Data.SBV.Control

Control sublanguage for interacting with SMT solvers.

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 allSat using 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

data Query a

A query is a user-guided mechanism to directly communicate and extract results from the solver.

Instances

Monad Query

Methods

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

(>>) :: Query a -> Query b -> Query b

return :: a -> Query a

fail :: String -> Query a

Functor Query

Methods

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

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

Applicative Query

Methods

pure :: a -> Query a

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

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

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

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

MonadIO Query

Methods

liftIO :: IO a -> Query a

MonadState State Query

Methods

get :: Query State

put :: State -> Query ()

state :: (State -> (a, State)) -> Query a

query :: Query a -> Symbolic a

Run a custom query

Create a fresh variable

freshVar_ :: forall a. SymWord a => Query (SBV a)

Similar to freshVar, except creates unnamed variable.

freshVar :: forall a. SymWord a => String -> Query (SBV a)

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.

Checking satisfiability

data CheckSatResult

Result of a checkSat or checkSatAssuming call.

Constructors

Sat

Satisfiable: A model is available, which can be queried with getValue.

Unsat

Unsatisfiable: No model is available. Unsat cores might be obtained via getUnsatCore.

Unk

Unknown: Use getUnknownReason to obtain an explanation why this might be the case.

Instances

Eq CheckSatResult

Methods

(==) :: CheckSatResult -> CheckSatResult -> Bool

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

Show CheckSatResult

Methods

showsPrec :: Int -> CheckSatResult -> ShowS

show :: CheckSatResult -> String

showList :: [CheckSatResult] -> ShowS

checkSat :: Query CheckSatResult

Check for satisfiability.

checkSatUsing :: String -> Query CheckSatResult

Check for satisfiability with a custom check-sat-using command.

checkSatAssuming :: [SBool] -> Query CheckSatResult

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])

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 $ ProduceUnsatAssumptions True) 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

A class which allows for sexpr-conversion to values

Methods

sexprToVal :: SExpr -> Maybe a

sexprToVal :: Read a => SExpr -> Maybe a

Instances

SMTValue Bool

Methods

sexprToVal :: SExpr -> Maybe Bool

SMTValue Char

Methods

sexprToVal :: SExpr -> Maybe Char

SMTValue Double

Methods

sexprToVal :: SExpr -> Maybe Double

SMTValue Float

Methods

sexprToVal :: SExpr -> Maybe Float

SMTValue Int8

Methods

sexprToVal :: SExpr -> Maybe Int8

SMTValue Int16

Methods

sexprToVal :: SExpr -> Maybe Int16

SMTValue Int32

Methods

sexprToVal :: SExpr -> Maybe Int32

SMTValue Int64

Methods

sexprToVal :: SExpr -> Maybe Int64

SMTValue Integer

Methods

sexprToVal :: SExpr -> Maybe Integer

SMTValue Word8

Methods

sexprToVal :: SExpr -> Maybe Word8

SMTValue Word16

Methods

sexprToVal :: SExpr -> Maybe Word16

SMTValue Word32

Methods

sexprToVal :: SExpr -> Maybe Word32

SMTValue Word64

Methods

sexprToVal :: SExpr -> Maybe Word64

SMTValue String

Methods

sexprToVal :: SExpr -> Maybe String

SMTValue AlgReal

Methods

sexprToVal :: SExpr -> Maybe AlgReal

SMTValue E

Methods

sexprToVal :: SExpr -> Maybe E

SMTValue Color

Methods

sexprToVal :: SExpr -> Maybe Color

SMTValue Nationality

Methods

sexprToVal :: SExpr -> Maybe Nationality

SMTValue Beverage

Methods

sexprToVal :: SExpr -> Maybe Beverage

SMTValue Pet

Methods

sexprToVal :: SExpr -> Maybe Pet

SMTValue Sport

Methods

sexprToVal :: SExpr -> Maybe Sport

SMTValue U2Member

Methods

sexprToVal :: SExpr -> Maybe U2Member

SMTValue Location

Methods

sexprToVal :: SExpr -> Maybe Location

SMTValue Day

Methods

sexprToVal :: SExpr -> Maybe Day

SMTValue BinOp

Methods

sexprToVal :: SExpr -> Maybe BinOp

SMTValue UnOp

Methods

sexprToVal :: SExpr -> Maybe UnOp

getValue :: SMTValue a => SBV a -> Query a

Get the value of a term.

getUninterpretedValue :: HasKind a => SBV a -> Query String

Get the value of an uninterpreted sort, as a String

getModel :: Query SMTModel

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)]

Retrieve the assignment. This is a lightweight version of getValue, where the solver returns the truth value for all named subterms of type Bool.

getSMTResult :: Query SMTResult

Issue check-sat and get an SMT Result out.

getUnknownReason :: Query String

Get the reason unknown. Only internally used.

