Data.SBV.Dynamic

Dynamically typed low-level API to the SBV library, for users who want to generate symbolic values at run-time. Note that with this API it is possible to create terms that are not type correct; use at your own risk!

Programming with symbolic values

Symbolic types

Abstract symbolic value type

data SVal

The Symbolic value. Either a constant (Left) or a symbolic value (Right Cached). Note that caching is essential for making sure sharing is preserved.

Instances

Eq SVal

This instance is only defined so that we can define an instance for Bits. == and /= simply throw an error.

Defined in Data.SBV.Core.Symbolic

Methods

(==) :: SVal -> SVal -> Bool

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

Show SVal

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> SVal -> ShowS

show :: SVal -> String

showList :: [SVal] -> ShowS

NFData SVal

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SVal -> ()

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

isUserSort :: 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

ArithOverflow SVal

Defined in Data.SBV.Tools.Overflow

Methods

bvAddO :: SVal -> SVal -> (SBool, SBool)

bvSubO :: SVal -> SVal -> (SBool, SBool)

bvMulO :: SVal -> SVal -> (SBool, SBool)

bvMulOFast :: SVal -> SVal -> (SBool, SBool)

bvDivO :: SVal -> SVal -> (SBool, SBool)

bvNegO :: SVal -> (SBool, SBool)

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

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

default kindOf :: (Read a, Data a) => 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

isUserSort :: 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

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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: () -> 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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 HumanHeightInCm

Symbolic instance simply follows the underlying type, just like Metres.

Defined in Documentation.SBV.Examples.Misc.Newtypes

Methods

kindOf :: HumanHeightInCm -> Kind

hasSign :: HumanHeightInCm -> Bool

intSizeOf :: HumanHeightInCm -> Int

isBoolean :: HumanHeightInCm -> Bool

isBounded :: HumanHeightInCm -> Bool

isReal :: HumanHeightInCm -> Bool

isFloat :: HumanHeightInCm -> Bool

isDouble :: HumanHeightInCm -> Bool

isUnbounded :: HumanHeightInCm -> Bool

isUserSort :: HumanHeightInCm -> Bool

isChar :: HumanHeightInCm -> Bool

isString :: HumanHeightInCm -> Bool

isList :: HumanHeightInCm -> Bool

isSet :: HumanHeightInCm -> Bool

isTuple :: HumanHeightInCm -> Bool

isMaybe :: HumanHeightInCm -> Bool

isEither :: HumanHeightInCm -> Bool

showType :: HumanHeightInCm -> String

HasKind Metres

To use Metres symbolically, we associate it with the underlying symbolic type's kind.

Defined in Documentation.SBV.Examples.Misc.Newtypes

Methods

kindOf :: Metres -> Kind

hasSign :: Metres -> Bool

intSizeOf :: Metres -> Int

isBoolean :: Metres -> Bool

isBounded :: Metres -> Bool

isReal :: Metres -> Bool

isFloat :: Metres -> Bool

isDouble :: Metres -> Bool

isUnbounded :: Metres -> Bool

isUserSort :: Metres -> Bool

isChar :: Metres -> Bool

isString :: Metres -> Bool

isList :: Metres -> Bool

isSet :: Metres -> Bool

isTuple :: Metres -> Bool

isMaybe :: Metres -> Bool

isEither :: Metres -> Bool

showType :: Metres -> 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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 Role

