module Data.SBV.BitVectors.Data
( SBool, SWord8, SWord16, SWord32, SWord64
, SInt8, SInt16, SInt32, SInt64, SInteger, SReal
, SymWord(..)
, CW(..), CWVal(..), cwSameType, cwIsBit, cwToBool
, mkConstCW ,liftCW2, mapCW, mapCW2
, SW(..), trueSW, falseSW, trueCW, falseCW
, SBV(..), NodeId(..), mkSymSBV
, ArrayContext(..), ArrayInfo, SymArray(..), SFunArray(..), mkSFunArray, SArray(..), arrayUIKind
, sbvToSW, sbvToSymSW
, SBVExpr(..), newExpr
, cache, Cached, uncache, uncacheAI, HasKind(..)
, Op(..), NamedSymVar, UnintKind(..), getTableIndex, SBVPgm(..), Symbolic, runSymbolic, runSymbolic', State, inProofMode, SBVRunMode(..), Kind(..), Outputtable(..), Result(..)
, getTraceInfo, getConstraints, addConstraint
, SBVType(..), newUninterpreted, unintFnUIKind, addAxiom
, Quantifier(..), needsExistentials
, SMTLibPgm(..), SMTLibVersion(..)
) where
import Control.DeepSeq (NFData(..))
import Control.Monad (when)
import Control.Monad.Reader (MonadReader, ReaderT, ask, runReaderT)
import Control.Monad.Trans (MonadIO, liftIO)
import Data.Char (isAlpha, isAlphaNum)
import Data.Generics (Data(..), dataTypeName, dataTypeOf, tyconUQname)
import Data.Int (Int8, Int16, Int32, Int64)
import Data.Word (Word8, Word16, Word32, Word64)
import Data.IORef (IORef, newIORef, modifyIORef, readIORef, writeIORef)
import Data.List (intercalate, sortBy)
import Data.Maybe (isJust, fromJust)
import qualified Data.IntMap as IMap (IntMap, empty, size, toAscList, lookup, insert, insertWith)
import qualified Data.Map as Map (Map, empty, toList, size, insert, lookup)
import qualified Data.Foldable as F (toList)
import qualified Data.Sequence as S (Seq, empty, (|>))
import System.Mem.StableName
import System.Random
import Data.SBV.BitVectors.AlgReals
import Data.SBV.Utils.Lib
data CWVal = CWAlgReal AlgReal
| CWInteger Integer
| CWUninterpreted String
instance Eq CWVal where
CWAlgReal a == CWAlgReal b = a `algRealStructuralEqual` b
CWInteger a == CWInteger b = a == b
CWUninterpreted a == CWUninterpreted b = a == b
_ == _ = False
instance Ord CWVal where
CWAlgReal a `compare` CWAlgReal b = a `algRealStructuralCompare` b
CWAlgReal _ `compare` CWInteger _ = LT
CWAlgReal _ `compare` CWUninterpreted _ = LT
CWInteger _ `compare` CWAlgReal _ = GT
CWInteger a `compare` CWInteger b = a `compare` b
CWInteger _ `compare` CWUninterpreted _ = LT
CWUninterpreted _ `compare` CWAlgReal _ = GT
CWUninterpreted _ `compare` CWInteger _ = GT
CWUninterpreted a `compare` CWUninterpreted b = a `compare` b
data CW = CW { cwKind :: !Kind
, cwVal :: !CWVal
}
deriving (Eq, Ord)
cwSameType :: CW -> CW -> Bool
cwSameType x y = cwKind x == cwKind y
cwIsBit :: CW -> Bool
cwIsBit x = case cwKind x of
KBounded False 1 -> True
_ -> False
cwToBool :: CW -> Bool
cwToBool x = cwVal x /= CWInteger 0
normCW :: CW -> CW
normCW c@(CW (KBounded signed sz) (CWInteger v)) = c { cwVal = CWInteger norm }
where norm | sz == 0 = 0
| signed = let rg = 2 ^ (sz 1)
in case divMod v rg of
(a, b) | even a -> b
(_, b) -> b rg
| True = v `mod` (2 ^ sz)
normCW c = c
data Kind = KBounded Bool Int
| KUnbounded
| KReal
| KUninterpreted String
deriving (Eq, Ord)
instance Show Kind where
show (KBounded False 1) = "SBool"
show (KBounded False n) = "SWord" ++ show n
