module Data.SBV.BitVectors.Model (
Mergeable(..), EqSymbolic(..), OrdSymbolic(..), BVDivisible(..), Uninterpreted(..)
, bitValue, setBitTo, allEqual, allDifferent, oneIf, blastBE, blastLE
, lsb, msb, SBVUF, sbvUFName, genFinVar, genFinVar_, forall, forall_, exists, exists_
, constrain, pConstrain
)
where
import Control.Monad (when)
import Data.Array (Array, Ix, listArray, elems, bounds, rangeSize)
import Data.Bits (Bits(..))
import Data.Int (Int8, Int16, Int32, Int64)
import Data.List (genericLength, genericIndex, genericSplitAt, unzip4, unzip5, unzip6, unzip7, intercalate)
import Data.Maybe (fromMaybe)
import Data.Word (Word8, Word16, Word32, Word64)
import Test.QuickCheck (Testable(..), Arbitrary(..))
import qualified Test.QuickCheck as QC (whenFail)
import qualified Test.QuickCheck.Monadic as QC (monadicIO, run)
import System.Random
import Data.SBV.BitVectors.Data
import Data.SBV.Utils.Boolean
liftSym1 :: (State -> (Bool, Size) -> SW -> IO SW) ->
(Integer -> Integer) -> SBV b -> SBV b
liftSym1 _ opC (SBV sgnsz (Left a)) = SBV sgnsz $ Left $ mapCW opC a
liftSym1 opS _ a@(SBV sgnsz _) = SBV sgnsz $ Right $ cache c
where c st = do swa <- sbvToSW st a
opS st sgnsz swa
liftSym2 :: (State -> (Bool, Size) -> SW -> SW -> IO SW) ->
(Integer -> Integer -> Integer) -> SBV b -> SBV b -> SBV b
liftSym2 _ opC (SBV sgnsz (Left a)) (SBV _ (Left b)) = SBV sgnsz $ Left $ mapCW2 opC a b
liftSym2 opS _ a@(SBV sgnsz _) b = SBV sgnsz $ Right $ cache c
where c st = do sw1 <- sbvToSW st a
sw2 <- sbvToSW st b
opS st sgnsz sw1 sw2
liftSym2B :: (State -> (Bool, Size) -> SW -> SW -> IO SW)
-> (Integer -> Integer -> Bool)
-> SBV b -> SBV b -> SBool
liftSym2B _ opC (SBV _ (Left a)) (SBV _ (Left b)) = literal (liftCW2 opC a b)
liftSym2B opS _ a b = SBV (False, Size (Just 1)) $ Right $ cache c
where c st = do sw1 <- sbvToSW st a
sw2 <- sbvToSW st b
opS st (False, Size (Just 1)) sw1 sw2
liftSym1Bool :: (State -> (Bool, Size) -> SW -> IO SW)
-> (Bool -> Bool)
-> SBool -> SBool
liftSym1Bool _ opC (SBV _ (Left a)) = literal $ opC $ cwToBool a
liftSym1Bool opS _ a = SBV (False, Size (Just 1)) $ Right $ cache c
where c st = do sw <- sbvToSW st a
opS st (False, Size (Just 1)) sw
liftSym2Bool :: (State -> (Bool, Size) -> SW -> SW -> IO SW)
-> (Bool -> Bool -> Bool)
-> SBool -> SBool -> SBool
liftSym2Bool _ opC (SBV _ (Left a)) (SBV _ (Left b)) = literal (cwToBool a `opC` cwToBool b)
liftSym2Bool opS _ a b = SBV (False, Size (Just 1)) $ Right $ cache c
where c st = do sw1 <- sbvToSW st a
sw2 <- sbvToSW st b
opS st (False, Size (Just 1)) sw1 sw2
mkSymOpSC :: (SW -> SW -> Maybe SW) -> Op -> State -> (Bool, Size) -> SW -> SW -> IO SW
mkSymOpSC shortCut op st sgnsz a b = maybe (newExpr st sgnsz (SBVApp op [a, b])) return (shortCut a b)
mkSymOp :: Op -> State -> (Bool, Size) -> SW -> SW -> IO SW
mkSymOp = mkSymOpSC (const (const Nothing))
mkSymOp1SC :: (SW -> Maybe SW) -> Op -> State -> (Bool, Size) -> SW -> IO SW
mkSymOp1SC shortCut op st sgnsz a = maybe (newExpr st sgnsz (SBVApp op [a])) return (shortCut a)
mkSymOp1 :: Op -> State -> (Bool, Size) -> SW -> IO SW
mkSymOp1 = mkSymOp1SC (const Nothing)
genFinVar :: (Random a, SymWord a) => Maybe Quantifier -> (Bool, Int) -> String -> Symbolic (SBV a)
genFinVar q (sg, sz) = mkSymSBV q (sg, Size (Just sz)) . Just
genFinVar_ :: (Random a, SymWord a) => Maybe Quantifier -> (Bool, Int) -> Symbolic (SBV a)
genFinVar_ q (sg, sz) = mkSymSBV q (sg, Size (Just sz)) Nothing
genFinLiteral :: Integral a => (Bool, Int) -> a -> SBV b
genFinLiteral (sg, sz) = SBV s . Left . mkConstCW s
where s = (sg, Size (Just sz))
genFromCW :: Integral a => CW -> a
genFromCW x = fromInteger (cwVal x)
instance SymWord Bool where
forall = genFinVar (Just ALL) (False, 1)
forall_ = genFinVar_ (Just ALL) (False, 1)
exists = genFinVar (Just EX) (False, 1)
exists_ = genFinVar_ (Just EX) (False, 1)
free = genFinVar Nothing (False, 1)
free_ = genFinVar_ Nothing (False, 1)
literal x = genFinLiteral (False, 1) (if x then (1::Integer) else 0)
fromCW = cwToBool
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Word8 where
forall = genFinVar (Just ALL) (False, 8)
forall_ = genFinVar_ (Just ALL) (False, 8)
exists = genFinVar (Just EX) (False, 8)
exists_ = genFinVar_ (Just EX) (False, 8)
free = genFinVar Nothing (False, 8)
free_ = genFinVar_ Nothing (False, 8)
literal = genFinLiteral (False, 8)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Int8 where
forall = genFinVar (Just ALL) (True, 8)
forall_ = genFinVar_ (Just ALL) (True, 8)
exists = genFinVar (Just EX) (True, 8)
exists_ = genFinVar_ (Just EX) (True, 8)
free = genFinVar Nothing (True, 8)
free_ = genFinVar_ Nothing (True, 8)
literal = genFinLiteral (True, 8)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Word16 where
