{-# LANGUAGE GeneralizedNewtypeDeriving #-} -- | -- Module : Z3.Monad -- Copyright : (c) Iago Abal, 2013-2015 -- (c) David Castro, 2013-2015 -- License : BSD3 -- Maintainer: Iago Abal <mail@iagoabal.eu>, -- David Castro <david.castro.dcp@gmail.com> -- -- A simple monadic interface to Z3 API. -- -- Examples: <https://bitbucket.org/iago/z3-haskell/src/tip/examples/Example/Monad> module Z3.Monad ( -- * Z3 monad MonadZ3(..) , Z3 , module Z3.Opts , Logic(..) , evalZ3 , evalZ3With -- ** Z3 enviroments , Z3Env , newEnv , evalZ3WithEnv -- * Types , Symbol , AST , Sort , FuncDecl , App , Pattern , Constructor , Model , Base.Context , FuncInterp , FuncEntry , Params , Solver , SortKind(..) , ASTKind(..) -- ** Satisfiability result , Result(..) -- * Parameters , mkParams , paramsSetBool , paramsSetUInt , paramsSetDouble , paramsSetSymbol , paramsToString -- * Symbols , mkIntSymbol , mkStringSymbol -- * Sorts , mkUninterpretedSort , mkBoolSort , mkIntSort , mkRealSort , mkBvSort , mkFiniteDomainSort , mkArraySort , mkTupleSort , mkConstructor , mkDatatype , mkDatatypes , mkSetSort -- * Constants and Applications , mkFuncDecl , mkApp , mkConst , mkFreshConst , mkFreshFuncDecl -- ** Helpers , mkVar , mkBoolVar , mkRealVar , mkIntVar , mkBvVar , mkFreshVar , mkFreshBoolVar , mkFreshRealVar , mkFreshIntVar , mkFreshBvVar -- * Propositional Logic and Equality , mkTrue , mkFalse , mkEq , mkNot , mkIte , mkIff , mkImplies , mkXor , mkAnd , mkOr , mkDistinct , mkDistinct1 -- ** Helpers , mkBool -- * Arithmetic: Integers and Reals , mkAdd , mkMul , mkSub , mkSub1 , mkUnaryMinus , mkDiv , mkMod , mkRem , mkLt , mkLe , mkGt , mkGe , mkInt2Real , mkReal2Int , mkIsInt -- * Bit-vectors , mkBvnot , mkBvredand , mkBvredor , mkBvand , mkBvor , mkBvxor , mkBvnand , mkBvnor , mkBvxnor , mkBvneg , mkBvadd , mkBvsub , mkBvmul , mkBvudiv , mkBvsdiv , mkBvurem , mkBvsrem , mkBvsmod , mkBvult , mkBvslt , mkBvule , mkBvsle , mkBvuge , mkBvsge , mkBvugt , mkBvsgt , mkConcat , mkExtract , mkSignExt , mkZeroExt , mkRepeat , mkBvshl , mkBvlshr , mkBvashr , mkRotateLeft , mkRotateRight , mkExtRotateLeft , mkExtRotateRight , mkInt2bv , mkBv2int , mkBvnegNoOverflow , mkBvaddNoOverflow , mkBvaddNoUnderflow , mkBvsubNoOverflow , mkBvsubNoUnderflow , mkBvmulNoOverflow , mkBvmulNoUnderflow , mkBvsdivNoOverflow -- * Arrays , mkSelect , mkStore , mkConstArray , mkMap , mkArrayDefault -- * Sets , mkEmptySet , mkFullSet , mkSetAdd , mkSetDel , mkSetUnion , mkSetIntersect , mkSetDifference , mkSetComplement , mkSetMember , mkSetSubset -- * Numerals , mkNumeral , mkInt , mkReal , mkUnsignedInt , mkInt64 , mkUnsignedInt64 -- ** Helpers , mkIntegral , mkRational , mkFixed , mkRealNum , mkInteger , mkIntNum , mkBitvector , mkBvNum -- * Quantifiers , mkPattern , mkBound , mkForall , mkExists , mkForallConst , mkExistsConst -- * Accessors , getSymbolString , getSortKind , getBvSortSize , getDatatypeSortConstructors , getDatatypeSortRecognizers , getDatatypeSortConstructorAccessors , getDeclName , getArity , getDomain , getRange , appToAst , getAppDecl , getAppNumArgs , getAppArg , getAppArgs , getSort , getArraySortDomain , getArraySortRange , getBoolValue , getAstKind , isApp , toApp , getNumeralString , simplify , simplifyEx , getIndexValue , isQuantifierForall , isQuantifierExists , getQuantifierWeight , getQuantifierNumPatterns , getQuantifierPatternAST , getQuantifierPatterns , getQuantifierNumNoPatterns , getQuantifierNoPatternAST , getQuantifierNoPatterns , getQuantifierNumBound , getQuantifierBoundName , getQuantifierBoundSort , getQuantifierBoundVars , getQuantifierBody -- ** Helpers , getBool , getInt , getReal , getBv -- * Modifiers , substituteVars -- * Models , modelEval , evalArray , getConstInterp , getFuncInterp , hasInterp , numConsts , numFuncs , getConstDecl , getFuncDecl , getConsts , getFuncs , isAsArray , addFuncInterp , addConstInterp , getAsArrayFuncDecl , funcInterpGetNumEntries , funcInterpGetEntry , funcInterpGetElse , funcInterpGetArity , funcEntryGetValue , funcEntryGetNumArgs , funcEntryGetArg , modelToString , showModel -- ** Helpers , EvalAst , eval , evalBool , evalInt , evalReal , evalBv , evalT , mapEval , FuncModel(..) , evalFunc -- * Tactics , mkTactic , andThenTactic , orElseTactic , skipTactic , tryForTactic , mkQuantifierEliminationTactic , mkAndInverterGraphTactic , applyTactic , getApplyResultNumSubgoals , getApplyResultSubgoal , getApplyResultSubgoals , mkGoal , goalAssert , getGoalSize , getGoalFormula , getGoalFormulas -- * String Conversion , ASTPrintMode(..) , setASTPrintMode , astToString , patternToString , sortToString , funcDeclToString , benchmarkToSMTLibString -- * Parser interface , parseSMTLib2String , parseSMTLib2File -- * Error Handling , Base.Z3Error(..) , Base.Z3ErrorCode(..) -- * Miscellaneous , Version(..) , getVersion -- * Fixedpoint , Fixedpoint , fixedpointPush , fixedpointPop , fixedpointAddRule , fixedpointSetParams , fixedpointRegisterRelation , fixedpointQueryRelations , fixedpointGetAnswer , fixedpointGetAssertions -- * Solvers , solverGetHelp , solverSetParams , solverPush , solverPop , solverReset , solverGetNumScopes , solverAssertCnstr , solverAssertAndTrack , solverCheck , solverCheckAssumptions , solverGetModel , solverGetUnsatCore , solverGetReasonUnknown , solverToString -- ** Helpers , assert , check , checkAssumptions , solverCheckAndGetModel , getModel , withModel , getUnsatCore , push , pop , local , reset , getNumScopes ) where import Z3.Opts import Z3.Base ( Symbol , AST , Sort , FuncDecl , App , Pattern , Constructor , Model , FuncInterp , FuncEntry , FuncModel(..) , Result(..) , Logic(..) , ASTPrintMode(..) , Version(..) , Params , Solver , Fixedpoint , SortKind(..) , ASTKind(..) , Tactic , ApplyResult , Goal ) import qualified Z3.Base as Base import Control.Applicative ( Applicative ) import Data.Fixed ( Fixed, HasResolution ) import Control.Monad.IO.Class ( MonadIO, liftIO ) import Control.Monad.Trans.Reader ( ReaderT, runReaderT, asks ) import Control.Monad.Fix ( MonadFix ) import Data.Int ( Int64 ) import Data.List.NonEmpty (NonEmpty) import Data.Word ( Word, Word64 ) import Data.Traversable ( Traversable ) import qualified Data.Traversable as T --------------------------------------------------------------------- -- The Z3 monad-class class (Applicative m, Monad m, MonadIO m) => MonadZ3 m where getSolver :: m Base.Solver getContext :: m Base.Context ------------------------------------------------- -- Lifting -- TODO: Rename to liftFun0 for consistency liftScalar :: MonadZ3 z3 => (Base.Context -> IO b) -> z3 b liftScalar f = liftIO . f =<< getContext liftFun1 :: MonadZ3 z3 => (Base.Context -> a -> IO b) -> a -> z3 b liftFun1 f a = getContext >>= \ctx -> liftIO (f ctx a) liftFun2 :: MonadZ3 z3 => (Base.Context -> a -> b -> IO c) -> a -> b -> z3 c liftFun2 f a b = getContext >>= \ctx -> liftIO (f ctx a b) liftFun3 :: MonadZ3 z3 => (Base.Context -> a -> b -> c -> IO d) -> a -> b -> c -> z3 d liftFun3 f a b c = getContext >>= \ctx -> liftIO (f ctx a b c) liftFun4 :: MonadZ3 z3 => (Base.Context -> a -> b -> c -> d -> IO e) -> a -> b -> c -> d -> z3 e liftFun4 f a b c d = getContext >>= \ctx -> liftIO (f ctx a b c d) liftFun5 :: MonadZ3 z3 => (Base.Context -> a1 -> a2 -> a3 -> a4 -> a5 -> IO b) -> a1 -> a2 -> a3 -> a4 -> a5-> z3 b liftFun5 f x1 x2 x3 x4 x5 = getContext >>= \ctx -> liftIO (f ctx x1 x2 x3 x4 x5) liftFun6 :: MonadZ3 z3 => (Base.Context -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> IO b) -> a1 -> a2 -> a3 -> a4 -> a5 -> a6 -> z3 b liftFun6 f x1 x2 x3 x4 x5 x6 = getContext >>= \ctx -> liftIO (f ctx x1 x2 x3 x4 x5 x6) liftSolver0 :: MonadZ3 z3 => (Base.Context -> Base.Solver -> IO b) -> z3 b liftSolver0 f_s = do ctx <- getContext liftIO . f_s ctx =<< getSolver liftSolver1 :: MonadZ3 z3 => (Base.Context -> Base.Solver -> a -> IO b) -> a -> z3 b liftSolver1 f_s a = do ctx <- getContext liftIO . (\s -> f_s ctx s a) =<< getSolver liftSolver2 :: MonadZ3 z3 => (Base.Context -> Base.Solver -> a -> b -> IO c) -> a -> b -> z3 c liftSolver2 f a b = do ctx <- getContext slv <- getSolver liftIO $ f ctx slv a b liftFixedpoint0 :: MonadFixedpoint z3 => (Base.Context -> Base.Fixedpoint -> IO b) -> z3 b liftFixedpoint0 f_s = do ctx <- getContext liftIO . f_s ctx =<< getFixedpoint liftFixedpoint1 :: MonadFixedpoint z3 => (Base.Context -> Base.Fixedpoint -> a -> IO b) -> a -> z3 b liftFixedpoint1 f_s a = do ctx <- getContext liftIO . (\s -> f_s ctx s