----------------------------------------------------------------------------- -- | -- Module : Data.SBV.Core.Data -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- -- Internal data-structures for the sbv library ----------------------------------------------------------------------------- {-# LANGUAGE CPP #-} {-# LANGUAGE TypeSynonymInstances #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE InstanceSigs #-} {-# LANGUAGE PatternGuards #-} {-# LANGUAGE DefaultSignatures #-} {-# LANGUAGE NamedFieldPuns #-} {-# LANGUAGE DeriveAnyClass #-} {-# LANGUAGE DeriveGeneric #-} module Data.SBV.Core.Data ( SBool, SWord8, SWord16, SWord32, SWord64 , SInt8, SInt16, SInt32, SInt64, SInteger, SReal, SFloat, SDouble, SChar, SString , nan, infinity, sNaN, sInfinity, RoundingMode(..), SRoundingMode , sRoundNearestTiesToEven, sRoundNearestTiesToAway, sRoundTowardPositive, sRoundTowardNegative, sRoundTowardZero , sRNE, sRNA, sRTP, sRTN, sRTZ , SymWord(..) , CW(..), CWVal(..), AlgReal(..), AlgRealPoly, ExtCW(..), GeneralizedCW(..), isRegularCW, cwSameType, cwToBool , mkConstCW ,liftCW2, mapCW, mapCW2 , SW(..), trueSW, falseSW, trueCW, falseCW, normCW , SVal(..) , SBV(..), NodeId(..), mkSymSBV , ArrayContext(..), ArrayInfo, SymArray(..), SFunArray(..), SArray(..) , sbvToSW, sbvToSymSW, forceSWArg , SBVExpr(..), newExpr , cache, Cached, uncache, uncacheAI, HasKind(..) , Op(..), PBOp(..), FPOp(..), StrOp(..), RegExp(..), NamedSymVar, getTableIndex , SBVPgm(..), Symbolic, runSymbolic, State, getPathCondition, extendPathCondition , inSMTMode, SBVRunMode(..), Kind(..), Outputtable(..), Result(..) , SolverContext(..), internalVariable, internalConstraint, isCodeGenMode , SBVType(..), newUninterpreted, addAxiom , Quantifier(..), needsExistentials , SMTLibPgm(..), SMTLibVersion(..), smtLibVersionExtension, smtLibReservedNames , SolverCapabilities(..) , extractSymbolicSimulationState , SMTScript(..), Solver(..), SMTSolver(..), SMTResult(..), SMTModel(..), SMTConfig(..) , OptimizeStyle(..), Penalty(..), Objective(..) , QueryState(..), Query(..), SMTProblem(..) ) where import GHC.Generics (Generic) import Control.DeepSeq (NFData(..)) import Control.Monad.Reader (ask) import Control.Monad.Trans (liftIO) import Data.Int (Int8, Int16, Int32, Int64) import Data.Word (Word8, Word16, Word32, Word64) import Data.List (elemIndex) import qualified Data.Generics as G (Data(..)) import System.Random import Data.SBV.Core.AlgReals import Data.SBV.Core.Kind import Data.SBV.Core.Concrete import Data.SBV.Core.Symbolic import Data.SBV.Core.Operations import Data.SBV.Control.Types import Data.SBV.SMT.SMTLibNames import Data.SBV.Utils.Lib import Data.SBV.Utils.Boolean -- | Get the current path condition getPathCondition :: State -> SBool getPathCondition st = SBV (getSValPathCondition st) -- | Extend the path condition with the given test value. extendPathCondition :: State -> (SBool -> SBool) -> State extendPathCondition st f = extendSValPathCondition st (unSBV . f . SBV) -- | The "Symbolic" value. The parameter 'a' is phantom, but is -- extremely important in keeping the user interface strongly typed. newtype SBV a = SBV { unSBV :: SVal } deriving (Generic, NFData) -- | A symbolic boolean/bit type SBool = SBV Bool -- | 8-bit unsigned symbolic value type SWord8 = SBV Word8 -- | 16-bit unsigned symbolic value type SWord16 = SBV Word16 -- | 32-bit unsigned symbolic value type SWord32 = SBV Word32 -- | 64-bit unsigned symbolic value type SWord64 = SBV Word64 -- | 8-bit signed symbolic value, 2's complement representation type SInt8 = SBV Int8 -- | 16-bit signed symbolic value, 2's complement representation type SInt16 = SBV Int16 -- | 32-bit signed symbolic value, 2's complement representation type SInt32 = SBV Int32 -- | 