forall = genFinVar (Just ALL) (False, 16)
forall_ = genFinVar_ (Just ALL) (False, 16)
exists = genFinVar (Just EX) (False, 16)
exists_ = genFinVar_ (Just EX) (False, 16)
free = genFinVar Nothing (False, 16)
free_ = genFinVar_ Nothing (False, 16)
literal = genFinLiteral (False, 16)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Int16 where
forall = genFinVar (Just ALL) (True, 16)
forall_ = genFinVar_ (Just ALL) (True, 16)
exists = genFinVar (Just EX) (True, 16)
exists_ = genFinVar_ (Just EX) (True, 16)
free = genFinVar Nothing (True, 16)
free_ = genFinVar_ Nothing (True, 16)
literal = genFinLiteral (True, 16)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Word32 where
forall = genFinVar (Just ALL) (False, 32)
forall_ = genFinVar_ (Just ALL) (False, 32)
exists = genFinVar (Just EX) (False, 32)
exists_ = genFinVar_ (Just EX) (False, 32)
free = genFinVar Nothing (False, 32)
free_ = genFinVar_ Nothing (False, 32)
literal = genFinLiteral (False, 32)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Int32 where
forall = genFinVar (Just ALL) (True, 32)
forall_ = genFinVar_ (Just ALL) (True, 32)
exists = genFinVar (Just EX) (True, 32)
exists_ = genFinVar_ (Just EX) (True, 32)
free = genFinVar Nothing (True, 32)
free_ = genFinVar_ Nothing (True, 32)
literal = genFinLiteral (True, 32)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Word64 where
forall = genFinVar (Just ALL) (False, 64)
forall_ = genFinVar_ (Just ALL) (False, 64)
exists = genFinVar (Just EX) (False, 64)
exists_ = genFinVar_ (Just EX) (False, 64)
free = genFinVar Nothing (False, 64)
free_ = genFinVar_ Nothing (False, 64)
literal = genFinLiteral (False, 64)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Int64 where
forall = genFinVar (Just ALL) (True, 64)
forall_ = genFinVar_ (Just ALL) (True, 64)
exists = genFinVar (Just EX) (True, 64)
exists_ = genFinVar_ (Just EX) (True, 64)
free = genFinVar Nothing (True, 64)
free_ = genFinVar_ Nothing (True, 64)
literal = genFinLiteral (True, 64)
fromCW = genFromCW
mbMaxBound = Just maxBound
mbMinBound = Just minBound
instance SymWord Integer where
forall = mkSymSBV (Just ALL) (True, Size Nothing) . Just
forall_ = mkSymSBV (Just ALL) (True, Size Nothing) Nothing
exists = mkSymSBV (Just EX) (True, Size Nothing) . Just
exists_ = mkSymSBV (Just EX) (True, Size Nothing) Nothing
free = mkSymSBV Nothing (True, Size Nothing) . Just
free_ = mkSymSBV Nothing (True, Size Nothing) Nothing
literal = SBV (True, Size Nothing) . Left . mkConstCW (True, Size Nothing)
fromCW = genFromCW
mbMaxBound = Nothing
mbMinBound = Nothing
infix 4 .==, ./=
class EqSymbolic a where
(.==), (./=) :: a -> a -> SBool
x ./= y = bnot (x .== y)
infix 4 .<, .<=, .>, .>=
class (Mergeable a, EqSymbolic a) => OrdSymbolic a where
(.<), (.<=), (.>), (.>=) :: a -> a -> SBool
smin, smax :: a -> a -> a
a .<= b = a .< b ||| a .== b
a .> b = b .< a
a .>= b = b .<= a
a `smin` b = ite (a .<= b) a b
a `smax` b = ite (a .<= b) b a
instance EqSymbolic (SBV a) where
(.==) = liftSym2B (mkSymOpSC (eqOpt trueSW) Equal) (==)
(./=) = liftSym2B (mkSymOpSC (eqOpt falseSW) NotEqual) (/=)
eqOpt :: SW -> SW -> SW -> Maybe SW
eqOpt w x y = if x == y then Just w else Nothing
instance SymWord a => OrdSymbolic (SBV a) where
x .< y
| Just mb <- mbMaxBound, x `isConcretely` (== mb) = false
| Just mb <- mbMinBound, y `isConcretely` (== mb) = false
| True = liftSym2B (mkSymOpSC (eqOpt falseSW) LessThan) (<) x y
x .<= y
| Just mb <- mbMinBound, x `isConcretely` (== mb) = true
| Just mb <- mbMaxBound, y `isConcretely` (== mb) = true
| True = liftSym2B (mkSymOpSC (eqOpt trueSW) LessEq) (<=) x y
x .> y
| Just mb <- mbMinBound, x `isConcretely` (== mb) = false
| Just mb <- mbMaxBound, y `isConcretely` (== mb) = false
| True = liftSym2B (mkSymOpSC (eqOpt falseSW) GreaterThan) (>) x y
x .>= y
| Just mb <- mbMaxBound, x `isConcretely` (== mb) = true
| Just mb <- mbMinBound, y `isConcretely` (== mb) = true
| True = liftSym2B (mkSymOpSC (eqOpt trueSW) GreaterEq) (>=) x y
instance EqSymbolic Bool where
x .== y = if x == y then true else false
instance EqSymbolic a => EqSymbolic [a] where
[] .== [] = true
(x:xs) .== (y:ys) = x .== y &&& xs .== ys
_ .== _ = false
instance OrdSymbolic a => OrdSymbolic [a] where
[] .< [] = false
[] .< _ = true
_ .< [] = false
(x:xs) .< (y:ys) = x .< y ||| (x .== y &&& xs .< ys)
instance EqSymbolic a => EqSymbolic (Maybe a) where
Nothing .== Nothing = true
Just a .== Just b = a .== b
_ .== _ = false
instance (OrdSymbolic a) => OrdSymbolic (Maybe a) where
Nothing .< Nothing = false
Nothing .< _ = true
Just _ .< Nothing = false
Just a .< Just b = a .< b
instance (EqSymbolic a, EqSymbolic b) => EqSymbolic (Either a b) where