show (KBounded True n) = "SInt" ++ show n
show KUnbounded = "SInteger"
show KReal = "SReal"
show (KUninterpreted s) = s
newtype NodeId = NodeId Int deriving (Eq, Ord)
data SW = SW Kind NodeId deriving (Eq, Ord)
data Quantifier = ALL | EX deriving Eq
needsExistentials :: [Quantifier] -> Bool
needsExistentials = (EX `elem`)
falseSW :: SW
falseSW = SW (KBounded False 1) $ NodeId (2)
trueSW :: SW
trueSW = SW (KBounded False 1) $ NodeId (1)
falseCW :: CW
falseCW = CW (KBounded False 1) (CWInteger 0)
trueCW :: CW
trueCW = CW (KBounded False 1) (CWInteger 1)
newtype SBVType = SBVType [Kind]
deriving (Eq, Ord)
typeArity :: SBVType -> Int
typeArity (SBVType xs) = length xs 1
instance Show SBVType where
show (SBVType []) = error "SBV: internal error, empty SBVType"
show (SBVType xs) = intercalate " -> " $ map show xs
data Op = Plus | Times | Minus
| Quot | Rem
| Equal | NotEqual
| LessThan | GreaterThan | LessEq | GreaterEq
| Ite
| And | Or | XOr | Not
| Shl Int | Shr Int | Rol Int | Ror Int
| Extract Int Int
| Join
| LkUp (Int, Kind, Kind, Int) !SW !SW
| ArrEq Int Int
| ArrRead Int
| Uninterpreted String
deriving (Eq, Ord)
data SBVExpr = SBVApp !Op ![SW]
deriving (Eq, Ord)
class HasKind a where
kindOf :: a -> Kind
hasSign :: a -> Bool
intSizeOf :: a -> Int
isBounded :: a -> Bool
isReal :: a -> Bool
isInteger :: a -> Bool
isUninterpreted :: a -> Bool
showType :: a -> String
hasSign x = case kindOf x of
KBounded b _ -> b
KUnbounded -> True
KReal -> True
KUninterpreted{} -> False
intSizeOf x = case kindOf x of
KBounded _ s -> s
KUnbounded -> error "SBV.HasKind.intSizeOf((S)Integer)"
KReal -> error "SBV.HasKind.intSizeOf((S)Real)"
KUninterpreted s -> error $ "SBV.HasKind.intSizeOf: Uninterpreted sort: " ++ s
isBounded x | KBounded{} <- kindOf x = True
| True = False
isReal x | KReal{} <- kindOf x = True
| True = False
isInteger x | KUnbounded{} <- kindOf x = True
| True = False
isUninterpreted x | KUninterpreted{} <- kindOf x = True
| True = False
showType = show . kindOf
default kindOf :: Data a => a -> Kind
kindOf = KUninterpreted . tyconUQname . dataTypeName . dataTypeOf
instance HasKind Bool where kindOf _ = KBounded False 1
instance HasKind Int8 where kindOf _ = KBounded True 8
instance HasKind Word8 where kindOf _ = KBounded False 8
instance HasKind Int16 where kindOf _ = KBounded True 16
instance HasKind Word16 where kindOf _ = KBounded False 16
instance HasKind Int32 where kindOf _ = KBounded True 32
instance HasKind Word32 where kindOf _ = KBounded False 32
instance HasKind Int64 where kindOf _ = KBounded True 64
instance HasKind Word64 where kindOf _ = KBounded False 64
instance HasKind Integer where kindOf _ = KUnbounded
instance HasKind AlgReal where kindOf _ = KReal
liftCW :: (AlgReal -> b) -> (Integer -> b) -> (String -> b) -> CW -> b
liftCW f _ _ (CW _ (CWAlgReal v)) = f v
liftCW _ g _ (CW _ (CWInteger v)) = g v
liftCW _ _ h (CW _ (CWUninterpreted v)) = h v
liftCW2 :: (AlgReal -> AlgReal -> b) -> (Integer -> Integer -> b) -> (String -> String -> b) -> CW -> CW -> b
liftCW2 f g h x y = case (cwVal x, cwVal y) of
(CWAlgReal a, CWAlgReal b) -> f a b
(CWInteger a, CWInteger b) -> g a b
(CWUninterpreted a, CWUninterpreted b) -> h a b
_ -> error $ "SBV.liftCW2: impossible, incompatible args received: " ++ show (x, y)