64-bit signed symbolic value, 2's complement representation type SInt64 = SBV Int64 -- | Infinite precision signed symbolic value type SInteger = SBV Integer -- | Infinite precision symbolic algebraic real value type SReal = SBV AlgReal -- | IEEE-754 single-precision floating point numbers type SFloat = SBV Float -- | IEEE-754 double-precision floating point numbers type SDouble = SBV Double -- | A symbolic character. Note that, as far as SBV's symbolic strings are concerned, a character -- is currently an 8-bit unsigned value, corresponding to the ISO-8859-1 (Latin-1) character -- set: . A Haskell 'Char', on the other hand, is based -- on unicode. Therefore, there isn't a 1-1 correspondence between a Haskell character and an SBV -- character for the time being. This limitation is due to the SMT-solvers only supporting this -- particular subset. However, there is a pending proposal to add support for unicode, and SBV -- will track these changes to have full unicode support as solvers become available. For -- details, see: type SChar = SBV Char -- | A symbolic string. Note that a symbolic string is /not/ a list of symbolic characters, -- that is, it is not the case that @SString = [SChar]@, unlike what one might expect following -- Haskell strings. An 'SString' is a symbolic value of its own, of possibly arbitrary length, -- and internally processed as one unit as opposed to a fixed-length list of characters. type SString = SBV String -- | Not-A-Number for 'Double' and 'Float'. Surprisingly, Haskell -- Prelude doesn't have this value defined, so we provide it here. nan :: Floating a => a nan = 0/0 -- | Infinity for 'Double' and 'Float'. Surprisingly, Haskell -- Prelude doesn't have this value defined, so we provide it here. infinity :: Floating a => a infinity = 1/0 -- | Symbolic variant of Not-A-Number. This value will inhabit both -- 'SDouble' and 'SFloat'. sNaN :: (Floating a, SymWord a) => SBV a sNaN = literal nan -- | Symbolic variant of infinity. This value will inhabit both -- 'SDouble' and 'SFloat'. sInfinity :: (Floating a, SymWord a) => SBV a sInfinity = literal infinity -- | Internal representation of a symbolic simulation result newtype SMTProblem = SMTProblem {smtLibPgm :: SMTConfig -> SMTLibPgm} -- ^ SMTLib representation, given the config -- Boolean combinators instance Boolean SBool where true = SBV (svBool True) false = SBV (svBool False) bnot (SBV b) = SBV (svNot b) SBV a &&& SBV b = SBV (svAnd a b) SBV a ||| SBV b = SBV (svOr a b) SBV a <+> SBV b = SBV (svXOr a b) -- | 'RoundingMode' can be used symbolically instance SymWord RoundingMode -- | The symbolic variant of 'RoundingMode' type SRoundingMode = SBV RoundingMode -- | Symbolic variant of 'RoundNearestTiesToEven' sRoundNearestTiesToEven :: SRoundingMode sRoundNearestTiesToEven = literal RoundNearestTiesToEven -- | Symbolic variant of 'RoundNearestTiesToAway' sRoundNearestTiesToAway :: SRoundingMode sRoundNearestTiesToAway = literal RoundNearestTiesToAway -- | Symbolic variant of 'RoundNearestPositive' sRoundTowardPositive :: SRoundingMode sRoundTowardPositive = literal RoundTowardPositive -- | Symbolic variant of 'RoundTowardNegative' sRoundTowardNegative :: SRoundingMode sRoundTowardNegative = literal RoundTowardNegative -- | Symbolic variant of 'RoundTowardZero' sRoundTowardZero :: SRoundingMode sRoundTowardZero = literal RoundTowardZero -- | Alias for 'sRoundNearestTiesToEven' sRNE :: SRoundingMode sRNE = sRoundNearestTiesToEven -- | Alias for 'sRoundNearestTiesToAway' sRNA :: SRoundingMode sRNA = sRoundNearestTiesToAway -- | Alias for 'sRoundTowardPositive' sRTP :: SRoundingMode sRTP = sRoundTowardPositive -- | Alias for 'sRoundTowardNegative' sRTN :: SRoundingMode sRTN = sRoundTowardNegative -- | Alias for 