLE :: SBV Word16 -> [SBool]

fromBitsBE :: [SBool] -> SBV Word16

fromBitsLE :: [SBool] -> SBV Word16

sTestBit :: SBV Word16 -> Int -> SBool

sExtractBits :: SBV Word16 -> [Int] -> [SBool]

sPopCount :: SBV Word16 -> SWord8

setBitTo :: SBV Word16 -> Int -> SBool -> SBV Word16

fullAdder :: SBV Word16 -> SBV Word16 -> (SBool, SBV Word16)

fullMultiplier :: SBV Word16 -> SBV Word16 -> (SBV Word16, SBV Word16)

sCountLeadingZeros :: SBV Word16 -> SWord8

sCountTrailingZeros :: SBV Word16 -> SWord8

SFiniteBits Word32

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Word32 -> Int

lsb :: SBV Word32 -> SBool

msb :: SBV Word32 -> SBool

blastBE :: SBV Word32 -> [SBool]

blastLE :: SBV Word32 -> [SBool]

fromBitsBE :: [SBool] -> SBV Word32

fromBitsLE :: [SBool] -> SBV Word32

sTestBit :: SBV Word32 -> Int -> SBool

sExtractBits :: SBV Word32 -> [Int] -> [SBool]

sPopCount :: SBV Word32 -> SWord8

setBitTo :: SBV Word32 -> Int -> SBool -> SBV Word32

fullAdder :: SBV Word32 -> SBV Word32 -> (SBool, SBV Word32)

fullMultiplier :: SBV Word32 -> SBV Word32 -> (SBV Word32, SBV Word32)

sCountLeadingZeros :: SBV Word32 -> SWord8

sCountTrailingZeros :: SBV Word32 -> SWord8

SFiniteBits Word64

Defined in Data.SBV.Core.Model

Methods

sFiniteBitSize :: SBV Word64 -> Int

lsb :: SBV Word64 -> SBool

msb :: SBV Word64 -> SBool

blastBE :: SBV Word64 -> [SBool]

blastLE :: SBV Word64 -> [SBool]

fromBitsBE :: [SBool] -> SBV Word64

fromBitsLE :: [SBool] -> SBV Word64

sTestBit :: SBV Word64 -> Int -> SBool

sExtractBits :: SBV Word64 -> [Int] -> [SBool]

sPopCount :: SBV Word64 -> SWord8

setBitTo :: SBV Word64 -> Int -> SBool -> SBV Word64

fullAdder :: SBV Word64 -> SBV Word64 -> (SBool, SBV Word64)

fullMultiplier :: SBV Word64 -> SBV Word64 -> (SBV Word64, SBV Word64)

sCountLeadingZeros :: SBV Word64 -> SWord8

sCountTrailingZeros :: SBV Word64 -> SWord8

Splitting, joining, and extending

class Splittable a b | b -> a where

Splitting an a into two b's and joining back. Intuitively, a is a larger bit-size word than b, typically double. The extend operation captures embedding of a b value into an a without changing its semantic value.

Methods

split :: a -> (b, b)

(#) :: b -> b -> a infixr 5

extend :: b -> a

Instances

Splittable Word8 Word4

Joiningsplitting tofrom Word8

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

split :: Word8 -> (Word4, Word4)

(#) :: Word4 -> Word4 -> Word8

extend :: Word4 -> Word8

Splittable Word16 Word8

Defined in Data.SBV.Core.Splittable

Methods

split :: Word16 -> (Word8, Word8)

(#) :: Word8 -> Word8 -> Word16

extend :: Word8 -> Word16

Splittable Word32 Word16

Defined in Data.SBV.Core.Splittable

Methods

split :: Word32 -> (Word16, Word16)

(#) :: Word16 -> Word16 -> Word32

extend :: Word16 -> Word32

Splittable Word64 Word32

Defined in Data.SBV.Core.Splittable

Methods

split :: Word64 -> (Word32, Word32)

(#) :: Word32 -> Word32 -> Word64

extend :: Word32 -> Word64

Splittable SWord64 SWord32

Defined in Data.SBV.Core.Splittable

Methods

split :: SWord64 -> (SWord32, SWord32)

(#) :: SWord32 -> SWord32 -> SWord64

extend :: SWord32 -> SWord64

Splittable SWord32 SWord16

Defined in Data.SBV.Core.Splittable

Methods

split :: SWord32 -> (SWord16, SWord16)

(#) :: SWord16 -> SWord16 -> SWord32

extend :: SWord16 -> SWord32

Splittable SWord16 SWord8

Defined in Data.SBV.Core.Splittable

Methods

split :: SWord16 -> (SWord8, SWord8)

(#) :: SWord8 -> SWord8 -> SWord16

extend :: SWord8 -> SWord16

Exponentiation

(.^) :: (Mergeable b, Num b, SIntegral e) => b -> SBV e -> b

Symbolic exponentiation using bit blasting and repeated squaring.

N.B. The exponent must be unsigned/bounded if symbolic. Signed exponents will be rejected.

IEEE-floating point numbers

class (SymVal a, RealFloat a) => IEEEFloating a where

A class of floating-point (IEEE754) operations, some of which behave differently based on rounding modes. Note that unless the rounding mode is concretely RoundNearestTiesToEven, we will not concretely evaluate these, but rather pass down to the SMT solver.

Minimal complete definition

Nothing

Methods

fpAbs :: SBV a -> SBV a

Compute the floating point absolute value.

fpNeg :: SBV a -> SBV a

Compute the unary negation. Note that 0 - x is not equivalent to -x for floating-point, since -0 and 0 are different.

fpAdd :: SRoundingMode -> SBV a -> SBV a -> SBV a

Add two floating point values, using the given rounding mode

fpSub :: SRoundingMode -> SBV a -> SBV a -> SBV a

Subtract two floating point values, using the given rounding mode

fpMul :: SRoundingMode -> SBV a -> SBV a -> SBV a

Multiply two floating point values, using the given rounding mode

fpDiv :: SRoundingMode -> SBV a -> SBV a -> SBV a

Divide two floating point values, using the given rounding mode

fpFMA :: SRoundingMode -> SBV a -> SBV a -> SBV a -> SBV a

Fused-multiply-add three floating point values, using the given rounding mode. fpFMA x y z = x*y+z but with only one rounding done for the whole operation; not two. Note that we will never concretely evaluate this function since Haskell lacks an FMA implementation.

fpSqrt :: SRoundingMode -> SBV a -> SBV a

Compute the square-root of a float, using the given rounding mode

fpRem :: SBV a -> SBV a -> SBV a

Compute the remainder: x - y * n, where n is the truncated integer nearest to x/y. The rounding mode is implicitly assumed to be RoundNearestTiesToEven.

fpRoundToIntegral :: SRoundingMode -> SBV a -> SBV a

Round to the nearest integral value, using the given rounding mode.

fpMin :: SBV a -> SBV a -> SBV a

Compute the minimum of two floats, respects infinity and NaN values

fpMax :: SBV a -> SBV a -> SBV a

Compute the maximum of two floats, respects infinity and NaN values

fpIsEqualObject :: SBV a -> SBV a -> SBool

Are the two given floats exactly the same. That is, NaN will compare equal to itself, +0 will not compare equal to -0 etc. This is the object level equality, as opposed to the semantic equality. (For the latter, just use .==.)

fpIsNormal :: SBV a -> SBool

Is the floating-point number a normal value. (i.e., not denormalized.)

fpIsSubnormal :: SBV a -> SBool

Is the floating-point number a subnormal value. (Also known as denormal.)

fpIsZero :: SBV a -> SBool

Is the floating-point number 0? (Note that both +0 and -0 will satisfy this predicate.)

fpIsInfinite :: SBV a -> SBool

Is the floating-point number infinity? (Note that both +oo and -oo will satisfy this predicate.)

fpIsNaN :: SBV a -> SBool

Is the floating-point number a NaN value?

fpIsNegative :: SBV a -> SBool

Is the floating-point number negative? Note that -0 satisfies this predicate but +0 does not.

fpIsPositive :: SBV a -> SBool

Is the floating-point number positive? Note that +0 satisfies this predicate but -0 does not.

fpIsNegativeZero :: SBV a -> SBool

Is the floating point number -0?

fpIsPositiveZero :: SBV a -> SBool

Is the floating point number +0?

fpIsPoint :: SBV a -> SBool

Is the floating-point number a regular floating point, i.e., not NaN, nor +oo, nor -oo. Normals or denormals are allowed.

Instances

IEEEFloating Double

SDouble instance

Defined in Data.SBV.Core.Floating

Methods

fpAbs :: SBV Double -> SBV Double

fpNeg :: SBV Double -> SBV Double

fpAdd :: SRoundingMode -> SBV Double -> SBV Double -> SBV Double

fpSub :: SRoundingMode -> SBV Double -> SBV Double -> SBV Double

fpMul :: SRoundingMode -> SBV Double -> SBV Double -> SBV Double

fpDiv :: SRoundingMode -> SBV Double -> SBV Double -> SBV Double

fpFMA :: SRoundingMode -> SBV Double -> SBV Double -> SBV Double -> SBV Double

fpSqrt :: SRoundingMode -> SBV Double -> SBV Double

fpRem :: SBV Double -> SBV Double -> SBV Double

fpRoundToIntegral :: SRoundingMode -> SBV Double -> SBV Double

fpMin :: SBV Double -> SBV Double -> SBV Double

fpMax :: SBV Double -> SBV Double -> SBV Double

fpIsEqualObject :: SBV Double -> SBV Double -> SBool

fpIsNormal :: SBV Double -> SBool

fpIsSubnormal :: SBV Double -> SBool

fpIsZero :: SBV Double -> SBool

fpIsInfinite :: SBV Double -> SBool

fpIsNaN :: SBV Double -> SBool

fpIsNegative :: SBV Double -> SBool

fpIsPositive :: SBV Double -> SBool

fpIsNegativeZero :: SBV Double -> SBool

fpIsPositiveZero :: SBV Double -> SBool

fpIsPoint :: SBV Double -> SBool

IEEEFloating Float

SFloat instance

Defined in Data.SBV.Core.Floating

Methods

fpAbs :: SBV Float -> SBV Float

fpNeg :: SBV Float -> SBV Float

fpAdd :: SRoundingMode -> SBV Float -> SBV Float -> SBV Float

fpSub :: SRoundingMode -> SBV Float -> SBV Float -> SBV Float

fpMul :: SRoundingMode -> SBV Float -> SBV Float -> SBV Float

fpDiv :: SRoundingMode -> SBV Float -> SBV Float -> SBV Float

fpFMA :: SRoundingMode -> SBV Float -> SBV Float -> SBV Float -> SBV Float

fpSqrt :: SRoundingMode -> SBV Float -> SBV Float

fpRem :: SBV Float -> SBV Float -> SBV Float

fpRoundToIntegral :: SRoundingMode -> SBV Float -> SBV Float

fpMin :: SBV Float -> SBV Float -> SBV Float

fpMax :: SBV Float -> SBV Float -> SBV Float

fpIsEqualObject :: SBV Float -> SBV Float -> SBool

fpIsNormal :: SBV Float -> SBool

fpIsSubnormal :: SBV Float -> SBool

fpIsZero :: SBV Float -> SBool

fpIsInfinite :: SBV Float -> SBool

fpIsNaN :: SBV Float -> SBool

fpIsNegative :: SBV Float -> SBool

fpIsPositive :: SBV Float -> SBool

fpIsNegativeZero :: SBV Float -> SBool

fpIsPositiveZero :: SBV Float -> SBool

fpIsPoint :: SBV Float -> SBool

data RoundingMode

Rounding mode to be used for the IEEE floating-point operations. Note that Haskell's default is RoundNearestTiesToEven. If you use a different rounding mode, then the counter-examples you get may not match what you observe in Haskell.

Constructors

RoundNearestTiesToEven

Round to nearest representable floating point value. If precisely at half-way, pick the even number. (In this context, even means the lowest-order bit is zero.)

RoundNearestTiesToAway

Round to nearest representable floating point value. If precisely at half-way, pick the number further away from 0. (That is, for positive values, pick the greater; for negative values, pick the smaller.)

RoundTowardPositive

Round towards positive infinity. (Also known as rounding-up or ceiling.)

RoundTowardNegative

Round towards negative infinity. (Also known as rounding-down or floor.)

RoundTowardZero

Round towards zero. (Also known as truncation.)

Instances

Bounded RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

minBound :: RoundingMode

maxBound :: RoundingMode

Enum RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

succ :: RoundingMode -> RoundingMode

pred :: RoundingMode -> RoundingMode

toEnum :: Int -> RoundingMode

fromEnum :: RoundingMode -> Int

enumFrom :: RoundingMode -> [RoundingMode]

enumFromThen :: RoundingMode -> RoundingMode -> [RoundingMode]

enumFromTo :: RoundingMode -> RoundingMode -> [RoundingMode]

enumFromThenTo :: RoundingMode -> RoundingMode -> RoundingMode -> [RoundingMode]

Eq RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

(==) :: RoundingMode -> RoundingMode -> Bool

(/=) :: RoundingMode -> RoundingMode -> Bool

Data RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> RoundingMode -> c RoundingMode

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c RoundingMode

toConstr :: RoundingMode -> Constr

dataTypeOf :: RoundingMode -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c RoundingMode)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c RoundingMode)

gmapT :: (forall b. Data b => b -> b) -> RoundingMode -> RoundingMode

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> RoundingMode -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> RoundingMode -> r

gmapQ :: (forall d. Data d => d -> u) -> RoundingMode -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> RoundingMode -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> RoundingMode -> m RoundingMode

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> RoundingMode -> m RoundingMode

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> RoundingMode -> m RoundingMode

Ord RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

compare :: RoundingMode -> RoundingMode -> Ordering

(<) :: RoundingMode -> RoundingMode -> Bool

(<=) :: RoundingMode -> RoundingMode -> Bool

(>) :: RoundingMode -> RoundingMode -> Bool

(>=) :: RoundingMode -> RoundingMode -> Bool

max :: RoundingMode -> RoundingMode -> RoundingMode

min :: RoundingMode -> RoundingMode -> RoundingMode

Read RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

readsPrec :: Int -> ReadS RoundingMode

readList :: ReadS [RoundingMode]

readPrec :: ReadPrec RoundingMode

readListPrec :: ReadPrec [RoundingMode]

Show RoundingMode

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> RoundingMode -> ShowS

show :: RoundingMode -> String

showList :: [RoundingMode] -> ShowS

HasKind RoundingMode

RoundingMode kind

Defined in Data.SBV.Core.Symbolic

Methods

kindOf :: RoundingMode -> Kind

hasSign :: RoundingMode -> Bool

intSizeOf :: RoundingMode -> Int

isBoolean :: RoundingMode -> Bool

isBounded :: RoundingMode -> Bool

isReal :: RoundingMode -> Bool

isFloat :: RoundingMode -> Bool

isDouble :: RoundingMode -> Bool

isUnbounded :: RoundingMode -> Bool

isUninterpreted :: RoundingMode -> Bool

isChar :: RoundingMode -> Bool

isString :: RoundingMode -> Bool

isList :: RoundingMode -> Bool

isSet :: RoundingMode -> Bool

isTuple :: RoundingMode -> Bool

isMaybe :: RoundingMode -> Bool

isEither :: RoundingMode -> Bool

showType :: RoundingMode -> String

SymVal RoundingMode

RoundingMode can be used symbolically

Defined in Data.SBV.Core.Data

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV RoundingMode)

literal :: RoundingMode -> SBV RoundingMode

fromCV :: CV -> RoundingMode

isConcretely :: SBV RoundingMode -> (RoundingMode -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV RoundingMode)

forall_ :: MonadSymbolic m => m (SBV RoundingMode)

mkForallVars :: MonadSymbolic m => Int -> m [SBV RoundingMode]

exists :: MonadSymbolic m => String -> m (SBV RoundingMode)

exists_ :: MonadSymbolic m => m (SBV RoundingMode)

mkExistVars :: MonadSymbolic m => Int -> m [SBV RoundingMode]

free :: MonadSymbolic m => String -> m (SBV RoundingMode)

free_ :: MonadSymbolic m => m (SBV RoundingMode)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV RoundingMode]

symbolic :: MonadSymbolic m => String -> m (SBV RoundingMode)

symbolics :: MonadSymbolic m => [String] -> m [SBV RoundingMode]

unliteral :: SBV RoundingMode -> Maybe RoundingMode

isConcrete :: SBV RoundingMode -> Bool

isSymbolic :: SBV RoundingMode -> Bool

SatModel RoundingMode

A rounding mode, extracted from a model. (Default definition suffices)

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (RoundingMode, [CV])

cvtModel :: (RoundingMode -> Maybe b) -> Maybe (RoundingMode, [CV]) -> Maybe (b, [CV])

type SRoundingMode = SBV RoundingMode

The symbolic variant of RoundingMode

nan :: Floating a => a

Not-A-Number for Double and Float. Surprisingly, Haskell Prelude doesn't have this value defined, so we provide it here.

infinity :: Floating a => a

Infinity for Double and Float. Surprisingly, Haskell Prelude doesn't have this value defined, so we provide it here.

sNaN :: (Floating a, SymVal a) => SBV a

Symbolic variant of Not-A-Number. This value will inhabit both SDouble and SFloat.

sInfinity :: (Floating a, SymVal a) => SBV a

Symbolic variant of infinity. This value will inhabit both SDouble and SFloat.

Rounding modes

sRoundNearestTiesToEven :: SRoundingMode

Symbolic variant of RoundNearestTiesToEven

sRoundNearestTiesToAway :: SRoundingMode

Symbolic variant of RoundNearestTiesToAway

sRoundTowardPositive :: SRoundingMode

Symbolic variant of RoundTowardPositive

sRoundTowardNegative :: SRoundingMode

Symbolic variant of RoundTowardNegative

sRoundTowardZero :: SRoundingMode

Symbolic variant of RoundTowardZero

sRNE :: SRoundingMode

Alias for sRoundNearestTiesToEven

sRNA :: SRoundingMode

Alias for sRoundNearestTiesToAway

sRTP :: SRoundingMode

Alias for sRoundTowardPositive

sRTN :: SRoundingMode

Alias for sRoundTowardNegative

sRTZ :: SRoundingMode

Alias for sRoundTowardZero

Conversion to/from floats

class SymVal a => IEEEFloatConvertible a where

Capture convertability from/to FloatingPoint representations.

Conversions to float: toSFloat and toSDouble simply return the nearest representable float from the given type based on the rounding mode provided.

Conversions from float: fromSFloat and fromSDouble functions do the reverse conversion. However some care is needed when given values that are not representable in the integral target domain. For instance, converting an SFloat to an SInt8 is problematic. The rules are as follows:

If the input value is a finite point and when rounded in the given rounding mode to an integral value lies within the target bounds, then that result is returned. (This is the regular interpretation of rounding in IEEE754.)

Otherwise (i.e., if the integral value in the float or double domain) doesn't fit into the target type, then the result is unspecified. Note that if the input is +oo, -oo, or NaN, then the result is unspecified.

Due to the unspecified nature of conversions, SBV will never constant fold conversions from floats to integral values. That is, you will always get a symbolic value as output. (Conversions from floats to other floats will be constant folded. Conversions from integral values to floats will also be constant folded.)

Note that unspecified really means unspecified: In particular, SBV makes no guarantees about matching the behavior between what you might get in Haskell, via SMT-Lib, or the C-translation. If the input value is out-of-bounds as defined above, or is NaN or oo or -oo, then all bets are off. In particular C and SMTLib are decidedly undefine this case, though that doesn't mean they do the same thing! Same goes for Haskell, which seems to convert via Int64, but we do not model that behavior in SBV as it doesn't seem to be intentional nor well documented.

You can check for NaN, oo and -oo, using the predicates fpIsNaN, fpIsInfinite, and fpIsPositive, fpIsNegative predicates, respectively; and do the proper conversion based on your needs. (0 is a good choice, as are min/max bounds of the target type.)

Currently, SBV provides no predicates to check if a value would lie within range for a particular conversion task, as this depends on the rounding mode and the types involved and can be rather tricky to determine. (See http://github.com/LeventErkok/sbv/issues/456 for a discussion of the issues involved.) In a future release, we hope to be able to provide underflow and overflow predicates for these conversions as well.

Minimal complete definition

Nothing

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV a

Convert from an IEEE74 single precision float.

toSFloat :: SRoundingMode -> SBV a -> SFloat

Convert to an IEEE-754 Single-precision float.

>>> :{
roundTrip :: forall a. (Eq a, IEEEFloatConvertible a) => SRoundingMode -> SBV a -> SBool
roundTrip m x = fromSFloat m (toSFloat m x) .== x
:}

>>> prove $ roundTrip @Int8
Q.E.D.
>>> prove $ roundTrip @Word8
Q.E.D.
>>> prove $ roundTrip @Int16
Q.E.D.
>>> prove $ roundTrip @Word16
Q.E.D.
>>> prove $ roundTrip @Int32
Falsifiable. Counter-example:
  s0 = RoundNearestTiesToEven :: RoundingMode
  s1 =            -2130176960 :: Int32

Note how we get a failure on Int32. The counter-example value is not representable exactly as a single precision float:

>>> toRational (-2130176960 :: Float)
(-2130177024) % 1

Note how the numerator is different, it is off by 64. This is hardly surprising, since floats become sparser as the magnitude increases to be able to cover all the integer values representable.

toSFloat :: Integral a => SRoundingMode -> SBV a -> SFloat

Convert to an IEEE-754 Single-precision float.

>>> :{
roundTrip :: forall a. (Eq a, IEEEFloatConvertible a) => SRoundingMode -> SBV a -> SBool
roundTrip m x = fromSFloat m (toSFloat m x) .== x
:}

>>> prove $ roundTrip @Int8
Q.E.D.
>>> prove $ roundTrip @Word8
Q.E.D.
>>> prove $ roundTrip @Int16
Q.E.D.
>>> prove $ roundTrip @Word16
Q.E.D.
>>> prove $ roundTrip @Int32
Falsifiable. Counter-example:
  s0 = RoundNearestTiesToEven :: RoundingMode
  s1 =            -2130176960 :: Int32

Note how we get a failure on Int32. The counter-example value is not representable exactly as a single precision float:

>>> toRational (-2130176960 :: Float)
(-2130177024) % 1

Note how the numerator is different, it is off by 64. This is hardly surprising, since floats become sparser as the magnitude increases to be able to cover all the integer values representable.

fromSDouble :: SRoundingMode -> SDouble -> SBV a

Convert from an IEEE74 double precision float.

toSDouble :: SRoundingMode -> SBV a -> SDouble

Convert to an IEEE-754 Double-precision float.

>>> :{
roundTrip :: forall a. (Eq a, IEEEFloatConvertible a) => SRoundingMode -> SBV a -> SBool
roundTrip m x = fromSDouble m (toSDouble m x) .== x
:}

>>> prove $ roundTrip @Int8
Q.E.D.
>>> prove $ roundTrip @Word8
Q.E.D.
>>> prove $ roundTrip @Int16
Q.E.D.
>>> prove $ roundTrip @Word16
Q.E.D.
>>> prove $ roundTrip @Int32
Q.E.D.
>>> prove $ roundTrip @Word32
Q.E.D.
>>> prove $ roundTrip @Int64
Falsifiable. Counter-example:
  s0 = RoundNearestTiesToEven :: RoundingMode
  s1 =    4611686018427387902 :: Int64

Just like in the SFloat case, once we reach 64-bits, we no longer can exactly represent the integer value for all possible values:

>>> toRational (4611686018427387902 ::Double)
4611686018427387904 % 1

In this case the numerator is off by 2!

toSDouble :: Integral a => SRoundingMode -> SBV a -> SDouble

Convert to an IEEE-754 Double-precision float.

>>> :{
roundTrip :: forall a. (Eq a, IEEEFloatConvertible a) => SRoundingMode -> SBV a -> SBool
roundTrip m x = fromSDouble m (toSDouble m x) .== x
:}

>>> prove $ roundTrip @Int8
Q.E.D.
>>> prove $ roundTrip @Word8
Q.E.D.
>>> prove $ roundTrip @Int16
Q.E.D.
>>> prove $ roundTrip @Word16
Q.E.D.
>>> prove $ roundTrip @Int32
Q.E.D.
>>> prove $ roundTrip @Word32
Q.E.D.
>>> prove $ roundTrip @Int64
Falsifiable. Counter-example:
  s0 = RoundNearestTiesToEven :: RoundingMode
  s1 =    4611686018427387902 :: Int64

Just like in the SFloat case, once we reach 64-bits, we no longer can exactly represent the integer value for all possible values:

>>> toRational (4611686018427387902 ::Double)
4611686018427387904 % 1

In this case the numerator is off by 2!

Instances

IEEEFloatConvertible Double

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Double

toSFloat :: SRoundingMode -> SBV Double -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Double

toSDouble :: SRoundingMode -> SBV Double -> SDouble

IEEEFloatConvertible Float

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Float

toSFloat :: SRoundingMode -> SBV Float -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Float

toSDouble :: SRoundingMode -> SBV Float -> SDouble

IEEEFloatConvertible Int8

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Int8

toSFloat :: SRoundingMode -> SBV Int8 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Int8

toSDouble :: SRoundingMode -> SBV Int8 -> SDouble

IEEEFloatConvertible Int16

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Int16

toSFloat :: SRoundingMode -> SBV Int16 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Int16

toSDouble :: SRoundingMode -> SBV Int16 -> SDouble

IEEEFloatConvertible Int32

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Int32

toSFloat :: SRoundingMode -> SBV Int32 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Int32

toSDouble :: SRoundingMode -> SBV Int32 -> SDouble

IEEEFloatConvertible Int64

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Int64

toSFloat :: SRoundingMode -> SBV Int64 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Int64

toSDouble :: SRoundingMode -> SBV Int64 -> SDouble

IEEEFloatConvertible Integer

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Integer

toSFloat :: SRoundingMode -> SBV Integer -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Integer

toSDouble :: SRoundingMode -> SBV Integer -> SDouble

IEEEFloatConvertible Word8

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Word8

toSFloat :: SRoundingMode -> SBV Word8 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Word8

toSDouble :: SRoundingMode -> SBV Word8 -> SDouble

IEEEFloatConvertible Word16

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Word16

toSFloat :: SRoundingMode -> SBV Word16 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Word16

toSDouble :: SRoundingMode -> SBV Word16 -> SDouble

IEEEFloatConvertible Word32

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Word32

toSFloat :: SRoundingMode -> SBV Word32 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Word32

toSDouble :: SRoundingMode -> SBV Word32 -> SDouble

IEEEFloatConvertible Word64

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV Word64

toSFloat :: SRoundingMode -> SBV Word64 -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV Word64

toSDouble :: SRoundingMode -> SBV Word64 -> SDouble

IEEEFloatConvertible AlgReal

Defined in Data.SBV.Core.Floating

Methods

fromSFloat :: SRoundingMode -> SFloat -> SBV AlgReal

toSFloat :: SRoundingMode -> SBV AlgReal -> SFloat

fromSDouble :: SRoundingMode -> SDouble -> SBV AlgReal

toSDouble :: SRoundingMode -> SBV AlgReal -> SDouble

Bit-pattern conversions

sFloatAsSWord32 :: SFloat -> SWord32

Convert an SFloat to an SWord32, preserving the bit-correspondence. Note that since the representation for NaNs are not unique, this function will return a symbolic value when given a concrete NaN.

Implementation note: Since there's no corresponding function in SMTLib for conversion to bit-representation due to partiality, we use a translation trick by allocating a new word variable, converting it to float, and requiring it to be equivalent to the input. In code-generation mode, we simply map it to a simple conversion.

sWord32AsSFloat :: SWord32 -> SFloat

Reinterpret the bits in a 32-bit word as a single-precision floating point number

sDoubleAsSWord64 :: SDouble -> SWord64

Convert an SDouble to an SWord64, preserving the bit-correspondence. Note that since the representation for NaNs are not unique, this function will return a symbolic value when given a concrete NaN.

See the implementation note for sFloatAsSWord32, as it applies here as well.

sWord64AsSDouble :: SWord64 -> SDouble

Reinterpret the bits in a 32-bit word as a single-precision floating point number

blastSFloat :: SFloat -> (SBool, [SBool], [SBool])

Extract the sign/exponent/mantissa of a single-precision float. The output will have 8 bits in the second argument for exponent, and 23 in the third for the mantissa.

blastSDouble :: SDouble -> (SBool, [SBool], [SBool])

Extract the sign/exponent/mantissa of a single-precision float. The output will have 11 bits in the second argument for exponent, and 52 in the third for the mantissa.

Enumerations

If the uninterpreted sort definition takes the form of an enumeration (i.e., a simple data type with all nullary constructors), then SBV will actually translate that as just such a data-type to SMT-Lib, and will use the constructors as the inhabitants of the said sort. A simple example is:

    data X = A | B | C
    mkSymbolicEnumeration ''X

Note the magic incantation mkSymbolicEnumeration ''X. For this to work, you need to have the following options turned on:

  LANGUAGE TemplateHaskell
  LANGUAGE StandaloneDeriving
  LANGUAGE DeriveDataTypeable
  LANGUAGE DeriveAnyClass

Now, the user can define

    type SX = SBV X

and treat SX as a regular symbolic type ranging over the values A, B, and C. Such values can be compared for equality, and with the usual other comparison operators, such as .==, ./=, .>, .>=, <, and <=.

Note that in this latter case the type is no longer uninterpreted, but is properly represented as a simple enumeration of the said elements. A simple query would look like:

     allSat $ x -> x .== (x :: SX)

which would list all three elements of this domain as satisfying solutions.

     Solution #1:
       s0 = A :: X
     Solution #2:
       s0 = B :: X
     Solution #3:
       s0 = C :: X
     Found 3 different solutions.

Note that the result is properly typed as X elements; these are not mere strings. So, in a getModelAssignment scenario, the user can recover actual elements of the domain and program further with those values as usual.

See Documentation.SBV.Examples.Misc.Enumerate for an extended example on how to use symbolic enumerations.

mkSymbolicEnumeration :: Name -> Q [Dec]

Make an enumeration a symbolic type.

Uninterpreted sorts, constants, and functions

Users can introduce new uninterpreted sorts simply by defining a data-type in Haskell and registering it as such. The following example demonstrates:

    data B = B () deriving (Eq, Ord, Show, Read, Data, SymVal, HasKind, SatModel)
 

(Note that you'll also need to use the language pragmas DeriveDataTypeable, DeriveAnyClass, and import Data.Generics for the above to work.)

This is all it takes to introduce B as an uninterpreted sort in SBV, which makes the type SBV B automagically become available as the type of symbolic values that ranges over B values. Note that the () argument is important to distinguish it from enumerations, which will be translated to proper SMT data-types.

Uninterpreted functions over both uninterpreted and regular sorts can be declared using the facilities introduced by the Uninterpreted class.

class Uninterpreted a where

Uninterpreted constants and functions. An uninterpreted constant is a value that is indexed by its name. The only property the prover assumes about these values are that they are equivalent to themselves; i.e., (for functions) they return the same results when applied to same arguments. We support uninterpreted-functions as a general means of black-box'ing operations that are irrelevant for the purposes of the proof; i.e., when the proofs can be performed without any knowledge about the function itself.