mapCW :: (AlgReal -> AlgReal) -> (Integer -> Integer) -> (String -> String) -> CW -> CW
mapCW f g h x = normCW $ CW (cwKind x) $ case cwVal x of
CWAlgReal a -> CWAlgReal (f a)
CWInteger a -> CWInteger (g a)
CWUninterpreted a -> CWUninterpreted (h a)
mapCW2 :: (AlgReal -> AlgReal -> AlgReal) -> (Integer -> Integer -> Integer) -> (String -> String -> String) -> CW -> CW -> CW
mapCW2 f g h x y = case (cwSameType x y, cwVal x, cwVal y) of
(True, CWAlgReal a, CWAlgReal b) -> normCW $ CW (cwKind x) (CWAlgReal (f a b))
(True, CWInteger a, CWInteger b) -> normCW $ CW (cwKind x) (CWInteger (g a b))
(True, CWUninterpreted a, CWUninterpreted b) -> normCW $ CW (cwKind x) (CWUninterpreted (h a b))
_ -> error $ "SBV.mapCW2: impossible, incompatible args received: " ++ show (x, y)
instance HasKind CW where
kindOf = cwKind
instance HasKind SW where
kindOf (SW k _) = k
instance Show CW where
show w | cwIsBit w = show (cwToBool w)
show w = liftCW show show id w ++ " :: " ++ showType w
instance Show SW where
show (SW _ (NodeId n))
| n < 0 = "s_" ++ show (abs n)
| True = 's' : show n
instance Show Op where
show (Shl i) = "<<" ++ show i
show (Shr i) = ">>" ++ show i
show (Rol i) = "<<<" ++ show i
show (Ror i) = ">>>" ++ show i
show (Extract i j) = "choose [" ++ show i ++ ":" ++ show j ++ "]"
show (LkUp (ti, at, rt, l) i e)
= "lookup(" ++ tinfo ++ ", " ++ show i ++ ", " ++ show e ++ ")"
where tinfo = "table" ++ show ti ++ "(" ++ show at ++ " -> " ++ show rt ++ ", " ++ show l ++ ")"
show (ArrEq i j) = "array_" ++ show i ++ " == array_" ++ show j
show (ArrRead i) = "select array_" ++ show i
show (Uninterpreted i) = "[uninterpreted] " ++ i
show op
| Just s <- op `lookup` syms = s
| True = error "impossible happened; can't find op!"
where syms = [ (Plus, "+"), (Times, "*"), (Minus, "-")
, (Quot, "quot")
, (Rem, "rem")
, (Equal, "=="), (NotEqual, "/=")
, (LessThan, "<"), (GreaterThan, ">"), (LessEq, "<"), (GreaterEq, ">")
, (Ite, "if_then_else")
, (And, "&"), (Or, "|"), (XOr, "^"), (Not, "~")
, (Join, "#")
]
reorder :: SBVExpr -> SBVExpr
reorder s = case s of
SBVApp op [a, b] | isCommutative op && a > b -> SBVApp op [b, a]
_ -> s
where isCommutative :: Op -> Bool
isCommutative o = o `elem` [Plus, Times, Equal, NotEqual, And, Or, XOr]
instance Show SBVExpr where
show (SBVApp Ite [t, a, b]) = unwords ["if", show t, "then", show a, "else", show b]
show (SBVApp (Shl i) [a]) = unwords [show a, "<<", show i]
show (SBVApp (Shr i) [a]) = unwords [show a, ">>", show i]
show (SBVApp (Rol i) [a]) = unwords [show a, "<<<", show i]
show (SBVApp (Ror i) [a]) = unwords [show a, ">>>", show i]
show (SBVApp op [a, b]) = unwords [show a, show op, show b]
show (SBVApp op args) = unwords (show op : map show args)
newtype SBVPgm = SBVPgm {pgmAssignments :: (S.Seq (SW, SBVExpr))}
type NamedSymVar = (SW, String)
data UnintKind = UFun Int String | UArr Int String
deriving Show
data Result = Result (Bool, Bool)
[String]
[(String, CW)]
[(String, [String])]
[(Quantifier, NamedSymVar)]
[(SW, CW)]
[((Int, Kind, Kind), [SW])]
[(Int, ArrayInfo)]
[(String, SBVType)]
[(String, [String])]
SBVPgm
[SW]
[SW]
getConstraints :: Result -> [SW]
getConstraints (Result _ _ _ _ _ _ _ _ _ _ _ cstrs _) = cstrs
getTraceInfo :: Result -> [(String, CW)]