Defined in Documentation.SBV.Examples.Puzzles.Murder

Methods

kindOf :: Role -> Kind

hasSign :: Role -> Bool

intSizeOf :: Role -> Int

isBoolean :: Role -> Bool

isBounded :: Role -> Bool

isReal :: Role -> Bool

isFloat :: Role -> Bool

isDouble :: Role -> Bool

isUnbounded :: Role -> Bool

isUserSort :: Role -> Bool

isChar :: Role -> Bool

isString :: Role -> Bool

isList :: Role -> Bool

isSet :: Role -> Bool

isTuple :: Role -> Bool

isMaybe :: Role -> Bool

isEither :: Role -> Bool

showType :: Role -> String

HasKind Sex

Defined in Documentation.SBV.Examples.Puzzles.Murder

Methods

kindOf :: Sex -> Kind

hasSign :: Sex -> Bool

intSizeOf :: Sex -> Int

isBoolean :: Sex -> Bool

isBounded :: Sex -> Bool

isReal :: Sex -> Bool

isFloat :: Sex -> Bool

isDouble :: Sex -> Bool

isUnbounded :: Sex -> Bool

isUserSort :: Sex -> Bool

isChar :: Sex -> Bool

isString :: Sex -> Bool

isList :: Sex -> Bool

isSet :: Sex -> Bool

isTuple :: Sex -> Bool

isMaybe :: Sex -> Bool

isEither :: Sex -> Bool

showType :: Sex -> String

HasKind Location

Defined in Documentation.SBV.Examples.Puzzles.Murder

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

isUserSort :: 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 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

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

isUserSort :: 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

isUserSort :: [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

isUserSort :: 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

isUserSort :: 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

isUserSort :: 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

(KnownNat n, IsNonZero n) => HasKind (IntN n)

IntN has a kind

Defined in Data.SBV.Core.Sized

Methods

kindOf :: IntN n -> Kind

hasSign :: IntN n -> Bool

intSizeOf :: IntN n -> Int

isBoolean :: IntN n -> Bool

isBounded :: IntN n -> Bool

isReal :: IntN n -> Bool

isFloat :: IntN n -> Bool

isDouble :: IntN n -> Bool

isUnbounded :: IntN n -> Bool

isUserSort :: IntN n -> Bool

isChar :: IntN n -> Bool

isString :: IntN n -> Bool

isList :: IntN n -> Bool

isSet :: IntN n -> Bool

isTuple :: IntN n -> Bool

isMaybe :: IntN n -> Bool

isEither :: IntN n -> Bool

showType :: IntN n -> String

(KnownNat n, IsNonZero n) => HasKind (WordN n)

WordN has a kind

Defined in Data.SBV.Core.Sized

Methods

kindOf :: WordN n -> Kind

hasSign :: WordN n -> Bool

intSizeOf :: WordN n -> Int

isBoolean :: WordN n -> Bool

isBounded :: WordN n -> Bool

isReal :: WordN n -> Bool

isFloat :: WordN n -> Bool

isDouble :: WordN n -> Bool

isUnbounded :: WordN n -> Bool

isUserSort :: WordN n -> Bool

isChar :: WordN n -> Bool

isString :: WordN n -> Bool

isList :: WordN n -> Bool

isSet :: WordN n -> Bool

isTuple :: WordN n -> Bool

isMaybe :: WordN n -> Bool

isEither :: WordN n -> Bool

showType :: WordN n -> 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

isUserSort :: 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

isUserSort :: (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

isUserSort :: 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

isUserSort :: (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

isUserSort :: (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

isUserSort :: (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

isUserSort :: (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

isUserSort :: (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

isUserSort :: (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

KUserSort String (Maybe [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

Data Kind

Defined in Data.SBV.Core.Kind

Methods

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

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

toConstr :: Kind -> Constr

dataTypeOf :: Kind -> DataType

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

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

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

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

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

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

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

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

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

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

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 KUserSort, 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

isUserSort :: 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

data CV

CV represents a concrete word of a fixed size: For signed words, the most significant digit is considered to be the sign.

Constructors

CV

Fields

• _cvKind :: !Kind
• cvVal :: !CVal

Instances

Eq CV

Defined in Data.SBV.Core.Concrete

Methods

(==) :: CV -> CV -> Bool

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

Ord CV

Defined in Data.SBV.Core.Concrete

Methods

compare :: CV -> CV -> Ordering

(<) :: CV -> CV -> Bool

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

(>) :: CV -> CV -> Bool

(>=) :: CV -> CV -> Bool

max :: CV -> CV -> CV

min :: CV -> CV -> CV

Show CV

Show instance for CV.