Minimal complete definition: sbvUninterpret. However, most instances in practice are already provided by SBV, so end-users should not need to define their own instances.

Minimal complete definition

sbvUninterpret

Methods

uninterpret :: String -> a

Uninterpret a value, receiving an object that can be used instead. Use this version when you do not need to add an axiom about this value.

cgUninterpret :: String -> [String] -> a -> a

Uninterpret a value, only for the purposes of code-generation. For execution and verification the value is used as is. For code-generation, the alternate definition is used. This is useful when we want to take advantage of native libraries on the target languages.

sbvUninterpret :: Maybe ([String], a) -> String -> a

Most generalized form of uninterpretation, this function should not be needed by end-user-code, but is rather useful for the library development.

Instances

HasKind a => Uninterpreted (SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV a

cgUninterpret :: String -> [String] -> SBV a -> SBV a

sbvUninterpret :: Maybe ([String], SBV a) -> String -> SBV a

(SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV c, SBV b) -> SBV a) -> (SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV c, SBV b) -> SBV a) -> String -> (SBV c, SBV b) -> SBV a

(SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV d, SBV c, SBV b) -> SBV a) -> (SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV d, SBV c, SBV b) -> SBV a

(SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal h, SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal h, SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV d -> SBV c -> SBV b -> SBV a) -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV c -> SBV b -> SBV a) -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV c -> SBV b -> SBV a) -> String -> SBV c -> SBV b -> SBV a

(SymVal b, HasKind a) => Uninterpreted (SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV b -> SBV a) -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV b -> SBV a) -> String -> SBV b -> SBV a

addAxiom :: String -> [String] -> Symbolic ()

Add a user specified axiom to the generated SMT-Lib file. The first argument is a mere string, use for commenting purposes. The second argument is intended to hold the multiple-lines of the axiom text as expressed in SMT-Lib notation. Note that we perform no checks on the axiom itself, to see whether it's actually well-formed or is sensical by any means. A separate formalization of SMT-Lib would be very useful here.

NB. For a version which generalizes over the underlying monad, see addAxiom

Properties, proofs, and satisfiability

The SBV library provides a "push-button" verification system via automated SMT solving. The design goal is to let SMT solvers be used without any knowledge of how SMT solvers work or how different logics operate. The details are hidden behind the SBV framework, providing Haskell programmers with a clean API that is unencumbered by the details of individual solvers. To that end, we use the SMT-Lib standard (http://smtlib.cs.uiowa.edu/) to communicate with arbitrary SMT solvers.

A note on reasoning in the presence of quantifers

Note that SBV allows reasoning with quantifiers: Inputs can be existentially or universally quantified. Predicates can be built with arbitrary nesting of such quantifiers as well. However, SBV always assumes that the input is in prenex-normal form: http://en.wikipedia.org/wiki/Prenex_normal_form. That is, all the input declarations are treated as happening at the beginning of a predicate, followed by the actual formula. Unfortunately, the way predicates are written can be misleading at times, since symbolic inputs can be created at arbitrary points; interleaving them with other code. The rule is simple, however: All inputs are assumed at the top, in the order declared, regardless of their quantifiers. SBV will apply skolemization to get rid of existentials before sending predicates to backend solvers. However, if you do want nested quantification, you will manually have to first convert to prenex-normal form (which produces an equisatisfiable but not necessarily equivalent formula), and code that explicitly in SBV. See http://github.com/LeventErkok/sbv/issues/256 for a detailed discussion of this issue.

Using multiple solvers

On a multi-core machine, it might be desirable to try a given property using multiple SMT solvers, using parallel threads. Even with machines with single-cores, threading can be helpful if you want to try out multiple-solvers but do not know which one would work the best for the problem at hand ahead of time.

SBV allows proving/satisfiability-checking with multiple backends at the same time. Each function comes in two variants, one that returns the results from all solvers, the other that returns the fastest one.

The All variants, (i.e., proveWithAll, satWithAll) run all solvers and return all the results. SBV internally makes sure that the result is lazily generated; so, the order of solvers given does not matter. In other words, the order of results will follow the order of the solvers as they finish, not as given by the user. These variants are useful when you want to make sure multiple-solvers agree (or disagree!) on a given problem.

The Any variants, (i.e., proveWithAny, satWithAny) will run all the solvers in parallel, and return the results of the first one finishing. The other threads will then be killed. These variants are useful when you do not care if the solvers produce the same result, but rather want to get the solution as quickly as possible, taking advantage of modern many-core machines.

Note that the function sbvAvailableSolvers will return all the installed solvers, which can be used as the first argument to all these functions, if you simply want to try all available solvers on a machine.

type Predicate = Symbolic SBool

A predicate is a symbolic program that returns a (symbolic) boolean value. For all intents and purposes, it can be treated as an n-ary function from symbolic-values to a boolean. The Symbolic monad captures the underlying representation, and can/should be ignored by the users of the library, unless you are building further utilities on top of SBV itself. Instead, simply use the Predicate type when necessary.

type Goal = Symbolic ()

A goal is a symbolic program that returns no values. The idea is that the constraints/min-max goals will serve as appropriate directives for sat/prove calls.

type Provable = MProvable IO

Provable is specialization of MProvable to the IO monad. Unless you are using transformers explicitly, this is the type you should prefer.

forAll_ :: Provable a => a -> Symbolic SBool

Turns a value into a universally quantified predicate, internally naming the inputs. In this case the sbv library will use names of the form s1, s2, etc. to name these variables Example:

 forAll_ $ \(x::SWord8) y -> x `shiftL` 2 .== y

is a predicate with two arguments, captured using an ordinary Haskell function. Internally, x will be named s0 and y will be named s1.

NB. For a version which generalizes over the underlying monad, see forAll_

forAll :: Provable a => [String] -> a -> Symbolic SBool

Turns a value into a predicate, allowing users to provide names for the inputs. If the user does not provide enough number of names for the variables, the remaining ones will be internally generated. Note that the names are only used for printing models and has no other significance; in particular, we do not check that they are unique. Example:

 forAll ["x", "y"] $ \(x::SWord8) y -> x `shiftL` 2 .== y

This is the same as above, except the variables will be named x and y respectively, simplifying the counter-examples when they are printed.

NB. For a version which generalizes over the underlying monad, see forAll

forSome_ :: Provable a => a -> Symbolic SBool

Turns a value into an existentially quantified predicate. (Indeed, exists would have been a better choice here for the name, but alas it's already taken.)

NB. For a version which generalizes over the underlying monad, see forSome_

forSome :: Provable a => [String] -> a -> Symbolic SBool

Version of forSome that allows user defined names.

NB. For a version which generalizes over the underlying monad, see forSome

prove :: Provable a => a -> IO ThmResult

Prove a predicate, using the default solver.

NB. For a version which generalizes over the underlying monad, see prove

proveWith :: Provable a => SMTConfig -> a -> IO ThmResult

Prove the predicate using the given SMT-solver.

NB. For a version which generalizes over the underlying monad, see proveWith

sat :: Provable a => a -> IO SatResult

Find a satisfying assignment for a predicate, using the default solver.

NB. For a version which generalizes over the underlying monad, see sat

satWith :: Provable a => SMTConfig -> a -> IO SatResult

Find a satisfying assignment using the given SMT-solver.

NB. For a version which generalizes over the underlying monad, see satWith

allSat :: Provable a => a -> IO AllSatResult

Find all satisfying assignments, using the default solver. Equivalent to allSatWith defaultSMTCfg. See allSatWith for details.

NB. For a version which generalizes over the underlying monad, see allSat

allSatWith :: Provable a => SMTConfig -> a -> IO AllSatResult

Return all satisfying assignments for a predicate. Note that this call will block until all satisfying assignments are found. If you have a problem with infinitely many satisfying models (consider SInteger) or a very large number of them, you might have to wait for a long time. To avoid such cases, use the allSatMaxModelCount parameter in the configuration.

NB. Uninterpreted constant/function values and counter-examples for array values are ignored for the purposes of allSat. That is, only the satisfying assignments modulo uninterpreted functions and array inputs will be returned. This is due to the limitation of not having a robust means of getting a function counter-example back from the SMT solver. Find all satisfying assignments using the given SMT-solver

NB. For a version which generalizes over the underlying monad, see allSatWith

optimize :: Provable a => OptimizeStyle -> a -> IO OptimizeResult

Optimize a given collection of Objectives.

NB. For a version which generalizes over the underlying monad, see optimize

optimizeWith :: Provable a => SMTConfig -> OptimizeStyle -> a -> IO OptimizeResult

Optimizes the objectives using the given SMT-solver.

NB. For a version which generalizes over the underlying monad, see optimizeWith

isVacuous :: Provable a => a -> IO Bool

Check if the constraints given are consistent, using the default solver.

NB. For a version which generalizes over the underlying monad, see isVacuous

isVacuousWith :: Provable a => SMTConfig -> a -> IO Bool

Determine if the constraints are vacuous using the given SMT-solver.

NB. For a version which generalizes over the underlying monad, see isVacuousWith

isTheorem :: Provable a => a -> IO Bool

Checks theoremhood using the default solver.

NB. For a version which generalizes over the underlying monad, see isTheorem

isTheoremWith :: Provable a => SMTConfig -> a -> IO Bool

Check whether a given property is a theorem.

NB. For a version which generalizes over the underlying monad, see isTheoremWith

isSatisfiable :: Provable a => a -> IO Bool

Checks satisfiability using the default solver.

NB. For a version which generalizes over the underlying monad, see isSatisfiable

isSatisfiableWith :: Provable a => SMTConfig -> a -> IO Bool

Check whether a given property is satisfiable.

NB. For a version which generalizes over the underlying monad, see isSatisfiableWith

proveWithAll :: Provable a => [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, ThmResult)]

Prove a property with multiple solvers, running them in separate threads. The results will be returned in the order produced.

proveWithAny :: Provable a => [SMTConfig] -> a -> IO (Solver, NominalDiffTime, ThmResult)

Prove a property with multiple solvers, running them in separate threads. Only the result of the first one to finish will be returned, remaining threads will be killed. Note that we send a ThreadKilled to the losing processes, but we do *not* actually wait for them to finish. In rare cases this can lead to zombie processes. In previous experiments, we found that some processes take their time to terminate. So, this solution favors quick turnaround.

satWithAll :: Provable a => [SMTConfig] -> a -> IO [(Solver, NominalDiffTime, SatResult)]

Find a satisfying assignment to a property with multiple solvers, running them in separate threads. The results will be returned in the order produced.

satWithAny :: Provable a => [SMTConfig] -> a -> IO (Solver, NominalDiffTime, SatResult)

Find a satisfying assignment to a property with multiple solvers, running them in separate threads. Only the result of the first one to finish will be returned, remaining threads will be killed. Note that we send a ThreadKilled to the losing processes, but we do *not* actually wait for them to finish. In rare cases this can lead to zombie processes. In previous experiments, we found that some processes take their time to terminate. So, this solution favors quick turnaround.

generateSMTBenchmark :: (MonadIO m, MProvable m a) => Bool -> a -> m String

Create an SMT-Lib2 benchmark. The Bool argument controls whether this is a SAT instance, i.e., translate the query directly, or a PROVE instance, i.e., translate the negated query.

solve :: [SBool] -> Symbolic SBool

Form the symbolic conjunction of a given list of boolean conditions. Useful in expressing problems with constraints, like the following:

  sat $ do [x, y, z] <- sIntegers ["x", "y", "z"]
           solve [x .> 5, y + z .< x]

NB. For a version which generalizes over the underlying monad, see solve

Constraints

A constraint is a means for restricting the input domain of a formula. Here's a simple example:

   do x <- exists "x"
      y <- exists "y"
      constrain $ x .> y
      constrain $ x + y .>= 12
      constrain $ y .>= 3
      ...

The first constraint requires x to be larger than y. The scond one says that sum of x and y must be at least 12, and the final one says that y to be at least 3. Constraints provide an easy way to assert additional properties on the input domain, right at the point of the introduction of variables.

Note that the proper reading of a constraint depends on the context:

• In a sat (or allSat) call: The constraint added is asserted conjunctively. That is, the resulting satisfying model (if any) will always satisfy all the constraints given.
• In a prove call: In this case, the constraint acts as an implication. The property is proved under the assumption that the constraint holds. In other words, the constraint says that we only care about the input space that satisfies the constraint.
• In a quickCheck call: The constraint acts as a filter for quickCheck; if the constraint does not hold, then the input value is considered to be irrelevant and is skipped. Note that this is similar to prove, but is stronger: We do not accept a test case to be valid just because the constraints fail on them, although semantically the implication does hold. We simply skip that test case as a bad test vector.
• In a genTest call: Similar to quickCheck and prove: If a constraint does not hold, the input value is ignored and is not included in the test set.

A good use case (in fact the motivating use case) for constrain is attaching a constraint to a forall or exists variable at the time of its creation. Also, the conjunctive semantics for sat and the implicative semantics for prove simplify programming by choosing the correct interpretation automatically. However, one should be aware of the semantic difference. For instance, in the presence of constraints, formulas that are provable are not necessarily satisfiable. To wit, consider:

   do x <- exists "x"
      constrain $ x .< x
      return $ x .< (x :: SWord8)

This predicate is unsatisfiable since no element of SWord8 is less than itself. But it's (vacuously) true, since it excludes the entire domain of values, thus making the proof trivial. Hence, this predicate is provable, but is not satisfiable. To make sure the given constraints are not vacuous, the functions isVacuous (and isVacuousWith) can be used.

Also note that this semantics imply that test case generation (genTest) and quick-check can take arbitrarily long in the presence of constraints, if the random input values generated rarely satisfy the constraints. (As an extreme case, consider constrain sFalse.)

constrain :: SolverContext m => SBool -> m ()

Add a constraint, any satisfying instance must satisfy this condition.

softConstrain :: SolverContext m => SBool -> m ()

Add a soft constraint. The solver will try to satisfy this condition if possible, but won't if it cannot.

Constraint Vacuity

When adding constraints, one has to be careful about making sure they are not inconsistent. The function isVacuous can be use for this purpose. Here is an example. Consider the following predicate:

>>> let pred = do { x <- free "x"; constrain $ x .< x; return $ x .>= (5 :: SWord8) }

This predicate asserts that all 8-bit values are larger than 5, subject to the constraint that the values considered satisfy x .< x, i.e., they are less than themselves. Since there are no values that satisfy this constraint, the proof will pass vacuously:

>>> prove pred
Q.E.D.

We can use isVacuous to make sure to see that the pass was vacuous:

>>> isVacuous pred
True

While the above example is trivial, things can get complicated if there are multiple constraints with non-straightforward relations; so if constraints are used one should make sure to check the predicate is not vacuously true. Here's an example that is not vacuous:

>>> let pred' = do { x <- free "x"; constrain $ x .> 6; return $ x .>= (5 :: SWord8) }

This time the proof passes as expected:

>>> prove pred'
Q.E.D.

And the proof is not vacuous:

>>> isVacuous pred'
False

Named constraints and attributes

Constraints can be given names:

 namedConstraint "a is at least 5" $ a .>= 5

Similarly, arbitrary term attributes can also be associated:

 constrainWithAttribute [(":solver-specific-attribute", "value")] $ a .>= 5

Note that a namedConstraint is equivalent to a constrainWithAttribute call, setting the `":named"' attribute.

namedConstraint :: SolverContext m => String -> SBool -> m ()

Add a named constraint. The name is used in unsat-core extraction.

constrainWithAttribute :: SolverContext m => [(String, String)] -> SBool -> m ()

Add a constraint, with arbitrary attributes. Used in interpolant generation.

Unsat cores

Named constraints are useful when used in conjunction with getUnsatCore function where the backend solver can be queried to obtain an unsat core in case the constraints are unsatisfiable. See getUnsatCore for details and Documentation.SBV.Examples.Queries.UnsatCore for an example use case.

Cardinality constraints

A pseudo-boolean function (http://en.wikipedia.org/wiki/Pseudo-Boolean_function) is a function from booleans to reals, basically treating True as 1 and False as 0. They are typically expressed in polynomial form. Such functions can be used to express cardinality constraints, where we want to count how many things satisfy a certain condition.

One can code such constraints using regular SBV programming: Simply walk over the booleans and the corresponding coefficients, and assert the required relation. For instance:

[b0, b1, b2, b3] `pbAtMost` 2

is precisely equivalent to:

sum (map (\b -> ite b 1 0) [b0, b1, b2, b3]) .<= 2

and they both express that at most two of b0, b1, b2, and b3 can be sTrue. However, the equivalent forms give rise to long formulas and the cardinality constraint can get lost in the translation. The idea here is that if you use these functions instead, SBV will produce better translations to SMTLib for more efficient solving of cardinality constraints, assuming the backend solver supports them. Currently, only Z3 supports pseudo-booleans directly. For all other solvers, SBV will translate these to equivalent terms that do not require special functions.

pbAtMost :: [SBool] -> Int -> SBool

sTrue if at most k of the input arguments are sTrue

pbAtLeast :: [SBool] -> Int -> SBool

sTrue if at least k of the input arguments are sTrue

pbExactly :: [SBool] -> Int -> SBool

sTrue if exactly k of the input arguments are sTrue

pbLe :: [(Int, SBool)] -> Int -> SBool

sTrue if the sum of coefficients for sTrue elements is at most k. Generalizes pbAtMost.

pbGe :: [(Int, SBool)] -> Int -> SBool

sTrue if the sum of coefficients for sTrue elements is at least k. Generalizes pbAtLeast.

pbEq :: [(Int, SBool)] -> Int -> SBool

sTrue if the sum of coefficients for sTrue elements is exactly least k. Useful for coding exactly K-of-N constraints, and in particular mutex constraints.

pbMutexed :: [SBool] -> SBool

sTrue if there is at most one set bit

pbStronglyMutexed :: [SBool] -> SBool

sTrue if there is exactly one set bit

Checking safety

The sAssert function allows users to introduce invariants to make sure certain properties hold at all times. This is another mechanism to provide further documentation/contract info into SBV code. The functions safe and safeWith can be used to statically discharge these proof assumptions. If a violation is found, SBV will print a model showing which inputs lead to the invariant being violated.

Here's a simple example. Let's assume we have a function that does subtraction, and requires its first argument to be larger than the second:

>>> let sub x y = sAssert Nothing "sub: x >= y must hold!" (x .>= y) (x - y)

Clearly, this function is not safe, as there's nothing that stops us from passing it a larger second argument. We can use safe to statically see if such a violation is possible before we use this function elsewhere.

>>> safe (sub :: SInt8 -> SInt8 -> SInt8)
[sub: x >= y must hold!: Violated. Model:
  s0 = 30 :: Int8
  s1 = 32 :: Int8]

What happens if we make sure to arrange for this invariant? Consider this version:

>>> let safeSub x y = ite (x .>= y) (sub x y) 0

Clearly, safeSub must be safe. And indeed, SBV can prove that:

>>> safe (safeSub :: SInt8 -> SInt8 -> SInt8)
[sub: x >= y must hold!: No violations detected]

Note how we used sub and safeSub polymorphically. We only need to monomorphise our types when a proof attempt is done, as we did in the safe calls.

If required, the user can pass a CallStack through the first argument to sAssert, which will be used by SBV to print a diagnostic info to pinpoint the failure.

Also see Documentation.SBV.Examples.Misc.NoDiv0 for the classic div-by-zero example.

sAssert :: HasKind a => Maybe CallStack -> String -> SBool -> SBV a -> SBV a

Symbolic assert. Check that the given boolean condition is always sTrue in the given path. The optional first argument can be used to provide call-stack info via GHC's location facilities.

isSafe :: SafeResult -> Bool

Check if a safe-call was safe or not, turning a SafeResult to a Bool.

class ExtractIO m => SExecutable m a

Symbolically executable program fragments. This class is mainly used for safe calls, and is sufficently populated internally to cover most use cases. Users can extend it as they wish to allow safe checks for SBV programs that return/take types that are user-defined.

Minimal complete definition

sName_, sName

Instances

ExtractIO m => SExecutable m ()

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: () -> SymbolicT m ()

sName :: [String] -> () -> SymbolicT m ()

safe :: () -> m [SafeResult]

safeWith :: SMTConfig -> () -> m [SafeResult]

ExtractIO m => SExecutable m [SBV a]

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: [SBV a] -> SymbolicT m ()

sName :: [String] -> [SBV a] -> SymbolicT m ()

safe :: [SBV a] -> m [SafeResult]

safeWith :: SMTConfig -> [SBV a] -> m [SafeResult]

ExtractIO m => SExecutable m (SBV a)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: SBV a -> SymbolicT m ()

sName :: [String] -> SBV a -> SymbolicT m ()

safe :: SBV a -> m [SafeResult]

safeWith :: SMTConfig -> SBV a -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SExecutable m p) => SExecutable m ((SBV a, SBV b) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m [SafeResult]

(SymVal a, SExecutable m p) => SExecutable m (SBV a -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a -> p) -> SymbolicT m ()

sName :: [String] -> (SBV a -> p) -> SymbolicT m ()

safe :: (SBV a -> p) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a -> p) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b) => SExecutable m (SBV a, SBV b)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b) -> SymbolicT m ()

safe :: (SBV a, SBV b) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b) -> m [SafeResult]

(ExtractIO m, NFData a) => SExecutable m (SymbolicT m a)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: SymbolicT m a -> SymbolicT m ()

sName :: [String] -> SymbolicT m a -> SymbolicT m ()

safe :: SymbolicT m a -> m [SafeResult]

safeWith :: SMTConfig -> SymbolicT m a -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c) => SExecutable m (SBV a, SBV b, SBV c)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d) => SExecutable m (SBV a, SBV b, SBV c, SBV d)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d, SBV e) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d, SBV e) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d, SBV e) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d, SBV e) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e, NFData f, SymVal f) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e, NFData f, SymVal f, NFData g, SymVal g) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> m [SafeResult]

sName_ :: SExecutable IO a => a -> Symbolic ()

NB. For a version which generalizes over the underlying monad, see sName_

sName :: SExecutable IO a => [String] -> a -> Symbolic ()

NB. For a version which generalizes over the underlying monad, see sName

safe :: SExecutable IO a => a -> IO [SafeResult]

Check safety using the default solver.

NB. For a version which generalizes over the underlying monad, see safe

safeWith :: SExecutable IO a => SMTConfig -> a -> IO [SafeResult]

Check if any of the sAssert calls can be violated.

NB. For a version which generalizes over the underlying monad, see safeWith

Quick-checking

sbvQuickCheck :: Symbolic SBool -> IO Bool

Quick check an SBV property. Note that a regular quickCheck call will work just as well. Use this variant if you want to receive the boolean result.

Optimization

SBV can optimize metric functions, i.e., those that generate both bounded SIntN, SWordN, and unbounded SInteger types, along with those produce SReals. That is, it can find models satisfying all the constraints while minimizing or maximizing user given metrics. Currently, optimization requires the use of the z3 SMT solver as the backend, and a good review of these features is given in this paper: http://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/nbjorner-scss2014.pdf.

Goals can be lexicographically (default), independently, or pareto-front optimized. The relevant functions are:

• minimize: Minimize a given arithmetic goal
• maximize: Minimize a given arithmetic goal

Goals can be optimized at a regular or an extended value: An extended value is either positive or negative infinity (for unbounded integers and reals) or positive or negative epsilon differential from a real value (for reals).

For instance, a call of the form

 minimize "name-of-goal" $ x + 2*y

minimizes the arithmetic goal x+2*y, where x and y can be signed/unsigned bit-vectors, reals, or integers.

A simple example

Here's an optimization example in action:

>>> optimize Lexicographic $ \x y -> minimize "goal" (x+2*(y::SInteger))
Optimal in an extension field:
  goal = -oo :: Integer

We will describe the role of the constructor Lexicographic shortly.

Of course, this becomes more useful when the result is not in an extension field:

>>> :{
    optimize Lexicographic $ do
                  x <- sInteger "x"
                  y <- sInteger "y"
                  constrain $ x .> 0
                  constrain $ x .< 6
                  constrain $ y .> 2
                  constrain $ y .< 12
                  minimize "goal" $ x + 2 * y
    :}
Optimal model:
  x    = 1 :: Integer
  y    = 3 :: Integer
  goal = 7 :: Integer

As usual, the programmatic API can be used to extract the values of objectives and model-values (getModelObjectives, getModelAssignment, etc.) to access these values and program with them further.

The following examples illustrate the use of basic optimization routines:

• Documentation.SBV.Examples.Optimization.LinearOpt: Simple linear-optimization example.
• Documentation.SBV.Examples.Optimization.Production: Scheduling machines in a shop
• Documentation.SBV.Examples.Optimization.VM: Scheduling virtual-machines in a data-center

Multiple optimization goals

Multiple goals can be specified, using the same syntax. In this case, the user gets to pick what style of optimization to perform, by passing the relevant OptimizeStyle as the first argument to optimize.

• [Lexicographic]. The solver will optimize the goals in the given order, optimizing the latter ones under the model that optimizes the previous ones.
• [Independent]. The solver will optimize the goals independently of each other. In this case the user will be presented a model for each goal given.
• [Pareto]. Finally, the user can query for pareto-fronts. A pareto front is an model such that no goal can be made "better" without making some other goal "worse."

Pareto fronts only make sense when the objectives are bounded. If there are unbounded objective values, then the backend solver can loop infinitely. (This is what z3 does currently.) If you are not sure the objectives are bounded, you should first use Independent mode to ensure the objectives are bounded, and then switch to pareto-mode to extract them further.

The optional number argument to Pareto specifies the maximum number of pareto-fronts the user is asking to get. If Nothing, SBV will query for all pareto-fronts. Note that pareto-fronts can be really large, so if Nothing is used, there is a potential for waiting indefinitely for the SBV-solver interaction to finish. (If you suspect this might be the case, run in verbose mode to see the interaction and put a limiting factor appropriately.)

data OptimizeStyle

Style of optimization. Note that in the pareto case the user is allowed to specify a max number of fronts to query the solver for, since there might potentially be an infinite number of them and there is no way to know exactly how many ahead of time. If Nothing is given, SBV will possibly loop forever if the number is really infinite.

Constructors

Lexicographic

Objectives are optimized in the order given, earlier objectives have higher priority.

Independent

Each objective is optimized independently.

Pareto (Maybe Int)

Objectives are optimized according to pareto front: That is, no objective can be made better without making some other worse.

Instances

Eq OptimizeStyle

Defined in Data.SBV.Core.Symbolic

Methods

(==) :: OptimizeStyle -> OptimizeStyle -> Bool

(/=) :: OptimizeStyle -> OptimizeStyle -> Bool

Show OptimizeStyle

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> OptimizeStyle -> ShowS

show :: OptimizeStyle -> String

showList :: [OptimizeStyle] -> ShowS

NFData OptimizeStyle

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: OptimizeStyle -> ()

Objectives and Metrics

data Objective a

Objective of optimization. We can minimize, maximize, or give a soft assertion with a penalty for not satisfying it.

Constructors

Minimize String a

Minimize this metric

Maximize String a

Maximize this metric

AssertWithPenalty String a Penalty

A soft assertion, with an associated penalty

Instances

Functor Objective

Defined in Data.SBV.Core.Symbolic

Methods

fmap :: (a -> b) -> Objective a -> Objective b

(<$) :: a -> Objective b -> Objective a

Show a => Show (Objective a)

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> Objective a -> ShowS

show :: Objective a -> String

showList :: [Objective a] -> ShowS

NFData a => NFData (Objective a)

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: Objective a -> ()

class Metric a where

Class of metrics we can optimize for. Currently, booleans, bounded signed/unsigned bit-vectors, unbounded integers, algebraic reals and floats can be optimized. You can add your instances, but bewared that the MetricSpace should map your type to something the backend solver understands, which are limited to unsigned bit-vectors, reals, and unbounded integers for z3.

A good reference on these features is given in the following paper: http://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/nbjorner-scss2014.pdf.

Minimal completion: None. However, if MetricSpace is not identical to the type, you want to define toMetricSpace and possbly 'minimize'/'maximize' to add extra constraints as necessary.

Minimal complete definition

Nothing

Associated Types

type MetricSpace a :: *

The metric space we optimize the goal over. Usually the same as the type itself, but not always! For instance, signed bit-vectors are optimized over their unsigned counterparts, floats are optimized over their Word32 comparable counterparts, etc.

Methods

toMetricSpace :: SBV a -> SBV (MetricSpace a)

Compute the metric value to optimize.

fromMetricSpace :: SBV (MetricSpace a) -> SBV a

Compute the value itself from the metric corresponding to it.

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV a -> m ()

Minimizing a metric space

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV a -> m ()

Maximizing a metric space

toMetricSpace :: a ~ MetricSpace a => SBV a -> SBV (MetricSpace a)

Compute the metric value to optimize.

fromMetricSpace :: a ~ MetricSpace a => SBV (MetricSpace a) -> SBV a

Compute the value itself from the metric corresponding to it.

Instances

Metric Bool

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Bool :: Type

Methods

toMetricSpace :: SBV Bool -> SBV (MetricSpace Bool)

fromMetricSpace :: SBV (MetricSpace Bool) -> SBV Bool

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Bool -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Bool -> m ()

Metric Double

Double instance for Metric goes through the lexicographic ordering on Word64. It implicitly makes sure that the value is not NaN.

Defined in Data.SBV.Core.Floating

Associated Types

type MetricSpace Double :: Type

Methods

toMetricSpace :: SBV Double -> SBV (MetricSpace Double)

fromMetricSpace :: SBV (MetricSpace Double) -> SBV Double

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Double -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Double -> m ()

Metric Float

Float instance for Metric goes through the lexicographic ordering on Word32. It implicitly makes sure that the value is not NaN.

