| Copyright | (c) Levent Erkok |
|---|---|
| License | BSD3 |
| Maintainer | erkokl@gmail.com |
| Stability | experimental |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.SBV.Control
Contents
- User queries
- Create a fresh variable
- Create a fresh array
- Checking satisfiability
- Querying the solver
- Getting solver information
- Entering and exiting assertion stack
- Higher level tactics
- Resetting the solver state
- Constructing assignments
- Terminating the query
- Controlling the solver behavior
- Miscellaneous
- Solver options
Description
Control sublanguage for interacting with SMT solvers.
Synopsis
- data Query a
- query :: Query a -> Symbolic a
- freshVar_ :: forall a. SymWord a => Query (SBV a)
- freshVar :: forall a. SymWord a => String -> Query (SBV a)
- freshArray_ :: (SymArray array, HasKind a, HasKind b) => Maybe (SBV b) -> Query (array a b)
- freshArray :: (SymArray array, HasKind a, HasKind b) => String -> Maybe (SBV b) -> Query (array a b)
- data CheckSatResult
- checkSat :: Query CheckSatResult
- checkSatUsing :: String -> Query CheckSatResult
- checkSatAssuming :: [SBool] -> Query CheckSatResult
- checkSatAssumingWithUnsatisfiableSet :: [SBool] -> Query (CheckSatResult, Maybe [SBool])
- class SMTValue a where
- getValue :: SMTValue a => SBV a -> Query a
- getUninterpretedValue :: HasKind a => SBV a -> Query String
- getModel :: Query SMTModel
- getAssignment :: Query [(String, Bool)]
- getSMTResult :: Query SMTResult
- getUnknownReason :: Query SMTReasonUnknown
- getUnsatCore :: Query [String]
- getProof :: Query String
- getInterpolant :: [String] -> Query String
- getAssertions :: Query [String]
- data SMTInfoFlag
- data SMTErrorBehavior
- data SMTInfoResponse
- getInfo :: SMTInfoFlag -> Query SMTInfoResponse
- getOption :: (a -> SMTOption) -> Query (Maybe SMTOption)
- getAssertionStackDepth :: Query Int
- push :: Int -> Query ()
- pop :: Int -> Query ()
- inNewAssertionStack :: Query a -> Query a
- caseSplit :: Bool -> [(String, SBool)] -> Query (Maybe (String, SMTResult))
- resetAssertions :: Query ()
- (|->) :: SymWord a => SBV a -> a -> Assignment
- mkSMTResult :: [Assignment] -> Query SMTResult
- exit :: Query ()
- ignoreExitCode :: SMTConfig -> Bool
- timeout :: Int -> Query a -> Query a
- queryDebug :: [String] -> Query ()
- echo :: String -> Query ()
- io :: IO a -> Query a
- data SMTOption
- = DiagnosticOutputChannel FilePath
- | ProduceAssertions Bool
- | ProduceAssignments Bool
- | ProduceProofs Bool
- | ProduceInterpolants Bool
- | ProduceUnsatAssumptions Bool
- | ProduceUnsatCores Bool
- | RandomSeed Integer
- | ReproducibleResourceLimit Integer
- | SMTVerbosity Integer
- | OptionKeyword String [String]
- | SetLogic Logic
- | SetInfo String [String]
Documentation
In certain cases, the user might want to take over the communication with the solver, programmatically querying the engine and issuing commands accordingly. Queries can be extremely powerful as they allow direct control of the solver. Here's a simple example:
module Test where
import Data.SBV
import Data.SBV.Control -- queries require this module to be imported!
test :: Symbolic (Maybe (Integer, Integer))
test = do x <- sInteger "x" -- a free variable named "x"
y <- sInteger "y" -- a free variable named "y"
-- require the sum to be 10
constrain $ x + y .== 10
-- Go into the Query mode
query $ do
-- Query the solver: Are the constraints satisfiable?
cs <- checkSat
case cs of
Unk -> error "Solver said unknown!"
Unsat -> return Nothing -- no solution!
Sat -> -- Query the values:
do xv <- getValue x
yv <- getValue y
io $ putStrLn $ "Solver returned: " ++ show (xv, yv)
-- We can now add new constraints,
-- Or perform arbitrary computations and tell
-- the solver anything we want!
constrain $ x .> literal xv + literal yv
-- call checkSat again
csNew <- checkSat
case csNew of
Unk -> error "Solver said unknown!"
Unsat -> return Nothing
Sat -> do xv2 <- getValue x
yv2 <- getValue y
return $ Just (xv2, yv2)
Note the type of test, it returns an optional pair of integers in the Symbolic monad. We turn
it into an IO value with the runSMT function: (There's also runSMTWith that uses a user specified
solver instead of the default.)
pair :: IO (Maybe (Integer, Integer))
pair = runSMT test
When run, this can return:
*Test> pair Solver returned: (10,0) Just (11,-1)
demonstrating that the user has full contact with the solver and can guide it as the program executes. SBV provides access to many SMTLib features in the query mode, as exported from this very module.