Defined in Data.SBV.Core.Concrete

Methods

showsPrec :: Int -> CV -> ShowS

show :: CV -> String

showList :: [CV] -> ShowS

NFData CV

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: CV -> ()

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

isUserSort :: 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

PrettyNum CV

Defined in Data.SBV.Utils.PrettyNum

Methods

hexS :: CV -> String

binS :: CV -> String

hexP :: CV -> String

binP :: CV -> String

hex :: CV -> String

bin :: CV -> String

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])

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

data CVal

A constant value

Constructors

CAlgReal !AlgReal

Algebraic real

CInteger !Integer

Bit-vector/unbounded integer

CFloat !Float

Float

CDouble !Double

Double

CChar !Char

Character

CString !String

String

CList ![CVal]

List

CSet !(RCSet CVal)

Set. Can be regular or complemented.

CUserSort !(Maybe Int, String)

Value of an uninterpreted/user kind. The Maybe Int shows index position for enumerations

CTuple ![CVal]

Tuple

CMaybe !(Maybe CVal)

Maybe

CEither !(Either CVal CVal)

Disjoint union

Instances

Eq CVal

Eq instance for CVVal. Note that we cannot simply derive Eq/Ord, since CVAlgReal doesn't have proper instances for these when values are infinitely precise reals. However, we do need a structural eq/ord for Map indexes; so define custom ones here:

Defined in Data.SBV.Core.Concrete

Methods

(==) :: CVal -> CVal -> Bool

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

Ord CVal

Ord instance for VWVal. Same comments as the Eq instance why this cannot be derived.

Defined in Data.SBV.Core.Concrete

Methods

compare :: CVal -> CVal -> Ordering

(<) :: CVal -> CVal -> Bool

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

(>) :: CVal -> CVal -> Bool

(>=) :: CVal -> CVal -> Bool

max :: CVal -> CVal -> CVal

min :: CVal -> CVal -> CVal

cvToBool :: CV -> Bool

Convert a CV to a Haskell boolean (NB. Assumes input is well-kinded)

SMT Arrays of symbolic values

data SArr

Arrays in terms of SMT-Lib arrays

readSArr :: SArr -> SVal -> SVal

Read the array element at a

writeSArr :: SArr -> SVal -> SVal -> SArr

Update the element at a to be b

mergeSArr :: SVal -> SArr -> SArr -> SArr

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

newSArr :: State -> (Kind, Kind) -> (Int -> String) -> Maybe SVal -> IO SArr

Create a named new array

eqSArr :: SArr -> SArr -> SVal

Compare two arrays for equality

Functional arrays of symbolic values

data SFunArr

Arrays managed internally

readSFunArr :: SFunArr -> SVal -> SVal

Read the array element at a. For efficiency purposes, we create a memo-table as we go along, as otherwise we suffer significant performance penalties. See: http://github.com/LeventErkok/sbv/issues/402 and http://github.com/LeventErkok/sbv/issues/396.

writeSFunArr :: SFunArr -> SVal -> SVal -> SFunArr

Update the element at address to be b

mergeSFunArr :: SVal -> SFunArr -> SFunArr -> SFunArr

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

newSFunArr :: State -> (Kind, Kind) -> (Int -> String) -> Maybe SVal -> IO SFunArr

Create a named new array

Creating a symbolic variable

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 Quantifier

Quantifiers: forall or exists. Note that we allow arbitrary nestings.