Defined in Data.SBV.Core.Floating

Associated Types

type MetricSpace Float :: Type

Methods

toMetricSpace :: SBV Float -> SBV (MetricSpace Float)

fromMetricSpace :: SBV (MetricSpace Float) -> SBV Float

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Float -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Float -> m ()

Metric Int8

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Int8 :: Type

Methods

toMetricSpace :: SBV Int8 -> SBV (MetricSpace Int8)

fromMetricSpace :: SBV (MetricSpace Int8) -> SBV Int8

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int8 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int8 -> m ()

Metric Int16

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Int16 :: Type

Methods

toMetricSpace :: SBV Int16 -> SBV (MetricSpace Int16)

fromMetricSpace :: SBV (MetricSpace Int16) -> SBV Int16

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int16 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int16 -> m ()

Metric Int32

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Int32 :: Type

Methods

toMetricSpace :: SBV Int32 -> SBV (MetricSpace Int32)

fromMetricSpace :: SBV (MetricSpace Int32) -> SBV Int32

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int32 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int32 -> m ()

Metric Int64

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Int64 :: Type

Methods

toMetricSpace :: SBV Int64 -> SBV (MetricSpace Int64)

fromMetricSpace :: SBV (MetricSpace Int64) -> SBV Int64

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int64 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Int64 -> m ()

Metric Integer

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Integer :: Type

Methods

toMetricSpace :: SBV Integer -> SBV (MetricSpace Integer)

fromMetricSpace :: SBV (MetricSpace Integer) -> SBV Integer

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Integer -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Integer -> m ()

Metric Word8

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Word8 :: Type

Methods

toMetricSpace :: SBV Word8 -> SBV (MetricSpace Word8)

fromMetricSpace :: SBV (MetricSpace Word8) -> SBV Word8

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word8 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word8 -> m ()

Metric Word16

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Word16 :: Type

Methods

toMetricSpace :: SBV Word16 -> SBV (MetricSpace Word16)

fromMetricSpace :: SBV (MetricSpace Word16) -> SBV Word16

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word16 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word16 -> m ()

Metric Word32

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Word32 :: Type

Methods

toMetricSpace :: SBV Word32 -> SBV (MetricSpace Word32)

fromMetricSpace :: SBV (MetricSpace Word32) -> SBV Word32

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word32 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word32 -> m ()

Metric Word64

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace Word64 :: Type

Methods

toMetricSpace :: SBV Word64 -> SBV (MetricSpace Word64)

fromMetricSpace :: SBV (MetricSpace Word64) -> SBV Word64

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word64 -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Word64 -> m ()

Metric AlgReal

Defined in Data.SBV.Core.Model

Associated Types

type MetricSpace AlgReal :: Type

Methods

toMetricSpace :: SBV AlgReal -> SBV (MetricSpace AlgReal)

fromMetricSpace :: SBV (MetricSpace AlgReal) -> SBV AlgReal

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV AlgReal -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV AlgReal -> m ()

Metric Day

Make day an optimizable value, by mapping it to Word8 in the most obvious way. We can map it to any value the underlying solver can optimize, but Word8 is the simplest and it'll fit the bill.

Defined in Documentation.SBV.Examples.Optimization.Enumerate

Associated Types

type MetricSpace Day :: Type

Methods

toMetricSpace :: SBV Day -> SBV (MetricSpace Day)

fromMetricSpace :: SBV (MetricSpace Day) -> SBV Day

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV Day -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV Day -> m ()

(SymVal a, Metric a, SymVal b, Metric b) => Metric (a, b)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b) :: Type

Methods

toMetricSpace :: SBV (a, b) -> SBV (MetricSpace (a, b))

fromMetricSpace :: SBV (MetricSpace (a, b)) -> SBV (a, b)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b) -> m ()

(SymVal a, Metric a, SymVal b, Metric b, SymVal c, Metric c) => Metric (a, b, c)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b, c) :: Type

Methods

toMetricSpace :: SBV (a, b, c) -> SBV (MetricSpace (a, b, c))

fromMetricSpace :: SBV (MetricSpace (a, b, c)) -> SBV (a, b, c)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c) -> m ()

(SymVal a, Metric a, SymVal b, Metric b, SymVal c, Metric c, SymVal d, Metric d) => Metric (a, b, c, d)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b, c, d) :: Type

Methods

toMetricSpace :: SBV (a, b, c, d) -> SBV (MetricSpace (a, b, c, d))

fromMetricSpace :: SBV (MetricSpace (a, b, c, d)) -> SBV (a, b, c, d)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d) -> m ()

(SymVal a, Metric a, SymVal b, Metric b, SymVal c, Metric c, SymVal d, Metric d, SymVal e, Metric e) => Metric (a, b, c, d, e)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b, c, d, e) :: Type

Methods

toMetricSpace :: SBV (a, b, c, d, e) -> SBV (MetricSpace (a, b, c, d, e))

fromMetricSpace :: SBV (MetricSpace (a, b, c, d, e)) -> SBV (a, b, c, d, e)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e) -> m ()

(SymVal a, Metric a, SymVal b, Metric b, SymVal c, Metric c, SymVal d, Metric d, SymVal e, Metric e, SymVal f, Metric f) => Metric (a, b, c, d, e, f)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b, c, d, e, f) :: Type

Methods

toMetricSpace :: SBV (a, b, c, d, e, f) -> SBV (MetricSpace (a, b, c, d, e, f))

fromMetricSpace :: SBV (MetricSpace (a, b, c, d, e, f)) -> SBV (a, b, c, d, e, f)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e, f) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e, f) -> m ()

(SymVal a, Metric a, SymVal b, Metric b, SymVal c, Metric c, SymVal d, Metric d, SymVal e, Metric e, SymVal f, Metric f, SymVal g, Metric g) => Metric (a, b, c, d, e, f, g)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b, c, d, e, f, g) :: Type

Methods

toMetricSpace :: SBV (a, b, c, d, e, f, g) -> SBV (MetricSpace (a, b, c, d, e, f, g))

fromMetricSpace :: SBV (MetricSpace (a, b, c, d, e, f, g)) -> SBV (a, b, c, d, e, f, g)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e, f, g) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e, f, g) -> m ()

(SymVal a, Metric a, SymVal b, Metric b, SymVal c, Metric c, SymVal d, Metric d, SymVal e, Metric e, SymVal f, Metric f, SymVal g, Metric g, SymVal h, Metric h) => Metric (a, b, c, d, e, f, g, h)

Defined in Data.SBV.Tuple

Associated Types

type MetricSpace (a, b, c, d, e, f, g, h) :: Type

Methods

toMetricSpace :: SBV (a, b, c, d, e, f, g, h) -> SBV (MetricSpace (a, b, c, d, e, f, g, h))

fromMetricSpace :: SBV (MetricSpace (a, b, c, d, e, f, g, h)) -> SBV (a, b, c, d, e, f, g, h)

msMinimize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e, f, g, h) -> m ()

msMaximize :: (MonadSymbolic m, SolverContext m) => String -> SBV (a, b, c, d, e, f, g, h) -> m ()

minimize :: Metric a => String -> SBV a -> Symbolic ()

Minimize a named metric

NB. For a version which generalizes over the underlying monad, see minimize

maximize :: Metric a => String -> SBV a -> Symbolic ()

Maximize a named metric

NB. For a version which generalizes over the underlying monad, see maximize

Soft assertions

Related to optimization, SBV implements soft-asserts via assertWithPenalty calls. A soft assertion is a hint to the SMT solver that we would like a particular condition to hold if **possible*. That is, if there is a solution satisfying it, then we would like it to hold, but it can be violated if there is no way to satisfy it. Each soft-assertion can be associated with a numeric penalty for not satisfying it, hence turning it into an optimization problem.

Note that assertWithPenalty works well with optimization goals ('minimize'/'maximize' etc.), and are most useful when we are optimizing a metric and thus some of the constraints can be relaxed with a penalty to obtain a good solution. Again see http://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/nbjorner-scss2014.pdf for a good overview of the features in Z3 that SBV is providing the bridge for.

A soft assertion can be specified in one of the following three main ways:

         assertWithPenalty "bounded_x" (x .< 5) DefaultPenalty
         assertWithPenalty "bounded_x" (x .< 5) (Penalty 2.3 Nothing)
         assertWithPenalty "bounded_x" (x .< 5) (Penalty 4.7 (Just "group-1"))

In the first form, we are saying that the constraint x .< 5 must be satisfied, if possible, but if this constraint can not be satisfied to find a model, it can be violated with the default penalty of 1.

In the second case, we are associating a penalty value of 2.3.

Finally in the third case, we are also associating this constraint with a group. The group name is only needed if we have classes of soft-constraints that should be considered together.

assertWithPenalty :: String -> SBool -> Penalty -> Symbolic ()

Introduce a soft assertion, with an optional penalty

NB. For a version which generalizes over the underlying monad, see assertWithPenalty

data Penalty

Penalty for a soft-assertion. The default penalty is 1, with all soft-assertions belonging to the same objective goal. A positive weight and an optional group can be provided by using the Penalty constructor.

Constructors

DefaultPenalty

Default: Penalty of 1 and no group attached

Penalty Rational (Maybe String)

Penalty with a weight and an optional group

Instances

Show Penalty

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> Penalty -> ShowS

show :: Penalty -> String

showList :: [Penalty] -> ShowS

NFData Penalty

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: Penalty -> ()

Field extensions

If an optimization results in an infinity/epsilon value, the returned CV value will be in the corresponding extension field.

data ExtCV

A simple expression type over extendent values, covering infinity, epsilon and intervals.

Constructors

Infinite Kind

Epsilon Kind

Interval ExtCV ExtCV

BoundedCV CV

AddExtCV ExtCV ExtCV

MulExtCV ExtCV ExtCV

Instances

Show ExtCV

Show instance, shows with the kind

Defined in Data.SBV.Core.Concrete

Methods

showsPrec :: Int -> ExtCV -> ShowS

show :: ExtCV -> String

showList :: [ExtCV] -> ShowS

HasKind ExtCV

Kind instance for Extended CV

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: ExtCV -> Kind

hasSign :: ExtCV -> Bool

intSizeOf :: ExtCV -> Int

isBoolean :: ExtCV -> Bool

isBounded :: ExtCV -> Bool

isReal :: ExtCV -> Bool

isFloat :: ExtCV -> Bool

isDouble :: ExtCV -> Bool

isUnbounded :: ExtCV -> Bool

isUninterpreted :: ExtCV -> Bool

isChar :: ExtCV -> Bool

isString :: ExtCV -> Bool

isList :: ExtCV -> Bool

isSet :: ExtCV -> Bool

isTuple :: ExtCV -> Bool

isMaybe :: ExtCV -> Bool

isEither :: ExtCV -> Bool

showType :: ExtCV -> String

data GeneralizedCV

A generalized CV allows for expressions involving infinite and epsilon values/intervals Used in optimization problems.

Constructors

ExtendedCV ExtCV

RegularCV CV

Instances

Show GeneralizedCV

Show instance for Generalized CV

Defined in Data.SBV.Core.Concrete

Methods

showsPrec :: Int -> GeneralizedCV -> ShowS

show :: GeneralizedCV -> String

showList :: [GeneralizedCV] -> ShowS

NFData GeneralizedCV

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: GeneralizedCV -> ()

HasKind GeneralizedCV

Kind instance for generalized CV

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: GeneralizedCV -> Kind

hasSign :: GeneralizedCV -> Bool

intSizeOf :: GeneralizedCV -> Int

isBoolean :: GeneralizedCV -> Bool

isBounded :: GeneralizedCV -> Bool

isReal :: GeneralizedCV -> Bool

isFloat :: GeneralizedCV -> Bool

isDouble :: GeneralizedCV -> Bool

isUnbounded :: GeneralizedCV -> Bool

isUninterpreted :: GeneralizedCV -> Bool

isChar :: GeneralizedCV -> Bool

isString :: GeneralizedCV -> Bool

isList :: GeneralizedCV -> Bool

isSet :: GeneralizedCV -> Bool

isTuple :: GeneralizedCV -> Bool

isMaybe :: GeneralizedCV -> Bool

isEither :: GeneralizedCV -> Bool

showType :: GeneralizedCV -> String

Model extraction

The default Show instances for prover calls provide all the counter-example information in a human-readable form and should be sufficient for most casual uses of sbv. However, tools built on top of sbv will inevitably need to look into the constructed models more deeply, programmatically extracting their results and performing actions based on them. The API provided in this section aims at simplifying this task.

Inspecting proof results

ThmResult, SatResult, and AllSatResult are simple newtype wrappers over SMTResult. Their main purpose is so that we can provide custom Show instances to print results accordingly.

newtype ThmResult

A prove call results in a ThmResult

Constructors

ThmResult SMTResult

Instances

Show ThmResult

Defined in Data.SBV.SMT.SMT

Methods

showsPrec :: Int -> ThmResult -> ShowS

show :: ThmResult -> String

showList :: [ThmResult] -> ShowS

NFData ThmResult

Defined in Data.SBV.SMT.SMT

Methods

rnf :: ThmResult -> ()

Modelable ThmResult

ThmResult as a generic model provider

Defined in Data.SBV.SMT.SMT

Methods

modelExists :: ThmResult -> Bool

getModelAssignment :: SatModel b => ThmResult -> Either String (Bool, b)

getModelDictionary :: ThmResult -> Map String CV

getModelValue :: SymVal b => String -> ThmResult -> Maybe b

getModelUninterpretedValue :: String -> ThmResult -> Maybe String

extractModel :: SatModel b => ThmResult -> Maybe b

getModelObjectives :: ThmResult -> Map String GeneralizedCV

getModelObjectiveValue :: String -> ThmResult -> Maybe GeneralizedCV

getModelUIFuns :: ThmResult -> Map String (SBVType, ([([CV], CV)], CV))

getModelUIFunValue :: String -> ThmResult -> Maybe (SBVType, ([([CV], CV)], CV))

newtype SatResult

A sat call results in a SatResult The reason for having a separate SatResult is to have a more meaningful Show instance.

Constructors

SatResult SMTResult

Instances

Show SatResult

Defined in Data.SBV.SMT.SMT

Methods

showsPrec :: Int -> SatResult -> ShowS

show :: SatResult -> String

showList :: [SatResult] -> ShowS

NFData SatResult

Defined in Data.SBV.SMT.SMT

Methods

rnf :: SatResult -> ()

Modelable SatResult

SatResult as a generic model provider

Defined in Data.SBV.SMT.SMT

Methods

modelExists :: SatResult -> Bool

getModelAssignment :: SatModel b => SatResult -> Either String (Bool, b)

getModelDictionary :: SatResult -> Map String CV

getModelValue :: SymVal b => String -> SatResult -> Maybe b

getModelUninterpretedValue :: String -> SatResult -> Maybe String

extractModel :: SatModel b => SatResult -> Maybe b

getModelObjectives :: SatResult -> Map String GeneralizedCV

getModelObjectiveValue :: String -> SatResult -> Maybe GeneralizedCV

getModelUIFuns :: SatResult -> Map String (SBVType, ([([CV], CV)], CV))

getModelUIFunValue :: String -> SatResult -> Maybe (SBVType, ([([CV], CV)], CV))

newtype AllSatResult

An allSat call results in a AllSatResult. The first boolean says whether we hit the max-model limit as we searched. The second boolean says whether there were prefix-existentials. The third boolean says whether we stopped because the solver returned Unknown.

Constructors

AllSatResult (Bool, Bool, Bool, [SMTResult])

Instances

Show AllSatResult

Defined in Data.SBV.SMT.SMT

Methods

showsPrec :: Int -> AllSatResult -> ShowS

show :: AllSatResult -> String

showList :: [AllSatResult] -> ShowS

newtype SafeResult

A safe call results in a SafeResult

Constructors

SafeResult (Maybe String, String, SMTResult)

Instances

Show SafeResult

Defined in Data.SBV.SMT.SMT

Methods

showsPrec :: Int -> SafeResult -> ShowS

show :: SafeResult -> String

showList :: [SafeResult] -> ShowS

data OptimizeResult

An optimize call results in a OptimizeResult. In the ParetoResult case, the boolean is True if we reached pareto-query limit and so there might be more unqueried results remaining. If False, it means that we have all the pareto fronts returned. See the Pareto OptimizeStyle for details.

Constructors

LexicographicResult SMTResult

ParetoResult (Bool, [SMTResult])

IndependentResult [(String, SMTResult)]

Instances

Show OptimizeResult

Defined in Data.SBV.SMT.SMT

Methods

showsPrec :: Int -> OptimizeResult -> ShowS

show :: OptimizeResult -> String

showList :: [OptimizeResult] -> ShowS

data SMTResult

The result of an SMT solver call. Each constructor is tagged with the SMTConfig that created it so that further tools can inspect it and build layers of results, if needed. For ordinary uses of the library, this type should not be needed, instead use the accessor functions on it. (Custom Show instances and model extractors.)

Constructors

Unsatisfiable SMTConfig (Maybe [String])

Unsatisfiable. If unsat-cores are enabled, they will be returned in the second parameter.

Satisfiable SMTConfig SMTModel

Satisfiable with model

SatExtField SMTConfig SMTModel

Prover returned a model, but in an extension field containing Infinite/epsilon

Unknown SMTConfig SMTReasonUnknown

Prover returned unknown, with the given reason

ProofError SMTConfig [String] (Maybe SMTResult)

Prover errored out, with possibly a bogus result

Instances

NFData SMTResult

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SMTResult -> ()

Modelable SMTResult

SMTResult as a generic model provider

Defined in Data.SBV.SMT.SMT

Methods

modelExists :: SMTResult -> Bool

getModelAssignment :: SatModel b => SMTResult -> Either String (Bool, b)

getModelDictionary :: SMTResult -> Map String CV

getModelValue :: SymVal b => String -> SMTResult -> Maybe b

getModelUninterpretedValue :: String -> SMTResult -> Maybe String

extractModel :: SatModel b => SMTResult -> Maybe b

getModelObjectives :: SMTResult -> Map String GeneralizedCV

getModelObjectiveValue :: String -> SMTResult -> Maybe GeneralizedCV

getModelUIFuns :: SMTResult -> Map String (SBVType, ([([CV], CV)], CV))

getModelUIFunValue :: String -> SMTResult -> Maybe (SBVType, ([([CV], CV)], CV))

data SMTReasonUnknown

Reason for reporting unknown.

Constructors

UnknownMemOut

UnknownIncomplete

UnknownTimeOut

UnknownOther String

Instances

Show SMTReasonUnknown

Show instance for unknown

Defined in Data.SBV.Control.Types

Methods

showsPrec :: Int -> SMTReasonUnknown -> ShowS

show :: SMTReasonUnknown -> String

showList :: [SMTReasonUnknown] -> ShowS

Generic SMTReasonUnknown

Defined in Data.SBV.Control.Types

Associated Types

type Rep SMTReasonUnknown :: Type -> Type

Methods

from :: SMTReasonUnknown -> Rep SMTReasonUnknown x

to :: Rep SMTReasonUnknown x -> SMTReasonUnknown

NFData SMTReasonUnknown

Defined in Data.SBV.Control.Types

Methods

rnf :: SMTReasonUnknown -> ()

type Rep SMTReasonUnknown

Defined in Data.SBV.Control.Types

type Rep SMTReasonUnknown = D1 (MetaData "SMTReasonUnknown" "Data.SBV.Control.Types" "sbv-8.3-KY4PN9PPbrH5uMg2KovlBp" False) ((C1 (MetaCons "UnknownMemOut" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "UnknownIncomplete" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "UnknownTimeOut" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "UnknownOther" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 String))))

Observing expressions

The observe command can be used to trace values of arbitrary expressions during a sat, prove, or perhaps more importantly, in a quickCheck call. This is useful for, for instance, recording expected/obtained expressions as a symbolic program is executing.

>>> :{
prove $ do a1 <- free "i1"
           a2 <- free "i2"
           let spec, res :: SWord8
               spec = a1 + a2
               res  = ite (a1 .== 12 .&& a2 .== 22)   -- insert a malicious bug!
                          1
                          (a1 + a2)
           return $ observe "Expected" spec .== observe "Result" res
:}
Falsifiable. Counter-example:
  Expected = 34 :: Word8
  Result   =  1 :: Word8
  i1       = 12 :: Word8
  i2       = 22 :: Word8

The observeIf variant allows the user to specify a boolean condition when the value is interesting to observe. Useful when you have lots of "debugging" points, but not all are of interest.

observe :: SymVal a => String -> SBV a -> SBV a

Observe the value of an expression, uncoditionally. See observeIf for a generalized version.

observeIf :: SymVal a => (a -> Bool) -> String -> SBV a -> SBV a

Observe the value of an expression, if the given condition holds. Such values are useful in model construction, as they are printed part of a satisfying model, or a counter-example. The same works for quick-check as well. Useful when we want to see intermediate values, or expected/obtained pairs in a particular run. Note that an observed expression is always symbolic, i.e., it won't be constant folded. Compare this to label which is used for putting a label in the generated SMTLib-C code.

Programmable model extraction

While default Show instances are sufficient for most use cases, it is sometimes desirable (especially for library construction) that the SMT-models are reinterpreted in terms of domain types. Programmable extraction allows getting arbitrarily typed models out of SMT models.

class SatModel a where

Instances of SatModel can be automatically extracted from models returned by the solvers. The idea is that the sbv infrastructure provides a stream of CV's (constant values) coming from the solver, and the type a is interpreted based on these constants. Many typical instances are already provided, so new instances can be declared with relative ease.

Minimum complete definition: parseCVs

Minimal complete definition

Nothing

Methods

parseCVs :: [CV] -> Maybe (a, [CV])

Given a sequence of constant-words, extract one instance of the type a, returning the remaining elements untouched. If the next element is not what's expected for this type you should return Nothing

cvtModel :: (a -> Maybe b) -> Maybe (a, [CV]) -> Maybe (b, [CV])

Given a parsed model instance, transform it using f, and return the result. The default definition for this method should be sufficient in most use cases.

parseCVs :: Read a => [CV] -> Maybe (a, [CV])

Given a sequence of constant-words, extract one instance of the type a, returning the remaining elements untouched. If the next element is not what's expected for this type you should return Nothing

Instances

SatModel Bool

Bool as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Bool, [CV])

cvtModel :: (Bool -> Maybe b) -> Maybe (Bool, [CV]) -> Maybe (b, [CV])

SatModel Double

Double as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Double, [CV])

cvtModel :: (Double -> Maybe b) -> Maybe (Double, [CV]) -> Maybe (b, [CV])

SatModel Float

Float as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Float, [CV])

cvtModel :: (Float -> Maybe b) -> Maybe (Float, [CV]) -> Maybe (b, [CV])

SatModel Int8

Int8 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Int8, [CV])

cvtModel :: (Int8 -> Maybe b) -> Maybe (Int8, [CV]) -> Maybe (b, [CV])

SatModel Int16

Int16 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Int16, [CV])

cvtModel :: (Int16 -> Maybe b) -> Maybe (Int16, [CV]) -> Maybe (b, [CV])

SatModel Int32

Int32 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Int32, [CV])

cvtModel :: (Int32 -> Maybe b) -> Maybe (Int32, [CV]) -> Maybe (b, [CV])

SatModel Int64

Int64 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Int64, [CV])

cvtModel :: (Int64 -> Maybe b) -> Maybe (Int64, [CV]) -> Maybe (b, [CV])

SatModel Integer

Integer as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Integer, [CV])

cvtModel :: (Integer -> Maybe b) -> Maybe (Integer, [CV]) -> Maybe (b, [CV])

SatModel Word8

Word8 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Word8, [CV])

cvtModel :: (Word8 -> Maybe b) -> Maybe (Word8, [CV]) -> Maybe (b, [CV])

SatModel Word16

Word16 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Word16, [CV])

cvtModel :: (Word16 -> Maybe b) -> Maybe (Word16, [CV]) -> Maybe (b, [CV])

SatModel Word32

Word32 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Word32, [CV])

cvtModel :: (Word32 -> Maybe b) -> Maybe (Word32, [CV]) -> Maybe (b, [CV])

SatModel Word64

Word64 as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (Word64, [CV])

cvtModel :: (Word64 -> Maybe b) -> Maybe (Word64, [CV]) -> Maybe (b, [CV])

SatModel ()

Base case for SatModel at unit type. Comes in handy if there are no real variables.

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((), [CV])

cvtModel :: (() -> Maybe b) -> Maybe ((), [CV]) -> Maybe (b, [CV])

SatModel AlgReal

AlgReal as extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (AlgReal, [CV])

cvtModel :: (AlgReal -> Maybe b) -> Maybe (AlgReal, [CV]) -> Maybe (b, [CV])

SatModel CV

CV as extracted from a model; trivial definition

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (CV, [CV])

cvtModel :: (CV -> Maybe b) -> Maybe (CV, [CV]) -> Maybe (b, [CV])

SatModel RoundingMode

A rounding mode, extracted from a model. (Default definition suffices)

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe (RoundingMode, [CV])

cvtModel :: (RoundingMode -> Maybe b) -> Maybe (RoundingMode, [CV]) -> Maybe (b, [CV])

SatModel State

Make State a symbolic enumeration

Defined in Documentation.SBV.Examples.Lists.BoundedMutex

Methods

parseCVs :: [CV] -> Maybe (State, [CV])

cvtModel :: (State -> Maybe b) -> Maybe (State, [CV]) -> Maybe (b, [CV])

SatModel E

Make E a symbolic value.

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

parseCVs :: [CV] -> Maybe (E, [CV])

cvtModel :: (E -> Maybe b) -> Maybe (E, [CV]) -> Maybe (b, [CV])

SatModel Word4

SatModel instance, merely uses the generic parsing method.

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

parseCVs :: [CV] -> Maybe (Word4, [CV])

cvtModel :: (Word4 -> Maybe b) -> Maybe (Word4, [CV]) -> Maybe (b, [CV])

SatModel Day

Make Day a symbolic value.

Defined in Documentation.SBV.Examples.Optimization.Enumerate

Methods

parseCVs :: [CV] -> Maybe (Day, [CV])

cvtModel :: (Day -> Maybe b) -> Maybe (Day, [CV]) -> Maybe (b, [CV])

SatModel Color

Make Color a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

parseCVs :: [CV] -> Maybe (Color, [CV])

cvtModel :: (Color -> Maybe b) -> Maybe (Color, [CV]) -> Maybe (b, [CV])

SatModel Nationality

Make Nationality a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

parseCVs :: [CV] -> Maybe (Nationality, [CV])

cvtModel :: (Nationality -> Maybe b) -> Maybe (Nationality, [CV]) -> Maybe (b, [CV])

SatModel Beverage

Make Beverage a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

parseCVs :: [CV] -> Maybe (Beverage, [CV])

cvtModel :: (Beverage -> Maybe b) -> Maybe (Beverage, [CV]) -> Maybe (b, [CV])

SatModel Pet

Make Pet a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

parseCVs :: [CV] -> Maybe (Pet, [CV])

cvtModel :: (Pet -> Maybe b) -> Maybe (Pet, [CV]) -> Maybe (b, [CV])

SatModel Sport

Make Sport a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

parseCVs :: [CV] -> Maybe (Sport, [CV])

cvtModel :: (Sport -> Maybe b) -> Maybe (Sport, [CV]) -> Maybe (b, [CV])

SatModel Color

Make Color a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.Garden

Methods

parseCVs :: [CV] -> Maybe (Color, [CV])

cvtModel :: (Color -> Maybe b) -> Maybe (Color, [CV]) -> Maybe (b, [CV])

SatModel Color

Make Color a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.HexPuzzle

Methods

parseCVs :: [CV] -> Maybe (Color, [CV])

cvtModel :: (Color -> Maybe b) -> Maybe (Color, [CV]) -> Maybe (b, [CV])

SatModel U2Member

Make U2Member a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

parseCVs :: [CV] -> Maybe (U2Member, [CV])

cvtModel :: (U2Member -> Maybe b) -> Maybe (U2Member, [CV]) -> Maybe (b, [CV])

SatModel Location

Make Location a symbolic value.

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

parseCVs :: [CV] -> Maybe (Location, [CV])

cvtModel :: (Location -> Maybe b) -> Maybe (Location, [CV]) -> Maybe (b, [CV])

SatModel Day

Make Day a symbolic value.

Defined in Documentation.SBV.Examples.Queries.Enums

Methods

parseCVs :: [CV] -> Maybe (Day, [CV])

cvtModel :: (Day -> Maybe b) -> Maybe (Day, [CV]) -> Maybe (b, [CV])

SatModel BinOp

Make BinOp a symbolic value.

Defined in Documentation.SBV.Examples.Queries.FourFours

Methods

parseCVs :: [CV] -> Maybe (BinOp, [CV])

cvtModel :: (BinOp -> Maybe b) -> Maybe (BinOp, [CV]) -> Maybe (b, [CV])

SatModel UnOp

Make UnOp a symbolic value.

Defined in Documentation.SBV.Examples.Queries.FourFours

Methods

parseCVs :: [CV] -> Maybe (UnOp, [CV])

cvtModel :: (UnOp -> Maybe b) -> Maybe (UnOp, [CV]) -> Maybe (b, [CV])

SatModel a => SatModel [a]

A list of values as extracted from a model. When reading a list, we go as long as we can (maximal-munch). Note that this never fails, as we can always return the empty list!

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ([a], [CV])

cvtModel :: ([a] -> Maybe b) -> Maybe ([a], [CV]) -> Maybe (b, [CV])

(SatModel a, SatModel b) => SatModel (a, b)

Tuples extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((a, b), [CV])

cvtModel :: ((a, b) -> Maybe b0) -> Maybe ((a, b), [CV]) -> Maybe (b0, [CV])

(SatModel a, SatModel b, SatModel c) => SatModel (a, b, c)

3-Tuples extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((a, b, c), [CV])

cvtModel :: ((a, b, c) -> Maybe b0) -> Maybe ((a, b, c), [CV]) -> Maybe (b0, [CV])

(SatModel a, SatModel b, SatModel c, SatModel d) => SatModel (a, b, c, d)

4-Tuples extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((a, b, c, d), [CV])

cvtModel :: ((a, b, c, d) -> Maybe b0) -> Maybe ((a, b, c, d), [CV]) -> Maybe (b0, [CV])

(SatModel a, SatModel b, SatModel c, SatModel d, SatModel e) => SatModel (a, b, c, d, e)

5-Tuples extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((a, b, c, d, e), [CV])

cvtModel :: ((a, b, c, d, e) -> Maybe b0) -> Maybe ((a, b, c, d, e), [CV]) -> Maybe (b0, [CV])

(SatModel a, SatModel b, SatModel c, SatModel d, SatModel e, SatModel f) => SatModel (a, b, c, d, e, f)

6-Tuples extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((a, b, c, d, e, f), [CV])

cvtModel :: ((a, b, c, d, e, f) -> Maybe b0) -> Maybe ((a, b, c, d, e, f), [CV]) -> Maybe (b0, [CV])

(SatModel a, SatModel b, SatModel c, SatModel d, SatModel e, SatModel f, SatModel g) => SatModel (a, b, c, d, e, f, g)

7-Tuples extracted from a model

Defined in Data.SBV.SMT.SMT

Methods

parseCVs :: [CV] -> Maybe ((a, b, c, d, e, f, g), [CV])

cvtModel :: ((a, b, c, d, e, f, g) -> Maybe b0) -> Maybe ((a, b, c, d, e, f, g), [CV]) -> Maybe (b0, [CV])

class Modelable a where

Various SMT results that we can extract models out of.