a) =<< getFixedpoint liftFixedpoint2 :: MonadFixedpoint z3 => (Base.Context -> Base.Fixedpoint -> a -> b -> IO c) -> a -> b -> z3 c liftFixedpoint2 f a b = do ctx <- getContext slv <- getFixedpoint liftIO $ f ctx slv a b ------------------------------------------------- -- A simple Z3 monad. newtype Z3 a = Z3 { _unZ3 :: ReaderT Z3Env IO a } deriving (Functor, Applicative, Monad, MonadIO, MonadFix) -- | Z3 environment. data Z3Env = Z3Env { envSolver :: Base.Solver , envContext :: Base.Context , envFixedpoint :: Base.Fixedpoint } instance MonadZ3 Z3 where getSolver = Z3 $ asks envSolver getContext = Z3 $ asks envContext instance MonadFixedpoint Z3 where getFixedpoint = Z3 $ asks envFixedpoint -- | Eval a Z3 script. evalZ3With :: Maybe Logic -> Opts -> Z3 a -> IO a evalZ3With mbLogic opts (Z3 s) = do env <- newEnv mbLogic opts runReaderT s env -- | Eval a Z3 script with default configuration options. evalZ3 :: Z3 a -> IO a evalZ3 = evalZ3With Nothing stdOpts newEnvWith :: (Base.Config -> IO Base.Context) -> Maybe Logic -> Opts -> IO Z3Env newEnvWith mkContext mbLogic opts = Base.withConfig $ \cfg -> do setOpts cfg opts ctx <- mkContext cfg solver <- maybe (Base.mkSolver ctx) (Base.mkSolverForLogic ctx) mbLogic fixedpoint <- Base.mkFixedpoint ctx return $ Z3Env solver ctx fixedpoint -- | Create a new Z3 environment. newEnv :: Maybe Logic -> Opts -> IO Z3Env newEnv = newEnvWith Base.mkContext -- | Eval a Z3 script with a given environment. -- -- Environments may facilitate running many queries under the same -- logical context. -- -- Note that an environment may change after each query. -- If you want to preserve the same environment then use 'local', as in -- @evalZ3WithEnv /env/ (local /query/)@. evalZ3WithEnv :: Z3 a -> Z3Env -> IO a evalZ3WithEnv (Z3 s) = runReaderT s --------------------------------------------------------------------- -- * Parameters -- | Create a Z3 (empty) parameter set. -- -- Starting at Z3 4.0, parameter sets are used to configure many components -- such as: simplifiers, tactics, solvers, etc. mkParams :: MonadZ3 z3 => z3 Params mkParams = liftScalar Base.mkParams -- | Add a Boolean parameter /k/ with value /v/ to the parameter set /p/. paramsSetBool :: MonadZ3 z3 => Params -> Symbol -> Bool -> z3 () paramsSetBool = liftFun3 Base.paramsSetBool -- | Add a unsigned parameter /k/ with value /v/ to the parameter set /p/. paramsSetUInt :: MonadZ3 z3 => Params -> Symbol -> Word -> z3 () paramsSetUInt = liftFun3 Base.paramsSetUInt -- | Add a double parameter /k/ with value /v/ to the parameter set /p/. paramsSetDouble :: MonadZ3 z3 => Params -> Symbol -> Double -> z3 () paramsSetDouble = liftFun3 Base.paramsSetDouble -- | Add a symbol parameter /k/ with value /v/ to the parameter set /p/. paramsSetSymbol :: MonadZ3 z3 => Params -> Symbol -> Symbol -> z3 () paramsSetSymbol = liftFun3 Base.paramsSetSymbol -- | Convert a parameter set into a string. -- -- This function is mainly used for printing the contents of a parameter set. paramsToString :: MonadZ3 z3 => Params -> z3 String paramsToString = liftFun1 Base.paramsToString -- TODO: Z3_params_validate --------------------------------------------------------------------- -- Symbols -- | Create a Z3 symbol using an integer. mkIntSymbol :: (MonadZ3 z3, Integral i) => i -> z3 Symbol mkIntSymbol = liftFun1 Base.mkIntSymbol -- | Create a Z3 symbol using a string. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gafebb0d3c212927cf7834c3a20a84ecae> mkStringSymbol :: MonadZ3 z3 => String -> z3 Symbol mkStringSymbol = liftFun1 Base.mkStringSymbol --------------------------------------------------------------------- -- Sorts -- | Create a free (uninterpreted) type using the given name (symbol). -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga736e88741af1c178cbebf94c49aa42de> mkUninterpretedSort :: MonadZ3 z3 => Symbol -> z3 Sort mkUninterpretedSort = liftFun1 Base.mkUninterpretedSort -- | Create the /boolean/ type. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gacdc73510b69a010b71793d429015f342> mkBoolSort :: MonadZ3 z3 => z3 Sort mkBoolSort = liftScalar Base.mkBoolSort -- | Create the /integer/ type. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga6cd426ab5748653b77d389fd3eac1015> mkIntSort :: MonadZ3 z3 => z3 Sort mkIntSort = liftScalar Base.mkIntSort -- | Create the /real/ type. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga40ef93b9738485caed6dc84631c3c1a0> mkRealSort :: MonadZ3 z3 => z3 Sort mkRealSort = liftScalar Base.mkRealSort -- | Create a bit-vector type of the given size. -- -- This type can also be seen as a machine integer. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaeed000a1bbb84b6ca6fdaac6cf0c1688> mkBvSort :: MonadZ3 z3 => Int -> z3 Sort mkBvSort = liftFun1 Base.mkBvSort -- | Create a finite-domain type. mkFiniteDomainSort :: MonadZ3 z3 => Symbol -> Word64 -> z3 Sort mkFiniteDomainSort = liftFun2 Base.mkFiniteDomainSort -- | Create an array type -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gafe617994cce1b516f46128e448c84445> -- mkArraySort :: MonadZ3 z3 => Sort -> Sort -> z3 Sort mkArraySort = liftFun2 Base.mkArraySort -- | Create a tuple type -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga7156b9c0a76a28fae46c81f8e3cdf0f1> mkTupleSort :: MonadZ3 z3 => Symbol -- ^ Name of the sort -> [(Symbol, Sort)] -- ^ Name and sort of each field -> z3 (Sort, FuncDecl, [FuncDecl]) -- ^ Resulting sort, and function -- declarations for the -- constructor and projections. mkTupleSort = liftFun2 Base.mkTupleSort -- | Create a contructor -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaa779e39f7050b9d51857887954b5f9b0> mkConstructor :: MonadZ3 z3 => Symbol -- ^ Name of the sonstructor -> Symbol -- ^ Name of recognizer function -> [(Symbol, Maybe Sort, Int)] -- ^ Name, sort option, and sortRefs -> z3 Constructor mkConstructor = liftFun3 Base.mkConstructor -- | Create datatype, such as lists, trees, records, enumerations or unions of -- records. The datatype may be recursive. Return the datatype sort. -- -- Reference <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gab6809d53327d807da9158abdf75df387> mkDatatype :: MonadZ3 z3 => Symbol -> [Constructor] -> z3 Sort mkDatatype = liftFun2 Base.mkDatatype -- | Create mutually recursive datatypes, such as a tree and forest. -- -- Returns the datatype sorts mkDatatypes :: MonadZ3 z3 => [Symbol] -> [[Constructor]] -> z3 [Sort] mkDatatypes = liftFun2 Base.mkDatatypes -- | Create a set type -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga6865879523e7e882d7e50a2d8445ac8b> -- mkSetSort :: MonadZ3 z3 => Sort -> z3 Sort mkSetSort = liftFun1 Base.mkSetSort --------------------------------------------------------------------- -- Constants and Applications -- | A Z3 function mkFuncDecl :: MonadZ3 z3 => Symbol -> [Sort] -> Sort -> z3 FuncDecl mkFuncDecl = liftFun3 Base.mkFuncDecl -- | Create a constant or function application. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga33a202d86bf628bfab9b6f437536cebe> mkApp :: MonadZ3 z3 => FuncDecl -> [AST] -> z3 AST mkApp = liftFun2 Base.mkApp -- | Declare and create a constant. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga093c9703393f33ae282ec5e8729354ef> mkConst :: MonadZ3 z3 => Symbol -> Sort -> z3 AST mkConst = liftFun2 Base.mkConst -- | Declare and create a constant. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga093c9703393f33ae282ec5e8729354ef> mkFreshConst :: MonadZ3 z3 => String -> Sort -> z3 AST mkFreshConst = liftFun2 Base.mkFreshConst -- | Declare a fresh constant or function. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga1f60c7eb41c5603e55a188a14dc929ec> mkFreshFuncDecl :: MonadZ3 z3 => String -> [Sort] -> Sort -> z3 FuncDecl mkFreshFuncDecl = liftFun3 Base.mkFreshFuncDecl ------------------------------------------------- -- ** Helpers -- | Declare and create a variable (aka /constant/). -- -- An alias for 'mkConst'. mkVar :: MonadZ3 z3 => Symbol -> Sort -> z3 AST mkVar = liftFun2 Base.mkVar -- | Declarate and create a variable of sort /bool/. -- -- See 'mkVar'. mkBoolVar :: MonadZ3 z3 => Symbol -> z3 AST mkBoolVar = liftFun1 Base.mkBoolVar -- | Declarate and create a variable of sort /real/. -- -- See 'mkVar'. mkRealVar :: MonadZ3 z3 => Symbol -> z3 AST mkRealVar = liftFun1 Base.mkRealVar -- | Declarate and create a variable of sort /int/. -- -- See 'mkVar'. mkIntVar :: MonadZ3 z3 => Symbol -> z3 AST mkIntVar = liftFun1 Base.mkIntVar -- | Declarate and create a variable of sort /bit-vector/. -- -- See 'mkVar'. mkBvVar :: MonadZ3 z3 => Symbol -> Int -- ^ bit-width -> z3 AST mkBvVar = liftFun2 Base.mkBvVar -- | Declare and create a /fresh/ variable (aka /constant/). -- -- An alias for 'mkFreshConst'. mkFreshVar :: MonadZ3 z3 => String -> Sort -> z3 AST mkFreshVar = liftFun2 Base.mkFreshConst -- | Declarate and create a /fresh/ variable of sort /bool/. -- -- See 'mkFreshVar'. mkFreshBoolVar :: MonadZ3 z3 => String -> z3 AST mkFreshBoolVar = liftFun1 Base.mkFreshBoolVar -- | Declarate and create a /fresh/ variable of sort /real/. -- -- See 'mkFreshVar'. mkFreshRealVar :: MonadZ3 z3 => String -> z3 AST mkFreshRealVar = liftFun1 Base.mkFreshRealVar -- | Declarate and create a /fresh/ variable of sort /int/. -- -- See 'mkFreshVar'. mkFreshIntVar :: MonadZ3 z3 => String -> z3 AST mkFreshIntVar = liftFun1 Base.mkFreshIntVar -- | Declarate and create a /fresh/ variable of sort /bit-vector/. -- -- See 'mkFreshVar'. mkFreshBvVar :: MonadZ3 z3 => String -> Int -- ^ bit-width -> z3 AST mkFreshBvVar = liftFun2 Base.mkFreshBvVar --------------------------------------------------------------------- -- Propositional Logic and Equality -- | Create an AST node representing /true/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gae898e7380409bbc57b56cc5205ef1db7> mkTrue :: MonadZ3 z3 => z3 AST mkTrue = liftScalar Base.mkTrue -- | Create an AST node representing /false/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga5952ac17671117a02001fed6575c778d> mkFalse :: MonadZ3 z3 => z3 AST mkFalse = liftScalar Base.mkFalse -- | Create an AST node representing /l = r/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga95a19ce675b70e22bb0401f7137af37c> mkEq :: MonadZ3 z3 => AST -> AST -> z3 AST mkEq = liftFun2 Base.mkEq -- | The distinct construct is used for declaring the arguments pairwise -- distinct. -- -- Requires a non-empty list. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaa076d3a668e0ec97d61744403153ecf7> mkDistinct :: MonadZ3 z3 => [AST] -> z3 AST mkDistinct = liftFun1 Base.mkDistinct -- | Same as 'mkDistinct' but type-safe. mkDistinct1 :: MonadZ3 z3 => NonEmpty AST -> z3 AST mkDistinct1 = liftFun1 Base.mkDistinct1 -- | Create an AST node representing /not(a)/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga3329538091996eb7b3dc677760a61072> mkNot :: MonadZ3 z3 => AST -> z3 AST mkNot = liftFun1 Base.mkNot -- | Create an AST node representing an if-then-else: /ite(t1, t2, t3)/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga94417eed5c36e1ad48bcfc8ad6e83547> mkIte :: MonadZ3 z3 => AST -> AST -> AST -> z3 AST mkIte = liftFun3 Base.mkIte -- | Create an AST node representing /t1 iff t2/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga930a8e844d345fbebc498ac43a696042> mkIff :: MonadZ3 z3 => AST -> AST -> z3 AST mkIff = liftFun2 Base.mkIff -- | Create an AST node representing /t1 implies t2/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac829c0e25bbbd30343bf073f7b524517> mkImplies :: MonadZ3 z3 => AST -> AST -> z3 AST mkImplies = liftFun2 Base.mkImplies -- | Create an AST node representing /t1 xor t2/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gacc6d1b848032dec0c4617b594d4229ec> mkXor :: MonadZ3 z3 => AST -> AST -> z3 AST mkXor = liftFun2 Base.mkXor -- | Create an AST node representing args[0] and ... and args[num_args-1]. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gacde98ce4a8ed1dde50b9669db4838c61> mkAnd :: MonadZ3 z3 => [AST] -> z3 AST mkAnd = liftFun1 Base.mkAnd -- | Create an AST node representing args[0] or ... or args[num_args-1]. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga00866d16331d505620a6c515302021f9> mkOr :: MonadZ3 z3 => [AST] -> z3 AST mkOr = liftFun1 Base.mkOr ------------------------------------------------- -- ** Helpers -- | Create an AST node representing the given boolean. mkBool :: MonadZ3 z3 => Bool -> z3 AST mkBool = liftFun1 Base.mkBool --------------------------------------------------------------------- -- Arithmetic: Integers and Reals -- | Create an AST node representing args[0] + ... + args[num_args-1]. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4e4ac0a4e53eee0b4b0ef159ed7d0cd5> mkAdd :: MonadZ3 z3 => [AST] -> z3 AST mkAdd = liftFun1 Base.mkAdd -- | Create an AST node representing args[0] * ... * args[num_args-1]. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gab9affbf8401a18eea474b59ad4adc890> mkMul :: MonadZ3 z3 => [AST] -> z3 AST mkMul = liftFun1 Base.mkMul -- | Create an AST node representing args[0] - ... - args[num_args - 1]. -- -- Requires a non-empty list. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4f5fea9b683f9e674fd8f14d676cc9a9> mkSub :: MonadZ3 z3 => [AST] -> z3 AST mkSub = liftFun1 Base.mkSub -- | Same as 'mkSub' but type-safe. mkSub1 :: MonadZ3 z3 => NonEmpty AST -> z3 AST mkSub1 = liftFun1 Base.mkSub1 -- | Create an AST node representing -arg. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gadcd2929ad732937e25f34277ce4988ea> mkUnaryMinus :: MonadZ3 z3 => AST -> z3 AST mkUnaryMinus = liftFun1 Base.mkUnaryMinus -- | Create an AST node representing arg1 div arg2. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga1ac60ee8307af8d0b900375914194ff3> mkDiv :: MonadZ3 z3 => AST -> AST -> z3 AST mkDiv = liftFun2 Base.mkDiv -- | Create an AST node representing arg1 mod arg2. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga8e350ac77e6b8fe805f57efe196e7713> mkMod :: MonadZ3 z3 => AST -> AST -> z3 AST mkMod = liftFun2 Base.mkMod -- | Create an AST node representing arg1 rem arg2. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga2fcdb17f9039bbdaddf8a30d037bd9ff> mkRem :: MonadZ3 z3 => AST -> AST -> z3 AST mkRem = liftFun2 Base.mkRem -- | Create less than. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga58a3dc67c5de52cf599c346803ba1534> mkLt :: MonadZ3 z3 => AST -> AST -> z3 AST mkLt = liftFun2 Base.mkLt -- | Create less than or equal to. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaa9a33d11096841f4e8c407f1578bc0bf> mkLe :: MonadZ3 z3 => AST -> AST -> z3 AST mkLe = liftFun2 Base.mkLe -- | Create greater than. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga46167b86067586bb742c0557d7babfd3> mkGt :: MonadZ3 z3 => AST -> AST -> z3 AST mkGt = liftFun2 Base.mkGt -- | Create greater than or equal to. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gad9245cbadb80b192323d01a8360fb942> mkGe :: MonadZ3 z3 => AST -> AST -> z3 AST mkGe = liftFun2 Base.mkGe -- | Coerce an integer to a real. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga7130641e614c7ebafd28ae16a7681a21> mkInt2Real :: MonadZ3 z3 => AST -> z3 AST mkInt2Real = liftFun1 Base.mkInt2Real -- | Coerce a real to an integer. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga759b6563ba1204aae55289009a3fdc6d> mkReal2Int :: MonadZ3 z3 => AST -> z3 AST mkReal2Int = liftFun1 Base.mkReal2Int -- | Check if a real number is an integer. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaac2ad0fb04e4900fdb4add438d137ad3> mkIsInt :: MonadZ3 z3 => AST -> z3 AST mkIsInt = liftFun1 Base.mkIsInt --------------------------------------------------------------------- -- Bit-vectors -- | Bitwise negation. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga36cf75c92c54c1ca633a230344f23080> mkBvnot :: MonadZ3 z3 => AST -> z3 AST mkBvnot = liftFun1 Base.mkBvnot -- | Take conjunction of bits in vector, return vector of length 1. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaccc04f2b58903279b1b3be589b00a7d8> mkBvredand :: MonadZ3 z3 => AST -> z3 AST mkBvredand = liftFun1 Base.mkBvredand -- | Take disjunction of bits in vector, return vector of length 1. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gafd18e127c0586abf47ad9cd96895f7d2> mkBvredor :: MonadZ3 z3 => AST -> z3 AST mkBvredor = liftFun1 Base.mkBvredor -- | Bitwise and. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gab96e0ea55334cbcd5a0e79323b57615d> mkBvand :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvand = liftFun2 Base.mkBvand -- | Bitwise or. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga77a6ae233fb3371d187c6d559b2843f5> mkBvor :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvor = liftFun2 Base.mkBvor -- | Bitwise exclusive-or. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga0a3821ea00b1c762205f73e4bc29e7d8> mkBvxor :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvxor = liftFun2 Base.mkBvxor -- | Bitwise nand. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga96dc37d36efd658fff5b2b4df49b0e61> mkBvnand :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvnand = liftFun2 Base.mkBvnand -- | Bitwise nor. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gabf15059e9e8a2eafe4929fdfd259aadb> mkBvnor :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvnor = liftFun2 Base.mkBvnor -- | Bitwise xnor. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga784f5ca36a4b03b93c67242cc94b21d6> mkBvxnor :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvxnor = liftFun2 Base.mkBvxnor -- | Standard two's complement unary minus. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga0c78be00c03eda4ed6a983224ed5c7b7 mkBvneg :: MonadZ3 z3 => AST -> z3 AST mkBvneg = liftFun1 Base.mkBvneg -- | Standard two's complement addition. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga819814e33573f3f9948b32fdc5311158> mkBvadd :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvadd = liftFun2 Base.mkBvadd -- | Standard two's complement subtraction. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga688c9aa1347888c7a51be4e46c19178e> mkBvsub :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsub = liftFun2 Base.mkBvsub -- | Standard two's complement multiplication. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga6abd3dde2a1ceff1704cf7221a72258c> mkBvmul :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvmul = liftFun2 Base.mkBvmul -- | Unsigned division. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga56ce0cd61666c6f8cf5777286f590544> mkBvudiv :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvudiv = liftFun2 Base.mkBvudiv -- | Two's complement signed division. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gad240fedb2fda1c1005b8e9d3c7f3d5a0> mkBvsdiv :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsdiv = liftFun2 Base.mkBvsdiv -- | Unsigned remainder. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga5df4298ec835e43ddc9e3e0bae690c8d> mkBvurem :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvurem = liftFun2 Base.mkBvurem -- | Two's complement signed remainder (sign follows dividend). -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga46c18a3042fca174fe659d3185693db1> mkBvsrem :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsrem = liftFun2 Base.mkBvsrem -- | Two's complement signed remainder (sign follows divisor). -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga95dac8e6eecb50f63cb82038560e0879> mkBvsmod :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsmod = liftFun2 Base.mkBvsmod -- | Unsigned less than. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga5774b22e93abcaf9b594672af6c7c3c4> mkBvult :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvult = liftFun2 Base.mkBvult -- | Two's complement signed less than. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga8ce08af4ed1fbdf08d4d6e63d171663a> mkBvslt :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvslt = liftFun2 Base.mkBvslt -- | Unsigned less than or equal to. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gab738b89de0410e70c089d3ac9e696e87> mkBvule :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvule = liftFun2 Base.mkBvule -- | Two's complement signed less than or equal to. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gab7c026feb93e7d2eab180e96f1e6255d> mkBvsle :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsle = liftFun2 Base.mkBvsle -- | Unsigned greater than or equal to. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gade58fbfcf61b67bf8c4a441490d3c4df> mkBvuge :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvuge = liftFun2 Base.mkBvuge -- | Two's complement signed greater than or equal to. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaeec3414c0e8a90a6aa5a23af36bf6dc5> mkBvsge :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsge = liftFun2 Base.mkBvsge -- | Unsigned greater than. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga063ab9f16246c99e5c1c893613927ee3> mkBvugt :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvugt = liftFun2 Base.mkBvugt -- | Two's complement signed greater than. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4e93a985aa2a7812c7c11a2c65d7c5f0> mkBvsgt :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsgt = liftFun2 Base.mkBvsgt -- | Concatenate the given bit-vectors. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gae774128fa5e9ff7458a36bd10e6ca0fa> mkConcat :: MonadZ3 z3 => AST -> AST -> z3 AST mkConcat = liftFun2 Base.mkConcat -- | Extract the bits high down to low from a bitvector of size m to yield a new -- bitvector of size /n/, where /n = high - low + 1/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga32d2fe7563f3e6b114c1b97b205d4317> mkExtract :: MonadZ3 z3 => Int -> Int -> AST -> z3 AST mkExtract = liftFun3 Base.mkExtract -- | Sign-extend of the given bit-vector to the (signed) equivalent bitvector -- of size /m+i/, where /m/ is the size of the given bit-vector. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gad29099270b36d0680bb54b560353c10e> mkSignExt :: MonadZ3 z3 => Int -> AST -> z3 AST mkSignExt = liftFun2 Base.mkSignExt -- | Extend the given bit-vector with zeros to the (unsigned) equivalent -- bitvector of size /m+i/, where /m/ is the size of the given bit-vector. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac9322fae11365a78640baf9078c428b3> mkZeroExt :: MonadZ3 z3 => Int -> AST -> z3 AST mkZeroExt = liftFun2 Base.mkZeroExt -- | Repeat the given bit-vector up length /i/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga03e81721502ea225c264d1f556c9119d> mkRepeat :: MonadZ3 z3 => Int -> AST -> z3 AST mkRepeat = liftFun2 Base.mkRepeat -- | Shift left. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac8d5e776c786c1172fa0d7dfede454e1> mkBvshl :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvshl = liftFun2 Base.mkBvshl -- | Logical shift right. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac59645a6edadad79a201f417e4e0c512> mkBvlshr :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvlshr = liftFun2 Base.mkBvlshr -- | Arithmetic shift right. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga674b580ad605ba1c2c9f9d3748be87c4> mkBvashr :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvashr = liftFun2 Base.mkBvashr -- | Rotate bits of /t1/ to the left /i/ times. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4932b7d08fea079dd903cd857a52dcda> mkRotateLeft :: MonadZ3 z3 => Int -> AST -> z3 AST mkRotateLeft = liftFun2 Base.mkRotateLeft -- | Rotate bits of /t1/ to the right /i/ times. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga3b94e1bf87ecd1a1858af8ebc1da4a1c> mkRotateRight :: MonadZ3 z3 => Int -> AST -> z3 AST mkRotateRight = liftFun2 Base.mkRotateRight -- | Rotate bits of /t1/ to the left /t2/ times. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaf46f1cb80e5a56044591a76e7c89e5e7> mkExtRotateLeft :: MonadZ3 z3 => AST -> AST -> z3 AST mkExtRotateLeft = liftFun2 Base.mkExtRotateLeft -- | Rotate bits of /t1/ to the right /t2/ times. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gabb227526c592b523879083f12aab281f> mkExtRotateRight :: MonadZ3 z3 => AST -> AST -> z3 AST mkExtRotateRight = liftFun2 Base.mkExtRotateRight -- | Create an /n/ bit bit-vector from the integer argument /t1/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga35f89eb05df43fbd9cce7200cc1f30b5> mkInt2bv :: MonadZ3 z3 => Int -> AST -> z3 AST mkInt2bv = liftFun2 Base.mkInt2bv -- | Create an integer from the bit-vector argument /t1/. If /is_signed/ is false, -- then the bit-vector /t1/ is treated as unsigned. So the result is non-negative -- and in the range [0..2^/N/-1], where /N/ are the number of bits in /t1/. -- If /is_signed/ is true, /t1/ is treated as a signed bit-vector. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac87b227dc3821d57258d7f53a28323d4> mkBv2int :: MonadZ3 z3 => AST -> Bool -> z3 AST mkBv2int = liftFun2 Base.mkBv2int -- | Create a predicate that checks that the bit-wise addition of /t1/ and /t2/ -- does not overflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga88f6b5ec876f05e0d7ba51e96c4b077f> mkBvaddNoOverflow :: MonadZ3 z3 => AST -> AST -> Bool -> z3 AST mkBvaddNoOverflow = liftFun3 Base.mkBvaddNoOverflow -- | Create a predicate that checks that the bit-wise signed addition of /t1/ -- and /t2/ does not underflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga1e2b1927cf4e50000c1600d47a152947> mkBvaddNoUnderflow :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvaddNoUnderflow = liftFun2 Base.mkBvaddNoUnderflow -- | Create a predicate that checks that the bit-wise signed subtraction of /t1/ -- and /t2/ does not overflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga785f8127b87e0b42130e6d8f52167d7c> mkBvsubNoOverflow :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsubNoOverflow = liftFun2 Base.mkBvsubNoOverflow -- | Create a predicate that checks that the bit-wise subtraction of /t1/ and -- /t2/ does not underflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga6480850f9fa01e14aea936c88ff184c4> mkBvsubNoUnderflow :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsubNoUnderflow = liftFun2 Base.mkBvsubNoUnderflow -- | Create a predicate that checks that the bit-wise signed division of /t1/ -- and /t2/ does not overflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaa17e7b2c33dfe2abbd74d390927ae83e> mkBvsdivNoOverflow :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvsdivNoOverflow = liftFun2 Base.mkBvsdivNoOverflow -- | Check that bit-wise negation does not overflow when /t1/ is interpreted as -- a signed bit-vector. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gae9c5d72605ddcd0e76657341eaccb6c7> mkBvnegNoOverflow :: MonadZ3 z3 => AST -> z3 AST mkBvnegNoOverflow = liftFun1 Base.mkBvnegNoOverflow -- | Create a predicate that checks that the bit-wise multiplication of /t1/ and -- /t2/ does not overflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga86f4415719d295a2f6845c70b3aaa1df> mkBvmulNoOverflow :: MonadZ3 z3 => AST -> AST -> Bool -> z3 AST mkBvmulNoOverflow = liftFun3 Base.mkBvmulNoOverflow -- | Create a predicate that checks that the bit-wise signed multiplication of -- /t1/ and /t2/ does not underflow. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga501ccc01d737aad3ede5699741717fda> mkBvmulNoUnderflow :: MonadZ3 z3 => AST -> AST -> z3 AST mkBvmulNoUnderflow = liftFun2 Base.mkBvmulNoUnderflow --------------------------------------------------------------------- -- Arrays -- | Array read. The argument a is the array and i is the index of the array -- that gets read. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga38f423f3683379e7f597a7fe59eccb67> mkSelect :: MonadZ3 z3 => AST -> AST -> z3 AST mkSelect = liftFun2 Base.mkSelect -- | Array update. Â -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gae305a4f54b4a64f7e5973ae6ccb13593> mkStore :: MonadZ3 z3 => AST -> AST -> AST -> z3 AST mkStore = liftFun3 Base.mkStore -- | Create the constant array. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga84ea6f0c32b99c70033feaa8f00e8f2d> mkConstArray :: MonadZ3 z3 => Sort -> AST -> z3 AST mkConstArray = liftFun2 Base.mkConstArray -- | map f on the the argument arrays. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga9150242d9430a8c3d55d2ca3b9a4362d> mkMap :: MonadZ3 z3 => FuncDecl -> [AST] -> z3 AST mkMap = liftFun2 Base.mkMap -- | Access the array default value. Produces the default range value, for -- arrays that can be represented as finite maps with a default range value. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga78e89cca82f0ab4d5f4e662e5e5fba7d> mkArrayDefault :: MonadZ3 z3 => AST -> z3 AST mkArrayDefault = liftFun1 Base.mkArrayDefault --------------------------------------------------------------------- -- Sets -- | Create the empty set. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga358b6b80509a567148f1c0ca9252118c> mkEmptySet :: MonadZ3 z3 => Sort -> z3 AST mkEmptySet = liftFun1 Base.mkEmptySet -- | Create the full set. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga5e92662c657374f7332aa32ce4503dd2> mkFullSet :: MonadZ3 z3 => Sort -> z3 AST mkFullSet = liftFun1 Base.mkFullSet -- | Add an element to a set. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga856c3d0e28ce720f53912c2bbdd76175> mkSetAdd :: MonadZ3 z3 => AST -> AST -> z3 AST mkSetAdd = liftFun2 Base.mkSetAdd -- | Remove an element from a set. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga80e883f39dd3b88f9d0745c8a5b91d1d> mkSetDel :: MonadZ3 z3 => AST -> AST -> z3 AST mkSetDel = liftFun2 Base.mkSetDel -- | Take the union of a list of sets. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4050162a13d539b8913200963bb4743c> mkSetUnion :: MonadZ3 z3 => [AST] -> z3 AST mkSetUnion = liftFun1 Base.mkSetUnion -- | Take the intersection of a list of sets. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga8a8abff0ebe6aeeaa6c919eaa013049d> mkSetIntersect :: MonadZ3 z3 => [AST] -> z3 AST mkSetIntersect = liftFun1 Base.mkSetIntersect -- | Take the set difference between two sets. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gabb49c62f70b8198362e1a29ba6d8bde1> mkSetDifference :: MonadZ3 z3 => AST -> AST -> z3 AST mkSetDifference = liftFun2 Base.mkSetDifference -- | Take the complement of a set. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga5c57143c9229cdf730c5103ff696590f> mkSetComplement :: MonadZ3 z3 => AST -> z3 AST mkSetComplement = liftFun1 Base.mkSetComplement -- | Check for set membership. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac6e516f3dce0bdd41095c6d6daf56063> mkSetMember :: MonadZ3 z3 => AST -> AST -> z3 AST mkSetMember = liftFun2 Base.mkSetMember -- | Check if the first set is a subset of the second set. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga139c5803af0e86464adc7cedc53e7f3a> mkSetSubset :: MonadZ3 z3 => AST -> AST -> z3 AST mkSetSubset = liftFun2 Base.mkSetSubset --------------------------------------------------------------------- -- * Numerals -- | Create a numeral of a given sort. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gac8aca397e32ca33618d8024bff32948c> mkNumeral :: MonadZ3 z3 => String -> Sort -> z3 AST mkNumeral = liftFun2 Base.mkNumeral -- | Create a numeral of sort /real/. mkReal :: MonadZ3 z3 => Int -> Int -> z3 AST mkReal = liftFun2 Base.mkReal -- | Create a numeral of an int, bit-vector, or finite-domain sort. -- -- This function can be use to create numerals that fit in a -- /machine integer/. -- It is slightly faster than 'mkNumeral' since it is not necessary -- to parse a string. mkInt :: MonadZ3 z3 => Int -> Sort -> z3 AST mkInt = liftFun2 Base.mkInt -- | Create a numeral of an int, bit-vector, or finite-domain sort. -- -- This function can be use to create numerals that fit in a -- /machine unsigned integer/. -- It is slightly faster than 'mkNumeral' since it is not necessary -- to parse a string. mkUnsignedInt :: MonadZ3 z3 => Word -> Sort -> z3 AST mkUnsignedInt = liftFun2 Base.mkUnsignedInt -- | Create a numeral of an int, bit-vector, or finite-domain sort. -- -- This function can be use to create numerals that fit in a -- /machine 64-bit integer/. -- It is slightly faster than 'mkNumeral' since it is not necessary -- to parse a string. mkInt64 :: MonadZ3 z3 => Int64 -> Sort -> z3 AST mkInt64 = liftFun2 Base.mkInt64 -- | Create a numeral of an int, bit-vector, or finite-domain sort. -- -- This function can be use to create numerals that fit in a -- /machine unsigned 64-bit integer/. -- It is slightly faster than 'mkNumeral' since it is not necessary -- to parse a string. mkUnsignedInt64 :: MonadZ3 z3 => Word64 -> Sort -> z3 AST mkUnsignedInt64 = liftFun2 Base.mkUnsignedInt64 ------------------------------------------------- -- ** Helpers -- | Create a numeral of an int, bit-vector, or finite-domain sort. mkIntegral :: (MonadZ3 z3, Integral a) => a -> Sort -> z3 AST mkIntegral = liftFun2 Base.mkIntegral -- | Create a numeral of sort /real/ from a 'Rational'. mkRational :: MonadZ3 z3 => Rational -> z3 AST mkRational = liftFun1 Base.mkRational -- | Create a numeral of sort /real/ from a 'Fixed'. mkFixed :: (MonadZ3 z3, HasResolution a) => Fixed a -> z3 AST mkFixed = liftFun1 Base.mkFixed -- | Create a numeral of sort /real/ from a 'Real'. mkRealNum :: (MonadZ3 z3, Real r) => r -> z3 AST mkRealNum = liftFun1 Base.mkRealNum -- | Create a numeral of sort /int/ from an 'Integer'. mkInteger :: MonadZ3 z3 => Integer -> z3 AST mkInteger = liftFun1 Base.mkInteger -- | Create a numeral of sort /int/ from an 'Integral'. mkIntNum :: (MonadZ3 z3, Integral a) => a -> z3 AST mkIntNum = liftFun1 Base.mkIntNum -- | Create a numeral of sort /Bit-vector/ from an 'Integer'. mkBitvector :: MonadZ3 z3 => Int -- ^ bit-width -> Integer -- ^ integer value -> z3 AST mkBitvector = liftFun2 Base.mkBitvector -- | Create a numeral of sort /Bit-vector/ from an 'Integral'. mkBvNum :: (MonadZ3 z3, Integral i) => Int -- ^ bit-width -> i -- ^ integer value -> z3 AST mkBvNum = liftFun2 Base.mkBvNum --------------------------------------------------------------------- -- Quantifiers mkPattern :: MonadZ3 z3 => [AST] -> z3 Pattern mkPattern = liftFun1 Base.mkPattern mkBound :: MonadZ3 z3 => Int -> Sort -> z3 AST mkBound = liftFun2 Base.mkBound mkForall :: MonadZ3 z3 => [Pattern] -> [Symbol] -> [Sort] -> AST -> z3 AST mkForall = liftFun4 Base.mkForall mkForallConst :: MonadZ3 z3 => [Pattern] -> [App] -> AST -> z3 AST mkForallConst = liftFun3 Base.mkForallConst mkExistsConst :: MonadZ3 z3 => [Pattern] -> [App] -> AST -> z3 AST mkExistsConst = liftFun3 Base.mkExistsConst mkExists :: MonadZ3 z3 => [Pattern] -> [Symbol] -> [Sort] -> AST -> z3 AST mkExists = liftFun4 Base.mkExists --------------------------------------------------------------------- -- Accessors -- | Return the symbol name. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaf1683d9464f377e5089ce6ebf2a9bd31> getSymbolString :: MonadZ3 z3 => Symbol -> z3 String getSymbolString = liftFun1 Base.getSymbolString -- | Return the sort kind. -- -- Reference: <http://z3prover.github.io/api/html/group__capi.html#gacd85d48842c7bfaa696596d16875681a> getSortKind :: MonadZ3 z3 => Sort -> z3 SortKind getSortKind = liftFun1 Base.getSortKind -- | Return the size of the given bit-vector sort. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga8fc3550edace7bc046e16d1f96ddb419> getBvSortSize :: MonadZ3 z3 => Sort -> z3 Int getBvSortSize = liftFun1 Base.getBvSortSize -- | Get list of constructors for datatype. getDatatypeSortConstructors :: MonadZ3 z3 => Sort -- ^ Datatype sort. -> z3 [FuncDecl] -- ^ Constructor declarations. getDatatypeSortConstructors = liftFun1 Base.getDatatypeSortConstructors -- | Get list of recognizers for datatype. getDatatypeSortRecognizers :: MonadZ3 z3 => Sort -- ^ Datatype sort. -> z3 [FuncDecl] -- ^ Constructor recognizers. getDatatypeSortRecognizers = liftFun1 Base.getDatatypeSortRecognizers -- | Get list of accessors for datatype. getDatatypeSortConstructorAccessors :: MonadZ3 z3 => Sort -- ^ Datatype sort. -> z3 [[FuncDecl]] -- ^ Constructor recognizers. getDatatypeSortConstructorAccessors = liftFun1 Base.getDatatypeSortConstructorAccessors -- | Return the constant declaration name as a symbol. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga741b1bf11cb92aa2ec9ef2fef73ff129> getDeclName :: MonadZ3 z3 => FuncDecl -> z3 Symbol getDeclName = liftFun1 Base.getDeclName -- | Returns the number of parameters of the given declaration getArity :: MonadZ3 z3 => FuncDecl -> z3 Int getArity = liftFun1 Base.getArity -- | Returns the sort of the i-th parameter of the given function declaration getDomain :: MonadZ3 z3 => FuncDecl -- ^ A function declaration -> Int -- ^ i -> z3 Sort getDomain = liftFun2 Base.getDomain -- | Returns the range of the given declaration. getRange :: MonadZ3 z3 => FuncDecl -> z3 Sort getRange = liftFun1 Base.getRange -- | Convert an app into AST. This is just type casting. appToAst :: MonadZ3 z3 => App -> z3 AST appToAst = liftFun1 Base.appToAst -- | Return the declaration of a constant or function application. getAppDecl :: MonadZ3 z3 => App -> z3 FuncDecl getAppDecl = liftFun1 Base.getAppDecl -- | Return the number of argument of an application. If t is an constant, then the number of arguments is 0. getAppNumArgs :: MonadZ3 z3 => App -> z3 Int getAppNumArgs = liftFun1 Base.getAppNumArgs -- | Return the i-th argument of the given application. getAppArg :: MonadZ3 z3 => App -> Int -> z3 AST getAppArg = liftFun2 Base.getAppArg -- | Return a list of all the arguments of the given application. getAppArgs :: MonadZ3 z3 => App -> z3 [AST] getAppArgs = liftFun1 Base.getAppArgs -- | Return the sort of an AST node. getSort :: MonadZ3 z3 => AST -> z3 Sort getSort = liftFun1 Base.getSort getArraySortDomain :: MonadZ3 z3 => Sort -> z3 Sort getArraySortDomain = liftFun1 Base.getArraySortDomain getArraySortRange :: MonadZ3 z3 => Sort -> z3 Sort getArraySortRange = liftFun1 Base.getArraySortRange -- | Returns @Just True@, @Just False@, or @Nothing@ for /undefined/. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga133aaa1ec31af9b570ed7627a3c8c5a4> getBoolValue :: MonadZ3 z3 => AST -> z3 (Maybe Bool) getBoolValue = liftFun1 Base.getBoolValue -- | Return the kind of the given AST. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4c43608feea4cae363ef9c520c239a5c> getAstKind :: MonadZ3 z3 => AST -> z3 ASTKind getAstKind = liftFun1 Base.getAstKind -- | Return True if an ast is APP_AST, False otherwise. isApp :: MonadZ3 z3 => AST -> z3 Bool isApp = liftFun1 Base.isApp -- | Cast AST into an App. toApp :: MonadZ3 z3 => AST -> z3 App toApp = liftFun1 Base.toApp -- | Return numeral value, as a string of a numeric constant term. getNumeralString :: MonadZ3 z3 => AST -> z3 String getNumeralString = liftFun1 Base.getNumeralString getIndexValue :: MonadZ3 z3 => AST -> z3 Int getIndexValue = liftFun1 Base.getIndexValue isQuantifierForall :: MonadZ3 z3 => AST -> z3 Bool isQuantifierForall = liftFun1 Base.isQuantifierForall isQuantifierExists :: MonadZ3 z3 => AST -> z3 Bool isQuantifierExists = liftFun1 Base.isQuantifierExists getQuantifierWeight :: MonadZ3 z3 => AST -> z3 Int getQuantifierWeight = liftFun1 Base.getQuantifierWeight getQuantifierNumPatterns :: MonadZ3 z3 => AST -> z3 Int getQuantifierNumPatterns = liftFun1 Base.getQuantifierNumPatterns getQuantifierPatternAST :: MonadZ3 z3 => AST -> Int -> z3 AST getQuantifierPatternAST = liftFun2 Base.getQuantifierPatternAST getQuantifierPatterns :: MonadZ3 z3 => AST -> z3 [AST] getQuantifierPatterns = liftFun1 Base.getQuantifierPatterns getQuantifierNumNoPatterns :: MonadZ3 z3 => AST -> z3 Int getQuantifierNumNoPatterns = liftFun1 Base.getQuantifierNumNoPatterns getQuantifierNoPatternAST :: MonadZ3 z3 => AST -> Int -> z3 AST getQuantifierNoPatternAST = liftFun2 Base.getQuantifierNoPatternAST getQuantifierNoPatterns :: MonadZ3 z3 => AST -> z3 [AST] getQuantifierNoPatterns = liftFun1 Base.getQuantifierNoPatterns getQuantifierNumBound :: MonadZ3 z3 => AST -> z3 Int getQuantifierNumBound = liftFun1 Base.getQuantifierNumBound getQuantifierBoundName :: MonadZ3 z3 => AST -> Int -> z3 Symbol getQuantifierBoundName = liftFun2 Base.getQuantifierBoundName getQuantifierBoundSort :: MonadZ3 z3 => AST -> Int -> z3 Sort getQuantifierBoundSort = liftFun2 Base.getQuantifierBoundSort getQuantifierBoundVars :: MonadZ3 z3 => AST -> z3 [AST] getQuantifierBoundVars = liftFun1 Base.getQuantifierBoundVars getQuantifierBody :: MonadZ3 z3 => AST -> z3 AST getQuantifierBody = liftFun1 Base.getQuantifierBody -- | Simplify the expression. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gada433553406475e5dd6a494ea957844c> simplify :: MonadZ3 z3 => AST -> z3 AST simplify = liftFun1 Base.simplify -- | Simplify the expression using the given parameters. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga34329d4c83ca8c98e18b2884b679008c> simplifyEx :: MonadZ3 z3 => AST -> Params -> z3 AST simplifyEx = liftFun2 Base.simplifyEx ------------------------------------------------- -- ** Helpers -- | Read a 'Bool' value from an 'AST' getBool :: MonadZ3 z3 => AST -> z3 Bool getBool = liftFun1 Base.getBool -- | Return the integer value getInt :: MonadZ3 z3 => AST -> z3 Integer getInt = liftFun1 Base.getInt -- | Return rational value getReal :: MonadZ3 z3 => AST -> z3 Rational getReal = liftFun1 Base.getReal -- | Read the 'Integer' value from an 'AST' of sort /bit-vector/. -- -- See 'mkBv2int'. getBv :: MonadZ3 z3 => AST -> Bool -- ^ signed? -> z3 Integer getBv = liftFun2 Base.getBv --------------------------------------------------------------------- -- Modifiers substituteVars :: MonadZ3 z3 => AST -> [AST] -> z3 AST substituteVars = liftFun2 Base.substituteVars --------------------------------------------------------------------- -- Models -- | Evaluate an AST node in the given model. -- -- The evaluation may fail for the following reasons: -- -- * /t/ contains a quantifier. -- * the model /m/ is partial. -- * /t/ is type incorrect. modelEval :: MonadZ3 z3 => Model -> AST -> Bool -- ^ Model completion? -> z3 (Maybe AST) modelEval = liftFun3 Base.modelEval -- | Get array as a list of argument/value pairs, if it is -- represented as a function (ie, using as-array). evalArray :: MonadZ3 z3 => Model -> AST -> z3 (Maybe FuncModel) evalArray = liftFun2 Base.evalArray getConstInterp :: MonadZ3 z3 => Model -> FuncDecl -> z3 (Maybe AST) getConstInterp = liftFun2 Base.getConstInterp -- | Return the interpretation of the function f in the model m. -- Return NULL, if the model does not assign an interpretation for f. -- That should be interpreted as: the f does not matter. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gafb9cc5eca9564d8a849c154c5a4a8633> getFuncInterp :: MonadZ3 z3 => Model -> FuncDecl -> z3 (Maybe FuncInterp) getFuncInterp = liftFun2 Base.getFuncInterp hasInterp :: MonadZ3 z3 => Model -> FuncDecl -> z3 Bool hasInterp = liftFun2 Base.hasInterp numConsts :: MonadZ3 z3 => Model -> z3 Word numConsts = liftFun1 Base.numConsts numFuncs :: MonadZ3 z3 => Model -> z3 Word numFuncs = liftFun1 Base.numFuncs getConstDecl :: MonadZ3 z3 => Model -> Word -> z3 FuncDecl getConstDecl = liftFun2 Base.getConstDecl getFuncDecl :: MonadZ3 z3 => Model -> Word -> z3 FuncDecl getFuncDecl = liftFun2 Base.getFuncDecl getConsts :: MonadZ3 z3 => Model -> z3 [FuncDecl] getConsts = liftFun1 Base.getConsts getFuncs :: MonadZ3 z3 => Model -> z3 [FuncDecl] getFuncs = liftFun1 Base.getFuncs -- | The (_ as-array f) AST node is a construct for assigning interpretations -- for arrays in Z3. It is the array such that forall indices i we have that -- (select (_ as-array f) i) is equal to (f i). This procedure returns Z3_TRUE -- if the a is an as-array AST node. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga4674da67d226bfb16861829b9f129cfa> isAsArray :: MonadZ3 z3 => AST -> z3 Bool isAsArray = liftFun1 Base.isAsArray addFuncInterp :: MonadZ3 z3 => Model -> FuncDecl -> AST -> z3 FuncInterp addFuncInterp = liftFun3 Base.addFuncInterp addConstInterp :: MonadZ3 z3 => Model -> FuncDecl -> AST -> z3 () addConstInterp = liftFun3 Base.addConstInterp -- | Return the function declaration f associated with a (_ as_array f) node. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga7d9262dc6e79f2aeb23fd4a383589dda> getAsArrayFuncDecl :: MonadZ3 z3 => AST -> z3 FuncDecl getAsArrayFuncDecl = liftFun1 Base.getAsArrayFuncDecl -- | Return the number of entries in the given function interpretation. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga2bab9ae1444940e7593729beec279844> funcInterpGetNumEntries :: MonadZ3 z3 => FuncInterp -> z3 Int funcInterpGetNumEntries = liftFun1 Base.funcInterpGetNumEntries -- | Return a "point" of the given function intepretation. -- It represents the value of f in a particular point. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaf157e1e1cd8c0cfe6a21be6370f659da> funcInterpGetEntry :: MonadZ3 z3 => FuncInterp -> Int -> z3 FuncEntry funcInterpGetEntry = liftFun2 Base.funcInterpGetEntry -- | Return the 'else' value of the given function interpretation. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga46de7559826ba71b8488d727cba1fb64> funcInterpGetElse :: MonadZ3 z3 => FuncInterp -> z3 AST funcInterpGetElse = liftFun1 Base.funcInterpGetElse -- | Return the arity (number of arguments) of the given function -- interpretation. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaca22cbdb6f7787aaae5d814f2ab383d8> funcInterpGetArity :: MonadZ3 z3 => FuncInterp -> z3 Int funcInterpGetArity = liftFun1 Base.funcInterpGetArity -- | Return the value of this point. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga9fd65e2ab039aa8e40608c2ecf7084da> funcEntryGetValue :: MonadZ3 z3 => FuncEntry -> z3 AST funcEntryGetValue = liftFun1 Base.funcEntryGetValue -- | Return the number of arguments in a Z3_func_entry object. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga51aed8c5bc4b1f53f0c371312de3ce1a> funcEntryGetNumArgs :: MonadZ3 z3 => FuncEntry -> z3 Int funcEntryGetNumArgs = liftFun1 Base.funcEntryGetNumArgs -- | Return an argument of a Z3_func_entry object. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga6fe03fe3c824fceb52766a4d8c2cbeab> funcEntryGetArg :: MonadZ3 z3 => FuncEntry -> Int -> z3 AST funcEntryGetArg = liftFun2 Base.funcEntryGetArg -- | Convert the given model into a string. modelToString :: MonadZ3 z3 => Model -> z3 String modelToString = liftFun1 Base.modelToString -- | Alias for 'modelToString'. showModel :: MonadZ3 z3 => Model -> z3 String showModel = modelToString ------------------------------------------------- -- ** Helpers -- | Type of an evaluation function for 'AST'. -- -- Evaluation may fail (i.e. return 'Nothing') for a few -- reasons, see 'modelEval'. type EvalAst m a = Model -> AST -> m (Maybe a) -- | An alias for 'modelEval' with model completion enabled. eval :: MonadZ3 z3 => EvalAst z3 AST eval = liftFun2 Base.eval -- | Evaluate an AST node of sort /bool/ in the given model. -- -- See 'modelEval' and 'getBool'. evalBool :: MonadZ3 z3 => EvalAst z3 Bool evalBool = liftFun2 Base.evalBool -- | Evaluate an AST node of sort /int/ in the given model. -- -- See 'modelEval' and 'getInt'. evalInt :: MonadZ3 z3 => EvalAst z3 Integer evalInt = liftFun2 Base.evalInt -- | Evaluate an AST node of sort /real/ in the given model. -- -- See 'modelEval' and 'getReal'. evalReal :: MonadZ3 z3 => EvalAst z3 Rational evalReal = liftFun2 Base.evalReal -- | Evaluate an AST node of sort /bit-vector/ in the given model. -- -- The flag /signed/ decides whether the bit-vector value is -- interpreted as a signed or unsigned integer. -- -- See 'modelEval' and 'getBv'. evalBv :: MonadZ3 z3 => Bool -- ^ signed? -> EvalAst z3 Integer evalBv = liftFun3 Base.evalBv -- | Evaluate a collection of AST nodes in the given model. evalT :: (MonadZ3 z3,Traversable t) => Model -> t AST -> z3 (Maybe (t AST)) evalT = liftFun2 Base.evalT -- | Run a evaluation function on a 'Traversable' data structure of 'AST's -- (e.g. @[AST]@, @Vector AST@, @Maybe AST@, etc). -- -- This a generic version of 'evalT' which can be used in combination with -- other helpers. For instance, @mapEval evalInt@ can be used to obtain -- the 'Integer' interpretation of a list of 'AST' of sort /int/. mapEval :: (MonadZ3 z3, Traversable t) => EvalAst z3 a -> Model -> t AST -> z3 (Maybe (t a)) mapEval f m = fmap T.sequence . T.mapM (f m) -- | Get function as a list of argument/value pairs. evalFunc :: MonadZ3 z3 => Model -> FuncDecl -> z3 (Maybe FuncModel) evalFunc = liftFun2 Base.evalFunc --------------------------------------------------------------------- -- Tactics mkTactic :: MonadZ3 z3 => String -> z3 Tactic mkTactic = liftFun1 Base.mkTactic andThenTactic :: MonadZ3 z3 => Tactic -> Tactic -> z3 Tactic andThenTactic = liftFun2 Base.andThenTactic orElseTactic :: MonadZ3 z3 => Tactic -> Tactic -> z3 Tactic orElseTactic = liftFun2 Base.andThenTactic skipTactic :: MonadZ3 z3 => z3 Tactic skipTactic = liftScalar Base.skipTactic tryForTactic :: MonadZ3 z3 => Tactic -> Int -> z3 Tactic tryForTactic = liftFun2 Base.tryForTactic mkQuantifierEliminationTactic :: MonadZ3 z3 => z3 Tactic mkQuantifierEliminationTactic = liftScalar Base.mkQuantifierEliminationTactic mkAndInverterGraphTactic :: MonadZ3 z3 => z3 Tactic mkAndInverterGraphTactic = liftScalar Base.mkAndInverterGraphTactic applyTactic :: MonadZ3 z3 => Tactic -> Goal -> z3 ApplyResult applyTactic = liftFun2 Base.applyTactic getApplyResultNumSubgoals :: MonadZ3 z3 => ApplyResult -> z3 Int getApplyResultNumSubgoals = liftFun1 Base.getApplyResultNumSubgoals getApplyResultSubgoal :: MonadZ3 z3 => ApplyResult -> Int -> z3 Goal getApplyResultSubgoal = liftFun2 Base.getApplyResultSubgoal getApplyResultSubgoals :: MonadZ3 z3 => ApplyResult -> z3 [Goal] getApplyResultSubgoals = liftFun1 Base.getApplyResultSubgoals mkGoal :: MonadZ3 z3 => Bool -> Bool -> Bool -> z3 Goal mkGoal = liftFun3 Base.mkGoal goalAssert :: MonadZ3 z3 => Goal -> AST -> z3 () goalAssert = liftFun2 Base.goalAssert getGoalSize :: MonadZ3 z3 => Goal -> z3 Int getGoalSize = liftFun1 Base.getGoalSize getGoalFormula :: MonadZ3 z3 => Goal -> Int -> z3 AST getGoalFormula = liftFun2 Base.getGoalFormula getGoalFormulas :: MonadZ3 z3 => Goal -> z3 [AST] getGoalFormulas = liftFun1 Base.getGoalFormulas --------------------------------------------------------------------- -- String Conversion -- | Set the mode for converting expressions to strings. setASTPrintMode :: MonadZ3 z3 => ASTPrintMode -> z3 () setASTPrintMode = liftFun1 Base.setASTPrintMode -- | Convert an AST to a string. astToString :: MonadZ3 z3 => AST -> z3 String astToString = liftFun1 Base.astToString -- | Convert a pattern to a string. patternToString :: MonadZ3 z3 => Pattern -> z3 String patternToString = liftFun1 Base.patternToString -- | Convert a sort to a string. sortToString :: MonadZ3 z3 => Sort -> z3 String sortToString = liftFun1 Base.sortToString -- | Convert a FuncDecl to a string. funcDeclToString :: MonadZ3 z3 => FuncDecl -> z3 String funcDeclToString = liftFun1 Base.funcDeclToString -- | Convert the given benchmark into SMT-LIB formatted string. -- -- The output format can be configured via 'setASTPrintMode'. benchmarkToSMTLibString :: MonadZ3 z3 => String -- ^ name -> String -- ^ logic -> String -- ^ status -> String -- ^ attributes -> [AST] -- ^ assumptions1 -> AST -- ^ formula -> z3 String benchmarkToSMTLibString = liftFun6 Base.benchmarkToSMTLibString --------------------------------------------------------------------- -- Parser interface -- | Parse SMT expressions from a string -- -- The sort and declaration arguments allow parsing in a context in which variables and functions have already been declared. They are almost never used. parseSMTLib2String :: MonadZ3 z3 => String -- ^ string to parse -> [Symbol] -- ^ sort names -> [Sort] -- ^ sorts -> [Symbol] -- ^ declaration names -> [FuncDecl] -- ^ declarations -> z3 AST parseSMTLib2String = liftFun5 Base.parseSMTLib2String -- | Parse SMT expressions from a file -- -- The sort and declaration arguments allow parsing in a context in which variables and functions have already been declared. They are almost never used. parseSMTLib2File :: MonadZ3 z3 => String -- ^ string to parse -> [Symbol] -- ^ sort names -> [Sort] -- ^ sorts -> [Symbol] -- ^ declaration names -> [FuncDecl] -- ^ declarations -> z3 AST parseSMTLib2File = liftFun5 Base.parseSMTLib2File --------------------------------------------------------------------- -- Miscellaneous -- | Return Z3 version number information. getVersion :: MonadZ3 z3 => z3 Version getVersion = liftIO Base.getVersion --------------------------------------------------------------------- -- Fixedpoint class MonadZ3 m => MonadFixedpoint m where getFixedpoint :: m Base.Fixedpoint fixedpointPush :: MonadFixedpoint z3 => z3 () fixedpointPush = liftFixedpoint0 Base.fixedpointPush fixedpointPop :: MonadFixedpoint z3 => z3 () fixedpointPop = liftFixedpoint0 Base.fixedpointPush fixedpointAddRule :: MonadFixedpoint z3 => AST -> Symbol -> z3 () fixedpointAddRule = liftFixedpoint2 Base.fixedpointAddRule fixedpointSetParams :: MonadFixedpoint z3 => Params -> z3 () fixedpointSetParams = liftFixedpoint1 Base.fixedpointSetParams fixedpointRegisterRelation :: MonadFixedpoint z3 => FuncDecl -> z3 () fixedpointRegisterRelation = liftFixedpoint1 Base.fixedpointRegisterRelation fixedpointQueryRelations :: MonadFixedpoint z3 => [FuncDecl] -> z3 Result fixedpointQueryRelations = liftFixedpoint1 Base.fixedpointQueryRelations fixedpointGetAnswer :: MonadFixedpoint z3 => z3 AST fixedpointGetAnswer = liftFixedpoint0 Base.fixedpointGetAnswer fixedpointGetAssertions :: MonadFixedpoint z3 => z3 [AST] fixedpointGetAssertions = liftFixedpoint0 Base.fixedpointGetAssertions --------------------------------------------------------------------- -- * Solvers -- mkSolver :: Context -> IO Solver -- mkSolver = liftFun0 z3_mk_solver -- mkSimpleSolver :: Context -> IO Solver -- mkSimpleSolver = liftFun0 z3_mk_simple_solver -- mkSolverForLogic :: Context -> Logic -> IO Solver -- mkSolverForLogic c logic = withContextError c $ \cPtr -> -- do sym <- mkStringSymbol c (show logic) -- c2h c =<< z3_mk_solver_for_logic cPtr (unSymbol sym) -- | Return a string describing all solver available parameters. solverGetHelp :: MonadZ3 z3 => z3 String solverGetHelp = liftSolver0 Base.solverGetHelp -- | Set the solver using the given parameters. solverSetParams :: MonadZ3 z3 => Params -> z3 () solverSetParams = liftSolver1 Base.solverSetParams -- | Create a backtracking point. solverPush :: MonadZ3 z3 => z3 () solverPush = liftSolver0 Base.solverPush -- | Backtrack /n/ backtracking points. solverPop :: MonadZ3 z3 => Int -> z3 () solverPop = liftSolver1 Base.solverPop solverReset :: MonadZ3 z3 => z3 () solverReset = liftSolver0 Base.solverReset -- | Number of backtracking points. solverGetNumScopes :: MonadZ3 z3 => z3 Int solverGetNumScopes = liftSolver0 Base.solverGetNumScopes -- | Assert a constraing into the logical context. -- -- Reference: <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#ga1a05ff73a564ae7256a2257048a4680a> solverAssertCnstr :: MonadZ3 z3 => AST -> z3 () solverAssertCnstr = liftSolver1 Base.solverAssertCnstr -- | Assert a constraint a into the solver, and track it -- (in the unsat) core using the Boolean constant /p/. -- -- This API is an alternative to Z3_solver_check_assumptions -- for extracting unsat cores. Both APIs can be used in the same -- solver. The unsat core will contain a combination of the Boolean -- variables provided using Z3_solver_assert_and_track and the -- Boolean literals provided using Z3_solver_check_assumptions. solverAssertAndTrack :: MonadZ3 z3 => AST -> AST -> z3 () solverAssertAndTrack = liftSolver2 Base.solverAssertAndTrack -- | Check whether the assertions in a given solver are consistent or not. solverCheck :: MonadZ3 z3 => z3 Result solverCheck = liftSolver0 Base.solverCheck -- | Check whether the assertions in the given solver and optional assumptions are consistent or not. solverCheckAssumptions :: MonadZ3 z3 => [AST] -> z3 Result solverCheckAssumptions = liftSolver1 Base.solverCheckAssumptions -- | Retrieve the model for the last 'solverCheck'. -- -- The error handler is invoked if a model is not available because -- the commands above were not invoked for the given solver, -- or if the result was 'Unsat'. solverGetModel :: MonadZ3 z3 => z3 Model solverGetModel = liftSolver0 Base.solverGetModel -- | Retrieve the unsat core for the last 'solverCheckAssumptions'; the unsat core is a subset of the assumptions solverGetUnsatCore :: MonadZ3 z3 => z3 [AST] solverGetUnsatCore = liftSolver0 Base.solverGetUnsatCore -- | Return a brief justification for an 'Unknown' result for the commands 'solverCheck' and 'solverCheckAssumptions'. solverGetReasonUnknown :: MonadZ3 z3 => z3 String solverGetReasonUnknown = liftSolver0 Base.solverGetReasonUnknown -- | Convert the given solver into a string. solverToString :: MonadZ3 z3 => z3 String solverToString = liftSolver0 Base.solverToString ------------------------------------------------- -- ** Helpers -- | Create a backtracking point. -- -- For @push; m; pop 1@ see 'local'. push :: MonadZ3 z3 => z3 () push = solverPush -- | Backtrack /n/ backtracking points. -- -- Contrary to 'solverPop' this funtion checks whether /n/ is within -- the size of the solver scope stack. pop :: MonadZ3 z3 => Int -> z3 () pop n = do scopes <- solverGetNumScopes if n <= scopes then solverPop n else error "Z3.Monad.safePop: too many scopes to backtrack" -- | Run a query and restore the initial logical context. -- -- This is a shorthand for 'push', run the query, and 'pop'. local :: MonadZ3 z3 => z3 a -> z3 a local q = do push r <- q pop 1 return r -- | Backtrack all the way. reset :: MonadZ3 z3 => z3 () reset = solverReset -- | Get number of backtracking points. getNumScopes :: MonadZ3 z3 => z3 Int getNumScopes = liftSolver0 Base.solverGetNumScopes assert :: MonadZ3 z3 => AST -> z3 () assert = solverAssertCnstr -- | Check whether the given logical context is consistent or not. check :: MonadZ3 z3 => z3 Result check = solverCheck -- | Check whether the assertions in the given solver and optional assumptions are consistent or not. checkAssumptions :: MonadZ3 z3 => [AST] -> z3 Result checkAssumptions = solverCheckAssumptions solverCheckAndGetModel :: MonadZ3 z3 => z3 (Result, Maybe Model) solverCheckAndGetModel = liftSolver0 Base.solverCheckAndGetModel -- | Get model. -- -- Reference : <http://research.microsoft.com/en-us/um/redmond/projects/z3/group__capi.html#gaff310fef80ac8a82d0a51417e073ec0a> getModel :: MonadZ3 z3 => z3 (Result, Maybe Model) getModel = solverCheckAndGetModel -- | Check satisfiability and, if /sat/, compute a value from the given model. -- -- E.g. -- @ -- withModel $ \\m -> -- fromJust \<$\> evalInt m x -- @ withModel :: (Applicative z3, MonadZ3 z3) => (Base.Model -> z3 a) -> z3 (Result, Maybe a) withModel f = do (r,mb_m) <- getModel mb_e <- T.traverse f mb_m return (r, mb_e) -- | Retrieve the unsat core for the last 'checkAssumptions'; the unsat core is a subset of the assumptions. getUnsatCore :: MonadZ3 z3 => z3 [AST] getUnsatCore = solverGetUnsatCore