Extracting the unsat core

getUnsatCore :: Query [String]

Retrieve the unsat-core. Note you must have arranged for unsat cores to be produced first (via setOption $ ProduceUnsatCores True) for this call to not error out!

Extracting a proof

getProof :: Query String

Retrieve the proof. Note you must have arranged for proofs to be produced first (via setOption $ ProduceProofs True) 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]

Retrieve interpolants after an Unsat result is obtained. Note you must have arranged for interpolants to be produced first (via setOption $ ProduceInterpolants True) for this call to not error out!

To get an interpolant for a pair of formulas A and B, use a namedConstraint to attach names to A and B. Then call getInterpolant ["A", "B"], assuming those are the names you gave to the formulas.

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.

Interpolants generalize to sequences: If you pass more than two formulas, then you will get a sequence of interpolants. In general, for N formulas that are not satisfiable together, you will be returned N-1 interpolants. If formulas are A1 .. An, then interpolants will be I1 .. I(N-1), such that A1 ==> I1, A2 /\ I1 ==> I2, A3 /\ I2 ==> I3, ..., and finally AN ===> not I(N-1).

Currently, SBV only returns simple and sequence interpolants, and does not support tree-interpolants. If you need these, please get in touch. Furthermore, the result will be a list of mere strings representing the interpolating formulas, as opposed to a more structured type. Please get in touch if you use this function and can suggest a better API.

Extracting assertions

getAssertions :: Query [String]

Retrieve assertions. Note you must have arranged for assertions to be available first (via setOption $ ProduceAssertions True) 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

Collectable information from the solver.

Constructors

AllStatistics

AssertionStackLevels

Authors

ErrorBehavior

Name

ReasonUnknown

Version

InfoKeyword String

Instances

Show SMTInfoFlag

Methods

showsPrec :: Int -> SMTInfoFlag -> ShowS

show :: SMTInfoFlag -> String

showList :: [SMTInfoFlag] -> ShowS

data SMTErrorBehavior

Behavior of the solver for errors.

Constructors

ErrorImmediateExit

ErrorContinuedExecution

Instances

Show SMTErrorBehavior

Methods

showsPrec :: Int -> SMTErrorBehavior -> ShowS

show :: SMTErrorBehavior -> String

showList :: [SMTErrorBehavior] -> ShowS

data SMTReasonUnknown

Reason for reporting unknown.

Constructors

UnknownMemOut

UnknownIncomplete

UnknownOther String

Instances

Show SMTReasonUnknown

Methods

showsPrec :: Int -> SMTReasonUnknown -> ShowS

show :: SMTReasonUnknown -> String

showList :: [SMTReasonUnknown] -> ShowS

data SMTInfoResponse

Collectable information from the solver.

Constructors

Resp_Unsupported

Resp_AllStatistics [(String, String)]

Resp_AssertionStackLevels Integer

Resp_Authors [String]

Resp_Error SMTErrorBehavior

Resp_Name String

Resp_ReasonUnknown SMTReasonUnknown

Resp_Version String

Resp_InfoKeyword String [String]

Instances

Show SMTInfoResponse

Methods

showsPrec :: Int -> SMTInfoResponse -> ShowS

show :: SMTInfoResponse -> String

showList :: [SMTInfoResponse] -> ShowS

getInfo :: SMTInfoFlag -> Query SMTInfoResponse

Ask solver for info.

getOption :: (a -> SMTOption) -> Query (Maybe SMTOption)

Retrieve the value of an 'SMTOption.' The curious function argument is on purpose here, simply pass the constructor name. Example: the call getOption ProduceUnsatCores will return either Nothing 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

getAssertionStackDepth :: Query Int

The current assertion stack depth, i.e., pops after start. Always non-negative.

push :: Int -> Query ()

Push the context, entering a new one. Pushes multiple levels if n > 1.

pop :: Int -> Query ()

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

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))

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 ()

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

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

Produce the query result from an assignment.

exit :: Query ()

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

If true, we shall ignore the exit code upon exit. Otherwise we require ExitSuccess.

timeout :: Int -> Query a -> Query a

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 ()

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 ()

Echo a string. Note that the echoing is done by the solver, not by SBV.

io :: IO a -> Query a

Perform an arbitrary IO action.