Minimal complete definition

modelExists, getModelAssignment, getModelDictionary, getModelObjectives, getModelUIFuns

Methods

modelExists :: a -> Bool

Is there a model?

getModelAssignment :: SatModel b => a -> Either String (Bool, b)

Extract assignments of a model, the result is a tuple where the first argument (if True) indicates whether the model was "probable". (i.e., if the solver returned unknown.)

getModelDictionary :: a -> Map String CV

Extract a model dictionary. Extract a dictionary mapping the variables to their respective values as returned by the SMT solver. Also see getModelDictionaries.

getModelValue :: SymVal b => String -> a -> Maybe b

Extract a model value for a given element. Also see getModelValues.

getModelUninterpretedValue :: String -> a -> Maybe String

Extract a representative name for the model value of an uninterpreted kind. This is supposed to correspond to the value as computed internally by the SMT solver; and is unportable from solver to solver. Also see getModelUninterpretedValues.

extractModel :: SatModel b => a -> Maybe b

A simpler variant of getModelAssignment to get a model out without the fuss.

getModelObjectives :: a -> Map String GeneralizedCV

Extract model objective values, for all optimization goals.

getModelObjectiveValue :: String -> a -> Maybe GeneralizedCV

Extract the value of an objective

getModelUIFuns :: a -> Map String (SBVType, ([([CV], CV)], CV))

Extract model uninterpreted-functions

getModelUIFunValue :: String -> a -> Maybe (SBVType, ([([CV], CV)], CV))

Extract the value of an uninterpreted-function as an association list

Instances

Modelable SMTResult

SMTResult as a generic model provider

Defined in Data.SBV.SMT.SMT

Methods

modelExists :: SMTResult -> Bool

getModelAssignment :: SatModel b => SMTResult -> Either String (Bool, b)

getModelDictionary :: SMTResult -> Map String CV

getModelValue :: SymVal b => String -> SMTResult -> Maybe b

getModelUninterpretedValue :: String -> SMTResult -> Maybe String

extractModel :: SatModel b => SMTResult -> Maybe b

getModelObjectives :: SMTResult -> Map String GeneralizedCV

getModelObjectiveValue :: String -> SMTResult -> Maybe GeneralizedCV

getModelUIFuns :: SMTResult -> Map String (SBVType, ([([CV], CV)], CV))

getModelUIFunValue :: String -> SMTResult -> Maybe (SBVType, ([([CV], CV)], CV))

Modelable SatResult

SatResult as a generic model provider

Defined in Data.SBV.SMT.SMT

Methods

modelExists :: SatResult -> Bool

getModelAssignment :: SatModel b => SatResult -> Either String (Bool, b)

getModelDictionary :: SatResult -> Map String CV

getModelValue :: SymVal b => String -> SatResult -> Maybe b

getModelUninterpretedValue :: String -> SatResult -> Maybe String

extractModel :: SatModel b => SatResult -> Maybe b

getModelObjectives :: SatResult -> Map String GeneralizedCV

getModelObjectiveValue :: String -> SatResult -> Maybe GeneralizedCV

getModelUIFuns :: SatResult -> Map String (SBVType, ([([CV], CV)], CV))

getModelUIFunValue :: String -> SatResult -> Maybe (SBVType, ([([CV], CV)], CV))

Modelable ThmResult

ThmResult as a generic model provider

Defined in Data.SBV.SMT.SMT

Methods

modelExists :: ThmResult -> Bool

getModelAssignment :: SatModel b => ThmResult -> Either String (Bool, b)

getModelDictionary :: ThmResult -> Map String CV

getModelValue :: SymVal b => String -> ThmResult -> Maybe b

getModelUninterpretedValue :: String -> ThmResult -> Maybe String

extractModel :: SatModel b => ThmResult -> Maybe b

getModelObjectives :: ThmResult -> Map String GeneralizedCV

getModelObjectiveValue :: String -> ThmResult -> Maybe GeneralizedCV

getModelUIFuns :: ThmResult -> Map String (SBVType, ([([CV], CV)], CV))

getModelUIFunValue :: String -> ThmResult -> Maybe (SBVType, ([([CV], CV)], CV))

displayModels :: SatModel a => (Int -> (Bool, a) -> IO ()) -> AllSatResult -> IO Int

Given an allSat call, we typically want to iterate over it and print the results in sequence. The displayModels function automates this task by calling disp on each result, consecutively. The first Int argument to disp 'is the current model number. The second argument is a tuple, where the first element indicates whether the model is alleged (i.e., if the solver is not sure, returing Unknown)

extractModels :: SatModel a => AllSatResult -> [a]

Return all the models from an allSat call, similar to extractModel but is suitable for the case of multiple results.

getModelDictionaries :: AllSatResult -> [Map String CV]

Get dictionaries from an all-sat call. Similar to getModelDictionary.

getModelValues :: SymVal b => String -> AllSatResult -> [Maybe b]

Extract value of a variable from an all-sat call. Similar to getModelValue.

getModelUninterpretedValues :: String -> AllSatResult -> [Maybe String]

Extract value of an uninterpreted variable from an all-sat call. Similar to getModelUninterpretedValue.

SMT Interface

data SMTConfig

Solver configuration. See also z3, yices, cvc4, boolector, mathSAT, etc. which are instantiations of this type for those solvers, with reasonable defaults. In particular, custom configuration can be created by varying those values. (Such as z3{verbose=True}.)

Most fields are self explanatory. The notion of precision for printing algebraic reals stems from the fact that such values does not necessarily have finite decimal representations, and hence we have to stop printing at some depth. It is important to emphasize that such values always have infinite precision internally. The issue is merely with how we print such an infinite precision value on the screen. The field printRealPrec controls the printing precision, by specifying the number of digits after the decimal point. The default value is 16, but it can be set to any positive integer.

When printing, SBV will add the suffix ... at the and of a real-value, if the given bound is not sufficient to represent the real-value exactly. Otherwise, the number will be written out in standard decimal notation. Note that SBV will always print the whole value if it is precise (i.e., if it fits in a finite number of digits), regardless of the precision limit. The limit only applies if the representation of the real value is not finite, i.e., if it is not rational.

The printBase field can be used to print numbers in base 2, 10, or 16. If base 2 or 16 is used, then floating-point values will be printed in their internal memory-layout format as well, which can come in handy for bit-precise analysis.

Constructors

SMTConfig

Fields

• verbose :: Bool

  Debug mode

• timing :: Timing

  Print timing information on how long different phases took (construction, solving, etc.)

• printBase :: Int

  Print integral literals in this base (2, 10, and 16 are supported.)

• printRealPrec :: Int

  Print algebraic real values with this precision. (SReal, default: 16)

• satCmd :: String

  Usually "(check-sat)". However, users might tweak it based on solver characteristics.

• allSatMaxModelCount :: Maybe Int

  In a allSat call, return at most this many models. If nothing, return all.

• allSatPrintAlong :: Bool

  In a allSat call, print models as they are found.

• satTrackUFs :: Bool

  In a sat call, should we try to extract values of uninterpreted functions?

• isNonModelVar :: String -> Bool

  When constructing a model, ignore variables whose name satisfy this predicate. (Default: (const False), i.e., don't ignore anything)

• validateModel :: Bool

  If set, SBV will attempt to validate the model it gets back from the solver.

• optimizeValidateConstraints :: Bool

  Validate optimization results. NB: Does NOT make sure the model is optimal, just checks they satisfy the constraints.

• transcript :: Maybe FilePath

  If Just, the entire interaction will be recorded as a playable file (for debugging purposes mostly)

• smtLibVersion :: SMTLibVersion

  What version of SMT-lib we use for the tool

• solver :: SMTSolver

  The actual SMT solver.

• allowQuantifiedQueries :: Bool

  Should we permit use of quantifiers in the query mode? (Default: False. See http://github.com/LeventErkok/sbv/issues/459 for why.)

• roundingMode :: RoundingMode

  Rounding mode to use for floating-point conversions

• solverSetOptions :: [SMTOption]

  Options to set as we start the solver

• ignoreExitCode :: Bool

  If true, we shall ignore the exit code upon exit. Otherwise we require ExitSuccess.

• redirectVerbose :: Maybe FilePath

  Redirect the verbose output to this file if given. If Nothing, stdout is implied.

Instances

NFData SMTConfig

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SMTConfig -> ()

data Timing

Specify how to save timing information, if at all.

Constructors

NoTiming

PrintTiming

SaveTiming (IORef NominalDiffTime)

data SMTLibVersion

Representation of SMTLib Program versions. As of June 2015, we're dropping support for SMTLib1, and supporting SMTLib2 only. We keep this data-type around in case SMTLib3 comes along and we want to support 2 and 3 simultaneously.

Constructors

SMTLib2

Instances

Bounded SMTLibVersion

Defined in Data.SBV.Core.Symbolic

Methods

minBound :: SMTLibVersion

maxBound :: SMTLibVersion

Enum SMTLibVersion

Defined in Data.SBV.Core.Symbolic

Methods

succ :: SMTLibVersion -> SMTLibVersion

pred :: SMTLibVersion -> SMTLibVersion

toEnum :: Int -> SMTLibVersion

fromEnum :: SMTLibVersion -> Int

enumFrom :: SMTLibVersion -> [SMTLibVersion]

enumFromThen :: SMTLibVersion -> SMTLibVersion -> [SMTLibVersion]

enumFromTo :: SMTLibVersion -> SMTLibVersion -> [SMTLibVersion]

enumFromThenTo :: SMTLibVersion -> SMTLibVersion -> SMTLibVersion -> [SMTLibVersion]

Eq SMTLibVersion

Defined in Data.SBV.Core.Symbolic

Methods

(==) :: SMTLibVersion -> SMTLibVersion -> Bool

(/=) :: SMTLibVersion -> SMTLibVersion -> Bool

Show SMTLibVersion

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> SMTLibVersion -> ShowS

show :: SMTLibVersion -> String

showList :: [SMTLibVersion] -> ShowS

NFData SMTLibVersion

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SMTLibVersion -> ()

data Solver

Solvers that SBV is aware of

Constructors

Z3

Yices

Boolector

CVC4

MathSAT

ABC

Instances

Bounded Solver

Defined in Data.SBV.Core.Symbolic

Methods

minBound :: Solver

maxBound :: Solver

Enum Solver

Defined in Data.SBV.Core.Symbolic

Methods

succ :: Solver -> Solver

pred :: Solver -> Solver

toEnum :: Int -> Solver

fromEnum :: Solver -> Int

enumFrom :: Solver -> [Solver]

enumFromThen :: Solver -> Solver -> [Solver]

enumFromTo :: Solver -> Solver -> [Solver]

enumFromThenTo :: Solver -> Solver -> Solver -> [Solver]

Show Solver

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> Solver -> ShowS

show :: Solver -> String

showList :: [Solver] -> ShowS

data SMTSolver

An SMT solver

Constructors

SMTSolver

Fields

• name :: Solver

  The solver in use

• executable :: String

  The path to its executable

• preprocess :: String -> String

  Each line sent to the solver will be passed through this function (typically id)

• options :: SMTConfig -> [String]

  Options to provide to the solver

• engine :: SMTEngine

  The solver engine, responsible for interpreting solver output

• capabilities :: SolverCapabilities

  Various capabilities of the solver

Controlling verbosity

SBV provides various levels of verbosity to aid in debugging, by using the SMTConfig fields:

• [verbose] Print on stdout a shortened account of what is sent/received. This is specifically trimmed to reduce noise and is good for quick debugging. The output is not supposed to be machine-readable.
• [redirectVerbose] Send the verbose output to a file. Note that you still have to set `verbose=True` for redirection to take effect. Otherwise, the output is the same as what you would see in verbose.
• [transcript] Produce a file that is valid SMTLib2 format, containing everything sent and received. In particular, one can directly feed this file to the SMT-solver outside of the SBV since it is machine-readable. This is good for offline analysis situations, where you want to have a full account of what happened. For instance, it will print time-stamps at every interaction point, so you can see how long each command took.

Solvers

boolector :: SMTConfig

Default configuration for the Boolector SMT solver

cvc4 :: SMTConfig

Default configuration for the CVC4 SMT Solver.

yices :: SMTConfig

Default configuration for the Yices SMT Solver.

z3 :: SMTConfig

Default configuration for the Z3 SMT solver

mathSAT :: SMTConfig

Default configuration for the MathSAT SMT solver

abc :: SMTConfig

Default configuration for the ABC synthesis and verification tool.

Configurations

defaultSolverConfig :: Solver -> SMTConfig

The default configs corresponding to supported SMT solvers

defaultSMTCfg :: SMTConfig

The default solver used by SBV. This is currently set to z3.

sbvCheckSolverInstallation :: SMTConfig -> IO Bool

Check whether the given solver is installed and is ready to go. This call does a simple call to the solver to ensure all is well.

sbvAvailableSolvers :: IO [SMTConfig]

Return the known available solver configs, installed on your machine.

setLogic :: SolverContext m => Logic -> m ()

Set the logic.

data Logic

SMT-Lib logics. If left unspecified SBV will pick the logic based on what it determines is needed. However, the user can override this choice using a call to setLogic This is especially handy if one is experimenting with custom logics that might be supported on new solvers. See http://smtlib.cs.uiowa.edu/logics.shtml for the official list.

Constructors

AUFLIA

Formulas over the theory of linear integer arithmetic and arrays extended with free sort and function symbols but restricted to arrays with integer indices and values.

AUFLIRA

Linear formulas with free sort and function symbols over one- and two-dimentional arrays of integer index and real value.

AUFNIRA

Formulas with free function and predicate symbols over a theory of arrays of arrays of integer index and real value.

LRA

Linear formulas in linear real arithmetic.

QF_ABV

Quantifier-free formulas over the theory of bitvectors and bitvector arrays.

QF_AUFBV

Quantifier-free formulas over the theory of bitvectors and bitvector arrays extended with free sort and function symbols.

QF_AUFLIA

Quantifier-free linear formulas over the theory of integer arrays extended with free sort and function symbols.

QF_AX

Quantifier-free formulas over the theory of arrays with extensionality.

QF_BV

Quantifier-free formulas over the theory of fixed-size bitvectors.

QF_IDL

Difference Logic over the integers. Boolean combinations of inequations of the form x - y < b where x and y are integer variables and b is an integer constant.

QF_LIA

Unquantified linear integer arithmetic. In essence, Boolean combinations of inequations between linear polynomials over integer variables.

QF_LRA

Unquantified linear real arithmetic. In essence, Boolean combinations of inequations between linear polynomials over real variables.

QF_NIA

Quantifier-free integer arithmetic.

QF_NRA

Quantifier-free real arithmetic.

QF_RDL

Difference Logic over the reals. In essence, Boolean combinations of inequations of the form x - y < b where x and y are real variables and b is a rational constant.

QF_UF

Unquantified formulas built over a signature of uninterpreted (i.e., free) sort and function symbols.

QF_UFBV

Unquantified formulas over bitvectors with uninterpreted sort function and symbols.

QF_UFIDL

Difference Logic over the integers (in essence) but with uninterpreted sort and function symbols.

QF_UFLIA

Unquantified linear integer arithmetic with uninterpreted sort and function symbols.

QF_UFLRA

Unquantified linear real arithmetic with uninterpreted sort and function symbols.

QF_UFNRA

Unquantified non-linear real arithmetic with uninterpreted sort and function symbols.

QF_UFNIRA

Unquantified non-linear real integer arithmetic with uninterpreted sort and function symbols.

UFLRA

Linear real arithmetic with uninterpreted sort and function symbols.

UFNIA

Non-linear integer arithmetic with uninterpreted sort and function symbols.

QF_FPBV

Quantifier-free formulas over the theory of floating point numbers, arrays, and bit-vectors.

QF_FP

Quantifier-free formulas over the theory of floating point numbers.

QF_FD

Quantifier-free finite domains.

QF_S

Quantifier-free formulas over the theory of strings.

Logic_ALL

The catch-all value.

Logic_NONE

Use this value when you want SBV to simply not set the logic.

CustomLogic String

In case you need a really custom string!

Instances

Show Logic

Defined in Data.SBV.Control.Types

Methods

showsPrec :: Int -> Logic -> ShowS

show :: Logic -> String

showList :: [Logic] -> ShowS

Generic Logic

Defined in Data.SBV.Control.Types

Associated Types

type Rep Logic :: Type -> Type

Methods

from :: Logic -> Rep Logic x

to :: Rep Logic x -> Logic

NFData Logic

Defined in Data.SBV.Control.Types

Methods

rnf :: Logic -> ()

GShow Logic

Defined in Data.SBV.Control.Types

Methods

gshowsPrec :: Int -> Logic -> ShowS

gshows :: Logic -> ShowS

gshow :: Logic -> String

gshowList :: [Logic] -> ShowS

type Rep Logic

Defined in Data.SBV.Control.Types

type Rep Logic = D1 (MetaData "Logic" "Data.SBV.Control.Types" "sbv-8.3-KY4PN9PPbrH5uMg2KovlBp" False) ((((C1 (MetaCons "AUFLIA" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "AUFLIRA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "AUFNIRA" PrefixI False) (U1 :: Type -> Type))) :+: ((C1 (MetaCons "LRA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_ABV" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "QF_AUFBV" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_AUFLIA" PrefixI False) (U1 :: Type -> Type)))) :+: (((C1 (MetaCons "QF_AX" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_BV" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "QF_IDL" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_LIA" PrefixI False) (U1 :: Type -> Type))) :+: ((C1 (MetaCons "QF_LRA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_NIA" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "QF_NRA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_RDL" PrefixI False) (U1 :: Type -> Type))))) :+: ((((C1 (MetaCons "QF_UF" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_UFBV" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "QF_UFIDL" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_UFLIA" PrefixI False) (U1 :: Type -> Type))) :+: ((C1 (MetaCons "QF_UFLRA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_UFNRA" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "QF_UFNIRA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "UFLRA" PrefixI False) (U1 :: Type -> Type)))) :+: (((C1 (MetaCons "UFNIA" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_FPBV" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "QF_FP" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "QF_FD" PrefixI False) (U1 :: Type -> Type))) :+: ((C1 (MetaCons "QF_S" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "Logic_ALL" PrefixI False) (U1 :: Type -> Type)) :+: (C1 (MetaCons "Logic_NONE" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "CustomLogic" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 String)))))))

setOption :: SolverContext m => SMTOption -> m ()

Set an option.

setInfo :: SolverContext m => String -> [String] -> m ()

Set info. Example: setInfo ":status" ["unsat"].

setTimeOut :: SolverContext m => Integer -> m ()

Set a solver time-out value, in milli-seconds. This function essentially translates to the SMTLib call (set-info :timeout val), and your backend solver may or may not support it! The amount given is in milliseconds. Also see the function timeOut for finer level control of time-outs, directly from SBV.

SBV exceptions

data SBVException

An exception thrown from SBV. If the solver ever responds with a non-success value for a command, SBV will throw an SBVException, it so the user can process it as required. The provided Show instance will render the failure nicely. Note that if you ever catch this exception, the solver is no longer alive: You should either -- throw the exception up, or do other proper clean-up before continuing.

Constructors

SBVException

Fields

• sbvExceptionDescription :: String
• sbvExceptionSent :: Maybe String
• sbvExceptionExpected :: Maybe String
• sbvExceptionReceived :: Maybe String
• sbvExceptionStdOut :: Maybe String
• sbvExceptionStdErr :: Maybe String
• sbvExceptionExitCode :: Maybe ExitCode
• sbvExceptionConfig :: SMTConfig
• sbvExceptionReason :: Maybe [String]
• sbvExceptionHint :: Maybe [String]

Instances

Show SBVException

A fairly nice rendering of the exception, for display purposes.

Defined in Data.SBV.SMT.Utils

Methods

showsPrec :: Int -> SBVException -> ShowS

show :: SBVException -> String

showList :: [SBVException] -> ShowS

Exception SBVException

SBVExceptions are throwable. A simple "show" will render this exception nicely though of course you can inspect the individual fields as necessary.

Defined in Data.SBV.SMT.Utils

Methods

toException :: SBVException -> SomeException

fromException :: SomeException -> Maybe SBVException

displayException :: SBVException -> String

Abstract SBV type

data SBV a

The Symbolic value. The parameter a is phantom, but is extremely important in keeping the user interface strongly typed.

Instances

IsString SString

Defined in Data.SBV.Core.Model

Methods

fromString :: String -> SString

Testable SBool

Defined in Data.SBV.Core.Model

Methods

property :: SBool -> Property

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> SBool) -> Property

SDivisible SInteger

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInteger -> SInteger -> (SInteger, SInteger)

sDivMod :: SInteger -> SInteger -> (SInteger, SInteger)

sQuot :: SInteger -> SInteger -> SInteger

sRem :: SInteger -> SInteger -> SInteger

sDiv :: SInteger -> SInteger -> SInteger

sMod :: SInteger -> SInteger -> SInteger

SDivisible SInt64

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt64 -> SInt64 -> (SInt64, SInt64)

sDivMod :: SInt64 -> SInt64 -> (SInt64, SInt64)

sQuot :: SInt64 -> SInt64 -> SInt64

sRem :: SInt64 -> SInt64 -> SInt64

sDiv :: SInt64 -> SInt64 -> SInt64

sMod :: SInt64 -> SInt64 -> SInt64

SDivisible SInt32

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt32 -> SInt32 -> (SInt32, SInt32)

sDivMod :: SInt32 -> SInt32 -> (SInt32, SInt32)

sQuot :: SInt32 -> SInt32 -> SInt32

sRem :: SInt32 -> SInt32 -> SInt32

sDiv :: SInt32 -> SInt32 -> SInt32

sMod :: SInt32 -> SInt32 -> SInt32

SDivisible SInt16

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt16 -> SInt16 -> (SInt16, SInt16)

sDivMod :: SInt16 -> SInt16 -> (SInt16, SInt16)

sQuot :: SInt16 -> SInt16 -> SInt16

sRem :: SInt16 -> SInt16 -> SInt16

sDiv :: SInt16 -> SInt16 -> SInt16

sMod :: SInt16 -> SInt16 -> SInt16

SDivisible SInt8

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SInt8 -> SInt8 -> (SInt8, SInt8)

sDivMod :: SInt8 -> SInt8 -> (SInt8, SInt8)

sQuot :: SInt8 -> SInt8 -> SInt8

sRem :: SInt8 -> SInt8 -> SInt8

sDiv :: SInt8 -> SInt8 -> SInt8

sMod :: SInt8 -> SInt8 -> SInt8

SDivisible SWord64

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord64 -> SWord64 -> (SWord64, SWord64)

sDivMod :: SWord64 -> SWord64 -> (SWord64, SWord64)

sQuot :: SWord64 -> SWord64 -> SWord64

sRem :: SWord64 -> SWord64 -> SWord64

sDiv :: SWord64 -> SWord64 -> SWord64

sMod :: SWord64 -> SWord64 -> SWord64

SDivisible SWord32

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord32 -> SWord32 -> (SWord32, SWord32)

sDivMod :: SWord32 -> SWord32 -> (SWord32, SWord32)

sQuot :: SWord32 -> SWord32 -> SWord32

sRem :: SWord32 -> SWord32 -> SWord32

sDiv :: SWord32 -> SWord32 -> SWord32

sMod :: SWord32 -> SWord32 -> SWord32

SDivisible SWord16

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord16 -> SWord16 -> (SWord16, SWord16)

sDivMod :: SWord16 -> SWord16 -> (SWord16, SWord16)

sQuot :: SWord16 -> SWord16 -> SWord16

sRem :: SWord16 -> SWord16 -> SWord16

sDiv :: SWord16 -> SWord16 -> SWord16

sMod :: SWord16 -> SWord16 -> SWord16

SDivisible SWord8

Defined in Data.SBV.Core.Model

Methods

sQuotRem :: SWord8 -> SWord8 -> (SWord8, SWord8)

sDivMod :: SWord8 -> SWord8 -> (SWord8, SWord8)

sQuot :: SWord8 -> SWord8 -> SWord8

sRem :: SWord8 -> SWord8 -> SWord8

sDiv :: SWord8 -> SWord8 -> SWord8

sMod :: SWord8 -> SWord8 -> SWord8

SDivisible SWord4

SDvisible instance, using default methods

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

sQuotRem :: SWord4 -> SWord4 -> (SWord4, SWord4)

sDivMod :: SWord4 -> SWord4 -> (SWord4, SWord4)

sQuot :: SWord4 -> SWord4 -> SWord4

sRem :: SWord4 -> SWord4 -> SWord4

sDiv :: SWord4 -> SWord4 -> SWord4

sMod :: SWord4 -> SWord4 -> SWord4

Polynomial SWord64

Defined in Data.SBV.Tools.Polynomial

Methods

polynomial :: [Int] -> SWord64

pAdd :: SWord64 -> SWord64 -> SWord64

pMult :: (SWord64, SWord64, [Int]) -> SWord64

pDiv :: SWord64 -> SWord64 -> SWord64

pMod :: SWord64 -> SWord64 -> SWord64

pDivMod :: SWord64 -> SWord64 -> (SWord64, SWord64)

showPoly :: SWord64 -> String

showPolynomial :: Bool -> SWord64 -> String

Polynomial SWord32

Defined in Data.SBV.Tools.Polynomial

Methods

polynomial :: [Int] -> SWord32

pAdd :: SWord32 -> SWord32 -> SWord32

pMult :: (SWord32, SWord32, [Int]) -> SWord32

pDiv :: SWord32 -> SWord32 -> SWord32

pMod :: SWord32 -> SWord32 -> SWord32

pDivMod :: SWord32 -> SWord32 -> (SWord32, SWord32)

showPoly :: SWord32 -> String

showPolynomial :: Bool -> SWord32 -> String

Polynomial SWord16

Defined in Data.SBV.Tools.Polynomial

Methods

polynomial :: [Int] -> SWord16

pAdd :: SWord16 -> SWord16 -> SWord16

pMult :: (SWord16, SWord16, [Int]) -> SWord16

pDiv :: SWord16 -> SWord16 -> SWord16

pMod :: SWord16 -> SWord16 -> SWord16

pDivMod :: SWord16 -> SWord16 -> (SWord16, SWord16)

showPoly :: SWord16 -> String

showPolynomial :: Bool -> SWord16 -> String

Polynomial SWord8

Defined in Data.SBV.Tools.Polynomial

Methods

polynomial :: [Int] -> SWord8

pAdd :: SWord8 -> SWord8 -> SWord8

pMult :: (SWord8, SWord8, [Int]) -> SWord8

pDiv :: SWord8 -> SWord8 -> SWord8

pMod :: SWord8 -> SWord8 -> SWord8

pDivMod :: SWord8 -> SWord8 -> (SWord8, SWord8)

showPoly :: SWord8 -> String

showPolynomial :: Bool -> SWord8 -> String

ArithOverflow SInt64

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SInt64 -> SInt64 -> (SBool, SBool)

bvSubO :: SInt64 -> SInt64 -> (SBool, SBool)

bvMulO :: SInt64 -> SInt64 -> (SBool, SBool)

bvMulOFast :: SInt64 -> SInt64 -> (SBool, SBool)

bvDivO :: SInt64 -> SInt64 -> (SBool, SBool)

bvNegO :: SInt64 -> (SBool, SBool)

ArithOverflow SInt32

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SInt32 -> SInt32 -> (SBool, SBool)

bvSubO :: SInt32 -> SInt32 -> (SBool, SBool)

bvMulO :: SInt32 -> SInt32 -> (SBool, SBool)

bvMulOFast :: SInt32 -> SInt32 -> (SBool, SBool)

bvDivO :: SInt32 -> SInt32 -> (SBool, SBool)

bvNegO :: SInt32 -> (SBool, SBool)

ArithOverflow SInt16

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SInt16 -> SInt16 -> (SBool, SBool)

bvSubO :: SInt16 -> SInt16 -> (SBool, SBool)

bvMulO :: SInt16 -> SInt16 -> (SBool, SBool)

bvMulOFast :: SInt16 -> SInt16 -> (SBool, SBool)

bvDivO :: SInt16 -> SInt16 -> (SBool, SBool)

bvNegO :: SInt16 -> (SBool, SBool)

ArithOverflow SInt8

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SInt8 -> SInt8 -> (SBool, SBool)

bvSubO :: SInt8 -> SInt8 -> (SBool, SBool)

bvMulO :: SInt8 -> SInt8 -> (SBool, SBool)

bvMulOFast :: SInt8 -> SInt8 -> (SBool, SBool)

bvDivO :: SInt8 -> SInt8 -> (SBool, SBool)

bvNegO :: SInt8 -> (SBool, SBool)

ArithOverflow SWord64

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SWord64 -> SWord64 -> (SBool, SBool)

bvSubO :: SWord64 -> SWord64 -> (SBool, SBool)

bvMulO :: SWord64 -> SWord64 -> (SBool, SBool)

bvMulOFast :: SWord64 -> SWord64 -> (SBool, SBool)

bvDivO :: SWord64 -> SWord64 -> (SBool, SBool)

bvNegO :: SWord64 -> (SBool, SBool)

ArithOverflow SWord32

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SWord32 -> SWord32 -> (SBool, SBool)

bvSubO :: SWord32 -> SWord32 -> (SBool, SBool)

bvMulO :: SWord32 -> SWord32 -> (SBool, SBool)

bvMulOFast :: SWord32 -> SWord32 -> (SBool, SBool)

bvDivO :: SWord32 -> SWord32 -> (SBool, SBool)

bvNegO :: SWord32 -> (SBool, SBool)

ArithOverflow SWord16

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SWord16 -> SWord16 -> (SBool, SBool)

bvSubO :: SWord16 -> SWord16 -> (SBool, SBool)

bvMulO :: SWord16 -> SWord16 -> (SBool, SBool)

bvMulOFast :: SWord16 -> SWord16 -> (SBool, SBool)

bvDivO :: SWord16 -> SWord16 -> (SBool, SBool)

bvNegO :: SWord16 -> (SBool, SBool)

ArithOverflow SWord8

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SWord8 -> SWord8 -> (SBool, SBool)

bvSubO :: SWord8 -> SWord8 -> (SBool, SBool)

bvMulO :: SWord8 -> SWord8 -> (SBool, SBool)

bvMulOFast :: SWord8 -> SWord8 -> (SBool, SBool)

bvDivO :: SWord8 -> SWord8 -> (SBool, SBool)

bvNegO :: SWord8 -> (SBool, SBool)

RegExpMatchable SString

Matching symbolic strings.

Defined in Data.SBV.RegExp

Methods

match :: SString -> RegExp -> SBool

RegExpMatchable SChar

Matching a character simply means the singleton string matches the regex.