For other examples see:
- Documentation.SBV.Examples.Queries.AllSat: Simulating SBV's
allSatusing queries. - Documentation.SBV.Examples.Queries.CaseSplit: Performing a case-split during a query.
- Documentation.SBV.Examples.Queries.Enums: Using enumerations in queries.
- Documentation.SBV.Examples.Queries.FourFours: Solution to a fun arithmetic puzzle, coded using queries.
- Documentation.SBV.Examples.Queries.GuessNumber: The famous number guessing game.
- Documentation.SBV.Examples.Queries.UnsatCore: Extracting unsat-cores using queries.
- Documentation.SBV.Examples.Queries.Interpolants: Extracting interpolants using queries.
User queries
A query is a user-guided mechanism to directly communicate and extract results from the solver.
Instances
| Monad Query Source # | |
| Functor Query Source # | |
| Applicative Query Source # | |
| MonadIO Query Source # | |
Defined in Data.SBV.Core.Symbolic | |
| SolverContext Query Source # |
|
Defined in Data.SBV.Control.Utils Methods constrain :: SBool -> Query () Source # softConstrain :: SBool -> Query () Source # namedConstraint :: String -> SBool -> Query () Source # constrainWithAttribute :: [(String, String)] -> SBool -> Query () Source # setInfo :: String -> [String] -> Query () Source # setOption :: SMTOption -> Query () Source # setLogic :: Logic -> Query () Source # setTimeOut :: Integer -> Query () Source # | |
| MonadState State Query Source # | |
Create a fresh variable
freshVar_ :: forall a. SymWord a => Query (SBV a) Source #
Similar to freshVar, except creates unnamed variable.
freshVar :: forall a. SymWord a => String -> Query (SBV a) Source #
Create a fresh variable in query mode. You should prefer
creating input variables using sBool, sInt32, etc., which act
as primary inputs to the model and can be existential or universal.
Use freshVar only in query mode for anonymous temporary variables.
Such variables are always existential. Note that freshVar should hardly be
needed: Your input variables and symbolic expressions should suffice for
most major use cases.
Create a fresh array
freshArray_ :: (SymArray array, HasKind a, HasKind b) => Maybe (SBV b) -> Query (array a b) Source #
Similar to freshArray, except creates unnamed array.
freshArray :: (SymArray array, HasKind a, HasKind b) => String -> Maybe (SBV b) -> Query (array a b) Source #
Create a fresh array in query mode. Again, you should prefer
creating arrays before the queries start using newArray, but this
method can come in handy in occasional cases where you need a new array
after you start the query based interaction.
Checking satisfiability
data CheckSatResult Source #
Result of a checkSat or checkSatAssuming call.
Constructors
| Sat | Satisfiable: A model is available, which can be queried with |
| Unsat | Unsatisfiable: No model is available. Unsat cores might be obtained via |
| Unk | Unknown: Use |
Instances
| Eq CheckSatResult Source # | |
Defined in Data.SBV.Control.Types Methods (==) :: CheckSatResult -> CheckSatResult -> Bool # (/=) :: CheckSatResult -> CheckSatResult -> Bool # | |
| Show CheckSatResult Source # | |
Defined in Data.SBV.Control.Types Methods showsPrec :: Int -> CheckSatResult -> ShowS # show :: CheckSatResult -> String # showList :: [CheckSatResult] -> ShowS # | |
checkSat :: Query CheckSatResult Source #
Check for satisfiability.
checkSatUsing :: String -> Query CheckSatResult Source #
Check for satisfiability with a custom check-sat-using command.
checkSatAssuming :: [SBool] -> Query CheckSatResult Source #
Check for satisfiability, under the given conditions. Similar to checkSat except it allows making
further assumptions as captured by the first argument of booleans. (Also see checkSatAssumingWithUnsatisfiableSet
for a variant that returns the subset of the given assumptions that led to the Unsat conclusion.)
checkSatAssumingWithUnsatisfiableSet :: [SBool] -> Query (CheckSatResult, Maybe [SBool]) Source #
Check for satisfiability, under the given conditions. Returns the unsatisfiable
set of assumptions. Similar to checkSat except it allows making further assumptions
as captured by the first argument of booleans. If the result is Unsat, the user will
also receive a subset of the given assumptions that led to the Unsat conclusion. Note
that while this set will be a subset of the inputs, it is not necessarily guaranteed to be minimal.
You must have arranged for the production of unsat assumptions first via
setOption$ProduceUnsatAssumptionsTrue
for this call to not error out!