Constructors

ALL

EX

Instances

Eq Quantifier

Defined in Data.SBV.Core.Symbolic

Methods

(==) :: Quantifier -> Quantifier -> Bool

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

Show Quantifier

Show instance for Quantifier

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> Quantifier -> ShowS

show :: Quantifier -> String

showList :: [Quantifier] -> ShowS

NFData Quantifier

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: Quantifier -> ()

svMkSymVar :: VarContext -> Kind -> Maybe String -> State -> IO SVal

Create a symbolic value, based on the quantifier we have. If an explicit quantifier is given, we just use that. If not, then we pick the quantifier appropriately based on the run-mode. randomCV is used for generating random values for this variable when used for quickCheck or genTest purposes.

sWordN :: MonadSymbolic m => Int -> String -> m SVal

Generalization of sWordN

sWordN_ :: MonadSymbolic m => Int -> m SVal

Generalization of sWordN_

sIntN :: MonadSymbolic m => Int -> String -> m SVal

Generalization of sIntN

sIntN_ :: MonadSymbolic m => Int -> m SVal

Generalization of sIntN_

Operations on symbolic values

Boolean literals

svTrue :: SVal

Boolean True.

svFalse :: SVal

Boolean False.

svBool :: Bool -> SVal

Convert from a Boolean.

svAsBool :: SVal -> Maybe Bool

Extract a bool, by properly interpreting the integer stored.

Integer literals

svInteger :: Kind -> Integer -> SVal

Convert from an Integer.

svAsInteger :: SVal -> Maybe Integer

Extract an integer from a concrete value.

Float literals

svFloat :: Float -> SVal

Convert from a Float

svDouble :: Double -> SVal

Convert from a Float

Algebraic reals (only from rationals)

svReal :: Rational -> SVal

Convert from a Rational

svNumerator :: SVal -> Maybe Integer

Grab the numerator of an SReal, if available

svDenominator :: SVal -> Maybe Integer

Grab the denominator of an SReal, if available

Symbolic equality

svEqual :: SVal -> SVal -> SVal

Equality.

svNotEqual :: SVal -> SVal -> SVal

Inequality.

Constructing concrete lists

svEnumFromThenTo :: SVal -> Maybe SVal -> SVal -> Maybe [SVal]

Constructing [x, y, .. z] and [x .. y]. Only works when all arguments are concrete and integral and the result is guaranteed finite Note that the it isn't "obviously" clear why the following works; after all we're doing the construction over Integer's and mapping it back to other types such as SIntN/SWordN. The reason is that the values we receive are guaranteed to be in their domains; and thus the lifting to Integers preserves the bounds; and then going back is just fine. So, things like [1, 5 .. 200] :: [SInt8] work just fine (end evaluate to empty list), since we see [1, 5 .. -56] in the Integer domain. Also note the explicit check for s /= f below to make sure we don't stutter and produce an infinite list.

Symbolic ordering

svLessThan :: SVal -> SVal -> SVal

Less than.

svGreaterThan :: SVal -> SVal -> SVal

Greater than.

svLessEq :: SVal -> SVal -> SVal

Less than or equal to.

svGreaterEq :: SVal -> SVal -> SVal

Greater than or equal to.

svStructuralLessThan :: SVal -> SVal -> SVal

Given a composite structure, figure out how to compare for less than

Arithmetic operations

svPlus :: SVal -> SVal -> SVal

Addition.

svTimes :: SVal -> SVal -> SVal

Multiplication.

svMinus :: SVal -> SVal -> SVal

Subtraction.

svUNeg :: SVal -> SVal

Unary minus.

svAbs :: SVal -> SVal

Absolute value.

svDivide :: SVal -> SVal -> SVal

Division.

svQuot :: SVal -> SVal -> SVal

Quotient: Overloaded operation whose meaning depends on the kind at which it is used: For unbounded integers, it corresponds to the SMT-Lib "div" operator (Euclidean division, which always has a non-negative remainder). For unsigned bitvectors, it is "bvudiv"; and for signed bitvectors it is "bvsdiv", which rounds toward zero. Division by 0 is defined s.t. x/0 = 0, which holds even when x itself is 0.

svRem :: SVal -> SVal -> SVal

Remainder: Overloaded operation whose meaning depends on the kind at which it is used: For unbounded integers, it corresponds to the SMT-Lib "mod" operator (always non-negative). For unsigned bitvectors, it is "bvurem"; and for signed bitvectors it is "bvsrem", which rounds toward zero (sign of remainder matches that of x). Division by 0 is defined s.t. x/0 = 0, which holds even when x itself is 0.