Defined in Data.SBV.RegExp

Methods

match :: SChar -> RegExp -> SBool

ExtractIO m => MProvable m SBool

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: SBool -> SymbolicT m SBool

forAll :: [String] -> SBool -> SymbolicT m SBool

forSome_ :: SBool -> SymbolicT m SBool

forSome :: [String] -> SBool -> SymbolicT m SBool

prove :: SBool -> m ThmResult

proveWith :: SMTConfig -> SBool -> m ThmResult

sat :: SBool -> m SatResult

satWith :: SMTConfig -> SBool -> m SatResult

allSat :: SBool -> m AllSatResult

allSatWith :: SMTConfig -> SBool -> m AllSatResult

optimize :: OptimizeStyle -> SBool -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> SBool -> m OptimizeResult

isVacuous :: SBool -> m Bool

isVacuousWith :: SMTConfig -> SBool -> m Bool

isTheorem :: SBool -> m Bool

isTheoremWith :: SMTConfig -> SBool -> m Bool

isSatisfiable :: SBool -> m Bool

isSatisfiableWith :: SMTConfig -> SBool -> m Bool

validate :: Bool -> SMTConfig -> SBool -> SMTResult -> m SMTResult

Splittable SWord64 SWord32

Defined in Data.SBV.Core.Splittable

Methods

split :: SWord64 -> (SWord32, SWord32)

(#) :: SWord32 -> SWord32 -> SWord64

extend :: SWord32 -> SWord64

Splittable SWord32 SWord16

Defined in Data.SBV.Core.Splittable

Methods

split :: SWord32 -> (SWord16, SWord16)

(#) :: SWord16 -> SWord16 -> SWord32

extend :: SWord16 -> SWord32

Splittable SWord16 SWord8

Defined in Data.SBV.Core.Splittable

Methods

split :: SWord16 -> (SWord8, SWord8)

(#) :: SWord8 -> SWord8 -> SWord16

extend :: SWord8 -> SWord16

Fresh IO (S SInteger)

Fresh instance for our state

Defined in Documentation.SBV.Examples.ProofTools.BMC

Methods

fresh :: QueryT IO (S SInteger)

Fresh IO (S SInteger)

Fresh instance for our state

Defined in Documentation.SBV.Examples.ProofTools.Fibonacci

Methods

fresh :: QueryT IO (S SInteger)

Fresh IO (S SInteger)

Fresh instance for our state

Defined in Documentation.SBV.Examples.ProofTools.Strengthen

Methods

fresh :: QueryT IO (S SInteger)

Fresh IO (S SInteger)

Fresh instance for our state

Defined in Documentation.SBV.Examples.ProofTools.Sum

Methods

fresh :: QueryT IO (S SInteger)

(SymVal a, SMTValue a) => Fresh IO (FibS (SBV a))

Fresh instance for the program state

Defined in Documentation.SBV.Examples.WeakestPreconditions.Fib

Methods

fresh :: QueryT IO (FibS (SBV a))

(SymVal a, SMTValue a) => Fresh IO (GCDS (SBV a))

Fresh instance for the program state

Defined in Documentation.SBV.Examples.WeakestPreconditions.GCD

Methods

fresh :: QueryT IO (GCDS (SBV a))

(SymVal a, SMTValue a) => Fresh IO (DivS (SBV a))

Fresh instance for the program state

Defined in Documentation.SBV.Examples.WeakestPreconditions.IntDiv

Methods

fresh :: QueryT IO (DivS (SBV a))

(SymVal a, SMTValue a) => Fresh IO (SqrtS (SBV a))

Fresh instance for the program state

Defined in Documentation.SBV.Examples.WeakestPreconditions.IntSqrt

Methods

fresh :: QueryT IO (SqrtS (SBV a))

(SymVal a, SMTValue a) => Fresh IO (SumS (SBV a))

Fresh instance for the program state

Defined in Documentation.SBV.Examples.WeakestPreconditions.Sum

Methods

fresh :: QueryT IO (SumS (SBV a))

ExtractIO m => SExecutable m [SBV a]

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: [SBV a] -> SymbolicT m ()

sName :: [String] -> [SBV a] -> SymbolicT m ()

safe :: [SBV a] -> m [SafeResult]

safeWith :: SMTConfig -> [SBV a] -> m [SafeResult]

ExtractIO m => SExecutable m (SBV a)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: SBV a -> SymbolicT m ()

sName :: [String] -> SBV a -> SymbolicT m ()

safe :: SBV a -> m [SafeResult]

safeWith :: SMTConfig -> SBV a -> m [SafeResult]

(MonadIO m, SymVal a, SMTValue a) => Queriable m (SBV a) a

Generic Queriable instance for 'SymVal'/'SMTValue' values

Defined in Data.SBV.Control.Utils

Methods

create :: QueryT m (SBV a)

project :: SBV a -> QueryT m a

embed :: a -> QueryT m (SBV a)

(MonadIO m, SymVal a, SMTValue a, Foldable t, Traversable t, Fresh m (t (SBV a))) => Queriable m (t (SBV a)) (t a)

Generic Queriable instance for things that are Fresh and look like containers:

Defined in Data.SBV.Control.Utils

Methods

create :: QueryT m (t (SBV a))

project :: t (SBV a) -> QueryT m (t a)

embed :: t a -> QueryT m (t (SBV a))

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c, SBV d) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SExecutable m p) => SExecutable m ((SBV a, SBV b, SBV c) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b, SBV c) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m [SafeResult]

(SymVal a, SymVal b, SExecutable m p) => SExecutable m ((SBV a, SBV b) -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: ((SBV a, SBV b) -> p) -> SymbolicT m ()

sName :: [String] -> ((SBV a, SBV b) -> p) -> SymbolicT m ()

safe :: ((SBV a, SBV b) -> p) -> m [SafeResult]

safeWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m [SafeResult]

(SymVal a, SExecutable m p) => SExecutable m (SBV a -> p)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a -> p) -> SymbolicT m ()

sName :: [String] -> (SBV a -> p) -> SymbolicT m ()

safe :: (SBV a -> p) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a -> p) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b) => SExecutable m (SBV a, SBV b)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b) -> SymbolicT m ()

safe :: (SBV a, SBV b) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b) -> m [SafeResult]

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m SBool

forAll :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m SBool

forSome_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m SBool

forSome :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SymbolicT m SBool

prove :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m ThmResult

proveWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m ThmResult

sat :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m SatResult

satWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m SatResult

allSat :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m AllSatResult

allSatWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m AllSatResult

optimize :: OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m OptimizeResult

isVacuous :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m Bool

isVacuousWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m Bool

isTheorem :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m Bool

isTheoremWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m Bool

isSatisfiable :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> m Bool

validate :: Bool -> SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> p) -> SMTResult -> m SMTResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m SBool

forAll :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m SBool

forSome_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m SBool

forSome :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SymbolicT m SBool

prove :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m ThmResult

proveWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m ThmResult

sat :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m SatResult

satWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m SatResult

allSat :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m AllSatResult

allSatWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m AllSatResult

optimize :: OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m OptimizeResult

isVacuous :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m Bool

isVacuousWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m Bool

isTheorem :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m Bool

isTheoremWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m Bool

isSatisfiable :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> m Bool

validate :: Bool -> SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> p) -> SMTResult -> m SMTResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m SBool

forAll :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m SBool

forSome_ :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m SBool

forSome :: [String] -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SymbolicT m SBool

prove :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m ThmResult

proveWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m ThmResult

sat :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m SatResult

satWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m SatResult

allSat :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m AllSatResult

allSatWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m AllSatResult

optimize :: OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m OptimizeResult

isVacuous :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m Bool

isVacuousWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m Bool

isTheorem :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m Bool

isTheoremWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m Bool

isSatisfiable :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> m Bool

validate :: Bool -> SMTConfig -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> p) -> SMTResult -> m SMTResult

(SymVal a, SymVal b, SymVal c, SymVal d, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c, SBV d) -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m SBool

forAll :: [String] -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m SBool

forSome_ :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m SBool

forSome :: [String] -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> SymbolicT m SBool

prove :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m ThmResult

proveWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m ThmResult

sat :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m SatResult

satWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m SatResult

allSat :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m AllSatResult

allSatWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m AllSatResult

optimize :: OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m OptimizeResult

isVacuous :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m Bool

isVacuousWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m Bool

isTheorem :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m Bool

isTheoremWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m Bool

isSatisfiable :: ((SBV a, SBV b, SBV c, SBV d) -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> m Bool

validate :: Bool -> SMTConfig -> ((SBV a, SBV b, SBV c, SBV d) -> p) -> SMTResult -> m SMTResult

(SymVal a, SymVal b, SymVal c, MProvable m p) => MProvable m ((SBV a, SBV b, SBV c) -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m SBool

forAll :: [String] -> ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m SBool

forSome_ :: ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m SBool

forSome :: [String] -> ((SBV a, SBV b, SBV c) -> p) -> SymbolicT m SBool

prove :: ((SBV a, SBV b, SBV c) -> p) -> m ThmResult

proveWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m ThmResult

sat :: ((SBV a, SBV b, SBV c) -> p) -> m SatResult

satWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m SatResult

allSat :: ((SBV a, SBV b, SBV c) -> p) -> m AllSatResult

allSatWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m AllSatResult

optimize :: OptimizeStyle -> ((SBV a, SBV b, SBV c) -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> ((SBV a, SBV b, SBV c) -> p) -> m OptimizeResult

isVacuous :: ((SBV a, SBV b, SBV c) -> p) -> m Bool

isVacuousWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m Bool

isTheorem :: ((SBV a, SBV b, SBV c) -> p) -> m Bool

isTheoremWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m Bool

isSatisfiable :: ((SBV a, SBV b, SBV c) -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> m Bool

validate :: Bool -> SMTConfig -> ((SBV a, SBV b, SBV c) -> p) -> SMTResult -> m SMTResult

(SymVal a, SymVal b, MProvable m p) => MProvable m ((SBV a, SBV b) -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: ((SBV a, SBV b) -> p) -> SymbolicT m SBool

forAll :: [String] -> ((SBV a, SBV b) -> p) -> SymbolicT m SBool

forSome_ :: ((SBV a, SBV b) -> p) -> SymbolicT m SBool

forSome :: [String] -> ((SBV a, SBV b) -> p) -> SymbolicT m SBool

prove :: ((SBV a, SBV b) -> p) -> m ThmResult

proveWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m ThmResult

sat :: ((SBV a, SBV b) -> p) -> m SatResult

satWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m SatResult

allSat :: ((SBV a, SBV b) -> p) -> m AllSatResult

allSatWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m AllSatResult

optimize :: OptimizeStyle -> ((SBV a, SBV b) -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> ((SBV a, SBV b) -> p) -> m OptimizeResult

isVacuous :: ((SBV a, SBV b) -> p) -> m Bool

isVacuousWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m Bool

isTheorem :: ((SBV a, SBV b) -> p) -> m Bool

isTheoremWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m Bool

isSatisfiable :: ((SBV a, SBV b) -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> ((SBV a, SBV b) -> p) -> m Bool

validate :: Bool -> SMTConfig -> ((SBV a, SBV b) -> p) -> SMTResult -> m SMTResult

(SymVal a, MProvable m p) => MProvable m (SBV a -> p)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: (SBV a -> p) -> SymbolicT m SBool

forAll :: [String] -> (SBV a -> p) -> SymbolicT m SBool

forSome_ :: (SBV a -> p) -> SymbolicT m SBool

forSome :: [String] -> (SBV a -> p) -> SymbolicT m SBool

prove :: (SBV a -> p) -> m ThmResult

proveWith :: SMTConfig -> (SBV a -> p) -> m ThmResult

sat :: (SBV a -> p) -> m SatResult

satWith :: SMTConfig -> (SBV a -> p) -> m SatResult

allSat :: (SBV a -> p) -> m AllSatResult

allSatWith :: SMTConfig -> (SBV a -> p) -> m AllSatResult

optimize :: OptimizeStyle -> (SBV a -> p) -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> (SBV a -> p) -> m OptimizeResult

isVacuous :: (SBV a -> p) -> m Bool

isVacuousWith :: SMTConfig -> (SBV a -> p) -> m Bool

isTheorem :: (SBV a -> p) -> m Bool

isTheoremWith :: SMTConfig -> (SBV a -> p) -> m Bool

isSatisfiable :: (SBV a -> p) -> m Bool

isSatisfiableWith :: SMTConfig -> (SBV a -> p) -> m Bool

validate :: Bool -> SMTConfig -> (SBV a -> p) -> SMTResult -> m SMTResult

ExtractIO m => MProvable m (SymbolicT m SBool)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: SymbolicT m SBool -> SymbolicT m SBool

forAll :: [String] -> SymbolicT m SBool -> SymbolicT m SBool

forSome_ :: SymbolicT m SBool -> SymbolicT m SBool

forSome :: [String] -> SymbolicT m SBool -> SymbolicT m SBool

prove :: SymbolicT m SBool -> m ThmResult

proveWith :: SMTConfig -> SymbolicT m SBool -> m ThmResult

sat :: SymbolicT m SBool -> m SatResult

satWith :: SMTConfig -> SymbolicT m SBool -> m SatResult

allSat :: SymbolicT m SBool -> m AllSatResult

allSatWith :: SMTConfig -> SymbolicT m SBool -> m AllSatResult

optimize :: OptimizeStyle -> SymbolicT m SBool -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> SymbolicT m SBool -> m OptimizeResult

isVacuous :: SymbolicT m SBool -> m Bool

isVacuousWith :: SMTConfig -> SymbolicT m SBool -> m Bool

isTheorem :: SymbolicT m SBool -> m Bool

isTheoremWith :: SMTConfig -> SymbolicT m SBool -> m Bool

isSatisfiable :: SymbolicT m SBool -> m Bool

isSatisfiableWith :: SMTConfig -> SymbolicT m SBool -> m Bool

validate :: Bool -> SMTConfig -> SymbolicT m SBool -> SMTResult -> m SMTResult

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c) => SExecutable m (SBV a, SBV b, SBV c)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d) => SExecutable m (SBV a, SBV b, SBV c, SBV d)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d, SBV e) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d, SBV e) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d, SBV e) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d, SBV e) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e, NFData f, SymVal f) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> m [SafeResult]

(ExtractIO m, NFData a, SymVal a, NFData b, SymVal b, NFData c, SymVal c, NFData d, SymVal d, NFData e, SymVal e, NFData f, SymVal f, NFData g, SymVal g) => SExecutable m (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> SymbolicT m ()

sName :: [String] -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> SymbolicT m ()

safe :: (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> m [SafeResult]

safeWith :: SMTConfig -> (SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> m [SafeResult]

SymVal [a] => IsList (SList a)

IsList instance allows list literals to be written compactly.

Defined in Data.SBV.Core.Data

Associated Types

type Item (SList a) :: Type

Methods

fromList :: [Item (SList a)] -> SList a

fromListN :: Int -> [Item (SList a)] -> SList a

toList :: SList a -> [Item (SList a)]

(SymVal a, Bounded a) => Bounded (SBV a)

Defined in Data.SBV.Core.Model

Methods

minBound :: SBV a

maxBound :: SBV a

(Show a, Bounded a, Integral a, Num a, SymVal a) => Enum (SBV a)

Defined in Data.SBV.Core.Model

Methods

succ :: SBV a -> SBV a

pred :: SBV a -> SBV a

toEnum :: Int -> SBV a

fromEnum :: SBV a -> Int

enumFrom :: SBV a -> [SBV a]

enumFromThen :: SBV a -> SBV a -> [SBV a]

enumFromTo :: SBV a -> SBV a -> [SBV a]

enumFromThenTo :: SBV a -> SBV a -> SBV a -> [SBV a]

Eq (SBV a)

This instance is only defined so that we can define an instance for Bits. == and /= simply throw an error. Use EqSymbolic instead.

Defined in Data.SBV.Core.Data

Methods

(==) :: SBV a -> SBV a -> Bool

(/=) :: SBV a -> SBV a -> Bool

(Ord a, SymVal a, Fractional a, Floating a) => Floating (SBV a)

Define Floating instance on SBV's; only for base types that are already floating; i.e., SFloat and SDouble Note that most of the fields are "undefined" for symbolic values, we add methods as they are supported by SMTLib. Currently, the only symbolicly available function in this class is sqrt.

Defined in Data.SBV.Core.Model

Methods

pi :: SBV a

exp :: SBV a -> SBV a

log :: SBV a -> SBV a

sqrt :: SBV a -> SBV a

(**) :: SBV a -> SBV a -> SBV a

logBase :: SBV a -> SBV a -> SBV a

sin :: SBV a -> SBV a

cos :: SBV a -> SBV a

tan :: SBV a -> SBV a

asin :: SBV a -> SBV a

acos :: SBV a -> SBV a

atan :: SBV a -> SBV a

sinh :: SBV a -> SBV a

cosh :: SBV a -> SBV a

tanh :: SBV a -> SBV a

asinh :: SBV a -> SBV a

acosh :: SBV a -> SBV a

atanh :: SBV a -> SBV a

log1p :: SBV a -> SBV a

expm1 :: SBV a -> SBV a

log1pexp :: SBV a -> SBV a

log1mexp :: SBV a -> SBV a

(Ord a, SymVal a, Fractional a) => Fractional (SBV a)

Defined in Data.SBV.Core.Model

Methods

(/) :: SBV a -> SBV a -> SBV a

recip :: SBV a -> SBV a

fromRational :: Rational -> SBV a

(Ord a, Num a, SymVal a) => Num (SBV a)

Defined in Data.SBV.Core.Model

Methods

(+) :: SBV a -> SBV a -> SBV a

(-) :: SBV a -> SBV a -> SBV a

(*) :: SBV a -> SBV a -> SBV a

negate :: SBV a -> SBV a

abs :: SBV a -> SBV a

signum :: SBV a -> SBV a

fromInteger :: Integer -> SBV a

Show (SBV a)

A Show instance is not particularly "desirable," when the value is symbolic, but we do need this instance as otherwise we cannot simply evaluate Haskell functions that return symbolic values and have their constant values printed easily!

Defined in Data.SBV.Core.Data

Methods

showsPrec :: Int -> SBV a -> ShowS

show :: SBV a -> String

showList :: [SBV a] -> ShowS

(SymVal a, Show a) => Show (FibS (SBV a))

Show instance for FibS. The above deriving clause would work just as well, but we want it to be a little prettier here, and hence the OVERLAPS directive.

Defined in Documentation.SBV.Examples.WeakestPreconditions.Fib

Methods

showsPrec :: Int -> FibS (SBV a) -> ShowS

show :: FibS (SBV a) -> String

showList :: [FibS (SBV a)] -> ShowS

(SymVal a, Show a) => Show (GCDS (SBV a))

Show instance for GCDS. The above deriving clause would work just as well, but we want it to be a little prettier here, and hence the OVERLAPS directive.

Defined in Documentation.SBV.Examples.WeakestPreconditions.GCD

Methods

showsPrec :: Int -> GCDS (SBV a) -> ShowS

show :: GCDS (SBV a) -> String

showList :: [GCDS (SBV a)] -> ShowS

(SymVal a, Show a) => Show (DivS (SBV a))

Show instance for DivS. The above deriving clause would work just as well, but we want it to be a little prettier here, and hence the OVERLAPS directive.

Defined in Documentation.SBV.Examples.WeakestPreconditions.IntDiv

Methods

showsPrec :: Int -> DivS (SBV a) -> ShowS

show :: DivS (SBV a) -> String

showList :: [DivS (SBV a)] -> ShowS

(SymVal a, Show a) => Show (SqrtS (SBV a))

Show instance for SqrtS. The above deriving clause would work just as well, but we want it to be a little prettier here, and hence the OVERLAPS directive.

Defined in Documentation.SBV.Examples.WeakestPreconditions.IntSqrt

Methods

showsPrec :: Int -> SqrtS (SBV a) -> ShowS

show :: SqrtS (SBV a) -> String

showList :: [SqrtS (SBV a)] -> ShowS

(SymVal a, Show a) => Show (SumS (SBV a))

Show instance for SumS. The above deriving clause would work just as well, but we want it to be a little prettier here, and hence the OVERLAPS directive.

Defined in Documentation.SBV.Examples.WeakestPreconditions.Sum

Methods

showsPrec :: Int -> SumS (SBV a) -> ShowS

show :: SumS (SBV a) -> String

showList :: [SumS (SBV a)] -> ShowS

Generic (SBV a)

Defined in Data.SBV.Core.Data

Associated Types

type Rep (SBV a) :: Type -> Type

Methods

from :: SBV a -> Rep (SBV a) x

to :: Rep (SBV a) x -> SBV a

Testable (Symbolic SBool)

Defined in Data.SBV.Core.Model

Methods

property :: Symbolic SBool -> Property

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> Symbolic SBool) -> Property

(SymVal a, Arbitrary a) => Arbitrary (SBV a)

Defined in Data.SBV.Core.Model

Methods

arbitrary :: Gen (SBV a)

shrink :: SBV a -> [SBV a]

(Ord a, Num a, Bits a, SymVal a) => Bits (SBV a)

Using popCount or testBit on non-concrete values will result in an error. Use sPopCount or sTestBit instead.

Defined in Data.SBV.Core.Model

Methods

(.&.) :: SBV a -> SBV a -> SBV a

(.|.) :: SBV a -> SBV a -> SBV a

xor :: SBV a -> SBV a -> SBV a

complement :: SBV a -> SBV a

shift :: SBV a -> Int -> SBV a

rotate :: SBV a -> Int -> SBV a

zeroBits :: SBV a

bit :: Int -> SBV a

setBit :: SBV a -> Int -> SBV a

clearBit :: SBV a -> Int -> SBV a

complementBit :: SBV a -> Int -> SBV a

testBit :: SBV a -> Int -> Bool

bitSizeMaybe :: SBV a -> Maybe Int

bitSize :: SBV a -> Int

isSigned :: SBV a -> Bool

shiftL :: SBV a -> Int -> SBV a

unsafeShiftL :: SBV a -> Int -> SBV a

shiftR :: SBV a -> Int -> SBV a

unsafeShiftR :: SBV a -> Int -> SBV a

rotateL :: SBV a -> Int -> SBV a

rotateR :: SBV a -> Int -> SBV a

popCount :: SBV a -> Int

NFData (SBV a)

Defined in Data.SBV.Core.Data

Methods

rnf :: SBV a -> ()

(Random a, SymVal a) => Random (SBV a)

Defined in Data.SBV.Core.Data

Methods

randomR :: RandomGen g => (SBV a, SBV a) -> g -> (SBV a, g)

random :: RandomGen g => g -> (SBV a, g)

randomRs :: RandomGen g => (SBV a, SBV a) -> g -> [SBV a]

randoms :: RandomGen g => g -> [SBV a]

randomRIO :: (SBV a, SBV a) -> IO (SBV a)

randomIO :: IO (SBV a)

HasKind a => HasKind (SBV a)

Defined in Data.SBV.Core.Data

Methods

kindOf :: SBV a -> Kind

hasSign :: SBV a -> Bool

intSizeOf :: SBV a -> Int

isBoolean :: SBV a -> Bool

isBounded :: SBV a -> Bool

isReal :: SBV a -> Bool

isFloat :: SBV a -> Bool

isDouble :: SBV a -> Bool

isUnbounded :: SBV a -> Bool

isUninterpreted :: SBV a -> Bool

isChar :: SBV a -> Bool

isString :: SBV a -> Bool

isList :: SBV a -> Bool

isSet :: SBV a -> Bool

isTuple :: SBV a -> Bool

isMaybe :: SBV a -> Bool

isEither :: SBV a -> Bool

showType :: SBV a -> String

Outputtable (SBV a)

Defined in Data.SBV.Core.Data

Methods

output :: MonadSymbolic m => SBV a -> m (SBV a)

(SymVal a, PrettyNum a) => PrettyNum (SBV a)

Defined in Data.SBV.Utils.PrettyNum

Methods

hexS :: SBV a -> String

binS :: SBV a -> String

hexP :: SBV a -> String

binP :: SBV a -> String

hex :: SBV a -> String

bin :: SBV a -> String

HasKind a => Uninterpreted (SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV a

cgUninterpret :: String -> [String] -> SBV a -> SBV a

sbvUninterpret :: Maybe ([String], SBV a) -> String -> SBV a

SymVal a => Mergeable (SBV a)

Defined in Data.SBV.Core.Model

Methods

symbolicMerge :: Bool -> SBool -> SBV a -> SBV a -> SBV a

select :: (Ord b, SymVal b, Num b) => [SBV a] -> SBV a -> SBV b -> SBV a

(Ord a, SymVal a) => OrdSymbolic (SBV a)

Defined in Data.SBV.Core.Model

Methods

(.<) :: SBV a -> SBV a -> SBool

(.<=) :: SBV a -> SBV a -> SBool

(.>) :: SBV a -> SBV a -> SBool

(.>=) :: SBV a -> SBV a -> SBool

smin :: SBV a -> SBV a -> SBV a

smax :: SBV a -> SBV a -> SBV a

inRange :: SBV a -> (SBV a, SBV a) -> SBool

EqSymbolic (SBV a)

Defined in Data.SBV.Core.Model

Methods

(.==) :: SBV a -> SBV a -> SBool

(./=) :: SBV a -> SBV a -> SBool

(.===) :: SBV a -> SBV a -> SBool

(./==) :: SBV a -> SBV a -> SBool

distinct :: [SBV a] -> SBool

allEqual :: [SBV a] -> SBool

sElem :: SBV a -> [SBV a] -> SBool

(SymVal a, SymVal b, EqSymbolic z) => Equality ((SBV a, SBV b) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b) -> z) -> ((SBV a, SBV b) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c) -> z) -> ((SBV a, SBV b, SBV c) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d) -> z) -> ((SBV a, SBV b, SBV c, SBV d) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d, SBV e) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d, SBV e) -> z) -> ((SBV a, SBV b, SBV c, SBV d, SBV e) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> z) -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, EqSymbolic z) => Equality ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> z) -> ((SBV a, SBV b, SBV c, SBV d, SBV e, SBV f, SBV g) -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> SBV g -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> SBV g -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> SBV g -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> SBV f -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> SBV e -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, SymVal d, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> SBV d -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> SBV d -> z) -> (SBV a -> SBV b -> SBV c -> SBV d -> z) -> IO ThmResult

(SymVal a, SymVal b, SymVal c, EqSymbolic z) => Equality (SBV a -> SBV b -> SBV c -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> SBV c -> z) -> (SBV a -> SBV b -> SBV c -> z) -> IO ThmResult

(SymVal a, SymVal b, EqSymbolic z) => Equality (SBV a -> SBV b -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> SBV b -> z) -> (SBV a -> SBV b -> z) -> IO ThmResult

(SymVal a, EqSymbolic z) => Equality (SBV a -> z)

Defined in Data.SBV.Core.Model

Methods

(===) :: (SBV a -> z) -> (SBV a -> z) -> IO ThmResult

(SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV c, SBV b) -> SBV a) -> (SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV c, SBV b) -> SBV a) -> String -> (SBV c, SBV b) -> SBV a

(SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV d, SBV c, SBV b) -> SBV a) -> (SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV d, SBV c, SBV b) -> SBV a

(SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal h, SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted ((SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

cgUninterpret :: String -> [String] -> ((SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

sbvUninterpret :: Maybe ([String], (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) -> String -> (SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a

(SymVal h, SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal g, SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal f, SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal e, SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV e -> SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV e -> SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal d, SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV d -> SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV d -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV d -> SBV c -> SBV b -> SBV a) -> SBV d -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV d -> SBV c -> SBV b -> SBV a) -> String -> SBV d -> SBV c -> SBV b -> SBV a

(SymVal c, SymVal b, HasKind a) => Uninterpreted (SBV c -> SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV c -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV c -> SBV b -> SBV a) -> SBV c -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV c -> SBV b -> SBV a) -> String -> SBV c -> SBV b -> SBV a

(SymVal b, HasKind a) => Uninterpreted (SBV b -> SBV a)

Defined in Data.SBV.Core.Model

Methods

uninterpret :: String -> SBV b -> SBV a

cgUninterpret :: String -> [String] -> (SBV b -> SBV a) -> SBV b -> SBV a

sbvUninterpret :: Maybe ([String], SBV b -> SBV a) -> String -> SBV b -> SBV a

SymVal e => Mergeable (STree i e)

Defined in Data.SBV.Tools.STree

Methods

symbolicMerge :: Bool -> SBool -> STree i e -> STree i e -> STree i e

select :: (Ord b, SymVal b, Num b) => [STree i e] -> STree i e -> SBV b -> STree i e

type Rep (SBV a)

Defined in Data.SBV.Core.Data

type Rep (SBV a) = D1 (MetaData "SBV" "Data.SBV.Core.Data" "sbv-8.3-KY4PN9PPbrH5uMg2KovlBp" True) (C1 (MetaCons "SBV" PrefixI True) (S1 (MetaSel (Just "unSBV") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 SVal)))

type Item (SList a)

Defined in Data.SBV.Core.Data

type Item (SList a) = a

class HasKind a where

A class for capturing values that have a sign and a size (finite or infinite) minimal complete definition: kindOf, unless you can take advantage of the default signature: This class can be automatically derived for data-types that have a Data instance; this is useful for creating uninterpreted sorts. So, in reality, end users should almost never need to define any methods.