Left a .== Left b = a .== b
Right a .== Right b = a .== b
_ .== _ = false
instance (OrdSymbolic a, OrdSymbolic b) => OrdSymbolic (Either a b) where
Left a .< Left b = a .< b
Left _ .< Right _ = true
Right _ .< Left _ = false
Right a .< Right b = a .< b
instance (EqSymbolic a, EqSymbolic b) => EqSymbolic (a, b) where
(a0, b0) .== (a1, b1) = a0 .== a1 &&& b0 .== b1
instance (OrdSymbolic a, OrdSymbolic b) => OrdSymbolic (a, b) where
(a0, b0) .< (a1, b1) = a0 .< a1 ||| (a0 .== a1 &&& b0 .< b1)
instance (EqSymbolic a, EqSymbolic b, EqSymbolic c) => EqSymbolic (a, b, c) where
(a0, b0, c0) .== (a1, b1, c1) = (a0, b0) .== (a1, b1) &&& c0 .== c1
instance (OrdSymbolic a, OrdSymbolic b, OrdSymbolic c) => OrdSymbolic (a, b, c) where
(a0, b0, c0) .< (a1, b1, c1) = (a0, b0) .< (a1, b1) ||| ((a0, b0) .== (a1, b1) &&& c0 .< c1)
instance (EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d) => EqSymbolic (a, b, c, d) where
(a0, b0, c0, d0) .== (a1, b1, c1, d1) = (a0, b0, c0) .== (a1, b1, c1) &&& d0 .== d1
instance (OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d) => OrdSymbolic (a, b, c, d) where
(a0, b0, c0, d0) .< (a1, b1, c1, d1) = (a0, b0, c0) .< (a1, b1, c1) ||| ((a0, b0, c0) .== (a1, b1, c1) &&& d0 .< d1)
instance (EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d, EqSymbolic e) => EqSymbolic (a, b, c, d, e) where
(a0, b0, c0, d0, e0) .== (a1, b1, c1, d1, e1) = (a0, b0, c0, d0) .== (a1, b1, c1, d1) &&& e0 .== e1
instance (OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d, OrdSymbolic e) => OrdSymbolic (a, b, c, d, e) where
(a0, b0, c0, d0, e0) .< (a1, b1, c1, d1, e1) = (a0, b0, c0, d0) .< (a1, b1, c1, d1) ||| ((a0, b0, c0, d0) .== (a1, b1, c1, d1) &&& e0 .< e1)
instance (EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d, EqSymbolic e, EqSymbolic f) => EqSymbolic (a, b, c, d, e, f) where
(a0, b0, c0, d0, e0, f0) .== (a1, b1, c1, d1, e1, f1) = (a0, b0, c0, d0, e0) .== (a1, b1, c1, d1, e1) &&& f0 .== f1
instance (OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d, OrdSymbolic e, OrdSymbolic f) => OrdSymbolic (a, b, c, d, e, f) where
(a0, b0, c0, d0, e0, f0) .< (a1, b1, c1, d1, e1, f1) = (a0, b0, c0, d0, e0) .< (a1, b1, c1, d1, e1)
||| ((a0, b0, c0, d0, e0) .== (a1, b1, c1, d1, e1) &&& f0 .< f1)
instance (EqSymbolic a, EqSymbolic b, EqSymbolic c, EqSymbolic d, EqSymbolic e, EqSymbolic f, EqSymbolic g) => EqSymbolic (a, b, c, d, e, f, g) where
(a0, b0, c0, d0, e0, f0, g0) .== (a1, b1, c1, d1, e1, f1, g1) = (a0, b0, c0, d0, e0, f0) .== (a1, b1, c1, d1, e1, f1) &&& g0 .== g1
instance (OrdSymbolic a, OrdSymbolic b, OrdSymbolic c, OrdSymbolic d, OrdSymbolic e, OrdSymbolic f, OrdSymbolic g) => OrdSymbolic (a, b, c, d, e, f, g) where
(a0, b0, c0, d0, e0, f0, g0) .< (a1, b1, c1, d1, e1, f1, g1) = (a0, b0, c0, d0, e0, f0) .< (a1, b1, c1, d1, e1, f1)
||| ((a0, b0, c0, d0, e0, f0) .== (a1, b1, c1, d1, e1, f1) &&& g0 .< g1)
instance Boolean SBool where
true = literal True
false = literal False
bnot b | b `isConcretely` (== False) = true
| b `isConcretely` (== True) = false
| True = liftSym1Bool (mkSymOp1 Not) not b
a &&& b | a `isConcretely` (== False) || b `isConcretely` (== False) = false
| a `isConcretely` (== True) = b
| b `isConcretely` (== True) = a
| True = liftSym2Bool (mkSymOpSC opt And) (&&) a b
where opt x y
| x == falseSW || y == falseSW = Just falseSW
| x == trueSW = Just y
| y == trueSW = Just x
| True = Nothing
a ||| b | a `isConcretely` (== True) || b `isConcretely` (== True) = true
| a `isConcretely` (== False) = b
| b `isConcretely` (== False) = a
| True = liftSym2Bool (mkSymOpSC opt Or) (||) a b
where opt x y
| x == trueSW || y == trueSW = Just trueSW
| x == falseSW = Just y
| y == falseSW = Just x
| True = Nothing
a <+> b | a `isConcretely` (== False) = b
| b `isConcretely` (== False) = a
| a `isConcretely` (== True) = bnot b
| b `isConcretely` (== True) = bnot a
| True = liftSym2Bool (mkSymOpSC opt XOr) (<+>) a b
where opt x y
| x == y = Just falseSW
| x == falseSW = Just y
| y == falseSW = Just x
| True = Nothing
allDifferent :: (Eq a, SymWord a) => [SBV a] -> SBool
allDifferent (x:xs@(_:_)) = bAll ((./=) x) xs &&& allDifferent xs
allDifferent _ = true
allEqual :: (Eq a, SymWord a) => [SBV a] -> SBool
allEqual (x:xs@(_:_)) = bAll ((.==) x) xs
allEqual _ = true
oneIf :: (Num a, SymWord a) => SBool -> SBV a
oneIf t = ite t 1 0
instance (Ord a, Num a, SymWord a) => Num (SBV a) where
fromInteger = literal . fromIntegral
x + y
| x `isConcretely` (== 0) = y
| y `isConcretely` (== 0) = x
| True = liftSym2 (mkSymOp Plus) (+) x y
x * y
| x `isConcretely` (== 0) = 0
| y `isConcretely` (== 0) = 0
| x `isConcretely` (== 1) = y
| y `isConcretely` (== 1) = x
| True = liftSym2 (mkSymOp Times) (*) x y