Solver options

data SMTOption

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, use ProduceAssertions instead.)
• :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

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]

Instances

Show SMTOption

Methods

showsPrec :: Int -> SMTOption -> ShowS

show :: SMTOption -> String

showList :: [SMTOption] -> ShowS

Generic SMTOption

Associated Types

type Rep SMTOption :: * -> *

Methods

from :: SMTOption -> Rep SMTOption x

to :: Rep SMTOption x -> SMTOption

NFData SMTOption

Methods

rnf :: SMTOption -> ()

type Rep SMTOption

type Rep SMTOption = D1 * (MetaData "SMTOption" "Data.SBV.Control.Types" "sbv-7.7-KHNFtBNwUNU1J81TmQfmcg" False) ((:+:) * ((:+:) * ((:+:) * (C1 * (MetaCons "DiagnosticOutputChannel" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * FilePath))) ((:+:) * (C1 * (MetaCons "ProduceAssertions" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool))) (C1 * (MetaCons "ProduceAssignments" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool))))) ((:+:) * (C1 * (MetaCons "ProduceProofs" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool))) ((:+:) * (C1 * (MetaCons "ProduceInterpolants" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool))) (C1 * (MetaCons "ProduceUnsatAssumptions" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))))) ((:+:) * ((:+:) * (C1 * (MetaCons "ProduceUnsatCores" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool))) ((:+:) * (C1 * (MetaCons "RandomSeed" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Integer))) (C1 * (MetaCons "ReproducibleResourceLimit" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Integer))))) ((:+:) * ((:+:) * (C1 * (MetaCons "SMTVerbosity" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Integer))) (C1 * (MetaCons "OptionKeyword" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * String)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * [String]))))) ((:+:) * (C1 * (MetaCons "SetLogic" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Logic))) (C1 * (MetaCons "SetInfo" PrefixI False) ((:*:) * (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * String)) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * [String]))))))))

Logics supported

data Logic

SMT-Lib logics. If left unspecified SBV will pick the logic based on what it determines is needed. However, the user can override this choice using a call to setLogic This is especially handy if one is experimenting with custom logics that might be supported on new solvers. See http://smtlib.cs.uiowa.edu/logics.shtml for the official list.

Constructors

AUFLIA

Formulas over the theory of linear integer arithmetic and arrays extended with free sort and function symbols but restricted to arrays with integer indices and values.

AUFLIRA

Linear formulas with free sort and function symbols over one- and two-dimentional arrays of integer index and real value.

AUFNIRA

Formulas with free function and predicate symbols over a theory of arrays of arrays of integer index and real value.

LRA

Linear formulas in linear real arithmetic.

QF_ABV

Quantifier-free formulas over the theory of bitvectors and bitvector arrays.

QF_AUFBV

Quantifier-free formulas over the theory of bitvectors and bitvector arrays extended with free sort and function symbols.

QF_AUFLIA

Quantifier-free linear formulas over the theory of integer arrays extended with free sort and function symbols.

QF_AX

Quantifier-free formulas over the theory of arrays with extensionality.

QF_BV

Quantifier-free formulas over the theory of fixed-size bitvectors.

QF_IDL

Difference Logic over the integers. Boolean combinations of inequations of the form x - y < b where x and y are integer variables and b is an integer constant.

QF_LIA

Unquantified linear integer arithmetic. In essence, Boolean combinations of inequations between linear polynomials over integer variables.

QF_LRA

Unquantified linear real arithmetic. In essence, Boolean combinations of inequations between linear polynomials over real variables.

QF_NIA

Quantifier-free integer arithmetic.

QF_NRA

Quantifier-free real arithmetic.