svQuotRem :: SVal -> SVal -> (SVal, SVal)

Combination of quot and rem

svExp :: SVal -> SVal -> SVal

Exponentiation.

svAddConstant :: Integral a => SVal -> a -> SVal

Add a constant value:

svIncrement :: SVal -> SVal

Increment:

svDecrement :: SVal -> SVal

Decrement:

Logical operations

svAnd :: SVal -> SVal -> SVal

Bitwise and.

svOr :: SVal -> SVal -> SVal

Bitwise or.

svXOr :: SVal -> SVal -> SVal

Bitwise xor.

svNot :: SVal -> SVal

Bitwise complement.

svShl :: SVal -> Int -> SVal

Shift left by a constant amount. Translates to the "bvshl" operation in SMT-Lib.

NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.

svShr :: SVal -> Int -> SVal

Shift right by a constant amount. Translates to either "bvlshr" (logical shift right) or "bvashr" (arithmetic shift right) in SMT-Lib, depending on whether x is a signed bitvector.

NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.

svRol :: SVal -> Int -> SVal

Rotate-left, by a constant.

NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.

svRor :: SVal -> Int -> SVal

Rotate-right, by a constant.

NB. Haskell spec says the behavior is undefined if the shift amount is negative. We arbitrarily return the value unchanged if this is the case.

Splitting, joining, and extending

svExtract :: Int -> Int -> SVal -> SVal

Extract bit-sequences.

svJoin :: SVal -> SVal -> SVal

Join two words, by concatenating

Sign-casting

svSign :: SVal -> SVal

Convert a symbolic bitvector from unsigned to signed.

svUnsign :: SVal -> SVal

Convert a symbolic bitvector from signed to unsigned.

Numeric conversions

svFromIntegral :: Kind -> SVal -> SVal

Convert a symbolic bitvector from one integral kind to another.

Indexed lookups

svSelect :: [SVal] -> SVal -> SVal -> SVal

Total indexing operation. svSelect xs default index is intuitively the same as xs !! index, except it evaluates to default if index overflows. Translates to SMT-Lib tables.

Word-level operations

svToWord1 :: SVal -> SVal

Convert an SVal from kind Bool to an unsigned bitvector of size 1.

svFromWord1 :: SVal -> SVal

Convert an SVal from a bitvector of size 1 (signed or unsigned) to kind Bool.

svTestBit :: SVal -> Int -> SVal

Test the value of a bit. Note that we do an extract here as opposed to masking and checking against zero, as we found extraction to be much faster with large bit-vectors.

svSetBit :: SVal -> Int -> SVal

Set a given bit at index

svShiftLeft :: SVal -> SVal -> SVal

Generalization of svShl, where the shift-amount is symbolic.

svShiftRight :: SVal -> SVal -> SVal

Generalization of svShr, where the shift-amount is symbolic.

NB. If the shiftee is signed, then this is an arithmetic shift; otherwise it's logical.

svRotateLeft :: SVal -> SVal -> SVal

Generalization of svRol, where the rotation amount is symbolic. If the first argument is not bounded, then the this is the same as shift.

svRotateRight :: SVal -> SVal -> SVal

Generalization of svRor, where the rotation amount is symbolic. If the first argument is not bounded, then the this is the same as shift.

svBarrelRotateLeft :: SVal -> SVal -> SVal

A variant of svRotateLeft that uses a barrel-rotate design, which can lead to better verification code. Only works when both arguments are finite and the second argument is unsigned.

svBarrelRotateRight :: SVal -> SVal -> SVal

A variant of svRotateLeft that uses a barrel-rotate design, which can lead to better verification code. Only works when both arguments are finite and the second argument is unsigned.

svWordFromBE :: [SVal] -> SVal

Un-bit-blast from little-endian representation to a word of the right size. The input is assumed to be unsigned.

svWordFromLE :: [SVal] -> SVal

Un-bit-blast from big-endian representation to a word of the right size. The input is assumed to be unsigned.

svBlastLE :: SVal -> [SVal]

Bit-blast: Little-endian. Assumes the input is a bit-vector.

svBlastBE :: SVal -> [SVal]

Bit-blast: Big-endian. Assumes the input is a bit-vector.