'sRoundTowardZero' sRTZ :: SRoundingMode sRTZ = sRoundTowardZero -- | A 'Show' instance is not particularly "desirable," when the value is symbolic, -- but we do need this instance as otherwise we cannot simply evaluate Haskell functions -- that return symbolic values and have their constant values printed easily! instance Show (SBV a) where show (SBV sv) = show sv -- | Equality constraint on SBV values. Not desirable since we can't really compare two -- symbolic values, but will do. Note that we do need this instance since we want -- Bits as a class for SBV that we implement, which necessiates the Eq class. instance Eq (SBV a) where SBV a == SBV b = a == b SBV a /= SBV b = a /= b instance HasKind (SBV a) where kindOf (SBV (SVal k _)) = k -- | Convert a symbolic value to a symbolic-word sbvToSW :: State -> SBV a -> IO SW sbvToSW st (SBV s) = svToSW st s ------------------------------------------------------------------------- -- * Symbolic Computations ------------------------------------------------------------------------- -- | Create a symbolic variable. mkSymSBV :: forall a. Maybe Quantifier -> Kind -> Maybe String -> Symbolic (SBV a) mkSymSBV mbQ k mbNm = SBV <$> (ask >>= liftIO . svMkSymVar mbQ k mbNm) -- | Convert a symbolic value to an SW, inside the Symbolic monad sbvToSymSW :: SBV a -> Symbolic SW sbvToSymSW sbv = do st <- ask liftIO $ sbvToSW st sbv -- | Actions we can do in a context: Either at problem description -- time or while we are dynamically querying. 'Symbolic' and 'Query' are -- two instances of this class. Note that we use this mechanism -- internally and do not export it from SBV. class SolverContext m where -- | Add a constraint, any satisfying instance must satisfy this condition constrain :: SBool -> m () -- | Add a soft constraint. The solver will try to satisfy this condition if possible, but won't if it cannot softConstrain :: SBool -> m () -- | Add a named constraint. The name is used in unsat-core extraction. namedConstraint :: String -> SBool -> m () -- | Add a constraint, with arbitrary attributes. Used in interpolant generation. constrainWithAttribute :: [(String, String)] -> SBool -> m () -- | Set info. Example: @setInfo ":status" ["unsat"]@. setInfo :: String -> [String] -> m () -- | Set an option. setOption :: SMTOption -> m () -- | Set the logic. setLogic :: Logic -> m () -- | Set a solver time-out value, in milli-seconds. This function -- essentially translates to the SMTLib call @(set-info :timeout val)@, -- and your backend solver may or may not support it! The amount given -- is in milliseconds. Also see the function 'timeOut' for finer level -- control of time-outs, directly from SBV. setTimeOut :: Integer -> m () -- time-out, logic, and info are simply options in our implementation, so default implementation suffices setTimeOut t = setOption $ OptionKeyword ":timeout" [show t] setLogic = setOption . SetLogic setInfo k = setOption . SetInfo k -- | A class representing what can be returned from a symbolic computation. class Outputtable a where -- | Mark an interim result as an output. Useful when constructing Symbolic programs -- that return multiple values, or when the result is programmatically computed. output :: a -> Symbolic a instance Outputtable (SBV a) where output i = do outputSVal (unSBV i) return i instance Outputtable a => Outputtable [a] where output = mapM output instance Outputtable () where output = return instance (Outputtable a, Outputtable b) => Outputtable (a, b) where output = mlift2 (,) output output instance (Outputtable a, Outputtable b, Outputtable c) => Outputtable (a, b, c) where output = mlift3 (,,) output output output instance (Outputtable a, Outputtable b, Outputtable c, Outputtable d) => Outputtable (a, b, c, d) where