Minimal complete definition

Nothing

Methods

kindOf :: a -> Kind

hasSign :: a -> Bool

intSizeOf :: a -> Int

isBoolean :: a -> Bool

isBounded :: a -> Bool

isReal :: a -> Bool

isFloat :: a -> Bool

isDouble :: a -> Bool

isUnbounded :: a -> Bool

isUninterpreted :: a -> Bool

isChar :: a -> Bool

isString :: a -> Bool

isList :: a -> Bool

isSet :: a -> Bool

isTuple :: a -> Bool

isMaybe :: a -> Bool

isEither :: a -> Bool

showType :: a -> String

kindOf :: (Read a, Data a) => a -> Kind

Instances

HasKind Bool

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Bool -> Kind

hasSign :: Bool -> Bool

intSizeOf :: Bool -> Int

isBoolean :: Bool -> Bool

isBounded :: Bool -> Bool

isReal :: Bool -> Bool

isFloat :: Bool -> Bool

isDouble :: Bool -> Bool

isUnbounded :: Bool -> Bool

isUninterpreted :: Bool -> Bool

isChar :: Bool -> Bool

isString :: Bool -> Bool

isList :: Bool -> Bool

isSet :: Bool -> Bool

isTuple :: Bool -> Bool

isMaybe :: Bool -> Bool

isEither :: Bool -> Bool

showType :: Bool -> String

HasKind Char

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Char -> Kind

hasSign :: Char -> Bool

intSizeOf :: Char -> Int

isBoolean :: Char -> Bool

isBounded :: Char -> Bool

isReal :: Char -> Bool

isFloat :: Char -> Bool

isDouble :: Char -> Bool

isUnbounded :: Char -> Bool

isUninterpreted :: Char -> Bool

isChar :: Char -> Bool

isString :: Char -> Bool

isList :: Char -> Bool

isSet :: Char -> Bool

isTuple :: Char -> Bool

isMaybe :: Char -> Bool

isEither :: Char -> Bool

showType :: Char -> String

HasKind Double

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Double -> Kind

hasSign :: Double -> Bool

intSizeOf :: Double -> Int

isBoolean :: Double -> Bool

isBounded :: Double -> Bool

isReal :: Double -> Bool

isFloat :: Double -> Bool

isDouble :: Double -> Bool

isUnbounded :: Double -> Bool

isUninterpreted :: Double -> Bool

isChar :: Double -> Bool

isString :: Double -> Bool

isList :: Double -> Bool

isSet :: Double -> Bool

isTuple :: Double -> Bool

isMaybe :: Double -> Bool

isEither :: Double -> Bool

showType :: Double -> String

HasKind Float

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Float -> Kind

hasSign :: Float -> Bool

intSizeOf :: Float -> Int

isBoolean :: Float -> Bool

isBounded :: Float -> Bool

isReal :: Float -> Bool

isFloat :: Float -> Bool

isDouble :: Float -> Bool

isUnbounded :: Float -> Bool

isUninterpreted :: Float -> Bool

isChar :: Float -> Bool

isString :: Float -> Bool

isList :: Float -> Bool

isSet :: Float -> Bool

isTuple :: Float -> Bool

isMaybe :: Float -> Bool

isEither :: Float -> Bool

showType :: Float -> String

HasKind Int8

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Int8 -> Kind

hasSign :: Int8 -> Bool

intSizeOf :: Int8 -> Int

isBoolean :: Int8 -> Bool

isBounded :: Int8 -> Bool

isReal :: Int8 -> Bool

isFloat :: Int8 -> Bool

isDouble :: Int8 -> Bool

isUnbounded :: Int8 -> Bool

isUninterpreted :: Int8 -> Bool

isChar :: Int8 -> Bool

isString :: Int8 -> Bool

isList :: Int8 -> Bool

isSet :: Int8 -> Bool

isTuple :: Int8 -> Bool

isMaybe :: Int8 -> Bool

isEither :: Int8 -> Bool

showType :: Int8 -> String

HasKind Int16

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Int16 -> Kind

hasSign :: Int16 -> Bool

intSizeOf :: Int16 -> Int

isBoolean :: Int16 -> Bool

isBounded :: Int16 -> Bool

isReal :: Int16 -> Bool

isFloat :: Int16 -> Bool

isDouble :: Int16 -> Bool

isUnbounded :: Int16 -> Bool

isUninterpreted :: Int16 -> Bool

isChar :: Int16 -> Bool

isString :: Int16 -> Bool

isList :: Int16 -> Bool

isSet :: Int16 -> Bool

isTuple :: Int16 -> Bool

isMaybe :: Int16 -> Bool

isEither :: Int16 -> Bool

showType :: Int16 -> String

HasKind Int32

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Int32 -> Kind

hasSign :: Int32 -> Bool

intSizeOf :: Int32 -> Int

isBoolean :: Int32 -> Bool

isBounded :: Int32 -> Bool

isReal :: Int32 -> Bool

isFloat :: Int32 -> Bool

isDouble :: Int32 -> Bool

isUnbounded :: Int32 -> Bool

isUninterpreted :: Int32 -> Bool

isChar :: Int32 -> Bool

isString :: Int32 -> Bool

isList :: Int32 -> Bool

isSet :: Int32 -> Bool

isTuple :: Int32 -> Bool

isMaybe :: Int32 -> Bool

isEither :: Int32 -> Bool

showType :: Int32 -> String

HasKind Int64

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Int64 -> Kind

hasSign :: Int64 -> Bool

intSizeOf :: Int64 -> Int

isBoolean :: Int64 -> Bool

isBounded :: Int64 -> Bool

isReal :: Int64 -> Bool

isFloat :: Int64 -> Bool

isDouble :: Int64 -> Bool

isUnbounded :: Int64 -> Bool

isUninterpreted :: Int64 -> Bool

isChar :: Int64 -> Bool

isString :: Int64 -> Bool

isList :: Int64 -> Bool

isSet :: Int64 -> Bool

isTuple :: Int64 -> Bool

isMaybe :: Int64 -> Bool

isEither :: Int64 -> Bool

showType :: Int64 -> String

HasKind Integer

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Integer -> Kind

hasSign :: Integer -> Bool

intSizeOf :: Integer -> Int

isBoolean :: Integer -> Bool

isBounded :: Integer -> Bool

isReal :: Integer -> Bool

isFloat :: Integer -> Bool

isDouble :: Integer -> Bool

isUnbounded :: Integer -> Bool

isUninterpreted :: Integer -> Bool

isChar :: Integer -> Bool

isString :: Integer -> Bool

isList :: Integer -> Bool

isSet :: Integer -> Bool

isTuple :: Integer -> Bool

isMaybe :: Integer -> Bool

isEither :: Integer -> Bool

showType :: Integer -> String

HasKind Word8

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Word8 -> Kind

hasSign :: Word8 -> Bool

intSizeOf :: Word8 -> Int

isBoolean :: Word8 -> Bool

isBounded :: Word8 -> Bool

isReal :: Word8 -> Bool

isFloat :: Word8 -> Bool

isDouble :: Word8 -> Bool

isUnbounded :: Word8 -> Bool

isUninterpreted :: Word8 -> Bool

isChar :: Word8 -> Bool

isString :: Word8 -> Bool

isList :: Word8 -> Bool

isSet :: Word8 -> Bool

isTuple :: Word8 -> Bool

isMaybe :: Word8 -> Bool

isEither :: Word8 -> Bool

showType :: Word8 -> String

HasKind Word16

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Word16 -> Kind

hasSign :: Word16 -> Bool

intSizeOf :: Word16 -> Int

isBoolean :: Word16 -> Bool

isBounded :: Word16 -> Bool

isReal :: Word16 -> Bool

isFloat :: Word16 -> Bool

isDouble :: Word16 -> Bool

isUnbounded :: Word16 -> Bool

isUninterpreted :: Word16 -> Bool

isChar :: Word16 -> Bool

isString :: Word16 -> Bool

isList :: Word16 -> Bool

isSet :: Word16 -> Bool

isTuple :: Word16 -> Bool

isMaybe :: Word16 -> Bool

isEither :: Word16 -> Bool

showType :: Word16 -> String

HasKind Word32

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Word32 -> Kind

hasSign :: Word32 -> Bool

intSizeOf :: Word32 -> Int

isBoolean :: Word32 -> Bool

isBounded :: Word32 -> Bool

isReal :: Word32 -> Bool

isFloat :: Word32 -> Bool

isDouble :: Word32 -> Bool

isUnbounded :: Word32 -> Bool

isUninterpreted :: Word32 -> Bool

isChar :: Word32 -> Bool

isString :: Word32 -> Bool

isList :: Word32 -> Bool

isSet :: Word32 -> Bool

isTuple :: Word32 -> Bool

isMaybe :: Word32 -> Bool

isEither :: Word32 -> Bool

showType :: Word32 -> String

HasKind Word64

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Word64 -> Kind

hasSign :: Word64 -> Bool

intSizeOf :: Word64 -> Int

isBoolean :: Word64 -> Bool

isBounded :: Word64 -> Bool

isReal :: Word64 -> Bool

isFloat :: Word64 -> Bool

isDouble :: Word64 -> Bool

isUnbounded :: Word64 -> Bool

isUninterpreted :: Word64 -> Bool

isChar :: Word64 -> Bool

isString :: Word64 -> Bool

isList :: Word64 -> Bool

isSet :: Word64 -> Bool

isTuple :: Word64 -> Bool

isMaybe :: Word64 -> Bool

isEither :: Word64 -> Bool

showType :: Word64 -> String

HasKind ()

Defined in Data.SBV.Core.Kind

Methods

kindOf :: () -> Kind

hasSign :: () -> Bool

intSizeOf :: () -> Int

isBoolean :: () -> Bool

isBounded :: () -> Bool

isReal :: () -> Bool

isFloat :: () -> Bool

isDouble :: () -> Bool

isUnbounded :: () -> Bool

isUninterpreted :: () -> Bool

isChar :: () -> Bool

isString :: () -> Bool

isList :: () -> Bool

isSet :: () -> Bool

isTuple :: () -> Bool

isMaybe :: () -> Bool

isEither :: () -> Bool

showType :: () -> String

HasKind AlgReal

Defined in Data.SBV.Core.Kind

Methods

kindOf :: AlgReal -> Kind

hasSign :: AlgReal -> Bool

intSizeOf :: AlgReal -> Int

isBoolean :: AlgReal -> Bool

isBounded :: AlgReal -> Bool

isReal :: AlgReal -> Bool

isFloat :: AlgReal -> Bool

isDouble :: AlgReal -> Bool

isUnbounded :: AlgReal -> Bool

isUninterpreted :: AlgReal -> Bool

isChar :: AlgReal -> Bool

isString :: AlgReal -> Bool

isList :: AlgReal -> Bool

isSet :: AlgReal -> Bool

isTuple :: AlgReal -> Bool

isMaybe :: AlgReal -> Bool

isEither :: AlgReal -> Bool

showType :: AlgReal -> String

HasKind Kind

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Kind -> Kind

hasSign :: Kind -> Bool

intSizeOf :: Kind -> Int

isBoolean :: Kind -> Bool

isBounded :: Kind -> Bool

isReal :: Kind -> Bool

isFloat :: Kind -> Bool

isDouble :: Kind -> Bool

isUnbounded :: Kind -> Bool

isUninterpreted :: Kind -> Bool

isChar :: Kind -> Bool

isString :: Kind -> Bool

isList :: Kind -> Bool

isSet :: Kind -> Bool

isTuple :: Kind -> Bool

isMaybe :: Kind -> Bool

isEither :: Kind -> Bool

showType :: Kind -> String

HasKind ExtCV

Kind instance for Extended CV

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: ExtCV -> Kind

hasSign :: ExtCV -> Bool

intSizeOf :: ExtCV -> Int

isBoolean :: ExtCV -> Bool

isBounded :: ExtCV -> Bool

isReal :: ExtCV -> Bool

isFloat :: ExtCV -> Bool

isDouble :: ExtCV -> Bool

isUnbounded :: ExtCV -> Bool

isUninterpreted :: ExtCV -> Bool

isChar :: ExtCV -> Bool

isString :: ExtCV -> Bool

isList :: ExtCV -> Bool

isSet :: ExtCV -> Bool

isTuple :: ExtCV -> Bool

isMaybe :: ExtCV -> Bool

isEither :: ExtCV -> Bool

showType :: ExtCV -> String

HasKind GeneralizedCV

Kind instance for generalized CV

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: GeneralizedCV -> Kind

hasSign :: GeneralizedCV -> Bool

intSizeOf :: GeneralizedCV -> Int

isBoolean :: GeneralizedCV -> Bool

isBounded :: GeneralizedCV -> Bool

isReal :: GeneralizedCV -> Bool

isFloat :: GeneralizedCV -> Bool

isDouble :: GeneralizedCV -> Bool

isUnbounded :: GeneralizedCV -> Bool

isUninterpreted :: GeneralizedCV -> Bool

isChar :: GeneralizedCV -> Bool

isString :: GeneralizedCV -> Bool

isList :: GeneralizedCV -> Bool

isSet :: GeneralizedCV -> Bool

isTuple :: GeneralizedCV -> Bool

isMaybe :: GeneralizedCV -> Bool

isEither :: GeneralizedCV -> Bool

showType :: GeneralizedCV -> String

HasKind CV

Kind instance for CV

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: CV -> Kind

hasSign :: CV -> Bool

intSizeOf :: CV -> Int

isBoolean :: CV -> Bool

isBounded :: CV -> Bool

isReal :: CV -> Bool

isFloat :: CV -> Bool

isDouble :: CV -> Bool

isUnbounded :: CV -> Bool

isUninterpreted :: CV -> Bool

isChar :: CV -> Bool

isString :: CV -> Bool

isList :: CV -> Bool

isSet :: CV -> Bool

isTuple :: CV -> Bool

isMaybe :: CV -> Bool

isEither :: CV -> Bool

showType :: CV -> String

HasKind RoundingMode

RoundingMode kind

Defined in Data.SBV.Core.Symbolic

Methods

kindOf :: RoundingMode -> Kind

hasSign :: RoundingMode -> Bool

intSizeOf :: RoundingMode -> Int

isBoolean :: RoundingMode -> Bool

isBounded :: RoundingMode -> Bool

isReal :: RoundingMode -> Bool

isFloat :: RoundingMode -> Bool

isDouble :: RoundingMode -> Bool

isUnbounded :: RoundingMode -> Bool

isUninterpreted :: RoundingMode -> Bool

isChar :: RoundingMode -> Bool

isString :: RoundingMode -> Bool

isList :: RoundingMode -> Bool

isSet :: RoundingMode -> Bool

isTuple :: RoundingMode -> Bool

isMaybe :: RoundingMode -> Bool

isEither :: RoundingMode -> Bool

showType :: RoundingMode -> String

HasKind SVal

Defined in Data.SBV.Core.Symbolic

Methods

kindOf :: SVal -> Kind

hasSign :: SVal -> Bool

intSizeOf :: SVal -> Int

isBoolean :: SVal -> Bool

isBounded :: SVal -> Bool

isReal :: SVal -> Bool

isFloat :: SVal -> Bool

isDouble :: SVal -> Bool

isUnbounded :: SVal -> Bool

isUninterpreted :: SVal -> Bool

isChar :: SVal -> Bool

isString :: SVal -> Bool

isList :: SVal -> Bool

isSet :: SVal -> Bool

isTuple :: SVal -> Bool

isMaybe :: SVal -> Bool

isEither :: SVal -> Bool

showType :: SVal -> String

HasKind SV

Defined in Data.SBV.Core.Symbolic

Methods

kindOf :: SV -> Kind

hasSign :: SV -> Bool

intSizeOf :: SV -> Int

isBoolean :: SV -> Bool

isBounded :: SV -> Bool

isReal :: SV -> Bool

isFloat :: SV -> Bool

isDouble :: SV -> Bool

isUnbounded :: SV -> Bool

isUninterpreted :: SV -> Bool

isChar :: SV -> Bool

isString :: SV -> Bool

isList :: SV -> Bool

isSet :: SV -> Bool

isTuple :: SV -> Bool

isMaybe :: SV -> Bool

isEither :: SV -> Bool

showType :: SV -> String

HasKind State

Defined in Documentation.SBV.Examples.Lists.BoundedMutex

Methods

kindOf :: State -> Kind

hasSign :: State -> Bool

intSizeOf :: State -> Int

isBoolean :: State -> Bool

isBounded :: State -> Bool

isReal :: State -> Bool

isFloat :: State -> Bool

isDouble :: State -> Bool

isUnbounded :: State -> Bool

isUninterpreted :: State -> Bool

isChar :: State -> Bool

isString :: State -> Bool

isList :: State -> Bool

isSet :: State -> Bool

isTuple :: State -> Bool

isMaybe :: State -> Bool

isEither :: State -> Bool

showType :: State -> String

HasKind E

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

kindOf :: E -> Kind

hasSign :: E -> Bool

intSizeOf :: E -> Int

isBoolean :: E -> Bool

isBounded :: E -> Bool

isReal :: E -> Bool

isFloat :: E -> Bool

isDouble :: E -> Bool

isUnbounded :: E -> Bool

isUninterpreted :: E -> Bool

isChar :: E -> Bool

isString :: E -> Bool

isList :: E -> Bool

isSet :: E -> Bool

isTuple :: E -> Bool

isMaybe :: E -> Bool

isEither :: E -> Bool

showType :: E -> String

HasKind Word4

HasKind instance; simply returning the underlying kind for the type

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

kindOf :: Word4 -> Kind

hasSign :: Word4 -> Bool

intSizeOf :: Word4 -> Int

isBoolean :: Word4 -> Bool

isBounded :: Word4 -> Bool

isReal :: Word4 -> Bool

isFloat :: Word4 -> Bool

isDouble :: Word4 -> Bool

isUnbounded :: Word4 -> Bool

isUninterpreted :: Word4 -> Bool

isChar :: Word4 -> Bool

isString :: Word4 -> Bool

isList :: Word4 -> Bool

isSet :: Word4 -> Bool

isTuple :: Word4 -> Bool

isMaybe :: Word4 -> Bool

isEither :: Word4 -> Bool

showType :: Word4 -> String

HasKind Day

Defined in Documentation.SBV.Examples.Optimization.Enumerate

Methods

kindOf :: Day -> Kind

hasSign :: Day -> Bool

intSizeOf :: Day -> Int

isBoolean :: Day -> Bool

isBounded :: Day -> Bool

isReal :: Day -> Bool

isFloat :: Day -> Bool

isDouble :: Day -> Bool

isUnbounded :: Day -> Bool

isUninterpreted :: Day -> Bool

isChar :: Day -> Bool

isString :: Day -> Bool

isList :: Day -> Bool

isSet :: Day -> Bool

isTuple :: Day -> Bool

isMaybe :: Day -> Bool

isEither :: Day -> Bool

showType :: Day -> String

HasKind Color

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

kindOf :: Color -> Kind

hasSign :: Color -> Bool

intSizeOf :: Color -> Int

isBoolean :: Color -> Bool

isBounded :: Color -> Bool

isReal :: Color -> Bool

isFloat :: Color -> Bool

isDouble :: Color -> Bool

isUnbounded :: Color -> Bool

isUninterpreted :: Color -> Bool

isChar :: Color -> Bool

isString :: Color -> Bool

isList :: Color -> Bool

isSet :: Color -> Bool

isTuple :: Color -> Bool

isMaybe :: Color -> Bool

isEither :: Color -> Bool

showType :: Color -> String

HasKind Nationality

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

kindOf :: Nationality -> Kind

hasSign :: Nationality -> Bool

intSizeOf :: Nationality -> Int

isBoolean :: Nationality -> Bool

isBounded :: Nationality -> Bool

isReal :: Nationality -> Bool

isFloat :: Nationality -> Bool

isDouble :: Nationality -> Bool

isUnbounded :: Nationality -> Bool

isUninterpreted :: Nationality -> Bool

isChar :: Nationality -> Bool

isString :: Nationality -> Bool

isList :: Nationality -> Bool

isSet :: Nationality -> Bool

isTuple :: Nationality -> Bool

isMaybe :: Nationality -> Bool

isEither :: Nationality -> Bool

showType :: Nationality -> String

HasKind Beverage

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

kindOf :: Beverage -> Kind

hasSign :: Beverage -> Bool

intSizeOf :: Beverage -> Int

isBoolean :: Beverage -> Bool

isBounded :: Beverage -> Bool

isReal :: Beverage -> Bool

isFloat :: Beverage -> Bool

isDouble :: Beverage -> Bool

isUnbounded :: Beverage -> Bool

isUninterpreted :: Beverage -> Bool

isChar :: Beverage -> Bool

isString :: Beverage -> Bool

isList :: Beverage -> Bool

isSet :: Beverage -> Bool

isTuple :: Beverage -> Bool

isMaybe :: Beverage -> Bool

isEither :: Beverage -> Bool

showType :: Beverage -> String

HasKind Pet

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

kindOf :: Pet -> Kind

hasSign :: Pet -> Bool

intSizeOf :: Pet -> Int

isBoolean :: Pet -> Bool

isBounded :: Pet -> Bool

isReal :: Pet -> Bool

isFloat :: Pet -> Bool

isDouble :: Pet -> Bool

isUnbounded :: Pet -> Bool

isUninterpreted :: Pet -> Bool

isChar :: Pet -> Bool

isString :: Pet -> Bool

isList :: Pet -> Bool

isSet :: Pet -> Bool

isTuple :: Pet -> Bool

isMaybe :: Pet -> Bool

isEither :: Pet -> Bool

showType :: Pet -> String

HasKind Sport

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

kindOf :: Sport -> Kind

hasSign :: Sport -> Bool

intSizeOf :: Sport -> Int

isBoolean :: Sport -> Bool

isBounded :: Sport -> Bool

isReal :: Sport -> Bool

isFloat :: Sport -> Bool

isDouble :: Sport -> Bool

isUnbounded :: Sport -> Bool

isUninterpreted :: Sport -> Bool

isChar :: Sport -> Bool

isString :: Sport -> Bool

isList :: Sport -> Bool

isSet :: Sport -> Bool

isTuple :: Sport -> Bool

isMaybe :: Sport -> Bool

isEither :: Sport -> Bool

showType :: Sport -> String

HasKind Color

Defined in Documentation.SBV.Examples.Puzzles.Garden

Methods

kindOf :: Color -> Kind

hasSign :: Color -> Bool

intSizeOf :: Color -> Int

isBoolean :: Color -> Bool

isBounded :: Color -> Bool

isReal :: Color -> Bool

isFloat :: Color -> Bool

isDouble :: Color -> Bool

isUnbounded :: Color -> Bool

isUninterpreted :: Color -> Bool

isChar :: Color -> Bool

isString :: Color -> Bool

isList :: Color -> Bool

isSet :: Color -> Bool

isTuple :: Color -> Bool

isMaybe :: Color -> Bool

isEither :: Color -> Bool

showType :: Color -> String

HasKind Color

Defined in Documentation.SBV.Examples.Puzzles.HexPuzzle

Methods

kindOf :: Color -> Kind

hasSign :: Color -> Bool

intSizeOf :: Color -> Int

isBoolean :: Color -> Bool

isBounded :: Color -> Bool

isReal :: Color -> Bool

isFloat :: Color -> Bool

isDouble :: Color -> Bool

isUnbounded :: Color -> Bool

isUninterpreted :: Color -> Bool

isChar :: Color -> Bool

isString :: Color -> Bool

isList :: Color -> Bool

isSet :: Color -> Bool

isTuple :: Color -> Bool

isMaybe :: Color -> Bool

isEither :: Color -> Bool

showType :: Color -> String

HasKind U2Member

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

kindOf :: U2Member -> Kind

hasSign :: U2Member -> Bool

intSizeOf :: U2Member -> Int

isBoolean :: U2Member -> Bool

isBounded :: U2Member -> Bool

isReal :: U2Member -> Bool

isFloat :: U2Member -> Bool

isDouble :: U2Member -> Bool

isUnbounded :: U2Member -> Bool

isUninterpreted :: U2Member -> Bool

isChar :: U2Member -> Bool

isString :: U2Member -> Bool

isList :: U2Member -> Bool

isSet :: U2Member -> Bool

isTuple :: U2Member -> Bool

isMaybe :: U2Member -> Bool

isEither :: U2Member -> Bool

showType :: U2Member -> String

HasKind Location

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

kindOf :: Location -> Kind

hasSign :: Location -> Bool

intSizeOf :: Location -> Int

isBoolean :: Location -> Bool

isBounded :: Location -> Bool

isReal :: Location -> Bool

isFloat :: Location -> Bool

isDouble :: Location -> Bool

isUnbounded :: Location -> Bool

isUninterpreted :: Location -> Bool

isChar :: Location -> Bool

isString :: Location -> Bool

isList :: Location -> Bool

isSet :: Location -> Bool

isTuple :: Location -> Bool

isMaybe :: Location -> Bool

isEither :: Location -> Bool

showType :: Location -> String

HasKind Day

Defined in Documentation.SBV.Examples.Queries.Enums

Methods

kindOf :: Day -> Kind

hasSign :: Day -> Bool

intSizeOf :: Day -> Int

isBoolean :: Day -> Bool

isBounded :: Day -> Bool

isReal :: Day -> Bool

isFloat :: Day -> Bool

isDouble :: Day -> Bool

isUnbounded :: Day -> Bool

isUninterpreted :: Day -> Bool

isChar :: Day -> Bool

isString :: Day -> Bool

isList :: Day -> Bool

isSet :: Day -> Bool

isTuple :: Day -> Bool

isMaybe :: Day -> Bool

isEither :: Day -> Bool

showType :: Day -> String

HasKind BinOp

Defined in Documentation.SBV.Examples.Queries.FourFours

Methods

kindOf :: BinOp -> Kind

hasSign :: BinOp -> Bool

intSizeOf :: BinOp -> Int

isBoolean :: BinOp -> Bool

isBounded :: BinOp -> Bool

isReal :: BinOp -> Bool

isFloat :: BinOp -> Bool

isDouble :: BinOp -> Bool

isUnbounded :: BinOp -> Bool

isUninterpreted :: BinOp -> Bool

isChar :: BinOp -> Bool

isString :: BinOp -> Bool

isList :: BinOp -> Bool

isSet :: BinOp -> Bool

isTuple :: BinOp -> Bool

isMaybe :: BinOp -> Bool

isEither :: BinOp -> Bool

showType :: BinOp -> String

HasKind UnOp

Defined in Documentation.SBV.Examples.Queries.FourFours

Methods

kindOf :: UnOp -> Kind

hasSign :: UnOp -> Bool

intSizeOf :: UnOp -> Int

isBoolean :: UnOp -> Bool

isBounded :: UnOp -> Bool

isReal :: UnOp -> Bool

isFloat :: UnOp -> Bool

isDouble :: UnOp -> Bool

isUnbounded :: UnOp -> Bool

isUninterpreted :: UnOp -> Bool

isChar :: UnOp -> Bool

isString :: UnOp -> Bool

isList :: UnOp -> Bool

isSet :: UnOp -> Bool

isTuple :: UnOp -> Bool

isMaybe :: UnOp -> Bool

isEither :: UnOp -> Bool

showType :: UnOp -> String

HasKind B

Defined in Documentation.SBV.Examples.Uninterpreted.Deduce

Methods

kindOf :: B -> Kind

hasSign :: B -> Bool

intSizeOf :: B -> Int

isBoolean :: B -> Bool

isBounded :: B -> Bool

isReal :: B -> Bool

isFloat :: B -> Bool

isDouble :: B -> Bool

isUnbounded :: B -> Bool

isUninterpreted :: B -> Bool

isChar :: B -> Bool

isString :: B -> Bool

isList :: B -> Bool

isSet :: B -> Bool

isTuple :: B -> Bool

isMaybe :: B -> Bool

isEither :: B -> Bool

showType :: B -> String

HasKind Q

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Methods

kindOf :: Q -> Kind

hasSign :: Q -> Bool

intSizeOf :: Q -> Int

isBoolean :: Q -> Bool

isBounded :: Q -> Bool

isReal :: Q -> Bool

isFloat :: Q -> Bool

isDouble :: Q -> Bool

isUnbounded :: Q -> Bool

isUninterpreted :: Q -> Bool

isChar :: Q -> Bool

isString :: Q -> Bool

isList :: Q -> Bool

isSet :: Q -> Bool

isTuple :: Q -> Bool

isMaybe :: Q -> Bool

isEither :: Q -> Bool

showType :: Q -> String

HasKind L

Similarly, HasKinds default implementation is sufficient.

Defined in Documentation.SBV.Examples.Uninterpreted.UISortAllSat

Methods

kindOf :: L -> Kind

hasSign :: L -> Bool

intSizeOf :: L -> Int

isBoolean :: L -> Bool

isBounded :: L -> Bool

isReal :: L -> Bool

isFloat :: L -> Bool

isDouble :: L -> Bool

isUnbounded :: L -> Bool

isUninterpreted :: L -> Bool

isChar :: L -> Bool

isString :: L -> Bool

isList :: L -> Bool

isSet :: L -> Bool

isTuple :: L -> Bool

isMaybe :: L -> Bool

isEither :: L -> Bool

showType :: L -> String

(Typeable a, HasKind a) => HasKind [a]

Defined in Data.SBV.Core.Kind

Methods

kindOf :: [a] -> Kind

hasSign :: [a] -> Bool

intSizeOf :: [a] -> Int

isBoolean :: [a] -> Bool

isBounded :: [a] -> Bool

isReal :: [a] -> Bool

isFloat :: [a] -> Bool

isDouble :: [a] -> Bool

isUnbounded :: [a] -> Bool

isUninterpreted :: [a] -> Bool

isChar :: [a] -> Bool

isString :: [a] -> Bool

isList :: [a] -> Bool

isSet :: [a] -> Bool

isTuple :: [a] -> Bool

isMaybe :: [a] -> Bool

isEither :: [a] -> Bool

showType :: [a] -> String

HasKind a => HasKind (Maybe a)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Maybe a -> Kind

hasSign :: Maybe a -> Bool

intSizeOf :: Maybe a -> Int

isBoolean :: Maybe a -> Bool

isBounded :: Maybe a -> Bool

isReal :: Maybe a -> Bool

isFloat :: Maybe a -> Bool

isDouble :: Maybe a -> Bool

isUnbounded :: Maybe a -> Bool

isUninterpreted :: Maybe a -> Bool

isChar :: Maybe a -> Bool

isString :: Maybe a -> Bool

isList :: Maybe a -> Bool

isSet :: Maybe a -> Bool

isTuple :: Maybe a -> Bool

isMaybe :: Maybe a -> Bool

isEither :: Maybe a -> Bool

showType :: Maybe a -> String

HasKind a => HasKind (RCSet a)

Defined in Data.SBV.Core.Concrete

Methods

kindOf :: RCSet a -> Kind

hasSign :: RCSet a -> Bool

intSizeOf :: RCSet a -> Int

isBoolean :: RCSet a -> Bool

isBounded :: RCSet a -> Bool

isReal :: RCSet a -> Bool

isFloat :: RCSet a -> Bool

isDouble :: RCSet a -> Bool

isUnbounded :: RCSet a -> Bool

isUninterpreted :: RCSet a -> Bool

isChar :: RCSet a -> Bool

isString :: RCSet a -> Bool

isList :: RCSet a -> Bool

isSet :: RCSet a -> Bool

isTuple :: RCSet a -> Bool

isMaybe :: RCSet a -> Bool

isEither :: RCSet a -> Bool

showType :: RCSet a -> String

HasKind a => HasKind (SBV a)

Defined in Data.SBV.Core.Data

Methods

kindOf :: SBV a -> Kind

hasSign :: SBV a -> Bool

intSizeOf :: SBV a -> Int

isBoolean :: SBV a -> Bool

isBounded :: SBV a -> Bool

isReal :: SBV a -> Bool

isFloat :: SBV a -> Bool

isDouble :: SBV a -> Bool

isUnbounded :: SBV a -> Bool

isUninterpreted :: SBV a -> Bool

isChar :: SBV a -> Bool

isString :: SBV a -> Bool

isList :: SBV a -> Bool

isSet :: SBV a -> Bool

isTuple :: SBV a -> Bool

isMaybe :: SBV a -> Bool

isEither :: SBV a -> Bool

showType :: SBV a -> String

(HasKind a, HasKind b) => HasKind (Either a b)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Either a b -> Kind

hasSign :: Either a b -> Bool

intSizeOf :: Either a b -> Int

isBoolean :: Either a b -> Bool

isBounded :: Either a b -> Bool

isReal :: Either a b -> Bool

isFloat :: Either a b -> Bool

isDouble :: Either a b -> Bool

isUnbounded :: Either a b -> Bool

isUninterpreted :: Either a b -> Bool

isChar :: Either a b -> Bool

isString :: Either a b -> Bool

isList :: Either a b -> Bool

isSet :: Either a b -> Bool

isTuple :: Either a b -> Bool

isMaybe :: Either a b -> Bool

isEither :: Either a b -> Bool

showType :: Either a b -> String

(HasKind a, HasKind b) => HasKind (a, b)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b) -> Kind

hasSign :: (a, b) -> Bool

intSizeOf :: (a, b) -> Int

isBoolean :: (a, b) -> Bool

isBounded :: (a, b) -> Bool

isReal :: (a, b) -> Bool

isFloat :: (a, b) -> Bool

isDouble :: (a, b) -> Bool

isUnbounded :: (a, b) -> Bool

isUninterpreted :: (a, b) -> Bool

isChar :: (a, b) -> Bool

isString :: (a, b) -> Bool

isList :: (a, b) -> Bool

isSet :: (a, b) -> Bool

isTuple :: (a, b) -> Bool

isMaybe :: (a, b) -> Bool

isEither :: (a, b) -> Bool

showType :: (a, b) -> String

HasKind a => HasKind (Proxy a)

This instance allows us to use the `kindOf (Proxy @a)` idiom instead of the `kindOf (undefined :: a)`, which is safer and looks more idiomatic.