x y
| y `isConcretely` (== 0) = x
| True = liftSym2 (mkSymOp Minus) () x y
abs a
| hasSign a = ite (a .< 0) (a) a
| True = a
signum a
| hasSign a = ite (a .< 0) (1) (ite (a .== 0) 0 1)
| True = oneIf (a ./= 0)
instance (Bits a, SymWord a) => Bits (SBV a) where
x .&. y
| x `isConcretely` (== 0) = 0
| x `isConcretely` (== 1) = y
| y `isConcretely` (== 0) = 0
| y `isConcretely` (== 1) = x
| True = liftSym2 (mkSymOp And) (.&.) x y
x .|. y
| x `isConcretely` (== 0) = y
| x `isConcretely` (== 1) = 1
| y `isConcretely` (== 0) = x
| y `isConcretely` (== 1) = 1
| True = liftSym2 (mkSymOp Or) (.|.) x y
x `xor` y
| x `isConcretely` (== 0) = y
| y `isConcretely` (== 0) = x
| True = liftSym2 (mkSymOp XOr) xor x y
complement = liftSym1 (mkSymOp1 Not) complement
bitSize _ = intSizeOf (undefined :: a)
isSigned _ = hasSign (undefined :: a)
shiftL x y
| y < 0 = shiftR x (y)
| y == 0 = x
| True = liftSym1 (mkSymOp1 (Shl y)) (`shiftL` y) x
shiftR x y
| y < 0 = shiftL x (y)
| y == 0 = x
| True = liftSym1 (mkSymOp1 (Shr y)) (`shiftR` y) x
rotateL x y
| y < 0 = rotateR x (y)
| y == 0 = x
| not (isInfPrec x) = let sz = bitSize x in liftSym1 (mkSymOp1 (Rol (y `mod` sz))) (rot True sz y) x
| True = shiftL x y
rotateR x y
| y < 0 = rotateL x (y)
| y == 0 = x
| not (isInfPrec x) = let sz = bitSize x in liftSym1 (mkSymOp1 (Ror (y `mod` sz))) (rot False sz y) x
| True = shiftR x y
rot :: Bool -> Int -> Int -> Integer -> Integer
rot toLeft sz amt x
| sz < 2 = x
| True = (norm x y') `shiftL` y .|. norm (x `shiftR` y') y
where (y, y') | toLeft = (amt `mod` sz, sz y)
| True = (sz y', amt `mod` sz)
norm v s = v .&. ((1 `shiftL` s) 1)
bitValue :: (Bits a, SymWord a) => SBV a -> Int -> SBool
bitValue x i = (x .&. bit i) ./= 0
setBitTo :: (Bits a, SymWord a) => SBV a -> Int -> SBool -> SBV a
setBitTo x i b = ite b (setBit x i) (clearBit x i)
blastLE :: (Bits a, SymWord a) => SBV a -> [SBool]
blastLE x
| isInfPrec x = error "SBV.blastLE: Called on an infinite precision value"
| True = map (bitValue x) [0 .. (intSizeOf x)1]
blastBE :: (Bits a, SymWord a) => SBV a -> [SBool]
blastBE = reverse . blastLE
lsb :: (Bits a, SymWord a) => SBV a -> SBool
lsb x = bitValue x 0
msb :: (Bits a, SymWord a) => SBV a -> SBool
msb x
| isInfPrec x = error "SBV.msb: Called on an infinite precision value"
| True = bitValue x ((intSizeOf x) 1)
instance (Show a, Bounded a, Integral a, Num a, SymWord a) => Enum (SBV a) where
succ x
| v == (maxBound :: a) = error $ "Enum.succ{" ++ showType x ++ "}: tried to take `succ' of maxBound"
| True = fromIntegral $ v + 1
where v = enumCvt "succ" x
pred x
| v == (minBound :: a) = error $ "Enum.pred{" ++ showType x ++ "}: tried to take `pred' of minBound"
| True = fromIntegral $ v 1
where v = enumCvt "pred" x
toEnum x
| xi < fromIntegral (minBound :: a) || xi > fromIntegral (maxBound :: a)
= error $ "Enum.toEnum{" ++ showType r ++ "}: " ++ show x ++ " is out-of-bounds " ++ show (minBound :: a, maxBound :: a)
| True
= r
where xi :: Integer
xi = fromIntegral x
r :: SBV a
r = fromIntegral x
fromEnum x
| r < fromIntegral (minBound :: Int) || r > fromIntegral (maxBound :: Int)
= error $ "Enum.fromEnum{" ++ showType x ++ "}: value " ++ show r ++ " is outside of Int's bounds " ++ show (minBound :: Int, maxBound :: Int)
| True
= fromIntegral r
where r :: Integer
r = enumCvt "fromEnum" x
enumFrom x = map fromIntegral [xi .. fromIntegral (maxBound :: a)]
where xi :: Integer
xi = enumCvt "enumFrom" x
enumFromThen x y
| yi >= xi = map fromIntegral [xi, yi .. fromIntegral (maxBound :: a)]
| True = map fromIntegral [xi, yi .. fromIntegral (minBound :: a)]
where xi, yi :: Integer
xi = enumCvt "enumFromThen.x" x
yi = enumCvt "enumFromThen.y" y
enumFromThenTo x y z = map fromIntegral [xi, yi .. zi]
where xi, yi, zi :: Integer
xi = enumCvt "enumFromThenTo.x" x
yi = enumCvt "enumFromThenTo.y" y
zi = enumCvt "enumFromThenTo.z" z
enumCvt :: (SymWord a, Integral a, Num b) => String -> SBV a -> b
enumCvt w x = case unliteral x of
Nothing -> error $ "Enum." ++ w ++ "{" ++ showType x ++ "}: Called on symbolic value " ++ show x
Just v -> fromIntegral v
class BVDivisible a where
bvQuotRem :: a -> a -> (a, a)
instance BVDivisible Word64 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Int64 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Word32 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Int32 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Word16 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Int16 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Word8 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Int8 where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible Integer where
bvQuotRem x 0 = (0, x)