output = mlift4 (,,,) output output output output instance (Outputtable a, Outputtable b, Outputtable c, Outputtable d, Outputtable e) => Outputtable (a, b, c, d, e) where output = mlift5 (,,,,) output output output output output instance (Outputtable a, Outputtable b, Outputtable c, Outputtable d, Outputtable e, Outputtable f) => Outputtable (a, b, c, d, e, f) where output = mlift6 (,,,,,) output output output output output output instance (Outputtable a, Outputtable b, Outputtable c, Outputtable d, Outputtable e, Outputtable f, Outputtable g) => Outputtable (a, b, c, d, e, f, g) where output = mlift7 (,,,,,,) output output output output output output output instance (Outputtable a, Outputtable b, Outputtable c, Outputtable d, Outputtable e, Outputtable f, Outputtable g, Outputtable h) => Outputtable (a, b, c, d, e, f, g, h) where output = mlift8 (,,,,,,,) output output output output output output output output ------------------------------------------------------------------------------- -- * Symbolic Words ------------------------------------------------------------------------------- -- | A 'SymWord' is a potential symbolic bitvector that can be created instances of -- to be fed to a symbolic program. Note that these methods are typically not needed -- in casual uses with 'prove', 'sat', 'allSat' etc, as default instances automatically -- provide the necessary bits. class (HasKind a, Ord a) => SymWord a where -- | Create a user named input (universal) forall :: String -> Symbolic (SBV a) -- | Create an automatically named input forall_ :: Symbolic (SBV a) -- | Get a bunch of new words mkForallVars :: Int -> Symbolic [SBV a] -- | Create an existential variable exists :: String -> Symbolic (SBV a) -- | Create an automatically named existential variable exists_ :: Symbolic (SBV a) -- | Create a bunch of existentials mkExistVars :: Int -> Symbolic [SBV a] -- | Create a free variable, universal in a proof, existential in sat free :: String -> Symbolic (SBV a) -- | Create an unnamed free variable, universal in proof, existential in sat free_ :: Symbolic (SBV a) -- | Create a bunch of free vars mkFreeVars :: Int -> Symbolic [SBV a] -- | Similar to free; Just a more convenient name symbolic :: String -> Symbolic (SBV a) -- | Similar to mkFreeVars; but automatically gives names based on the strings symbolics :: [String] -> Symbolic [SBV a] -- | Turn a literal constant to symbolic literal :: a -> SBV a -- | Extract a literal, if the value is concrete unliteral :: SBV a -> Maybe a -- | Extract a literal, from a CW representation fromCW :: CW -> a -- | Is the symbolic word concrete? isConcrete :: SBV a -> Bool -- | Is the symbolic word really symbolic? isSymbolic :: SBV a -> Bool -- | Does it concretely satisfy the given predicate? isConcretely :: SBV a -> (a -> Bool) -> Bool -- | One stop allocator mkSymWord :: Maybe Quantifier -> Maybe String -> Symbolic (SBV a) -- minimal complete definition:: Nothing. -- Giving no instances is ok when defining an uninterpreted/enumerated sort, but otherwise you really -- want to define: literal, fromCW, mkSymWord forall = mkSymWord (Just ALL) . Just forall_ = mkSymWord (Just ALL) Nothing exists = mkSymWord (Just EX) . Just exists_ = mkSymWord (Just EX) Nothing free = mkSymWord Nothing . Just free_ = mkSymWord Nothing Nothing mkForallVars n = mapM (const forall_) [1 .. n] mkExistVars n = mapM (const exists_) [1 .. n] mkFreeVars n = mapM (const free_) [1 .. n] symbolic = free symbolics = mapM symbolic unliteral (SBV (SVal _ (Left c))) = Just $ fromCW c unliteral _ = Nothing isConcrete (SBV (SVal _ (Left _))) = True isConcrete _ = False isSymbolic = not . isConcrete isConcretely s p | Just i <- unliteral s = p i | True = False default literal :: Show a => a -> SBV a literal x = let k@(KUserSort _ conts) = kindOf x sx = show x mbIdx = case conts of Right xs -> sx `elemIndex` xs _ -> Nothing in SBV $ SVal k (Left (CW k (CWUserSort (mbIdx, sx)))) default fromCW :: Read a => CW -> a fromCW (CW _ (CWUserSort (_, s))) = read s fromCW cw = error $ "Cannot convert CW " ++ show cw ++ " to kind " ++ show (kindOf (undefined :: a)) default mkSymWord :: (Read a, G.Data a) => Maybe Quantifier -> Maybe String -> Symbolic (SBV a) mkSymWord mbQ mbNm = SBV <$> (ask >>= liftIO . svMkSymVar mbQ k mbNm) where k = constructUKind (undefined :: a) instance (Random a, SymWord a) => Random (SBV a) where randomR (l, h) g = case (unliteral l, unliteral h) of (Just lb, Just hb) -> let (v, g') = randomR (lb, hb) g in (literal (v :: a), g') _ -> error "SBV.Random: Cannot generate random values with symbolic bounds" random g = let (v, g') = random g in (literal (v :: a) , g') --------------------------------------------------------------------------------- -- * Symbolic Arrays --------------------------------------------------------------------------------- -- | Flat arrays of symbolic values -- An @array a b@ is an array indexed by the type @'SBV' a@, with elements of type @'SBV' b@. -- -- If a default value is supplied, then all the array elements will be initialized to this value. -- Otherwise, they will be left unspecified, i.e., a read from an unwritten location will produce -- an uninterpreted constant. -- -- While it's certainly possible for user to create instances of 'SymArray', the -- 'SArray' and 'SFunArray' instances already provided should cover most use cases -- in practice. Note that there are a few differences between these two models in -- terms of use models: -- -- * 'SArray' produces SMTLib arrays, and requires a solver that understands the -- array theory. 'SFunArray' is internally handled, and thus can be used with -- any solver. (Note that all solvers except 'abc' support arrays, so this isn't -- a big decision factor.) -- -- * For both arrays, if a default value is supplied, then reading from uninitialized -- cell will return that value. If the default is not given, then reading from -- uninitialized cells is still OK for both arrays, and will produce an uninterpreted -- constant in both cases. -- -- * Only 'SArray' supports checking equality of arrays. (That is, checking if an entire -- array is equivalent to another.) 'SFunArray's cannot be checked for equality. In general, -- checking wholesale equality of arrays is a difficult decision problem and should be -- avoided if possible. -- -- * Only 'SFunArray' supports compilation to C. Programs using 'SArray' will not be -- accepted by the C-code generator. -- -- * You cannot use quickcheck on programs that contain these arrays. (Neither 'SArray' -- nor 'SFunArray'.) -- -- * With 'SArray', SBV transfers all array-processing to the SMT-solver. So, it can generate -- programs more quickly, but they might end up being too hard for the solver to handle. With -- 'SFunArray', SBV only generates code for individual elements and the array itself never -- shows up in the resulting SMTLib program. This puts more onus on the SBV side and might -- have some performance impacts, but it might generate problems that are easier for the SMT -- solvers to handle. -- -- As a rule of thumb, try 'SArray' first. These should generate compact code. However, if -- the backend solver has hard time solving the generated problems, switch to -- 'SFunArray'. If you still have issues, please report so we can see what the problem might be! class SymArray array where -- | Create a new anonymous array, possibly with a default initial value. newArray_ :: (HasKind a, HasKind b) => Maybe (SBV b) -> Symbolic (array a