QF_RDL

Difference Logic over the reals. In essence, Boolean combinations of inequations of the form x - y < b where x and y are real variables and b is a rational constant.

QF_UF

Unquantified formulas built over a signature of uninterpreted (i.e., free) sort and function symbols.

QF_UFBV

Unquantified formulas over bitvectors with uninterpreted sort function and symbols.

QF_UFIDL

Difference Logic over the integers (in essence) but with uninterpreted sort and function symbols.

QF_UFLIA

Unquantified linear integer arithmetic with uninterpreted sort and function symbols.

QF_UFLRA

Unquantified linear real arithmetic with uninterpreted sort and function symbols.

QF_UFNRA

Unquantified non-linear real arithmetic with uninterpreted sort and function symbols.

QF_UFNIRA

Unquantified non-linear real integer arithmetic with uninterpreted sort and function symbols.

UFLRA

Linear real arithmetic with uninterpreted sort and function symbols.

UFNIA

Non-linear integer arithmetic with uninterpreted sort and function symbols.

QF_FPBV

Quantifier-free formulas over the theory of floating point numbers, arrays, and bit-vectors.

QF_FP

Quantifier-free formulas over the theory of floating point numbers.

QF_FD

Quantifier-free finite domains.

QF_S

Quantifier-free formulas over the theory of strings.

Logic_ALL

The catch-all value.

Logic_NONE

Use this value when you want SBV to simply not set the logic.

CustomLogic String

In case you need a really custom string!

Instances

Show Logic

Methods

showsPrec :: Int -> Logic -> ShowS

show :: Logic -> String

showList :: [Logic] -> ShowS

Generic Logic

Associated Types

type Rep Logic :: * -> *

Methods

from :: Logic -> Rep Logic x

to :: Rep Logic x -> Logic

NFData Logic

Methods

rnf :: Logic -> ()

GShow Logic

Methods

gshowsPrec :: Int -> Logic -> ShowS

gshows :: Logic -> ShowS

gshow :: Logic -> String

type Rep Logic

type Rep Logic = D1 * (MetaData "Logic" "Data.SBV.Control.Types" "sbv-7.7-KHNFtBNwUNU1J81TmQfmcg" False) ((:+:) * ((:+:) * ((:+:) * ((:+:) * (C1 * (MetaCons "AUFLIA" PrefixI False) (U1 *)) ((:+:) * (C1 * (MetaCons "AUFLIRA" PrefixI False) (U1 *)) (C1 * (MetaCons "AUFNIRA" PrefixI False) (U1 *)))) ((:+:) * ((:+:) * (C1 * (MetaCons "LRA" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_ABV" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "QF_AUFBV" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_AUFLIA" PrefixI False) (U1 *))))) ((:+:) * ((:+:) * ((:+:) * (C1 * (MetaCons "QF_AX" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_BV" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "QF_IDL" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_LIA" PrefixI False) (U1 *)))) ((:+:) * ((:+:) * (C1 * (MetaCons "QF_LRA" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_NIA" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "QF_NRA" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_RDL" PrefixI False) (U1 *)))))) ((:+:) * ((:+:) * ((:+:) * ((:+:) * (C1 * (MetaCons "QF_UF" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_UFBV" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "QF_UFIDL" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_UFLIA" PrefixI False) (U1 *)))) ((:+:) * ((:+:) * (C1 * (MetaCons "QF_UFLRA" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_UFNRA" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "QF_UFNIRA" PrefixI False) (U1 *)) (C1 * (MetaCons "UFLRA" PrefixI False) (U1 *))))) ((:+:) * ((:+:) * ((:+:) * (C1 * (MetaCons "UFNIA" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_FPBV" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "QF_FP" PrefixI False) (U1 *)) (C1 * (MetaCons "QF_FD" PrefixI False) (U1 *)))) ((:+:) * ((:+:) * (C1 * (MetaCons "QF_S" PrefixI False) (U1 *)) (C1 * (MetaCons "Logic_ALL" PrefixI False) (U1 *))) ((:+:) * (C1 * (MetaCons "Logic_NONE" PrefixI False) (U1 *)) (C1 * (MetaCons "CustomLogic" PrefixI False) (S1 * (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * String))))))))