getTraceInfo (Result _ _ tvals _ _ _ _ _ _ _ _ _ _) = tvals
instance Show Result where
show (Result _ _ _ _ _ cs _ _ [] [] _ [] [r])
| Just c <- r `lookup` cs
= show c
show (Result _ sorts _ cgs is cs ts as uis axs xs cstrs os) = intercalate "\n" $
(if null sorts then [] else "SORTS" : map (" " ++) sorts)
++ ["INPUTS"]
++ map shn is
++ ["CONSTANTS"]
++ map shc cs
++ ["TABLES"]
++ map sht ts
++ ["ARRAYS"]
++ map sha as
++ ["UNINTERPRETED CONSTANTS"]
++ map shui uis
++ ["USER GIVEN CODE SEGMENTS"]
++ concatMap shcg cgs
++ ["AXIOMS"]
++ map shax axs
++ ["DEFINE"]
++ map (\(s, e) -> " " ++ shs s ++ " = " ++ show e) (F.toList (pgmAssignments xs))
++ ["CONSTRAINTS"]
++ map ((" " ++) . show) cstrs
++ ["OUTPUTS"]
++ map ((" " ++) . show) os
where shs sw = show sw ++ " :: " ++ showType sw
sht ((i, at, rt), es) = " Table " ++ show i ++ " : " ++ show at ++ "->" ++ show rt ++ " = " ++ show es
shc (sw, cw) = " " ++ show sw ++ " = " ++ show cw
shcg (s, ss) = ("Variable: " ++ s) : map (" " ++) ss
shn (q, (sw, nm)) = " " ++ ni ++ " :: " ++ showType sw ++ ex ++ alias
where ni = show sw
ex | q == ALL = ""
| True = ", existential"
alias | ni == nm = ""
| True = ", aliasing " ++ show nm
sha (i, (nm, (ai, bi), ctx)) = " " ++ ni ++ " :: " ++ show ai ++ " -> " ++ show bi ++ alias
++ "\n Context: " ++ show ctx
where ni = "array_" ++ show i
alias | ni == nm = ""
| True = ", aliasing " ++ show nm
shui (nm, t) = " [uninterpreted] " ++ nm ++ " :: " ++ show t
shax (nm, ss) = " -- user defined axiom: " ++ nm ++ "\n " ++ intercalate "\n " ss
data ArrayContext = ArrayFree (Maybe SW)
| ArrayReset Int SW
| ArrayMutate Int SW SW
| ArrayMerge SW Int Int
instance Show ArrayContext where
show (ArrayFree Nothing) = " initialized with random elements"
show (ArrayFree (Just s)) = " initialized with " ++ show s ++ " :: " ++ showType s
show (ArrayReset i s) = " reset array_" ++ show i ++ " with " ++ show s ++ " :: " ++ showType s
show (ArrayMutate i a b) = " cloned from array_" ++ show i ++ " with " ++ show a ++ " :: " ++ showType a ++ " |-> " ++ show b ++ " :: " ++ showType b
show (ArrayMerge s i j) = " merged arrays " ++ show i ++ " and " ++ show j ++ " on condition " ++ show s
type ExprMap = Map.Map SBVExpr SW
type CnstMap = Map.Map CW SW
type TableMap = Map.Map [SW] (Int, Kind, Kind)
type ArrayInfo = (String, (Kind, Kind), ArrayContext)
type ArrayMap = IMap.IntMap ArrayInfo
type UIMap = Map.Map String SBVType
type CgMap = Map.Map String [String]
type Cache a = IMap.IntMap [(StableName (State -> IO a), a)]
unintFnUIKind :: (String, SBVType) -> (String, UnintKind)
unintFnUIKind (s, t) = (s, UFun (typeArity t) s)
arrayUIKind :: (Int, ArrayInfo) -> Maybe (String, UnintKind)
arrayUIKind (i, (nm, _, ctx))
| external ctx = Just ("array_" ++ show i, UArr 1 nm)
| True = Nothing
where external (ArrayFree{}) = True
external (ArrayReset{}) = False
external (ArrayMutate{}) = False
external (ArrayMerge{}) = False
data SBVRunMode = Proof Bool
| CodeGen
| Concrete StdGen
isConcreteMode :: SBVRunMode -> Bool
isConcreteMode (Concrete _) = True
isConcreteMode (Proof{}) = False
isConcreteMode CodeGen = False
data State = State { runMode :: SBVRunMode
, rStdGen :: IORef StdGen
, rCInfo :: IORef [(String, CW)]
, rctr :: IORef Int