Conditionals: Mergeable values

svIte :: SVal -> SVal -> SVal -> SVal

If-then-else. This one will force branches.

svLazyIte :: Kind -> SVal -> SVal -> SVal -> SVal

Lazy If-then-else. This one will delay forcing the branches unless it's really necessary.

svSymbolicMerge :: Kind -> Bool -> SVal -> SVal -> SVal -> SVal

Merge two symbolic values, at kind k, possibly force'ing the branches to make sure they do not evaluate to the same result.

Uninterpreted sorts, constants, and functions

svUninterpreted :: Kind -> String -> Maybe [String] -> [SVal] -> SVal

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.

Properties, proofs, and satisfiability

Proving properties

proveWith :: SMTConfig -> Symbolic SVal -> IO ThmResult

Proves the predicate using the given SMT-solver

Checking satisfiability

satWith :: SMTConfig -> Symbolic SVal -> IO SatResult

Find a satisfying assignment using the given SMT-solver

allSatWith :: SMTConfig -> Symbolic SVal -> IO AllSatResult

Find all satisfying assignments using the given SMT-solver

Checking safety

safeWith :: SMTConfig -> Symbolic SVal -> IO [SafeResult]

Check safety using the given SMT-solver

Proving properties using multiple solvers

proveWithAll :: [SMTConfig] -> Symbolic SVal -> 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 :: [SMTConfig] -> Symbolic SVal -> 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.

satWithAll :: [SMTConfig] -> Symbolic SVal -> 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 :: [SMTConfig] -> Symbolic SVal -> 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.

Proving properties using multiple threads

proveConcurrentWithAll :: SMTConfig -> Symbolic SVal -> [Query SVal] -> IO [(Solver, NominalDiffTime, ThmResult)]

Prove a property with query mode using multiple threads. Each query computation will spawn a thread and a unique instance of your solver to run asynchronously. The Symbolic SVal is duplicated for each thread. This function will block until all child threads return.

proveConcurrentWithAny :: SMTConfig -> Symbolic SVal -> [Query SVal] -> IO (Solver, NominalDiffTime, ThmResult)

Prove a property with query mode using multiple threads. Each query computation will spawn a thread and a unique instance of your solver to run asynchronously. The Symbolic SVal is duplicated for each thread. This function will return the first query computation that completes, killing the others.

satConcurrentWithAny :: SMTConfig -> [Query b] -> Symbolic SVal -> IO (Solver, NominalDiffTime, SatResult)

Find a satisfying assignment to a property with multiple threads in query mode. The Symbolic SVal represents what is known to all child query threads. Each query thread will spawn a unique instance of the solver. Only the first one to finish will be returned and the other threads will be killed.

satConcurrentWithAll :: SMTConfig -> [Query b] -> Symbolic SVal -> IO [(Solver, NominalDiffTime, SatResult)]

Find a satisfying assignment to a property with multiple threads in query mode. The Symbolic SVal represents what is known to all child query threads. Each query thread will spawn a unique instance of the solver. This function will block until all child threads have completed.

Quick-check

svQuickCheck :: Symbolic SVal -> IO Bool

Dynamic variant of quick-check

Model extraction

Inspecting proof results

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))

data AllSatResult

An allSat call results in a AllSatResult

Constructors

AllSatResult

Fields

• allSatMaxModelCountReached :: Bool

  Did we reach the user given model count limit?

• allSatHasPrefixExistentials :: Bool

  Were there quantifiers in the problem (unique upto prefix existentials)

• allSatSolverReturnedUnknown :: Bool

  Did the solver report unknown at the end?