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Proxy a -> Kind

hasSign :: Proxy a -> Bool

intSizeOf :: Proxy a -> Int

isBoolean :: Proxy a -> Bool

isBounded :: Proxy a -> Bool

isReal :: Proxy a -> Bool

isFloat :: Proxy a -> Bool

isDouble :: Proxy a -> Bool

isUnbounded :: Proxy a -> Bool

isUninterpreted :: Proxy a -> Bool

isChar :: Proxy a -> Bool

isString :: Proxy a -> Bool

isList :: Proxy a -> Bool

isSet :: Proxy a -> Bool

isTuple :: Proxy a -> Bool

isMaybe :: Proxy a -> Bool

isEither :: Proxy a -> Bool

showType :: Proxy a -> String

(HasKind a, HasKind b, HasKind c) => HasKind (a, b, c)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c) -> Kind

hasSign :: (a, b, c) -> Bool

intSizeOf :: (a, b, c) -> Int

isBoolean :: (a, b, c) -> Bool

isBounded :: (a, b, c) -> Bool

isReal :: (a, b, c) -> Bool

isFloat :: (a, b, c) -> Bool

isDouble :: (a, b, c) -> Bool

isUnbounded :: (a, b, c) -> Bool

isUninterpreted :: (a, b, c) -> Bool

isChar :: (a, b, c) -> Bool

isString :: (a, b, c) -> Bool

isList :: (a, b, c) -> Bool

isSet :: (a, b, c) -> Bool

isTuple :: (a, b, c) -> Bool

isMaybe :: (a, b, c) -> Bool

isEither :: (a, b, c) -> Bool

showType :: (a, b, c) -> String

(HasKind a, HasKind b, HasKind c, HasKind d) => HasKind (a, b, c, d)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d) -> Kind

hasSign :: (a, b, c, d) -> Bool

intSizeOf :: (a, b, c, d) -> Int

isBoolean :: (a, b, c, d) -> Bool

isBounded :: (a, b, c, d) -> Bool

isReal :: (a, b, c, d) -> Bool

isFloat :: (a, b, c, d) -> Bool

isDouble :: (a, b, c, d) -> Bool

isUnbounded :: (a, b, c, d) -> Bool

isUninterpreted :: (a, b, c, d) -> Bool

isChar :: (a, b, c, d) -> Bool

isString :: (a, b, c, d) -> Bool

isList :: (a, b, c, d) -> Bool

isSet :: (a, b, c, d) -> Bool

isTuple :: (a, b, c, d) -> Bool

isMaybe :: (a, b, c, d) -> Bool

isEither :: (a, b, c, d) -> Bool

showType :: (a, b, c, d) -> String

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e) => HasKind (a, b, c, d, e)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e) -> Kind

hasSign :: (a, b, c, d, e) -> Bool

intSizeOf :: (a, b, c, d, e) -> Int

isBoolean :: (a, b, c, d, e) -> Bool

isBounded :: (a, b, c, d, e) -> Bool

isReal :: (a, b, c, d, e) -> Bool

isFloat :: (a, b, c, d, e) -> Bool

isDouble :: (a, b, c, d, e) -> Bool

isUnbounded :: (a, b, c, d, e) -> Bool

isUninterpreted :: (a, b, c, d, e) -> Bool

isChar :: (a, b, c, d, e) -> Bool

isString :: (a, b, c, d, e) -> Bool

isList :: (a, b, c, d, e) -> Bool

isSet :: (a, b, c, d, e) -> Bool

isTuple :: (a, b, c, d, e) -> Bool

isMaybe :: (a, b, c, d, e) -> Bool

isEither :: (a, b, c, d, e) -> Bool

showType :: (a, b, c, d, e) -> String

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e, HasKind f) => HasKind (a, b, c, d, e, f)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e, f) -> Kind

hasSign :: (a, b, c, d, e, f) -> Bool

intSizeOf :: (a, b, c, d, e, f) -> Int

isBoolean :: (a, b, c, d, e, f) -> Bool

isBounded :: (a, b, c, d, e, f) -> Bool

isReal :: (a, b, c, d, e, f) -> Bool

isFloat :: (a, b, c, d, e, f) -> Bool

isDouble :: (a, b, c, d, e, f) -> Bool

isUnbounded :: (a, b, c, d, e, f) -> Bool

isUninterpreted :: (a, b, c, d, e, f) -> Bool

isChar :: (a, b, c, d, e, f) -> Bool

isString :: (a, b, c, d, e, f) -> Bool

isList :: (a, b, c, d, e, f) -> Bool

isSet :: (a, b, c, d, e, f) -> Bool

isTuple :: (a, b, c, d, e, f) -> Bool

isMaybe :: (a, b, c, d, e, f) -> Bool

isEither :: (a, b, c, d, e, f) -> Bool

showType :: (a, b, c, d, e, f) -> String

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e, HasKind f, HasKind g) => HasKind (a, b, c, d, e, f, g)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e, f, g) -> Kind

hasSign :: (a, b, c, d, e, f, g) -> Bool

intSizeOf :: (a, b, c, d, e, f, g) -> Int

isBoolean :: (a, b, c, d, e, f, g) -> Bool

isBounded :: (a, b, c, d, e, f, g) -> Bool

isReal :: (a, b, c, d, e, f, g) -> Bool

isFloat :: (a, b, c, d, e, f, g) -> Bool

isDouble :: (a, b, c, d, e, f, g) -> Bool

isUnbounded :: (a, b, c, d, e, f, g) -> Bool

isUninterpreted :: (a, b, c, d, e, f, g) -> Bool

isChar :: (a, b, c, d, e, f, g) -> Bool

isString :: (a, b, c, d, e, f, g) -> Bool

isList :: (a, b, c, d, e, f, g) -> Bool

isSet :: (a, b, c, d, e, f, g) -> Bool

isTuple :: (a, b, c, d, e, f, g) -> Bool

isMaybe :: (a, b, c, d, e, f, g) -> Bool

isEither :: (a, b, c, d, e, f, g) -> Bool

showType :: (a, b, c, d, e, f, g) -> String

(HasKind a, HasKind b, HasKind c, HasKind d, HasKind e, HasKind f, HasKind g, HasKind h) => HasKind (a, b, c, d, e, f, g, h)

Defined in Data.SBV.Core.Kind

Methods

kindOf :: (a, b, c, d, e, f, g, h) -> Kind

hasSign :: (a, b, c, d, e, f, g, h) -> Bool

intSizeOf :: (a, b, c, d, e, f, g, h) -> Int

isBoolean :: (a, b, c, d, e, f, g, h) -> Bool

isBounded :: (a, b, c, d, e, f, g, h) -> Bool

isReal :: (a, b, c, d, e, f, g, h) -> Bool

isFloat :: (a, b, c, d, e, f, g, h) -> Bool

isDouble :: (a, b, c, d, e, f, g, h) -> Bool

isUnbounded :: (a, b, c, d, e, f, g, h) -> Bool

isUninterpreted :: (a, b, c, d, e, f, g, h) -> Bool

isChar :: (a, b, c, d, e, f, g, h) -> Bool

isString :: (a, b, c, d, e, f, g, h) -> Bool

isList :: (a, b, c, d, e, f, g, h) -> Bool

isSet :: (a, b, c, d, e, f, g, h) -> Bool

isTuple :: (a, b, c, d, e, f, g, h) -> Bool

isMaybe :: (a, b, c, d, e, f, g, h) -> Bool

isEither :: (a, b, c, d, e, f, g, h) -> Bool

showType :: (a, b, c, d, e, f, g, h) -> String

data Kind

Kind of symbolic value

Constructors

KBool

KBounded !Bool !Int

KUnbounded

KReal

KUninterpreted String (Either String [String])

KFloat

KDouble

KChar

KString

KList Kind

KSet Kind

KTuple [Kind]

KMaybe Kind

KEither Kind Kind

Instances

Eq Kind

Defined in Data.SBV.Core.Kind

Methods

(==) :: Kind -> Kind -> Bool

(/=) :: Kind -> Kind -> Bool

Ord Kind

Defined in Data.SBV.Core.Kind

Methods

compare :: Kind -> Kind -> Ordering

(<) :: Kind -> Kind -> Bool

(<=) :: Kind -> Kind -> Bool

(>) :: Kind -> Kind -> Bool

(>=) :: Kind -> Kind -> Bool

max :: Kind -> Kind -> Kind

min :: Kind -> Kind -> Kind

Show Kind

The interesting about the show instance is that it can tell apart two kinds nicely; since it conveniently ignores the enumeration constructors. Also, when we construct a KUninterpreted, we make sure we don't use any of the reserved names; see constructUKind for details.

Defined in Data.SBV.Core.Kind

Methods

showsPrec :: Int -> Kind -> ShowS

show :: Kind -> String

showList :: [Kind] -> ShowS

NFData Kind

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: Kind -> ()

HasKind Kind

Defined in Data.SBV.Core.Kind

Methods

kindOf :: Kind -> Kind

hasSign :: Kind -> Bool

intSizeOf :: Kind -> Int

isBoolean :: Kind -> Bool

isBounded :: Kind -> Bool

isReal :: Kind -> Bool

isFloat :: Kind -> Bool

isDouble :: Kind -> Bool

isUnbounded :: Kind -> Bool

isUninterpreted :: Kind -> Bool

isChar :: Kind -> Bool

isString :: Kind -> Bool

isList :: Kind -> Bool

isSet :: Kind -> Bool

isTuple :: Kind -> Bool

isMaybe :: Kind -> Bool

isEither :: Kind -> Bool

showType :: Kind -> String

class (HasKind a, Typeable a) => SymVal a

A SymVal is a potential symbolic value that can be created instances of to be fed to a symbolic program.

Instances

SymVal Bool

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Bool)

literal :: Bool -> SBV Bool

fromCV :: CV -> Bool

isConcretely :: SBV Bool -> (Bool -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Bool)

forall_ :: MonadSymbolic m => m (SBV Bool)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Bool]

exists :: MonadSymbolic m => String -> m (SBV Bool)

exists_ :: MonadSymbolic m => m (SBV Bool)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Bool]

free :: MonadSymbolic m => String -> m (SBV Bool)

free_ :: MonadSymbolic m => m (SBV Bool)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Bool]

symbolic :: MonadSymbolic m => String -> m (SBV Bool)

symbolics :: MonadSymbolic m => [String] -> m [SBV Bool]

unliteral :: SBV Bool -> Maybe Bool

isConcrete :: SBV Bool -> Bool

isSymbolic :: SBV Bool -> Bool

SymVal Char

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Char)

literal :: Char -> SBV Char

fromCV :: CV -> Char

isConcretely :: SBV Char -> (Char -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Char)

forall_ :: MonadSymbolic m => m (SBV Char)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Char]

exists :: MonadSymbolic m => String -> m (SBV Char)

exists_ :: MonadSymbolic m => m (SBV Char)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Char]

free :: MonadSymbolic m => String -> m (SBV Char)

free_ :: MonadSymbolic m => m (SBV Char)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Char]

symbolic :: MonadSymbolic m => String -> m (SBV Char)

symbolics :: MonadSymbolic m => [String] -> m [SBV Char]

unliteral :: SBV Char -> Maybe Char

isConcrete :: SBV Char -> Bool

isSymbolic :: SBV Char -> Bool

SymVal Double

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Double)

literal :: Double -> SBV Double

fromCV :: CV -> Double

isConcretely :: SBV Double -> (Double -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Double)

forall_ :: MonadSymbolic m => m (SBV Double)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Double]

exists :: MonadSymbolic m => String -> m (SBV Double)

exists_ :: MonadSymbolic m => m (SBV Double)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Double]

free :: MonadSymbolic m => String -> m (SBV Double)

free_ :: MonadSymbolic m => m (SBV Double)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Double]

symbolic :: MonadSymbolic m => String -> m (SBV Double)

symbolics :: MonadSymbolic m => [String] -> m [SBV Double]

unliteral :: SBV Double -> Maybe Double

isConcrete :: SBV Double -> Bool

isSymbolic :: SBV Double -> Bool

SymVal Float

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Float)

literal :: Float -> SBV Float

fromCV :: CV -> Float

isConcretely :: SBV Float -> (Float -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Float)

forall_ :: MonadSymbolic m => m (SBV Float)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Float]

exists :: MonadSymbolic m => String -> m (SBV Float)

exists_ :: MonadSymbolic m => m (SBV Float)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Float]

free :: MonadSymbolic m => String -> m (SBV Float)

free_ :: MonadSymbolic m => m (SBV Float)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Float]

symbolic :: MonadSymbolic m => String -> m (SBV Float)

symbolics :: MonadSymbolic m => [String] -> m [SBV Float]

unliteral :: SBV Float -> Maybe Float

isConcrete :: SBV Float -> Bool

isSymbolic :: SBV Float -> Bool

SymVal Int8

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Int8)

literal :: Int8 -> SBV Int8

fromCV :: CV -> Int8

isConcretely :: SBV Int8 -> (Int8 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Int8)

forall_ :: MonadSymbolic m => m (SBV Int8)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Int8]

exists :: MonadSymbolic m => String -> m (SBV Int8)

exists_ :: MonadSymbolic m => m (SBV Int8)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Int8]

free :: MonadSymbolic m => String -> m (SBV Int8)

free_ :: MonadSymbolic m => m (SBV Int8)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Int8]

symbolic :: MonadSymbolic m => String -> m (SBV Int8)

symbolics :: MonadSymbolic m => [String] -> m [SBV Int8]

unliteral :: SBV Int8 -> Maybe Int8

isConcrete :: SBV Int8 -> Bool

isSymbolic :: SBV Int8 -> Bool

SymVal Int16

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Int16)

literal :: Int16 -> SBV Int16

fromCV :: CV -> Int16

isConcretely :: SBV Int16 -> (Int16 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Int16)

forall_ :: MonadSymbolic m => m (SBV Int16)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Int16]

exists :: MonadSymbolic m => String -> m (SBV Int16)

exists_ :: MonadSymbolic m => m (SBV Int16)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Int16]

free :: MonadSymbolic m => String -> m (SBV Int16)

free_ :: MonadSymbolic m => m (SBV Int16)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Int16]

symbolic :: MonadSymbolic m => String -> m (SBV Int16)

symbolics :: MonadSymbolic m => [String] -> m [SBV Int16]

unliteral :: SBV Int16 -> Maybe Int16

isConcrete :: SBV Int16 -> Bool

isSymbolic :: SBV Int16 -> Bool

SymVal Int32

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Int32)

literal :: Int32 -> SBV Int32

fromCV :: CV -> Int32

isConcretely :: SBV Int32 -> (Int32 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Int32)

forall_ :: MonadSymbolic m => m (SBV Int32)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Int32]

exists :: MonadSymbolic m => String -> m (SBV Int32)

exists_ :: MonadSymbolic m => m (SBV Int32)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Int32]

free :: MonadSymbolic m => String -> m (SBV Int32)

free_ :: MonadSymbolic m => m (SBV Int32)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Int32]

symbolic :: MonadSymbolic m => String -> m (SBV Int32)

symbolics :: MonadSymbolic m => [String] -> m [SBV Int32]

unliteral :: SBV Int32 -> Maybe Int32

isConcrete :: SBV Int32 -> Bool

isSymbolic :: SBV Int32 -> Bool

SymVal Int64

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Int64)

literal :: Int64 -> SBV Int64

fromCV :: CV -> Int64

isConcretely :: SBV Int64 -> (Int64 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Int64)

forall_ :: MonadSymbolic m => m (SBV Int64)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Int64]

exists :: MonadSymbolic m => String -> m (SBV Int64)

exists_ :: MonadSymbolic m => m (SBV Int64)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Int64]

free :: MonadSymbolic m => String -> m (SBV Int64)

free_ :: MonadSymbolic m => m (SBV Int64)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Int64]

symbolic :: MonadSymbolic m => String -> m (SBV Int64)

symbolics :: MonadSymbolic m => [String] -> m [SBV Int64]

unliteral :: SBV Int64 -> Maybe Int64

isConcrete :: SBV Int64 -> Bool

isSymbolic :: SBV Int64 -> Bool

SymVal Integer

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Integer)

literal :: Integer -> SBV Integer

fromCV :: CV -> Integer

isConcretely :: SBV Integer -> (Integer -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Integer)

forall_ :: MonadSymbolic m => m (SBV Integer)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Integer]

exists :: MonadSymbolic m => String -> m (SBV Integer)

exists_ :: MonadSymbolic m => m (SBV Integer)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Integer]

free :: MonadSymbolic m => String -> m (SBV Integer)

free_ :: MonadSymbolic m => m (SBV Integer)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Integer]

symbolic :: MonadSymbolic m => String -> m (SBV Integer)

symbolics :: MonadSymbolic m => [String] -> m [SBV Integer]

unliteral :: SBV Integer -> Maybe Integer

isConcrete :: SBV Integer -> Bool

isSymbolic :: SBV Integer -> Bool

SymVal Word8

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Word8)

literal :: Word8 -> SBV Word8

fromCV :: CV -> Word8

isConcretely :: SBV Word8 -> (Word8 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Word8)

forall_ :: MonadSymbolic m => m (SBV Word8)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Word8]

exists :: MonadSymbolic m => String -> m (SBV Word8)

exists_ :: MonadSymbolic m => m (SBV Word8)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Word8]

free :: MonadSymbolic m => String -> m (SBV Word8)

free_ :: MonadSymbolic m => m (SBV Word8)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Word8]

symbolic :: MonadSymbolic m => String -> m (SBV Word8)

symbolics :: MonadSymbolic m => [String] -> m [SBV Word8]

unliteral :: SBV Word8 -> Maybe Word8

isConcrete :: SBV Word8 -> Bool

isSymbolic :: SBV Word8 -> Bool

SymVal Word16

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Word16)

literal :: Word16 -> SBV Word16

fromCV :: CV -> Word16

isConcretely :: SBV Word16 -> (Word16 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Word16)

forall_ :: MonadSymbolic m => m (SBV Word16)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Word16]

exists :: MonadSymbolic m => String -> m (SBV Word16)

exists_ :: MonadSymbolic m => m (SBV Word16)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Word16]

free :: MonadSymbolic m => String -> m (SBV Word16)

free_ :: MonadSymbolic m => m (SBV Word16)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Word16]

symbolic :: MonadSymbolic m => String -> m (SBV Word16)

symbolics :: MonadSymbolic m => [String] -> m [SBV Word16]

unliteral :: SBV Word16 -> Maybe Word16

isConcrete :: SBV Word16 -> Bool

isSymbolic :: SBV Word16 -> Bool

SymVal Word32

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Word32)

literal :: Word32 -> SBV Word32

fromCV :: CV -> Word32

isConcretely :: SBV Word32 -> (Word32 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Word32)

forall_ :: MonadSymbolic m => m (SBV Word32)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Word32]

exists :: MonadSymbolic m => String -> m (SBV Word32)

exists_ :: MonadSymbolic m => m (SBV Word32)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Word32]

free :: MonadSymbolic m => String -> m (SBV Word32)

free_ :: MonadSymbolic m => m (SBV Word32)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Word32]

symbolic :: MonadSymbolic m => String -> m (SBV Word32)

symbolics :: MonadSymbolic m => [String] -> m [SBV Word32]

unliteral :: SBV Word32 -> Maybe Word32

isConcrete :: SBV Word32 -> Bool

isSymbolic :: SBV Word32 -> Bool

SymVal Word64

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Word64)

literal :: Word64 -> SBV Word64

fromCV :: CV -> Word64

isConcretely :: SBV Word64 -> (Word64 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Word64)

forall_ :: MonadSymbolic m => m (SBV Word64)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Word64]

exists :: MonadSymbolic m => String -> m (SBV Word64)

exists_ :: MonadSymbolic m => m (SBV Word64)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Word64]

free :: MonadSymbolic m => String -> m (SBV Word64)

free_ :: MonadSymbolic m => m (SBV Word64)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Word64]

symbolic :: MonadSymbolic m => String -> m (SBV Word64)

symbolics :: MonadSymbolic m => [String] -> m [SBV Word64]

unliteral :: SBV Word64 -> Maybe Word64

isConcrete :: SBV Word64 -> Bool

isSymbolic :: SBV Word64 -> Bool

SymVal ()

SymVal for 0-tuple (i.e., unit)

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV ())

literal :: () -> SBV ()

fromCV :: CV -> ()

isConcretely :: SBV () -> (() -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV ())

forall_ :: MonadSymbolic m => m (SBV ())

mkForallVars :: MonadSymbolic m => Int -> m [SBV ()]

exists :: MonadSymbolic m => String -> m (SBV ())

exists_ :: MonadSymbolic m => m (SBV ())

mkExistVars :: MonadSymbolic m => Int -> m [SBV ()]

free :: MonadSymbolic m => String -> m (SBV ())

free_ :: MonadSymbolic m => m (SBV ())

mkFreeVars :: MonadSymbolic m => Int -> m [SBV ()]

symbolic :: MonadSymbolic m => String -> m (SBV ())

symbolics :: MonadSymbolic m => [String] -> m [SBV ()]

unliteral :: SBV () -> Maybe ()

isConcrete :: SBV () -> Bool

isSymbolic :: SBV () -> Bool

SymVal AlgReal

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV AlgReal)

literal :: AlgReal -> SBV AlgReal

fromCV :: CV -> AlgReal

isConcretely :: SBV AlgReal -> (AlgReal -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV AlgReal)

forall_ :: MonadSymbolic m => m (SBV AlgReal)

mkForallVars :: MonadSymbolic m => Int -> m [SBV AlgReal]

exists :: MonadSymbolic m => String -> m (SBV AlgReal)

exists_ :: MonadSymbolic m => m (SBV AlgReal)

mkExistVars :: MonadSymbolic m => Int -> m [SBV AlgReal]

free :: MonadSymbolic m => String -> m (SBV AlgReal)

free_ :: MonadSymbolic m => m (SBV AlgReal)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV AlgReal]

symbolic :: MonadSymbolic m => String -> m (SBV AlgReal)

symbolics :: MonadSymbolic m => [String] -> m [SBV AlgReal]

unliteral :: SBV AlgReal -> Maybe AlgReal

isConcrete :: SBV AlgReal -> Bool

isSymbolic :: SBV AlgReal -> Bool

SymVal RoundingMode

RoundingMode can be used symbolically

Defined in Data.SBV.Core.Data

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV RoundingMode)

literal :: RoundingMode -> SBV RoundingMode

fromCV :: CV -> RoundingMode

isConcretely :: SBV RoundingMode -> (RoundingMode -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV RoundingMode)

forall_ :: MonadSymbolic m => m (SBV RoundingMode)

mkForallVars :: MonadSymbolic m => Int -> m [SBV RoundingMode]

exists :: MonadSymbolic m => String -> m (SBV RoundingMode)

exists_ :: MonadSymbolic m => m (SBV RoundingMode)

mkExistVars :: MonadSymbolic m => Int -> m [SBV RoundingMode]

free :: MonadSymbolic m => String -> m (SBV RoundingMode)

free_ :: MonadSymbolic m => m (SBV RoundingMode)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV RoundingMode]

symbolic :: MonadSymbolic m => String -> m (SBV RoundingMode)

symbolics :: MonadSymbolic m => [String] -> m [SBV RoundingMode]

unliteral :: SBV RoundingMode -> Maybe RoundingMode

isConcrete :: SBV RoundingMode -> Bool

isSymbolic :: SBV RoundingMode -> Bool

SymVal State

Defined in Documentation.SBV.Examples.Lists.BoundedMutex

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV State)

literal :: State -> SBV State

fromCV :: CV -> State

isConcretely :: SBV State -> (State -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV State)

forall_ :: MonadSymbolic m => m (SBV State)

mkForallVars :: MonadSymbolic m => Int -> m [SBV State]

exists :: MonadSymbolic m => String -> m (SBV State)

exists_ :: MonadSymbolic m => m (SBV State)

mkExistVars :: MonadSymbolic m => Int -> m [SBV State]

free :: MonadSymbolic m => String -> m (SBV State)

free_ :: MonadSymbolic m => m (SBV State)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV State]

symbolic :: MonadSymbolic m => String -> m (SBV State)

symbolics :: MonadSymbolic m => [String] -> m [SBV State]

unliteral :: SBV State -> Maybe State

isConcrete :: SBV State -> Bool

isSymbolic :: SBV State -> Bool

SymVal E

Defined in Documentation.SBV.Examples.Misc.Enumerate

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV E)

literal :: E -> SBV E

fromCV :: CV -> E

isConcretely :: SBV E -> (E -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV E)

forall_ :: MonadSymbolic m => m (SBV E)

mkForallVars :: MonadSymbolic m => Int -> m [SBV E]

exists :: MonadSymbolic m => String -> m (SBV E)

exists_ :: MonadSymbolic m => m (SBV E)

mkExistVars :: MonadSymbolic m => Int -> m [SBV E]

free :: MonadSymbolic m => String -> m (SBV E)

free_ :: MonadSymbolic m => m (SBV E)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV E]

symbolic :: MonadSymbolic m => String -> m (SBV E)

symbolics :: MonadSymbolic m => [String] -> m [SBV E]

unliteral :: SBV E -> Maybe E

isConcrete :: SBV E -> Bool

isSymbolic :: SBV E -> Bool

SymVal Word4

SymVal instance, allowing this type to be used in proofs/sat etc.

Defined in Documentation.SBV.Examples.Misc.Word4

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Word4)

literal :: Word4 -> SBV Word4

fromCV :: CV -> Word4

isConcretely :: SBV Word4 -> (Word4 -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Word4)

forall_ :: MonadSymbolic m => m (SBV Word4)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Word4]

exists :: MonadSymbolic m => String -> m (SBV Word4)

exists_ :: MonadSymbolic m => m (SBV Word4)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Word4]

free :: MonadSymbolic m => String -> m (SBV Word4)

free_ :: MonadSymbolic m => m (SBV Word4)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Word4]

symbolic :: MonadSymbolic m => String -> m (SBV Word4)

symbolics :: MonadSymbolic m => [String] -> m [SBV Word4]

unliteral :: SBV Word4 -> Maybe Word4

isConcrete :: SBV Word4 -> Bool

isSymbolic :: SBV Word4 -> Bool

SymVal Day

Defined in Documentation.SBV.Examples.Optimization.Enumerate

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Day)

literal :: Day -> SBV Day

fromCV :: CV -> Day

isConcretely :: SBV Day -> (Day -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Day)

forall_ :: MonadSymbolic m => m (SBV Day)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Day]

exists :: MonadSymbolic m => String -> m (SBV Day)

exists_ :: MonadSymbolic m => m (SBV Day)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Day]

free :: MonadSymbolic m => String -> m (SBV Day)

free_ :: MonadSymbolic m => m (SBV Day)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Day]

symbolic :: MonadSymbolic m => String -> m (SBV Day)

symbolics :: MonadSymbolic m => [String] -> m [SBV Day]

unliteral :: SBV Day -> Maybe Day

isConcrete :: SBV Day -> Bool

isSymbolic :: SBV Day -> Bool

SymVal Color

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Color)

literal :: Color -> SBV Color

fromCV :: CV -> Color

isConcretely :: SBV Color -> (Color -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Color)

forall_ :: MonadSymbolic m => m (SBV Color)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Color]

exists :: MonadSymbolic m => String -> m (SBV Color)

exists_ :: MonadSymbolic m => m (SBV Color)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Color]

free :: MonadSymbolic m => String -> m (SBV Color)

free_ :: MonadSymbolic m => m (SBV Color)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Color]

symbolic :: MonadSymbolic m => String -> m (SBV Color)

symbolics :: MonadSymbolic m => [String] -> m [SBV Color]

unliteral :: SBV Color -> Maybe Color

isConcrete :: SBV Color -> Bool

isSymbolic :: SBV Color -> Bool

SymVal Nationality

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Nationality)

literal :: Nationality -> SBV Nationality

fromCV :: CV -> Nationality

isConcretely :: SBV Nationality -> (Nationality -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Nationality)

forall_ :: MonadSymbolic m => m (SBV Nationality)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Nationality]

exists :: MonadSymbolic m => String -> m (SBV Nationality)

exists_ :: MonadSymbolic m => m (SBV Nationality)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Nationality]

free :: MonadSymbolic m => String -> m (SBV Nationality)

free_ :: MonadSymbolic m => m (SBV Nationality)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Nationality]

symbolic :: MonadSymbolic m => String -> m (SBV Nationality)

symbolics :: MonadSymbolic m => [String] -> m [SBV Nationality]

unliteral :: SBV Nationality -> Maybe Nationality

isConcrete :: SBV Nationality -> Bool

isSymbolic :: SBV Nationality -> Bool

SymVal Beverage

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Beverage)

literal :: Beverage -> SBV Beverage

fromCV :: CV -> Beverage

isConcretely :: SBV Beverage -> (Beverage -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Beverage)

forall_ :: MonadSymbolic m => m (SBV Beverage)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Beverage]

exists :: MonadSymbolic m => String -> m (SBV Beverage)

exists_ :: MonadSymbolic m => m (SBV Beverage)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Beverage]

free :: MonadSymbolic m => String -> m (SBV Beverage)

free_ :: MonadSymbolic m => m (SBV Beverage)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Beverage]

symbolic :: MonadSymbolic m => String -> m (SBV Beverage)

symbolics :: MonadSymbolic m => [String] -> m [SBV Beverage]

unliteral :: SBV Beverage -> Maybe Beverage

isConcrete :: SBV Beverage -> Bool

isSymbolic :: SBV Beverage -> Bool

SymVal Pet

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Pet)

literal :: Pet -> SBV Pet

fromCV :: CV -> Pet

isConcretely :: SBV Pet -> (Pet -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Pet)

forall_ :: MonadSymbolic m => m (SBV Pet)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Pet]

exists :: MonadSymbolic m => String -> m (SBV Pet)

exists_ :: MonadSymbolic m => m (SBV Pet)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Pet]

free :: MonadSymbolic m => String -> m (SBV Pet)

free_ :: MonadSymbolic m => m (SBV Pet)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Pet]

symbolic :: MonadSymbolic m => String -> m (SBV Pet)

symbolics :: MonadSymbolic m => [String] -> m [SBV Pet]

unliteral :: SBV Pet -> Maybe Pet

isConcrete :: SBV Pet -> Bool

isSymbolic :: SBV Pet -> Bool

SymVal Sport

Defined in Documentation.SBV.Examples.Puzzles.Fish

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Sport)

literal :: Sport -> SBV Sport

fromCV :: CV -> Sport

isConcretely :: SBV Sport -> (Sport -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Sport)

forall_ :: MonadSymbolic m => m (SBV Sport)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Sport]

exists :: MonadSymbolic m => String -> m (SBV Sport)

exists_ :: MonadSymbolic m => m (SBV Sport)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Sport]

free :: MonadSymbolic m => String -> m (SBV Sport)

free_ :: MonadSymbolic m => m (SBV Sport)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Sport]

symbolic :: MonadSymbolic m => String -> m (SBV Sport)

symbolics :: MonadSymbolic m => [String] -> m [SBV Sport]

unliteral :: SBV Sport -> Maybe Sport

isConcrete :: SBV Sport -> Bool

isSymbolic :: SBV Sport -> Bool

SymVal Color

Defined in Documentation.SBV.Examples.Puzzles.Garden

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Color)

literal :: Color -> SBV Color

fromCV :: CV -> Color

isConcretely :: SBV Color -> (Color -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Color)

forall_ :: MonadSymbolic m => m (SBV Color)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Color]

exists :: MonadSymbolic m => String -> m (SBV Color)

exists_ :: MonadSymbolic m => m (SBV Color)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Color]

free :: MonadSymbolic m => String -> m (SBV Color)

free_ :: MonadSymbolic m => m (SBV Color)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Color]

symbolic :: MonadSymbolic m => String -> m (SBV Color)

symbolics :: MonadSymbolic m => [String] -> m [SBV Color]

unliteral :: SBV Color -> Maybe Color

isConcrete :: SBV Color -> Bool

isSymbolic :: SBV Color -> Bool

SymVal Color

Defined in Documentation.SBV.Examples.Puzzles.HexPuzzle

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Color)