, rUnBounded :: IORef (Bool, Bool)
, rinps :: IORef [(Quantifier, NamedSymVar)]
, rConstraints :: IORef [SW]
, routs :: IORef [SW]
, rtblMap :: IORef TableMap
, spgm :: IORef SBVPgm
, rconstMap :: IORef CnstMap
, rexprMap :: IORef ExprMap
, rArrayMap :: IORef ArrayMap
, rUIMap :: IORef UIMap
, rCgMap :: IORef CgMap
, raxioms :: IORef [(String, [String])]
, rSWCache :: IORef (Cache SW)
, rAICache :: IORef (Cache Int)
, rSorts :: IORef [String]
}
inProofMode :: State -> Bool
inProofMode s = case runMode s of
Proof{} -> True
CodeGen -> False
Concrete{} -> False
data SBV a = SBV !Kind !(Either CW (Cached SW))
type SBool = SBV Bool
type SWord8 = SBV Word8
type SWord16 = SBV Word16
type SWord32 = SBV Word32
type SWord64 = SBV Word64
type SInt8 = SBV Int8
type SInt16 = SBV Int16
type SInt32 = SBV Int32
type SInt64 = SBV Int64
type SInteger = SBV Integer
type SReal = SBV AlgReal
instance Show (SBV a) where
show (SBV _ (Left c)) = show c
show (SBV k (Right _)) = "<symbolic> :: " ++ show k
instance Eq (SBV a) where
SBV _ (Left a) == SBV _ (Left b) = a == b
a == b = error $ "Comparing symbolic bit-vectors; Use (.==) instead. Received: " ++ show (a, b)
SBV _ (Left a) /= SBV _ (Left b) = a /= b
a /= b = error $ "Comparing symbolic bit-vectors; Use (./=) instead. Received: " ++ show (a, b)
instance HasKind a => HasKind (SBV a) where
kindOf _ = kindOf (undefined :: a)
incCtr :: State -> IO Int
incCtr s = do ctr <- readIORef (rctr s)
let i = ctr + 1
i `seq` writeIORef (rctr s) i
return ctr
throwDice :: State -> IO Double
throwDice st = do g <- readIORef (rStdGen st)
let (r, g') = randomR (0, 1) g
writeIORef (rStdGen st) g'
return r
newUninterpreted :: State -> String -> SBVType -> Maybe [String] -> IO ()
newUninterpreted st nm t mbCode
| null nm || not (isAlpha (head nm)) || not (all validChar (tail nm))
= error $ "Bad uninterpreted constant name: " ++ show nm ++ ". Must be a valid identifier."
| True = do
uiMap <- readIORef (rUIMap st)
case nm `Map.lookup` uiMap of
Just t' -> if t /= t'
then error $ "Uninterpreted constant " ++ show nm ++ " used at incompatible types\n"
++ " Current type : " ++ show t ++ "\n"
++ " Previously used at: " ++ show t'
else return ()
Nothing -> do modifyIORef (rUIMap st) (Map.insert nm t)
when (isJust mbCode) $ modifyIORef (rCgMap st) (Map.insert nm (fromJust mbCode))
where validChar x = isAlphaNum x || x `elem` "_"
newConst :: State -> CW -> IO SW
newConst st c = do
constMap <- readIORef (rconstMap st)
case c `Map.lookup` constMap of
Just sw -> return sw
Nothing -> do ctr <- incCtr st
let k = kindOf c
sw = SW k (NodeId ctr)
() <- case kindOf c of
KUnbounded -> modifyIORef (rUnBounded st) (\(_, y) -> (True, y))
KReal -> modifyIORef (rUnBounded st) (\(x, _) -> (x, True))
_ -> return ()
modifyIORef (rconstMap st) (Map.insert c sw)
return sw
getTableIndex :: State -> Kind -> Kind -> [SW] -> IO Int
getTableIndex st at rt elts = do
tblMap <- readIORef (rtblMap st)
case elts `Map.lookup` tblMap of
Just (i, _, _) -> return i
Nothing -> do let i = Map.size tblMap
modifyIORef (rtblMap st) (Map.insert elts (i, at, rt))
return i
mkConstCW :: Integral a => Kind -> a -> CW
mkConstCW KReal a = normCW $ CW KReal (CWAlgReal (fromInteger (toInteger a)))