• allSatSolverReturnedDSat :: Bool

  Did the solver report delta-satisfiable at the end?

• allSatResults :: [SMTResult]

  All satisfying models

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

DeltaSat SMTConfig (Maybe String) SMTModel

Delta satisfiable with queried string if available and 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))

Programmable model extraction

genParse :: Integral a => Kind -> [CV] -> Maybe (a, [CV])

Parse a signed/sized value from a sequence of CVs

getModelAssignment :: SMTResult -> Either String (Bool, [CV])

Extract 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 :: SMTResult -> 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.

SMT Interface: Configurations and solvers

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 :: Text -> 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

• dsatPrecision :: Maybe Double

  Delta-sat precision

• solver :: SMTSolver

  The actual SMT solver.

• extraArgs :: [String]

  Extra command line arguments to pass to the 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

Show SMTConfig

We show the name of the solver for the config. Arguably this is misleading, but better than nothing.

Defined in Data.SBV.Core.Symbolic

Methods

showsPrec :: Int -> SMTConfig -> ShowS

show :: SMTConfig -> String

showList :: [SMTConfig] -> ShowS

NFData SMTConfig

Defined in Data.SBV.Core.Symbolic

Methods

rnf :: SMTConfig -> ()

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

ABC

Boolector

CVC4

DReal

MathSAT

Yices

Z3

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

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.

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.

getAvailableSolvers :: IO [SMTConfig]

Return the known available solver configs, installed on your machine.

Symbolic computations

outputSVal :: MonadSymbolic m => SVal -> m ()

Generalization of outputSVal

Code generation from symbolic programs

data SBVCodeGen a

The code-generation monad. Allows for precise layout of input values reference parameters (for returning composite values in languages such as C), and return values.

Instances

Monad SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

(>>=) :: SBVCodeGen a -> (a -> SBVCodeGen b) -> SBVCodeGen b

(>>) :: SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen b

return :: a -> SBVCodeGen a

Functor SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

fmap :: (a -> b) -> SBVCodeGen a -> SBVCodeGen b

(<$) :: a -> SBVCodeGen b -> SBVCodeGen a

MonadFail SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

fail :: String -> SBVCodeGen a

Applicative SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

pure :: a -> SBVCodeGen a

(<*>) :: SBVCodeGen (a -> b) -> SBVCodeGen a -> SBVCodeGen b

liftA2 :: (a -> b -> c) -> SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen c

(*>) :: SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen b

(<*) :: SBVCodeGen a -> SBVCodeGen b -> SBVCodeGen a

MonadIO SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

liftIO :: IO a -> SBVCodeGen a

MonadSymbolic SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

symbolicEnv :: SBVCodeGen State

MonadState CgState SBVCodeGen

Defined in Data.SBV.Compilers.CodeGen

Methods

get :: SBVCodeGen CgState

put :: CgState -> SBVCodeGen ()

state :: (CgState -> (a, CgState)) -> SBVCodeGen a

Setting code-generation options

cgPerformRTCs :: Bool -> SBVCodeGen ()

Sets RTC (run-time-checks) for index-out-of-bounds, shift-with-large value etc. on/off. Default: False.

cgSetDriverValues :: [Integer] -> SBVCodeGen ()

Sets driver program run time values, useful for generating programs with fixed drivers for testing. Default: None, i.e., use random values.

cgGenerateDriver :: Bool -> SBVCodeGen ()

Should we generate a driver program? Default: True. When a library is generated, it will have a driver if any of the constituent functions has a driver. (See compileToCLib.)

cgGenerateMakefile :: Bool -> SBVCodeGen ()

Should we generate a Makefile? Default: True.

Designating inputs

svCgInput :: Kind -> String -> SBVCodeGen SVal

Creates an atomic input in the generated code.

svCgInputArr :: Kind -> Int -> String -> SBVCodeGen [SVal]

Creates an array input in the generated code.