bvQuotRem x y = x `quotRem` y
instance BVDivisible CW where
bvQuotRem x y
| cwSameType x y = let (r1, r2) = bvQuotRem (cwVal x) (cwVal y)
in (x { cwVal = r1 }, y { cwVal = r2 })
bvQuotRem x y = error $ "SBV.liftQRem: impossible, unexpected args received: " ++ show (x, y)
instance BVDivisible SWord64 where
bvQuotRem = liftQRem
instance BVDivisible SInt64 where
bvQuotRem = liftQRem
instance BVDivisible SWord32 where
bvQuotRem = liftQRem
instance BVDivisible SInt32 where
bvQuotRem = liftQRem
instance BVDivisible SWord16 where
bvQuotRem = liftQRem
instance BVDivisible SInt16 where
bvQuotRem = liftQRem
instance BVDivisible SWord8 where
bvQuotRem = liftQRem
instance BVDivisible SInt8 where
bvQuotRem = liftQRem
instance BVDivisible SInteger where
bvQuotRem = liftQRem
liftQRem :: (SymWord a, Num a, BVDivisible a) => SBV a -> SBV a -> (SBV a, SBV a)
liftQRem x y = ite (y .== 0) (0, x) (qr x y)
where qr (SBV sgnsz (Left a)) (SBV _ (Left b)) = let (q, r) = bvQuotRem a b in (SBV sgnsz (Left q), SBV sgnsz (Left r))
qr a@(SBV sgnsz _) b = (SBV sgnsz (Right (cache (mk Quot))), SBV sgnsz (Right (cache (mk Rem))))
where mk o st = do sw1 <- sbvToSW st a
sw2 <- sbvToSW st b
mkSymOp o st sgnsz sw1 sw2
instance (SymWord b, Arbitrary b) => Arbitrary (SFunArray a b) where
arbitrary = arbitrary >>= \r -> return $ SFunArray (const r)
instance (SymWord a, Arbitrary a) => Arbitrary (SBV a) where
arbitrary = arbitrary >>= return . literal
class Mergeable a where
symbolicMerge :: SBool -> a -> a -> a
ite :: SBool -> a -> a -> a
select :: (Bits b, SymWord b, Integral b) => [a] -> a -> SBV b -> a
ite s a b
| Just t <- unliteral s = if t then a else b
| True = symbolicMerge s a b
select [] err _ = err
select xs err ind
| hasSign ind = ite (ind .< 0) err $ result
| True = result
where result = go xs $ reverse (zip [(0::Integer)..] bits)
bits = map (ind `bitValue`) [0 .. bitSize ind 1]
go [] _ = err
go (x:_) [] = x
go elts ((n, b):nbs) = let (ys, zs) = genericSplitAt ((2::Integer) ^ n) elts
in ite b (go zs nbs) (go ys nbs)
instance SymWord a => Mergeable (SBV a) where
symbolicMerge t a b
| Just c1 <- unliteral a, Just c2 <- unliteral b, c1 == c2
= a
| True
= SBV sgnsz $ Right $ cache c
where sgnsz = (hasSign a, sizeOf a)
c st = do swt <- sbvToSW st t
case () of
() | swt == trueSW -> sbvToSW st a
() | swt == falseSW -> sbvToSW st b
() -> do swa <- sbvToSW st a
swb <- sbvToSW st b
case () of
() | swa == swb -> return swa
() | swa == trueSW && swb == falseSW -> return swt
() | swa == falseSW && swa == trueSW -> newExpr st sgnsz (SBVApp Not [swt])
() -> newExpr st sgnsz (SBVApp Ite [swt, swa, swb])
select xs err ind
| Just i <- unliteral ind
= let i' :: Integer
i' = fromIntegral i
in if i' < 0 || i' >= genericLength xs then err else genericIndex xs i'
select [] err _ = err
select xs err ind = SBV sgnszElt $ Right $ cache r
where sgnszInd = (hasSign ind, sizeOf ind)
sgnszElt = (hasSign err, sizeOf err)
r st = do sws <- mapM (sbvToSW st) xs
swe <- sbvToSW st err
if all (== swe) sws
then return swe
else do idx <- getTableIndex st sgnszInd sgnszElt sws
swi <- sbvToSW st ind
let len = length xs
newExpr st sgnszElt (SBVApp (LkUp (idx, sgnszInd, sgnszElt, len) swi swe) [])
instance Mergeable () where
symbolicMerge _ _ _ = ()
select _ _ _ = ()
instance Mergeable a => Mergeable [a] where
symbolicMerge t xs ys
| lxs == lys = zipWith (symbolicMerge t) xs ys
| True = error $ "SBV.Mergeable.List: No least-upper-bound for lists of differing size " ++ show (lxs, lys)
where (lxs, lys) = (length xs, length ys)
instance Mergeable a => Mergeable (Maybe a) where
symbolicMerge _ Nothing Nothing = Nothing
symbolicMerge t (Just a) (Just b) = Just $ symbolicMerge t a b
symbolicMerge _ a b = error $ "SBV.Mergeable.Maybe: No least-upper-bound for " ++ show (k a, k b)
where k Nothing = "Nothing"
k _ = "Just"
instance (Mergeable a, Mergeable b) => Mergeable (Either a b) where
symbolicMerge t (Left a) (Left b) = Left $ symbolicMerge t a b
symbolicMerge t (Right a) (Right b) = Right $ symbolicMerge t a b
symbolicMerge _ a b = error $ "SBV.Mergeable.Either: No least-upper-bound for " ++ show (k a, k b)
where k (Left _) = "Left"
k (Right _) = "Right"
instance (Ix a, Mergeable b) => Mergeable (Array a b) where
symbolicMerge t a b
| ba == bb = listArray ba (zipWith (symbolicMerge t) (elems a) (elems b))
| True = error $ "SBV.Mergeable.Array: No least-upper-bound for rangeSizes" ++ show (k ba, k bb)
where [ba, bb] = map bounds [a, b]
k = rangeSize
instance Mergeable b => Mergeable (a -> b) where
symbolicMerge t f g = \x -> symbolicMerge t (f x) (g x)
select xs err ind = \x -> select (map ($ x) xs) (err x) ind
instance (Mergeable a, Mergeable b) => Mergeable (a, b) where