mkConstCW k a = normCW $ CW k (CWInteger (toInteger a))
newExpr :: State -> Kind -> SBVExpr -> IO SW
newExpr st k app = do
let e = reorder app
exprMap <- readIORef (rexprMap st)
case e `Map.lookup` exprMap of
Just sw -> return sw
Nothing -> do ctr <- incCtr st
let sw = SW k (NodeId ctr)
() <- case k of
KUnbounded -> modifyIORef (rUnBounded st) (\(_, y) -> (True, y))
KReal -> modifyIORef (rUnBounded st) (\(x, _) -> (x, True))
_ -> return ()
modifyIORef (spgm st) (\(SBVPgm xs) -> SBVPgm (xs S.|> (sw, e)))
modifyIORef (rexprMap st) (Map.insert e sw)
return sw
sbvToSW :: State -> SBV a -> IO SW
sbvToSW st (SBV _ (Left c)) = newConst st c
sbvToSW st (SBV _ (Right f)) = uncache f st
newtype Symbolic a = Symbolic (ReaderT State IO a)
deriving (Functor, Monad, MonadIO, MonadReader State)
mkSymSBV :: forall a. (Random a, SymWord a) => Maybe Quantifier -> Kind -> Maybe String -> Symbolic (SBV a)
mkSymSBV mbQ k mbNm = do
st <- ask
let q = case (mbQ, runMode st) of
(Just x, _) -> x
(Nothing, Concrete{}) -> ALL
(Nothing, Proof True) -> EX
(Nothing, Proof False) -> ALL
(Nothing, CodeGen) -> ALL
case runMode st of
Concrete _ | q == EX -> case mbNm of
Nothing -> error $ "Cannot quick-check in the presence of existential variables, type: " ++ showType (undefined :: SBV a)
Just nm -> error $ "Cannot quick-check in the presence of existential variable " ++ nm ++ " :: " ++ showType (undefined :: SBV a)
Concrete _ -> do v@(SBV _ (Left cw)) <- liftIO randomIO
liftIO $ modifyIORef (rCInfo st) ((maybe "_" id mbNm, cw):)
return v
_ -> do ctr <- liftIO $ incCtr st
let nm = maybe ('s':show ctr) id mbNm
sw = SW k (NodeId ctr)
() <- case k of
KUnbounded -> liftIO $ modifyIORef (rUnBounded st) (\(_, y) -> (True, y))
KReal -> liftIO $ modifyIORef (rUnBounded st) (\(x, _) -> (x, True))
_ -> return ()
liftIO $ modifyIORef (rinps st) ((q, (sw, nm)):)
return $ SBV k $ Right $ cache (const (return sw))
sbvToSymSW :: SBV a -> Symbolic SW
sbvToSymSW sbv = do
st <- ask
liftIO $ sbvToSW st sbv
class Outputtable a where
output :: a -> Symbolic a
instance Outputtable (SBV a) where
output i@(SBV _ (Left c)) = do
st <- ask
sw <- liftIO $ newConst st c
liftIO $ modifyIORef (routs st) (sw:)
return i
output i@(SBV _ (Right f)) = do
st <- ask
sw <- liftIO $ uncache f st
liftIO $ modifyIORef (routs st) (sw:)
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
addAxiom :: String -> [String] -> Symbolic ()
addAxiom nm ax = do
st <- ask
liftIO $ modifyIORef (raxioms st) ((nm, ax) :)
runSymbolic :: Bool -> Symbolic a -> IO Result
runSymbolic b c = snd `fmap` runSymbolic' (Proof b) c
runSymbolic' :: SBVRunMode -> Symbolic a -> IO (a, Result)
runSymbolic' currentRunMode (Symbolic c) = do
ctr <- newIORef (2)
cInfo <- newIORef []
pgm <- newIORef (SBVPgm S.empty)
emap <- newIORef Map.empty
cmap <- newIORef Map.empty
inps <- newIORef []
outs <- newIORef []
tables <- newIORef Map.empty
arrays <- newIORef IMap.empty
uis <- newIORef Map.empty
cgs <- newIORef Map.empty
axioms <- newIORef []
swCache <- newIORef IMap.empty
aiCache <- newIORef IMap.empty
unbounded <- newIORef (False, False)
cstrs <- newIORef []
sorts <- newIORef []
rGen <- case currentRunMode of
Concrete g -> newIORef g
_ -> newStdGen >>= newIORef
let st = State { runMode = currentRunMode