Designating outputs

svCgOutput :: String -> SVal -> SBVCodeGen ()

Creates an atomic output in the generated code.

svCgOutputArr :: String -> [SVal] -> SBVCodeGen ()

Creates an array output in the generated code.

Designating return values

svCgReturn :: SVal -> SBVCodeGen ()

Creates a returned (unnamed) value in the generated code.

svCgReturnArr :: [SVal] -> SBVCodeGen ()

Creates a returned (unnamed) array value in the generated code.

Code generation with uninterpreted functions

cgAddPrototype :: [String] -> SBVCodeGen ()

Adds the given lines to the header file generated, useful for generating programs with uninterpreted functions.

cgAddDecl :: [String] -> SBVCodeGen ()

Adds the given lines to the program file generated, useful for generating programs with uninterpreted functions.

cgAddLDFlags :: [String] -> SBVCodeGen ()

Adds the given words to the compiler options in the generated Makefile, useful for linking extra stuff in.

cgIgnoreSAssert :: Bool -> SBVCodeGen ()

Ignore assertions (those generated by sAssert calls) in the generated C code

Code generation with SInteger and SReal types

cgIntegerSize :: Int -> SBVCodeGen ()

Sets number of bits to be used for representing the SInteger type in the generated C code. The argument must be one of 8, 16, 32, or 64. Note that this is essentially unsafe as the semantics of unbounded Haskell integers becomes reduced to the corresponding bit size, as typical in most C implementations.

cgSRealType :: CgSRealType -> SBVCodeGen ()

Sets the C type to be used for representing the SReal type in the generated C code. The setting can be one of C's "float", "double", or "long double", types, depending on the precision needed. Note that this is essentially unsafe as the semantics of infinite precision SReal values becomes reduced to the corresponding floating point type in C, and hence it is subject to rounding errors.

data CgSRealType

Possible mappings for the SReal type when translated to C. Used in conjunction with the function cgSRealType. Note that the particular characteristics of the mapped types depend on the platform and the compiler used for compiling the generated C program. See http://en.wikipedia.org/wiki/C_data_types for details.

Constructors

CgFloat

float

CgDouble

double

CgLongDouble

long double

Instances

Eq CgSRealType

Defined in Data.SBV.Compilers.CodeGen

Methods

(==) :: CgSRealType -> CgSRealType -> Bool

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

Show CgSRealType

Defined in Data.SBV.Compilers.CodeGen

Methods

showsPrec :: Int -> CgSRealType -> ShowS

show :: CgSRealType -> String

showList :: [CgSRealType] -> ShowS

Compilation to C

compileToC :: Maybe FilePath -> String -> SBVCodeGen a -> IO a

Given a symbolic computation, render it as an equivalent collection of files that make up a C program:

• The first argument is the directory name under which the files will be saved. To save files in the current directory pass Just ".". Use Nothing for printing to stdout.
• The second argument is the name of the C function to generate.
• The final argument is the function to be compiled.

Compilation will also generate a Makefile, a header file, and a driver (test) program, etc. As a result, we return whatever the code-gen function returns. Most uses should simply have () as the return type here, but the value can be useful if you want to chain the result of one compilation act to the next.

compileToCLib :: Maybe FilePath -> String -> [(String, SBVCodeGen a)] -> IO [a]

Create code to generate a library archive (.a) from given symbolic functions. Useful when generating code from multiple functions that work together as a library.

• The first argument is the directory name under which the files will be saved. To save files in the current directory pass Just ".". Use Nothing for printing to stdout.
• The second argument is the name of the archive to generate.
• The third argument is the list of functions to include, in the form of function-name/code pairs, similar to the second and third arguments of compileToC, except in a list.

Compilation to SMTLib

generateSMTBenchmark :: Bool -> Symbolic SVal -> IO String

Create SMT-Lib benchmarks. The first argument is the basename of the file, we will automatically add ".smt2" per SMT-Lib2 convention. 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.