Usage note: getUnsatCore is usually easier to use than checkSatAssumingWithUnsatisfiableSet, as it
allows the use of named assertions, as obtained by namedAssert. If getUnsatCore
fills your needs, you should definitely prefer it over checkSatAssumingWithUnsatisfiableSet.
Querying the solver
Extracting values
class SMTValue a where Source #
A class which allows for sexpr-conversion to values
Instances
getUninterpretedValue :: HasKind a => SBV a -> Query String Source #
Get the value of an uninterpreted sort, as a String
getModel :: Query SMTModel Source #
Collect model values. It is implicitly assumed that we are in a check-sat
context. See getSMTResult for a variant that issues a check-sat first and
returns an SMTResult.
getAssignment :: Query [(String, Bool)] Source #
Retrieve the assignment. This is a lightweight version of getValue, where the
solver returns the truth value for all named subterms of type Bool.
You must have first arranged for assignments to be produced via
setOption$ProduceAssignmentsTrue
for this call to not error out!
getSMTResult :: Query SMTResult Source #
Issue check-sat and get an SMT Result out.
getUnknownReason :: Query SMTReasonUnknown Source #
Get the reason unknown. Only internally used.
Extracting the unsat core
getUnsatCore :: Query [String] Source #
Retrieve the unsat-core. Note you must have arranged for unsat cores to be produced first via
setOption$ProduceUnsatCoresTrue
for this call to not error out!
NB. There is no notion of a minimal unsat-core, in case unsatisfiability can be derived in multiple ways. Furthermore, Z3 does not guarantee that the generated unsat core does not have any redundant assertions either, as doing so can incur a performance penalty. (There might be assertions in the set that is not needed.) To ensure all the assertions in the core are relevant, use:
setOption$OptionKeyword":smt.core.minimize" ["true"]
Note that this only works with Z3.
Extracting a proof
getProof :: Query String Source #
Retrieve the proof. Note you must have arranged for proofs to be produced first via
setOption$ProduceProofsTrue
for this call to not error out!
A proof is simply a String, as returned by the solver. In the future, SBV might
provide a better datatype, depending on the use cases. Please get in touch if you
use this function and can suggest a better API.
Extracting interpolants
getInterpolant :: [String] -> Query String Source #
Retrieve an interpolant after an Unsat result is obtained. Note you must have arranged for
interpolants to be produced first via
setOption$ProduceInterpolantsTrue
for this call to not error out!
To get an interpolant for a pair of formulas A and B, use a constrainWithAttribute call to attach
interplation groups to A and B. Then call getInterpolant ["A"], assuming those are the names
you gave to the formulas in the A group.
An interpolant for A and B is a formula I such that:
A ==> I and B ==> not I
That is, it's evidence that A and B cannot be true together
since A implies I but B implies not I; establishing that A and B cannot
be satisfied at the same time. Furthermore, I will have only the symbols that are common
to A and B.
N.B. As of Z3 version 4.8.0; Z3 no longer supports interpolants. Use the MathSAT backend for extracting interpolants. See Documentation.SBV.Examples.Queries.Interpolants for an example.
Extracting assertions
getAssertions :: Query [String] Source #
Retrieve assertions. Note you must have arranged for assertions to be available first via
setOption$ProduceAssertionsTrue
for this call to not error out!
Note that the set of assertions returned is merely a list of strings, just like the
case for getProof. In the future, SBV might provide a better datatype, depending
on the use cases. Please get in touch if you use this function and can suggest
a better API.
Getting solver information
data SMTInfoFlag Source #
Collectable information from the solver.
Constructors
| AllStatistics | |
| AssertionStackLevels | |
| Authors | |
| ErrorBehavior | |
| Name | |
| ReasonUnknown | |
| Version | |
| InfoKeyword String |
Instances
| Show SMTInfoFlag Source # | |
Defined in Data.SBV.Control.Types Methods showsPrec :: Int -> SMTInfoFlag -> ShowS # show :: SMTInfoFlag -> String # showList :: [SMTInfoFlag] -> ShowS # | |
data SMTErrorBehavior Source #
Behavior of the solver for errors.
Constructors
| ErrorImmediateExit | |
| ErrorContinuedExecution |
Instances
| Show SMTErrorBehavior Source # | |
Defined in Data.SBV.Control.Types Methods showsPrec :: Int -> SMTErrorBehavior -> ShowS # show :: SMTErrorBehavior -> String # showList :: [SMTErrorBehavior] -> ShowS # | |
data SMTInfoResponse Source #
Collectable information from the solver.