b) -- | Create a named new array, possibly with a default initial value. newArray :: (HasKind a, HasKind b) => String -> Maybe (SBV b) -> Symbolic (array a b) -- | Read the array element at @a@ readArray :: array a b -> SBV a -> SBV b -- | Update the element at @a@ to be @b@ writeArray :: SymWord b => array a b -> SBV a -> SBV b -> array a b -- | Merge two given arrays on the symbolic condition -- Intuitively: @mergeArrays cond a b = if cond then a else b@. -- Merging pushes the if-then-else choice down on to elements mergeArrays :: SymWord b => SBV Bool -> array a b -> array a b -> array a b -- | Internal function, not exported to the user newArrayInState :: (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (array a b) {-# MINIMAL readArray, writeArray, mergeArrays, newArrayInState #-} newArray_ mbVal = ask >>= liftIO . newArrayInState Nothing mbVal newArray nm mbVal = ask >>= liftIO . newArrayInState (Just nm) mbVal -- | Arrays implemented in terms of SMT-arrays: -- -- * Maps directly to SMT-lib arrays -- -- * Reading from an unintialized value is OK. If the default value is given in 'newArray', it will -- be the result. Otherwise, the read yields an uninterpreted constant. -- -- * Can check for equality of these arrays -- -- * Cannot be used in code-generation (i.e., compilation to C) -- -- * Cannot quick-check theorems using @SArray@ values -- -- * Typically slower as it heavily relies on SMT-solving for the array theory newtype SArray a b = SArray { unSArray :: SArr } instance (HasKind a, HasKind b) => Show (SArray a b) where show SArray{} = "SArray<" ++ showType (undefined :: a) ++ ":" ++ showType (undefined :: b) ++ ">" instance SymArray SArray where readArray (SArray arr) (SBV a) = SBV (readSArr arr a) writeArray (SArray arr) (SBV a) (SBV b) = SArray (writeSArr arr a b) mergeArrays (SBV t) (SArray a) (SArray b) = SArray (mergeSArr t a b) newArrayInState :: forall a b. (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (SArray a b) newArrayInState mbNm mbVal st = do mapM_ (registerKind st) [aknd, bknd] SArray <$> newSArr st (aknd, bknd) (mkNm mbNm) (unSBV <$> mbVal) where mkNm Nothing t = "array_" ++ show t mkNm (Just nm) _ = nm aknd = kindOf (undefined :: a) bknd = kindOf (undefined :: b) -- | Arrays implemented internally, without translating to SMT-Lib functions: -- -- * Internally handled by the library and not mapped to SMT-Lib, hence can -- be used with solvers that don't support arrays. (Such as abc.) -- -- * Reading from an unintialized value is OK. If the default value is given in 'newArray', it will -- be the result. Otherwise, the read yields an uninterpreted constant. -- -- * Cannot check for equality of arrays. -- -- * Can be used in code-generation (i.e., compilation to C). -- -- * Can not quick-check theorems using @SFunArray@ values -- -- * Typically faster as it gets compiled away during translation. newtype SFunArray a b = SFunArray { unSFunArray :: SFunArr } instance (HasKind a, HasKind b) => Show (SFunArray a b) where show SFunArray{} = "SFunArray<" ++ showType (undefined :: a) ++ ":" ++ showType (undefined :: b) ++ ">" instance SymArray SFunArray where readArray (SFunArray arr) (SBV a) = SBV (readSFunArr arr a) writeArray (SFunArray arr) (SBV a) (SBV b) = SFunArray (writeSFunArr arr a b) mergeArrays (SBV t) (SFunArray a) (SFunArray b) = SFunArray (mergeSFunArr t a b) newArrayInState :: forall a b. (HasKind a, HasKind b) => Maybe String -> Maybe (SBV b) -> State -> IO (SFunArray a b) newArrayInState mbNm mbVal st = do mapM_ (registerKind st) [aknd, bknd] SFunArray <$> newSFunArr st (aknd, bknd) (mkNm mbNm) (unSBV <$> mbVal) where mkNm Nothing t = "funArray_" ++ show t mkNm (Just nm) _ = nm aknd = kindOf (undefined :: a) bknd = kindOf (undefined :: b)