literal :: Color -> SBV Color

fromCV :: CV -> Color

isConcretely :: SBV Color -> (Color -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Color)

forall_ :: MonadSymbolic m => m (SBV Color)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Color]

exists :: MonadSymbolic m => String -> m (SBV Color)

exists_ :: MonadSymbolic m => m (SBV Color)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Color]

free :: MonadSymbolic m => String -> m (SBV Color)

free_ :: MonadSymbolic m => m (SBV Color)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Color]

symbolic :: MonadSymbolic m => String -> m (SBV Color)

symbolics :: MonadSymbolic m => [String] -> m [SBV Color]

unliteral :: SBV Color -> Maybe Color

isConcrete :: SBV Color -> Bool

isSymbolic :: SBV Color -> Bool

SymVal U2Member

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV U2Member)

literal :: U2Member -> SBV U2Member

fromCV :: CV -> U2Member

isConcretely :: SBV U2Member -> (U2Member -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV U2Member)

forall_ :: MonadSymbolic m => m (SBV U2Member)

mkForallVars :: MonadSymbolic m => Int -> m [SBV U2Member]

exists :: MonadSymbolic m => String -> m (SBV U2Member)

exists_ :: MonadSymbolic m => m (SBV U2Member)

mkExistVars :: MonadSymbolic m => Int -> m [SBV U2Member]

free :: MonadSymbolic m => String -> m (SBV U2Member)

free_ :: MonadSymbolic m => m (SBV U2Member)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV U2Member]

symbolic :: MonadSymbolic m => String -> m (SBV U2Member)

symbolics :: MonadSymbolic m => [String] -> m [SBV U2Member]

unliteral :: SBV U2Member -> Maybe U2Member

isConcrete :: SBV U2Member -> Bool

isSymbolic :: SBV U2Member -> Bool

SymVal Location

Defined in Documentation.SBV.Examples.Puzzles.U2Bridge

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Location)

literal :: Location -> SBV Location

fromCV :: CV -> Location

isConcretely :: SBV Location -> (Location -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Location)

forall_ :: MonadSymbolic m => m (SBV Location)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Location]

exists :: MonadSymbolic m => String -> m (SBV Location)

exists_ :: MonadSymbolic m => m (SBV Location)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Location]

free :: MonadSymbolic m => String -> m (SBV Location)

free_ :: MonadSymbolic m => m (SBV Location)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Location]

symbolic :: MonadSymbolic m => String -> m (SBV Location)

symbolics :: MonadSymbolic m => [String] -> m [SBV Location]

unliteral :: SBV Location -> Maybe Location

isConcrete :: SBV Location -> Bool

isSymbolic :: SBV Location -> Bool

SymVal Day

Defined in Documentation.SBV.Examples.Queries.Enums

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Day)

literal :: Day -> SBV Day

fromCV :: CV -> Day

isConcretely :: SBV Day -> (Day -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Day)

forall_ :: MonadSymbolic m => m (SBV Day)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Day]

exists :: MonadSymbolic m => String -> m (SBV Day)

exists_ :: MonadSymbolic m => m (SBV Day)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Day]

free :: MonadSymbolic m => String -> m (SBV Day)

free_ :: MonadSymbolic m => m (SBV Day)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Day]

symbolic :: MonadSymbolic m => String -> m (SBV Day)

symbolics :: MonadSymbolic m => [String] -> m [SBV Day]

unliteral :: SBV Day -> Maybe Day

isConcrete :: SBV Day -> Bool

isSymbolic :: SBV Day -> Bool

SymVal BinOp

Defined in Documentation.SBV.Examples.Queries.FourFours

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV BinOp)

literal :: BinOp -> SBV BinOp

fromCV :: CV -> BinOp

isConcretely :: SBV BinOp -> (BinOp -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV BinOp)

forall_ :: MonadSymbolic m => m (SBV BinOp)

mkForallVars :: MonadSymbolic m => Int -> m [SBV BinOp]

exists :: MonadSymbolic m => String -> m (SBV BinOp)

exists_ :: MonadSymbolic m => m (SBV BinOp)

mkExistVars :: MonadSymbolic m => Int -> m [SBV BinOp]

free :: MonadSymbolic m => String -> m (SBV BinOp)

free_ :: MonadSymbolic m => m (SBV BinOp)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV BinOp]

symbolic :: MonadSymbolic m => String -> m (SBV BinOp)

symbolics :: MonadSymbolic m => [String] -> m [SBV BinOp]

unliteral :: SBV BinOp -> Maybe BinOp

isConcrete :: SBV BinOp -> Bool

isSymbolic :: SBV BinOp -> Bool

SymVal UnOp

Defined in Documentation.SBV.Examples.Queries.FourFours

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV UnOp)

literal :: UnOp -> SBV UnOp

fromCV :: CV -> UnOp

isConcretely :: SBV UnOp -> (UnOp -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV UnOp)

forall_ :: MonadSymbolic m => m (SBV UnOp)

mkForallVars :: MonadSymbolic m => Int -> m [SBV UnOp]

exists :: MonadSymbolic m => String -> m (SBV UnOp)

exists_ :: MonadSymbolic m => m (SBV UnOp)

mkExistVars :: MonadSymbolic m => Int -> m [SBV UnOp]

free :: MonadSymbolic m => String -> m (SBV UnOp)

free_ :: MonadSymbolic m => m (SBV UnOp)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV UnOp]

symbolic :: MonadSymbolic m => String -> m (SBV UnOp)

symbolics :: MonadSymbolic m => [String] -> m [SBV UnOp]

unliteral :: SBV UnOp -> Maybe UnOp

isConcrete :: SBV UnOp -> Bool

isSymbolic :: SBV UnOp -> Bool

SymVal B

Defined in Documentation.SBV.Examples.Uninterpreted.Deduce

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV B)

literal :: B -> SBV B

fromCV :: CV -> B

isConcretely :: SBV B -> (B -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV B)

forall_ :: MonadSymbolic m => m (SBV B)

mkForallVars :: MonadSymbolic m => Int -> m [SBV B]

exists :: MonadSymbolic m => String -> m (SBV B)

exists_ :: MonadSymbolic m => m (SBV B)

mkExistVars :: MonadSymbolic m => Int -> m [SBV B]

free :: MonadSymbolic m => String -> m (SBV B)

free_ :: MonadSymbolic m => m (SBV B)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV B]

symbolic :: MonadSymbolic m => String -> m (SBV B)

symbolics :: MonadSymbolic m => [String] -> m [SBV B]

unliteral :: SBV B -> Maybe B

isConcrete :: SBV B -> Bool

isSymbolic :: SBV B -> Bool

SymVal Q

Defined in Documentation.SBV.Examples.Uninterpreted.Sort

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV Q)

literal :: Q -> SBV Q

fromCV :: CV -> Q

isConcretely :: SBV Q -> (Q -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV Q)

forall_ :: MonadSymbolic m => m (SBV Q)

mkForallVars :: MonadSymbolic m => Int -> m [SBV Q]

exists :: MonadSymbolic m => String -> m (SBV Q)

exists_ :: MonadSymbolic m => m (SBV Q)

mkExistVars :: MonadSymbolic m => Int -> m [SBV Q]

free :: MonadSymbolic m => String -> m (SBV Q)

free_ :: MonadSymbolic m => m (SBV Q)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV Q]

symbolic :: MonadSymbolic m => String -> m (SBV Q)

symbolics :: MonadSymbolic m => [String] -> m [SBV Q]

unliteral :: SBV Q -> Maybe Q

isConcrete :: SBV Q -> Bool

isSymbolic :: SBV Q -> Bool

SymVal L

Declare instances to make L a usable uninterpreted sort. First we need the SymVal instance, with the default definition sufficing.

Defined in Documentation.SBV.Examples.Uninterpreted.UISortAllSat

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV L)

literal :: L -> SBV L

fromCV :: CV -> L

isConcretely :: SBV L -> (L -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV L)

forall_ :: MonadSymbolic m => m (SBV L)

mkForallVars :: MonadSymbolic m => Int -> m [SBV L]

exists :: MonadSymbolic m => String -> m (SBV L)

exists_ :: MonadSymbolic m => m (SBV L)

mkExistVars :: MonadSymbolic m => Int -> m [SBV L]

free :: MonadSymbolic m => String -> m (SBV L)

free_ :: MonadSymbolic m => m (SBV L)

mkFreeVars :: MonadSymbolic m => Int -> m [SBV L]

symbolic :: MonadSymbolic m => String -> m (SBV L)

symbolics :: MonadSymbolic m => [String] -> m [SBV L]

unliteral :: SBV L -> Maybe L

isConcrete :: SBV L -> Bool

isSymbolic :: SBV L -> Bool

SymVal a => SymVal [a]

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV [a])

literal :: [a] -> SBV [a]

fromCV :: CV -> [a]

isConcretely :: SBV [a] -> ([a] -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV [a])

forall_ :: MonadSymbolic m => m (SBV [a])

mkForallVars :: MonadSymbolic m => Int -> m [SBV [a]]

exists :: MonadSymbolic m => String -> m (SBV [a])

exists_ :: MonadSymbolic m => m (SBV [a])

mkExistVars :: MonadSymbolic m => Int -> m [SBV [a]]

free :: MonadSymbolic m => String -> m (SBV [a])

free_ :: MonadSymbolic m => m (SBV [a])

mkFreeVars :: MonadSymbolic m => Int -> m [SBV [a]]

symbolic :: MonadSymbolic m => String -> m (SBV [a])

symbolics :: MonadSymbolic m => [String] -> m [SBV [a]]

unliteral :: SBV [a] -> Maybe [a]

isConcrete :: SBV [a] -> Bool

isSymbolic :: SBV [a] -> Bool

SymVal a => SymVal (Maybe a)

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (Maybe a))

literal :: Maybe a -> SBV (Maybe a)

fromCV :: CV -> Maybe a

isConcretely :: SBV (Maybe a) -> (Maybe a -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (Maybe a))

forall_ :: MonadSymbolic m => m (SBV (Maybe a))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (Maybe a)]

exists :: MonadSymbolic m => String -> m (SBV (Maybe a))

exists_ :: MonadSymbolic m => m (SBV (Maybe a))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (Maybe a)]

free :: MonadSymbolic m => String -> m (SBV (Maybe a))

free_ :: MonadSymbolic m => m (SBV (Maybe a))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (Maybe a)]

symbolic :: MonadSymbolic m => String -> m (SBV (Maybe a))

symbolics :: MonadSymbolic m => [String] -> m [SBV (Maybe a)]

unliteral :: SBV (Maybe a) -> Maybe (Maybe a)

isConcrete :: SBV (Maybe a) -> Bool

isSymbolic :: SBV (Maybe a) -> Bool

(Ord a, SymVal a) => SymVal (RCSet a)

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (RCSet a))

literal :: RCSet a -> SBV (RCSet a)

fromCV :: CV -> RCSet a

isConcretely :: SBV (RCSet a) -> (RCSet a -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (RCSet a))

forall_ :: MonadSymbolic m => m (SBV (RCSet a))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (RCSet a)]

exists :: MonadSymbolic m => String -> m (SBV (RCSet a))

exists_ :: MonadSymbolic m => m (SBV (RCSet a))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (RCSet a)]

free :: MonadSymbolic m => String -> m (SBV (RCSet a))

free_ :: MonadSymbolic m => m (SBV (RCSet a))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (RCSet a)]

symbolic :: MonadSymbolic m => String -> m (SBV (RCSet a))

symbolics :: MonadSymbolic m => [String] -> m [SBV (RCSet a)]

unliteral :: SBV (RCSet a) -> Maybe (RCSet a)

isConcrete :: SBV (RCSet a) -> Bool

isSymbolic :: SBV (RCSet a) -> Bool

(SymVal a, SymVal b) => SymVal (Either a b)

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (Either a b))

literal :: Either a b -> SBV (Either a b)

fromCV :: CV -> Either a b

isConcretely :: SBV (Either a b) -> (Either a b -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (Either a b))

forall_ :: MonadSymbolic m => m (SBV (Either a b))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (Either a b)]

exists :: MonadSymbolic m => String -> m (SBV (Either a b))

exists_ :: MonadSymbolic m => m (SBV (Either a b))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (Either a b)]

free :: MonadSymbolic m => String -> m (SBV (Either a b))

free_ :: MonadSymbolic m => m (SBV (Either a b))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (Either a b)]

symbolic :: MonadSymbolic m => String -> m (SBV (Either a b))

symbolics :: MonadSymbolic m => [String] -> m [SBV (Either a b)]

unliteral :: SBV (Either a b) -> Maybe (Either a b)

isConcrete :: SBV (Either a b) -> Bool

isSymbolic :: SBV (Either a b) -> Bool

(SymVal a, SymVal b) => SymVal (a, b)

SymVal for 2-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b))

literal :: (a, b) -> SBV (a, b)

fromCV :: CV -> (a, b)

isConcretely :: SBV (a, b) -> ((a, b) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b))

forall_ :: MonadSymbolic m => m (SBV (a, b))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b)]

exists :: MonadSymbolic m => String -> m (SBV (a, b))

exists_ :: MonadSymbolic m => m (SBV (a, b))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b)]

free :: MonadSymbolic m => String -> m (SBV (a, b))

free_ :: MonadSymbolic m => m (SBV (a, b))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b)]

unliteral :: SBV (a, b) -> Maybe (a, b)

isConcrete :: SBV (a, b) -> Bool

isSymbolic :: SBV (a, b) -> Bool

(SymVal a, SymVal b, SymVal c) => SymVal (a, b, c)

SymVal for 3-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b, c))

literal :: (a, b, c) -> SBV (a, b, c)

fromCV :: CV -> (a, b, c)

isConcretely :: SBV (a, b, c) -> ((a, b, c) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b, c))

forall_ :: MonadSymbolic m => m (SBV (a, b, c))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b, c)]

exists :: MonadSymbolic m => String -> m (SBV (a, b, c))

exists_ :: MonadSymbolic m => m (SBV (a, b, c))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b, c)]

free :: MonadSymbolic m => String -> m (SBV (a, b, c))

free_ :: MonadSymbolic m => m (SBV (a, b, c))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b, c)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b, c))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b, c)]

unliteral :: SBV (a, b, c) -> Maybe (a, b, c)

isConcrete :: SBV (a, b, c) -> Bool

isSymbolic :: SBV (a, b, c) -> Bool

(SymVal a, SymVal b, SymVal c, SymVal d) => SymVal (a, b, c, d)

SymVal for 4-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b, c, d))

literal :: (a, b, c, d) -> SBV (a, b, c, d)

fromCV :: CV -> (a, b, c, d)

isConcretely :: SBV (a, b, c, d) -> ((a, b, c, d) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b, c, d))

forall_ :: MonadSymbolic m => m (SBV (a, b, c, d))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d)]

exists :: MonadSymbolic m => String -> m (SBV (a, b, c, d))

exists_ :: MonadSymbolic m => m (SBV (a, b, c, d))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d)]

free :: MonadSymbolic m => String -> m (SBV (a, b, c, d))

free_ :: MonadSymbolic m => m (SBV (a, b, c, d))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b, c, d))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b, c, d)]

unliteral :: SBV (a, b, c, d) -> Maybe (a, b, c, d)

isConcrete :: SBV (a, b, c, d) -> Bool

isSymbolic :: SBV (a, b, c, d) -> Bool

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e) => SymVal (a, b, c, d, e)

SymVal for 5-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b, c, d, e))

literal :: (a, b, c, d, e) -> SBV (a, b, c, d, e)

fromCV :: CV -> (a, b, c, d, e)

isConcretely :: SBV (a, b, c, d, e) -> ((a, b, c, d, e) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e))

forall_ :: MonadSymbolic m => m (SBV (a, b, c, d, e))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e)]

exists :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e))

exists_ :: MonadSymbolic m => m (SBV (a, b, c, d, e))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e)]

free :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e))

free_ :: MonadSymbolic m => m (SBV (a, b, c, d, e))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b, c, d, e)]

unliteral :: SBV (a, b, c, d, e) -> Maybe (a, b, c, d, e)

isConcrete :: SBV (a, b, c, d, e) -> Bool

isSymbolic :: SBV (a, b, c, d, e) -> Bool

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f) => SymVal (a, b, c, d, e, f)

SymVal for 6-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b, c, d, e, f))

literal :: (a, b, c, d, e, f) -> SBV (a, b, c, d, e, f)

fromCV :: CV -> (a, b, c, d, e, f)

isConcretely :: SBV (a, b, c, d, e, f) -> ((a, b, c, d, e, f) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f))

forall_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f)]

exists :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f))

exists_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f)]

free :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f))

free_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b, c, d, e, f)]

unliteral :: SBV (a, b, c, d, e, f) -> Maybe (a, b, c, d, e, f)

isConcrete :: SBV (a, b, c, d, e, f) -> Bool

isSymbolic :: SBV (a, b, c, d, e, f) -> Bool

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g) => SymVal (a, b, c, d, e, f, g)

SymVal for 7-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b, c, d, e, f, g))

literal :: (a, b, c, d, e, f, g) -> SBV (a, b, c, d, e, f, g)

fromCV :: CV -> (a, b, c, d, e, f, g)

isConcretely :: SBV (a, b, c, d, e, f, g) -> ((a, b, c, d, e, f, g) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g))

forall_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f, g))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f, g)]

exists :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g))

exists_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f, g))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f, g)]

free :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g))

free_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f, g))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f, g)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b, c, d, e, f, g)]

unliteral :: SBV (a, b, c, d, e, f, g) -> Maybe (a, b, c, d, e, f, g)

isConcrete :: SBV (a, b, c, d, e, f, g) -> Bool

isSymbolic :: SBV (a, b, c, d, e, f, g) -> Bool

(SymVal a, SymVal b, SymVal c, SymVal d, SymVal e, SymVal f, SymVal g, SymVal h) => SymVal (a, b, c, d, e, f, g, h)

SymVal for 8-tuples

Defined in Data.SBV.Core.Model

Methods

mkSymVal :: MonadSymbolic m => Maybe Quantifier -> Maybe String -> m (SBV (a, b, c, d, e, f, g, h))

literal :: (a, b, c, d, e, f, g, h) -> SBV (a, b, c, d, e, f, g, h)

fromCV :: CV -> (a, b, c, d, e, f, g, h)

isConcretely :: SBV (a, b, c, d, e, f, g, h) -> ((a, b, c, d, e, f, g, h) -> Bool) -> Bool

forall :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g, h))

forall_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f, g, h))

mkForallVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f, g, h)]

exists :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g, h))

exists_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f, g, h))

mkExistVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f, g, h)]

free :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g, h))

free_ :: MonadSymbolic m => m (SBV (a, b, c, d, e, f, g, h))

mkFreeVars :: MonadSymbolic m => Int -> m [SBV (a, b, c, d, e, f, g, h)]

symbolic :: MonadSymbolic m => String -> m (SBV (a, b, c, d, e, f, g, h))

symbolics :: MonadSymbolic m => [String] -> m [SBV (a, b, c, d, e, f, g, h)]

unliteral :: SBV (a, b, c, d, e, f, g, h) -> Maybe (a, b, c, d, e, f, g, h)

isConcrete :: SBV (a, b, c, d, e, f, g, h) -> Bool

isSymbolic :: SBV (a, b, c, d, e, f, g, h) -> Bool

forall :: SymVal a => String -> Symbolic (SBV a)

Create a user named input (universal)

NB. For a version which generalizes over the underlying monad, see forall

forall_ :: SymVal a => Symbolic (SBV a)

Create an automatically named input

NB. For a version which generalizes over the underlying monad, see forall_

mkForallVars :: SymVal a => Int -> Symbolic [SBV a]

Get a bunch of new words

NB. For a version which generalizes over the underlying monad, see mkForallVars

exists :: SymVal a => String -> Symbolic (SBV a)

Create an existential variable

NB. For a version which generalizes over the underlying monad, see exists

exists_ :: SymVal a => Symbolic (SBV a)

Create an automatically named existential variable

NB. For a version which generalizes over the underlying monad, see exists_

mkExistVars :: SymVal a => Int -> Symbolic [SBV a]

Create a bunch of existentials

NB. For a version which generalizes over the underlying monad, see mkExistVars

free :: SymVal a => String -> Symbolic (SBV a)

Create a free variable, universal in a proof, existential in sat

NB. For a version which generalizes over the underlying monad, see free

free_ :: SymVal a => Symbolic (SBV a)

Create an unnamed free variable, universal in proof, existential in sat

NB. For a version which generalizes over the underlying monad, see free_

mkFreeVars :: SymVal a => Int -> Symbolic [SBV a]

Create a bunch of free vars

NB. For a version which generalizes over the underlying monad, see mkFreeVars

symbolic :: SymVal a => String -> Symbolic (SBV a)

Similar to free; Just a more convenient name

NB. For a version which generalizes over the underlying monad, see symbolic

symbolics :: SymVal a => [String] -> Symbolic [SBV a]

Similar to mkFreeVars; but automatically gives names based on the strings

NB. For a version which generalizes over the underlying monad, see symbolics

literal :: SymVal a => a -> SBV a

Turn a literal constant to symbolic

unliteral :: SymVal a => SBV a -> Maybe a

Extract a literal, if the value is concrete

fromCV :: SymVal a => CV -> a

Extract a literal, from a CV representation

isConcrete :: SymVal a => SBV a -> Bool

Is the symbolic word concrete?

isSymbolic :: SymVal a => SBV a -> Bool

Is the symbolic word really symbolic?

isConcretely :: SymVal a => SBV a -> (a -> Bool) -> Bool

Does it concretely satisfy the given predicate?

mkSymVal :: SymVal a => Maybe Quantifier -> Maybe String -> Symbolic (SBV a)

One stop allocator

NB. For a version which generalizes over the underlying monad, see mkSymVal

class MonadIO m => MonadSymbolic m where

A Symbolic computation. Represented by a reader monad carrying the state of the computation, layered on top of IO for creating unique references to hold onto intermediate results.

Computations which support symbolic operations

Minimal complete definition

Nothing

Methods

symbolicEnv :: m State

symbolicEnv :: (MonadTrans t, MonadSymbolic m', m ~ t m') => m State

Instances

MonadSymbolic Query

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: Query State

MonadSymbolic SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

symbolicEnv :: SBVCodeGen State

MonadSymbolic Alloc

Defined in Documentation.SBV.Examples.Transformers.SymbolicEval

Methods

symbolicEnv :: Alloc State

MonadSymbolic m => MonadSymbolic (MaybeT m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: MaybeT m State

MonadIO m => MonadSymbolic (SymbolicT m)

MonadSymbolic instance for `SymbolicT m`

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: SymbolicT m State

MonadSymbolic m => MonadSymbolic (ExceptT e m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: ExceptT e m State

MonadSymbolic m => MonadSymbolic (StateT s m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: StateT s m State

MonadSymbolic m => MonadSymbolic (StateT s m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: StateT s m State

(MonadSymbolic m, Monoid w) => MonadSymbolic (WriterT w m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: WriterT w m State

(MonadSymbolic m, Monoid w) => MonadSymbolic (WriterT w m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: WriterT w m State

MonadSymbolic m => MonadSymbolic (ReaderT r m)

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: ReaderT r m State

type Symbolic = SymbolicT IO

Symbolic is specialization of SymbolicT to the IO monad. Unless you are using transformers explicitly, this is the type you should prefer.

data SymbolicT m a

A generalization of Symbolic.

Instances

MonadTrans SymbolicT

Defined in Data.SBV.Core.Symbolic

Methods

lift :: Monad m => m a -> SymbolicT m a

MonadWriter w m => MonadWriter w (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

writer :: (a, w) -> SymbolicT m a

tell :: w -> SymbolicT m ()

listen :: SymbolicT m a -> SymbolicT m (a, w)

pass :: SymbolicT m (a, w -> w) -> SymbolicT m a

MonadState s m => MonadState s (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

get :: SymbolicT m s

put :: s -> SymbolicT m ()

state :: (s -> (a, s)) -> SymbolicT m a

MonadReader r m => MonadReader r (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

ask :: SymbolicT m r

local :: (r -> r) -> SymbolicT m a -> SymbolicT m a

reader :: (r -> a) -> SymbolicT m a

MonadError e m => MonadError e (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

throwError :: e -> SymbolicT m a

catchError :: SymbolicT m a -> (e -> SymbolicT m a) -> SymbolicT m a

(ExtractIO m, NFData a) => SExecutable m (SymbolicT m a)

Defined in Data.SBV.Provers.Prover

Methods

sName_ :: SymbolicT m a -> SymbolicT m ()

sName :: [String] -> SymbolicT m a -> SymbolicT m ()

safe :: SymbolicT m a -> m [SafeResult]

safeWith :: SMTConfig -> SymbolicT m a -> m [SafeResult]

ExtractIO m => MProvable m (SymbolicT m SBool)

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: SymbolicT m SBool -> SymbolicT m SBool

forAll :: [String] -> SymbolicT m SBool -> SymbolicT m SBool

forSome_ :: SymbolicT m SBool -> SymbolicT m SBool

forSome :: [String] -> SymbolicT m SBool -> SymbolicT m SBool

prove :: SymbolicT m SBool -> m ThmResult

proveWith :: SMTConfig -> SymbolicT m SBool -> m ThmResult

sat :: SymbolicT m SBool -> m SatResult

satWith :: SMTConfig -> SymbolicT m SBool -> m SatResult

allSat :: SymbolicT m SBool -> m AllSatResult

allSatWith :: SMTConfig -> SymbolicT m SBool -> m AllSatResult

optimize :: OptimizeStyle -> SymbolicT m SBool -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> SymbolicT m SBool -> m OptimizeResult

isVacuous :: SymbolicT m SBool -> m Bool

isVacuousWith :: SMTConfig -> SymbolicT m SBool -> m Bool

isTheorem :: SymbolicT m SBool -> m Bool

isTheoremWith :: SMTConfig -> SymbolicT m SBool -> m Bool

isSatisfiable :: SymbolicT m SBool -> m Bool

isSatisfiableWith :: SMTConfig -> SymbolicT m SBool -> m Bool

validate :: Bool -> SMTConfig -> SymbolicT m SBool -> SMTResult -> m SMTResult

ExtractIO m => MProvable m (SymbolicT m ())

Defined in Data.SBV.Provers.Prover

Methods

forAll_ :: SymbolicT m () -> SymbolicT m SBool

forAll :: [String] -> SymbolicT m () -> SymbolicT m SBool

forSome_ :: SymbolicT m () -> SymbolicT m SBool

forSome :: [String] -> SymbolicT m () -> SymbolicT m SBool

prove :: SymbolicT m () -> m ThmResult

proveWith :: SMTConfig -> SymbolicT m () -> m ThmResult

sat :: SymbolicT m () -> m SatResult

satWith :: SMTConfig -> SymbolicT m () -> m SatResult

allSat :: SymbolicT m () -> m AllSatResult

allSatWith :: SMTConfig -> SymbolicT m () -> m AllSatResult

optimize :: OptimizeStyle -> SymbolicT m () -> m OptimizeResult

optimizeWith :: SMTConfig -> OptimizeStyle -> SymbolicT m () -> m OptimizeResult

isVacuous :: SymbolicT m () -> m Bool

isVacuousWith :: SMTConfig -> SymbolicT m () -> m Bool

isTheorem :: SymbolicT m () -> m Bool

isTheoremWith :: SMTConfig -> SymbolicT m () -> m Bool

isSatisfiable :: SymbolicT m () -> m Bool

isSatisfiableWith :: SMTConfig -> SymbolicT m () -> m Bool

validate :: Bool -> SMTConfig -> SymbolicT m () -> SMTResult -> m SMTResult

Monad m => Monad (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

(>>=) :: SymbolicT m a -> (a -> SymbolicT m b) -> SymbolicT m b

(>>) :: SymbolicT m a -> SymbolicT m b -> SymbolicT m b

return :: a -> SymbolicT m a

fail :: String -> SymbolicT m a

Functor m => Functor (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

fmap :: (a -> b) -> SymbolicT m a -> SymbolicT m b

(<$) :: a -> SymbolicT m b -> SymbolicT m a

MonadFail m => MonadFail (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

fail :: String -> SymbolicT m a

Applicative m => Applicative (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

pure :: a -> SymbolicT m a

(<*>) :: SymbolicT m (a -> b) -> SymbolicT m a -> SymbolicT m b

liftA2 :: (a -> b -> c) -> SymbolicT m a -> SymbolicT m b -> SymbolicT m c

(*>) :: SymbolicT m a -> SymbolicT m b -> SymbolicT m b

(<*) :: SymbolicT m a -> SymbolicT m b -> SymbolicT m a

Testable (Symbolic SVal)

Defined in Data.SBV.Core.Model

Methods

property :: Symbolic SVal -> Property

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> Symbolic SVal) -> Property

Testable (Symbolic SBool)

Defined in Data.SBV.Core.Model

Methods

property :: Symbolic SBool -> Property

propertyForAllShrinkShow :: Gen a -> (a -> [a]) -> (a -> [String]) -> (a -> Symbolic SBool) -> Property

MonadIO m => MonadIO (SymbolicT m)

Defined in Data.SBV.Core.Symbolic

Methods

liftIO :: IO a -> SymbolicT m a

MonadIO m => MonadSymbolic (SymbolicT m)

MonadSymbolic instance for `SymbolicT m`

Defined in Data.SBV.Core.Symbolic

Methods

symbolicEnv :: SymbolicT m State

MonadIO m => SolverContext (SymbolicT m)

Symbolic computations provide a context for writing symbolic programs.

Defined in Data.SBV.Core.Model

Methods

constrain :: SBool -> SymbolicT m ()

softConstrain :: SBool -> SymbolicT m ()

namedConstraint :: String -> SBool -> SymbolicT m ()

constrainWithAttribute :: [(String, String)] -> SBool -> SymbolicT m ()

setInfo :: String -> [String] -> SymbolicT m ()

setOption :: SMTOption -> SymbolicT m ()

setLogic :: Logic -> SymbolicT m ()

setTimeOut :: Integer -> SymbolicT m ()

contextState :: SymbolicT m State

label :: SymVal a => String -> SBV a -> SBV a

label: Label the result of an expression. This is essentially a no-op, but useful as it generates a comment in the generated C/SMT-Lib code. Note that if the argument is a constant, then the label is dropped completely, per the usual constant folding strategy. Compare this to observe which is good for printing counter-examples.

output :: Outputtable a => a -> Symbolic a

Mark an interim result as an output. Useful when constructing Symbolic programs that return multiple values, or when the result is programmatically computed.

NB. For a version which generalizes over the underlying monad, see output

runSMT :: Symbolic a -> IO a

Run an arbitrary symbolic computation, equivalent to runSMTWith defaultSMTCfg

NB. For a version which generalizes over the underlying monad, see runSMT

runSMTWith :: SMTConfig -> Symbolic a -> IO a

Runs an arbitrary symbolic computation, exposed to the user in SAT mode

NB. For a version which generalizes over the underlying monad, see runSMTWith

Module exports

The SBV library exports the following modules wholesale, as user programs will have to import these modules to make any sensible use of the SBV functionality.

module Data.Bits

module Data.Word

module Data.Int

module Data.Ratio