Constructors
Instances
| Show SMTInfoResponse Source # | |
Defined in Data.SBV.Control.Types Methods showsPrec :: Int -> SMTInfoResponse -> ShowS # show :: SMTInfoResponse -> String # showList :: [SMTInfoResponse] -> ShowS # | |
getInfo :: SMTInfoFlag -> Query SMTInfoResponse Source #
Ask solver for info.
getOption :: (a -> SMTOption) -> Query (Maybe SMTOption) Source #
Retrieve the value of an 'SMTOption.' The curious function argument is on purpose here,
simply pass the constructor name. Example: the call getOption ProduceUnsatCoresNothing or Just (ProduceUnsatCores True) or Just (ProduceUnsatCores False).
Result will be Nothing if the solver does not support this option.
Entering and exiting assertion stack
push :: Int -> Query () Source #
Push the context, entering a new one. Pushes multiple levels if n > 1.
pop :: Int -> Query () Source #
Pop the context, exiting a new one. Pops multiple levels if n > 1. It's an error to pop levels that don't exist.
inNewAssertionStack :: Query a -> Query a Source #
Run the query in a new assertion stack. That is, we push the context, run the query commands, and pop it back.
Higher level tactics
caseSplit :: Bool -> [(String, SBool)] -> Query (Maybe (String, SMTResult)) Source #
Search for a result via a sequence of case-splits, guided by the user. If one of
the conditions lead to a satisfiable result, returns Just that result. If none of them
do, returns Nothing. Note that we automatically generate a coverage case and search
for it automatically as well. In that latter case, the string returned will be Coverage.
The first argument controls printing progress messages See Documentation.SBV.Examples.Queries.CaseSplit
for an example use case.
Resetting the solver state
resetAssertions :: Query () Source #
Reset the solver, by forgetting all the assertions. However, bindings are kept as is,
as opposed to reset. Use this variant to clean-up the solver state while leaving the bindings
intact. Pops all assertion levels. Declarations and definitions resulting from the setLogic
command are unaffected. Note that SBV implicitly uses global-declarations, so bindings will remain intact.
Constructing assignments
(|->) :: SymWord a => SBV a -> a -> Assignment infix 1 Source #
Make an assignment. The type Assignment is abstract, the result is typically passed
to mkSMTResult:
mkSMTResult [ a |-> 332
, b |-> 2.3
, c |-> True
]
End users should use getModel for automatically constructing models from the current solver state.
However, an explicit Assignment might be handy in complex scenarios where a model needs to be
created manually.
Terminating the query
mkSMTResult :: [Assignment] -> Query SMTResult Source #
Produce the query result from an assignment.
Exit the solver. This action will cause the solver to terminate. Needless to say, trying to communicate with the solver after issuing "exit" will simply fail.
Controlling the solver behavior
ignoreExitCode :: SMTConfig -> Bool Source #
If true, we shall ignore the exit code upon exit. Otherwise we require ExitSuccess.
timeout :: Int -> Query a -> Query a Source #
Timeout a query action, typically a command call to the underlying SMT solver.
The duration is in microseconds (1/10^6 seconds). If the duration
is negative, then no timeout is imposed. When specifying long timeouts, be careful not to exceed
maxBound :: Int. (On a 64 bit machine, this bound is practically infinite. But on a 32 bit
machine, it corresponds to about 36 minutes!)
Semantics: The call timeout n q causes the timeout value to be applied to all interactive calls that take place
as we execute the query q. That is, each call that happens during the execution of q gets a separate
time-out value, as opposed to one timeout value that limits the whole query. This is typically the intended behavior.
It is advisible to apply this combinator to calls that involve a single call to the solver for
finer control, as opposed to an entire set of interactions. However, different use cases might call for different scenarios.
If the solver responds within the time-out specified, then we continue as usual. However, if the backend solver times-out using this mechanism, there is no telling what the state of the solver will be. Thus, we raise an error in this case.
Miscellaneous
queryDebug :: [String] -> Query () Source #
If verbose is True, print the message, useful for debugging messages
in custom queries. Note that redirectVerbose will be respected: If a
file redirection is given, the output will go to the file.
echo :: String -> Query () Source #
Echo a string. Note that the echoing is done by the solver, not by SBV.
Solver options
Option values that can be set in the solver, following the SMTLib specification http://smtlib.cs.uiowa.edu/language.shtml.
Note that not all solvers may support all of these!
Furthermore, SBV doesn't support the following options allowed by SMTLib.
:interactive-mode(Deprecated in SMTLib, useProduceAssertionsinstead.):print-success(SBV critically needs this to be True in query mode.):produce-models(SBV always sets this option so it can extract models.):regular-output-channel(SBV always requires regular output to come on stdout for query purposes.):global-declarations(SBV always uses global declarations since definitions are accumulative.)
Note that SetLogic and SetInfo are, strictly speaking, not SMTLib options. However, we treat it as such here
uniformly, as it fits better with how options work.
Constructors