symbolicMerge t (i0, i1) (j0, j1) = (i i0 j0, i i1 j1)
where i a b = symbolicMerge t a b
select xs (err1, err2) ind = (select as err1 ind, select bs err2 ind)
where (as, bs) = unzip xs
instance (Mergeable a, Mergeable b, Mergeable c) => Mergeable (a, b, c) where
symbolicMerge t (i0, i1, i2) (j0, j1, j2) = (i i0 j0, i i1 j1, i i2 j2)
where i a b = symbolicMerge t a b
select xs (err1, err2, err3) ind = (select as err1 ind, select bs err2 ind, select cs err3 ind)
where (as, bs, cs) = unzip3 xs
instance (Mergeable a, Mergeable b, Mergeable c, Mergeable d) => Mergeable (a, b, c, d) where
symbolicMerge t (i0, i1, i2, i3) (j0, j1, j2, j3) = (i i0 j0, i i1 j1, i i2 j2, i i3 j3)
where i a b = symbolicMerge t a b
select xs (err1, err2, err3, err4) ind = (select as err1 ind, select bs err2 ind, select cs err3 ind, select ds err4 ind)
where (as, bs, cs, ds) = unzip4 xs
instance (Mergeable a, Mergeable b, Mergeable c, Mergeable d, Mergeable e) => Mergeable (a, b, c, d, e) where
symbolicMerge t (i0, i1, i2, i3, i4) (j0, j1, j2, j3, j4) = (i i0 j0, i i1 j1, i i2 j2, i i3 j3, i i4 j4)
where i a b = symbolicMerge t a b
select xs (err1, err2, err3, err4, err5) ind = (select as err1 ind, select bs err2 ind, select cs err3 ind, select ds err4 ind, select es err5 ind)
where (as, bs, cs, ds, es) = unzip5 xs
instance (Mergeable a, Mergeable b, Mergeable c, Mergeable d, Mergeable e, Mergeable f) => Mergeable (a, b, c, d, e, f) where
symbolicMerge t (i0, i1, i2, i3, i4, i5) (j0, j1, j2, j3, j4, j5) = (i i0 j0, i i1 j1, i i2 j2, i i3 j3, i i4 j4, i i5 j5)
where i a b = symbolicMerge t a b
select xs (err1, err2, err3, err4, err5, err6) ind = (select as err1 ind, select bs err2 ind, select cs err3 ind, select ds err4 ind, select es err5 ind, select fs err6 ind)
where (as, bs, cs, ds, es, fs) = unzip6 xs
instance (Mergeable a, Mergeable b, Mergeable c, Mergeable d, Mergeable e, Mergeable f, Mergeable g) => Mergeable (a, b, c, d, e, f, g) where
symbolicMerge t (i0, i1, i2, i3, i4, i5, i6) (j0, j1, j2, j3, j4, j5, j6) = (i i0 j0, i i1 j1, i i2 j2, i i3 j3, i i4 j4, i i5 j5, i i6 j6)
where i a b = symbolicMerge t a b
select xs (err1, err2, err3, err4, err5, err6, err7) ind = (select as err1 ind, select bs err2 ind, select cs err3 ind, select ds err4 ind, select es err5 ind, select fs err6 ind, select gs err7 ind)
where (as, bs, cs, ds, es, fs, gs) = unzip7 xs
instance (SymWord a, Bounded a) => Bounded (SBV a) where
minBound = literal minBound
maxBound = literal maxBound
instance EqSymbolic (SArray a b) where
(SArray _ a) .== (SArray _ b) = SBV (False, Size (Just 1)) $ Right $ cache c
where c st = do ai <- uncacheAI a st
bi <- uncacheAI b st
newExpr st (False, Size (Just 1)) (SBVApp (ArrEq ai bi) [])
instance SymWord b => Mergeable (SArray a b) where
symbolicMerge = mergeArrays
instance SymArray SFunArray where
newArray _ = newArray_
newArray_ mbiVal = return $ SFunArray $ const $ maybe (error "Reading from an uninitialized array entry") id mbiVal
readArray (SFunArray f) a = f a
resetArray (SFunArray _) a = SFunArray $ const a
writeArray (SFunArray f) a b = SFunArray (\a' -> ite (a .== a') b (f a'))
mergeArrays t (SFunArray f) (SFunArray g) = SFunArray (\x -> ite t (f x) (g x))
instance SymWord b => Mergeable (SFunArray a b) where
symbolicMerge = mergeArrays
newtype SBVUF = SBVUF String
sbvUFName :: SBVUF -> String
sbvUFName (SBVUF s) = s
mkUFName :: String -> SBVUF
mkUFName nm = SBVUF $ "uninterpreted_" ++ nm
class Uninterpreted a where
uninterpret :: String -> a
uninterpretWithHandle :: String -> (SBVUF, a)
cgUninterpret :: String -> [String] -> a -> a
sbvUninterpret :: Maybe ([String], a) -> String -> (SBVUF, a)
uninterpret = snd . uninterpretWithHandle
uninterpretWithHandle = sbvUninterpret Nothing
cgUninterpret nm code v = snd $ sbvUninterpret (Just (code, v)) nm
instance HasSignAndSize a => Uninterpreted (SBV a) where
sbvUninterpret mbCgData nm
| Just (_, v) <- mbCgData = (mkUFName nm, v)
| True = (mkUFName nm, SBV sgnsza $ Right $ cache result)
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st v
| True = do newUninterpreted st nm (SBVType [sgnsza]) (fst `fmap` mbCgData)
newExpr st sgnsza $ SBVApp (Uninterpreted nm) []
forceArg :: SW -> IO ()
forceArg (SW (b, s) n) = b `seq` s `seq` n `seq` return ()
instance (SymWord b, HasSignAndSize a) => Uninterpreted (SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0
| Just (_, v) <- mbCgData, isConcrete arg0
= v arg0
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0)
| True = do newUninterpreted st nm (SBVType [sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
mapM_ forceArg [sw0]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0]