, rStdGen = rGen
, rCInfo = cInfo
, rctr = ctr
, rUnBounded = unbounded
, rinps = inps
, routs = outs
, rtblMap = tables
, spgm = pgm
, rconstMap = cmap
, rArrayMap = arrays
, rexprMap = emap
, rUIMap = uis
, rCgMap = cgs
, raxioms = axioms
, rSWCache = swCache
, rAICache = aiCache
, rConstraints = cstrs
, rSorts = sorts
}
_ <- newConst st (mkConstCW (KBounded False 1) (0::Integer))
_ <- newConst st (mkConstCW (KBounded False 1) (1::Integer))
r <- runReaderT c st
SBVPgm rpgm <- readIORef pgm
inpsO <- reverse `fmap` readIORef inps
outsO <- reverse `fmap` readIORef outs
let swap (a, b) = (b, a)
cmp (a, _) (b, _) = a `compare` b
cnsts <- (sortBy cmp . map swap . Map.toList) `fmap` readIORef (rconstMap st)
tbls <- (sortBy (\((x, _, _), _) ((y, _, _), _) -> x `compare` y) . map swap . Map.toList) `fmap` readIORef tables
arrs <- IMap.toAscList `fmap` readIORef arrays
unint <- Map.toList `fmap` readIORef uis
axs <- reverse `fmap` readIORef axioms
boundInfo <- readIORef unbounded
cgMap <- Map.toList `fmap` readIORef cgs
traceVals <- reverse `fmap` readIORef cInfo
extraCstrs <- reverse `fmap` readIORef cstrs
usorts <- reverse `fmap` readIORef sorts
return $ (r, Result boundInfo usorts traceVals cgMap inpsO cnsts tbls arrs unint axs (SBVPgm rpgm) extraCstrs outsO)
class (HasKind a, Ord a) => SymWord a where
forall :: String -> Symbolic (SBV a)
forall_ :: Symbolic (SBV a)
mkForallVars :: Int -> Symbolic [SBV a]
exists :: String -> Symbolic (SBV a)
exists_ :: Symbolic (SBV a)
mkExistVars :: Int -> Symbolic [SBV a]
free :: String -> Symbolic (SBV a)
free_ :: Symbolic (SBV a)
mkFreeVars :: Int -> Symbolic [SBV a]
symbolic :: String -> Symbolic (SBV a)
symbolics :: [String] -> Symbolic [SBV a]
literal :: a -> SBV a
unliteral :: SBV a -> Maybe a
fromCW :: CW -> a
isConcrete :: SBV a -> Bool
isSymbolic :: SBV a -> Bool
isConcretely :: SBV a -> (a -> Bool) -> Bool
mbMaxBound, mbMinBound :: Maybe a
mkSymWord :: Maybe Quantifier -> Maybe String -> Symbolic (SBV a)
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 _ (Left c)) = Just $ fromCW c
unliteral _ = Nothing
isConcrete (SBV _ (Left _)) = True
isConcrete _ = False
isSymbolic = not . isConcrete
isConcretely s p
| Just i <- unliteral s = p i
| True = False
mbMaxBound = Nothing
mbMinBound = Nothing
literal x = error $ "Cannot create symbolic literals for kind: " ++ show (kindOf x)
fromCW cw = error $ "Cannot convert CW " ++ show cw ++ " to kind " ++ show (kindOf (undefined :: a))
default mkSymWord :: Data a => Maybe Quantifier -> Maybe String -> Symbolic (SBV a)
mkSymWord mbQ mbNm = do
let sortName = tyconUQname . dataTypeName . dataTypeOf $ (undefined :: a)
st <- ask
let
reserved = ["Int", "Real", "List", "Array", "Bool"]
when (sortName `elem` reserved) $ error $ "SBV.registerSort: " ++ show sortName ++ " is a reserved sort; please use a different name"
curSorts <- liftIO $ readIORef (rSorts st)
when (sortName `notElem` curSorts) $ liftIO $ modifyIORef (rSorts st) (sortName :)
let k = KUninterpreted sortName
q = case (mbQ, runMode st) of
(Just x, _) -> x
(Nothing, Proof True) -> EX
(Nothing, Proof False) -> ALL
(Nothing, Concrete{}) -> error $ "SBV.registerSort: Uninterpreted sort " ++ sortName ++ " can not be used in concrete simulation mode."