instance (SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted (SBV c -> SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0 arg1
| Just (_, v) <- mbCgData, isConcrete arg0, isConcrete arg1
= v arg0 arg1
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
sgnszc = (hasSign (undefined :: c), sizeOf (undefined :: c))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0 arg1)
| True = do newUninterpreted st nm (SBVType [sgnszc, sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
sw1 <- sbvToSW st arg1
mapM_ forceArg [sw0, sw1]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0, sw1]
instance (SymWord d, SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted (SBV d -> SBV c -> SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0 arg1 arg2
| Just (_, v) <- mbCgData, isConcrete arg0, isConcrete arg1, isConcrete arg2
= v arg0 arg1 arg2
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
sgnszc = (hasSign (undefined :: c), sizeOf (undefined :: c))
sgnszd = (hasSign (undefined :: d), sizeOf (undefined :: d))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0 arg1 arg2)
| True = do newUninterpreted st nm (SBVType [sgnszd, sgnszc, sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
sw1 <- sbvToSW st arg1
sw2 <- sbvToSW st arg2
mapM_ forceArg [sw0, sw1, sw2]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0, sw1, sw2]
instance (SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted (SBV e -> SBV d -> SBV c -> SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0 arg1 arg2 arg3
| Just (_, v) <- mbCgData, isConcrete arg0, isConcrete arg1, isConcrete arg2, isConcrete arg3
= v arg0 arg1 arg2 arg3
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
sgnszc = (hasSign (undefined :: c), sizeOf (undefined :: c))
sgnszd = (hasSign (undefined :: d), sizeOf (undefined :: d))
sgnsze = (hasSign (undefined :: e), sizeOf (undefined :: e))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0 arg1 arg2 arg3)
| True = do newUninterpreted st nm (SBVType [sgnsze, sgnszd, sgnszc, sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
sw1 <- sbvToSW st arg1
sw2 <- sbvToSW st arg2
sw3 <- sbvToSW st arg3
mapM_ forceArg [sw0, sw1, sw2, sw3]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0, sw1, sw2, sw3]
instance (SymWord f, SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted (SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0 arg1 arg2 arg3 arg4
| Just (_, v) <- mbCgData, isConcrete arg0, isConcrete arg1, isConcrete arg2, isConcrete arg3, isConcrete arg4
= v arg0 arg1 arg2 arg3 arg4
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
sgnszc = (hasSign (undefined :: c), sizeOf (undefined :: c))
sgnszd = (hasSign (undefined :: d), sizeOf (undefined :: d))
sgnsze = (hasSign (undefined :: e), sizeOf (undefined :: e))
sgnszf = (hasSign (undefined :: f), sizeOf (undefined :: f))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0 arg1 arg2 arg3 arg4)
| True = do newUninterpreted st nm (SBVType [sgnszf, sgnsze, sgnszd, sgnszc, sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
sw1 <- sbvToSW st arg1
sw2 <- sbvToSW st arg2
sw3 <- sbvToSW st arg3
sw4 <- sbvToSW st arg4
mapM_ forceArg [sw0, sw1, sw2, sw3, sw4]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0, sw1, sw2, sw3, sw4]
instance (SymWord g, SymWord f, SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted (SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0 arg1 arg2 arg3 arg4 arg5
| Just (_, v) <- mbCgData, isConcrete arg0, isConcrete arg1, isConcrete arg2, isConcrete arg3, isConcrete arg4, isConcrete arg5
= v arg0 arg1 arg2 arg3 arg4 arg5
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
sgnszc = (hasSign (undefined :: c), sizeOf (undefined :: c))
sgnszd = (hasSign (undefined :: d), sizeOf (undefined :: d))
sgnsze = (hasSign (undefined :: e), sizeOf (undefined :: e))
sgnszf = (hasSign (undefined :: f), sizeOf (undefined :: f))
sgnszg = (hasSign (undefined :: g), sizeOf (undefined :: g))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0 arg1 arg2 arg3 arg4 arg5)
| True = do newUninterpreted st nm (SBVType [sgnszg, sgnszf, sgnsze, sgnszd, sgnszc, sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
sw1 <- sbvToSW st arg1
sw2 <- sbvToSW st arg2
sw3 <- sbvToSW st arg3
sw4 <- sbvToSW st arg4
sw5 <- sbvToSW st arg5
mapM_ forceArg [sw0, sw1, sw2, sw3, sw4, sw5]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0, sw1, sw2, sw3, sw4, sw5]
instance (SymWord h, SymWord g, SymWord f, SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a)
=> Uninterpreted (SBV h -> SBV g -> SBV f -> SBV e -> SBV d -> SBV c -> SBV b -> SBV a) where
sbvUninterpret mbCgData nm = (mkUFName nm, f)
where f arg0 arg1 arg2 arg3 arg4 arg5 arg6
| Just (_, v) <- mbCgData, isConcrete arg0, isConcrete arg1, isConcrete arg2, isConcrete arg3, isConcrete arg4, isConcrete arg5, isConcrete arg6
= v arg0 arg1 arg2 arg3 arg4 arg5 arg6
| True
= SBV sgnsza $ Right $ cache result
where sgnsza = (hasSign (undefined :: a), sizeOf (undefined :: a))
sgnszb = (hasSign (undefined :: b), sizeOf (undefined :: b))
sgnszc = (hasSign (undefined :: c), sizeOf (undefined :: c))
sgnszd = (hasSign (undefined :: d), sizeOf (undefined :: d))
sgnsze = (hasSign (undefined :: e), sizeOf (undefined :: e))
sgnszf = (hasSign (undefined :: f), sizeOf (undefined :: f))
sgnszg = (hasSign (undefined :: g), sizeOf (undefined :: g))
sgnszh = (hasSign (undefined :: h), sizeOf (undefined :: h))
result st | Just (_, v) <- mbCgData, inProofMode st = sbvToSW st (v arg0 arg1 arg2 arg3 arg4 arg5 arg6)
| True = do newUninterpreted st nm (SBVType [sgnszh, sgnszg, sgnszf, sgnsze, sgnszd, sgnszc, sgnszb, sgnsza]) (fst `fmap` mbCgData)
sw0 <- sbvToSW st arg0
sw1 <- sbvToSW st arg1
sw2 <- sbvToSW st arg2
sw3 <- sbvToSW st arg3
sw4 <- sbvToSW st arg4
sw5 <- sbvToSW st arg5
sw6 <- sbvToSW st arg6
mapM_ forceArg [sw0, sw1, sw2, sw3, sw4, sw5, sw6]
newExpr st sgnsza $ SBVApp (Uninterpreted nm) [sw0, sw1, sw2, sw3, sw4, sw5, sw6]
instance (SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted ((SBV c, SBV b) -> SBV a) where
sbvUninterpret mbCgData nm = let (h, f) = sbvUninterpret (uc2 `fmap` mbCgData) nm in (h, \(arg0, arg1) -> f arg0 arg1)
where uc2 (cs, fn) = (cs, \a b -> fn (a, b))
instance (SymWord d, SymWord c, SymWord b, HasSignAndSize a) => Uninterpreted ((SBV d, SBV c, SBV b) -> SBV a) where
sbvUninterpret mbCgData nm = let (h, f) = sbvUninterpret (uc3 `fmap` mbCgData) nm in (h, \(arg0, arg1, arg2) -> f arg0 arg1 arg2)
where uc3 (cs, fn) = (cs, \a b c -> fn (a, b, c))
instance (SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a)
=> Uninterpreted ((SBV e, SBV d, SBV c, SBV b) -> SBV a) where
sbvUninterpret mbCgData nm = let (h, f) = sbvUninterpret (uc4 `fmap` mbCgData) nm in (h, \(arg0, arg1, arg2, arg3) -> f arg0 arg1 arg2 arg3)
where uc4 (cs, fn) = (cs, \a b c d -> fn (a, b, c, d))
instance (SymWord f, SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a)
=> Uninterpreted ((SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) where
sbvUninterpret mbCgData nm = let (h, f) = sbvUninterpret (uc5 `fmap` mbCgData) nm in (h, \(arg0, arg1, arg2, arg3, arg4) -> f arg0 arg1 arg2 arg3 arg4)
where uc5 (cs, fn) = (cs, \a b c d e -> fn (a, b, c, d, e))
instance (SymWord g, SymWord f, SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a)
=> Uninterpreted ((SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) where
sbvUninterpret mbCgData nm = let (h, f) = sbvUninterpret (uc6 `fmap` mbCgData) nm in (h, \(arg0, arg1, arg2, arg3, arg4, arg5) -> f arg0 arg1 arg2 arg3 arg4 arg5)
where uc6 (cs, fn) = (cs, \a b c d e f -> fn (a, b, c, d, e, f))
instance (SymWord h, SymWord g, SymWord f, SymWord e, SymWord d, SymWord c, SymWord b, HasSignAndSize a)
=> Uninterpreted ((SBV h, SBV g, SBV f, SBV e, SBV d, SBV c, SBV b) -> SBV a) where
sbvUninterpret mbCgData nm = let (h, f) = sbvUninterpret (uc7 `fmap` mbCgData) nm in (h, \(arg0, arg1, arg2, arg3, arg4, arg5, arg6) -> f arg0 arg1 arg2 arg3 arg4 arg5 arg6)
where uc7 (cs, fn) = (cs, \a b c d e f g -> fn (a, b, c, d, e, f, g))
constrain :: SBool -> Symbolic ()
constrain c = addConstraint Nothing c (bnot c)
pConstrain :: Double -> SBool -> Symbolic ()
pConstrain t c = addConstraint (Just t) c (bnot c)
instance Testable SBool where
property (SBV _ (Left b)) = property (cwToBool b)
property s = error $ "Cannot quick-check in the presence of uninterpreted constants! (" ++ show s ++ ")"
instance Testable (Symbolic SBool) where
property m = QC.whenFail (putStrLn msg) $ QC.monadicIO test
where runOnce g = do (r, Result _ tvals _ _ cs _ _ _ _ _ cstrs _) <- runSymbolic' (Concrete g) m
let cval = fromMaybe (error "Cannot quick-check in the presence of uninterpeted constants!") . (`lookup` cs)
cond = all (cwToBool . cval) cstrs
when (isSymbolic r) $ error $ "Cannot quick-check in the presence of uninterpreted constants! (" ++ show r ++ ")"
if cond then if r `isConcretely` id
then return False
else do putStrLn $ complain tvals
return True
else runOnce g
test = do die <- QC.run $ newStdGen >>= runOnce
when die $ fail "Falsifiable"
msg = "*** SBV: See the custom counter example reported above."
complain [] = "*** SBV Counter Example: Predicate contains no universally quantified variables."
complain qcInfo = intercalate "\n" $ "*** SBV Counter Example:" : map ((" " ++) . info) qcInfo
where maxLen = maximum (0:[length s | (s, _) <- qcInfo])
shN s = s ++ replicate (maxLen length s) ' '
info (n, cw) = shN n ++ " = " ++ show cw