(Nothing, CodeGen) -> error $ "SBV.registerSort: Uninterpreted sort " ++ sortName ++ " can not be used in code-generation mode."
ctr <- liftIO $ incCtr st
let sw = SW k (NodeId ctr)
nm = maybe ('s':show ctr) id mbNm
liftIO $ modifyIORef (rinps st) ((q, (sw, nm)):)
return $ SBV k $ Right $ cache (const (return sw))
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')
class SymArray array where
newArray_ :: (HasKind a, HasKind b) => Maybe (SBV b) -> Symbolic (array a b)
newArray :: (HasKind a, HasKind b) => String -> Maybe (SBV b) -> Symbolic (array a b)
readArray :: array a b -> SBV a -> SBV b
resetArray :: SymWord b => array a b -> SBV b -> array a b
writeArray :: SymWord b => array a b -> SBV a -> SBV b -> array a b
mergeArrays :: SymWord b => SBV Bool -> array a b -> array a b -> array a b
data SArray a b = SArray (Kind, Kind) (Cached ArrayIndex)
type ArrayIndex = Int
instance (HasKind a, HasKind b) => Show (SArray a b) where
show (SArray{}) = "SArray<" ++ showType (undefined :: a) ++ ":" ++ showType (undefined :: b) ++ ">"
instance SymArray SArray where
newArray_ = declNewSArray (\t -> "array_" ++ show t)
newArray n = declNewSArray (const n)
readArray (SArray (_, bk) f) a = SBV bk $ Right $ cache r
where r st = do arr <- uncacheAI f st
i <- sbvToSW st a
newExpr st bk (SBVApp (ArrRead arr) [i])
resetArray (SArray ainfo f) b = SArray ainfo $ cache g
where g st = do amap <- readIORef (rArrayMap st)
val <- sbvToSW st b
i <- uncacheAI f st
let j = IMap.size amap
j `seq` modifyIORef (rArrayMap st) (IMap.insert j ("array_" ++ show j, ainfo, ArrayReset i val))
return j
writeArray (SArray ainfo f) a b = SArray ainfo $ cache g
where g st = do arr <- uncacheAI f st
addr <- sbvToSW st a
val <- sbvToSW st b
amap <- readIORef (rArrayMap st)
let j = IMap.size amap
j `seq` modifyIORef (rArrayMap st) (IMap.insert j ("array_" ++ show j, ainfo, ArrayMutate arr addr val))
return j
mergeArrays t (SArray ainfo a) (SArray _ b) = SArray ainfo $ cache h
where h st = do ai <- uncacheAI a st
bi <- uncacheAI b st
ts <- sbvToSW st t
amap <- readIORef (rArrayMap st)
let k = IMap.size amap
k `seq` modifyIORef (rArrayMap st) (IMap.insert k ("array_" ++ show k, ainfo, ArrayMerge ts ai bi))
return k
declNewSArray :: forall a b. (HasKind a, HasKind b) => (Int -> String) -> Maybe (SBV b) -> Symbolic (SArray a b)
declNewSArray mkNm mbInit = do
let aknd = kindOf (undefined :: a)
bknd = kindOf (undefined :: b)
st <- ask
amap <- liftIO $ readIORef $ rArrayMap st
let i = IMap.size amap
nm = mkNm i
actx <- liftIO $ case mbInit of
Nothing -> return $ ArrayFree Nothing
Just ival -> sbvToSW st ival >>= \sw -> return $ ArrayFree (Just sw)
liftIO $ modifyIORef (rArrayMap st) (IMap.insert i (nm, (aknd, bknd), actx))
return $ SArray (aknd, bknd) $ cache $ const $ return i
data SFunArray a b = SFunArray (SBV a -> SBV b)
instance (HasKind a, HasKind b) => Show (SFunArray a b) where
show (SFunArray _) = "SFunArray<" ++ showType (undefined :: a) ++ ":" ++ showType (undefined :: b) ++ ">"
mkSFunArray :: (SBV a -> SBV b) -> SFunArray a b
mkSFunArray = SFunArray
imposeConstraint :: SBool -> Symbolic ()
imposeConstraint c = do st <- ask
case runMode st of
CodeGen -> error "SBV: constraints are not allowed in code-generation"
_ -> do liftIO $ do v <- sbvToSW st c
modifyIORef (rConstraints st) (v:)
addConstraint :: Maybe Double -> SBool -> SBool -> Symbolic ()
addConstraint Nothing c _ = imposeConstraint c
addConstraint (Just t) c c'
| t < 0 || t > 1
= error $ "SBV: pConstrain: Invalid probability threshold: " ++ show t ++ ", must be in [0, 1]."
| True
= do st <- ask
when (not (isConcreteMode (runMode st))) $ error "SBV: pConstrain only allowed in 'genTest' or 'quickCheck' contexts."
case () of
() | t > 0 && t < 1 -> liftIO (throwDice st) >>= \d -> imposeConstraint (if d <= t then c else c')
| t > 0 -> imposeConstraint c
| True -> imposeConstraint c'
newtype Cached a = Cached (State -> IO a)
cache :: (State -> IO a) -> Cached a
cache = Cached
uncache :: Cached SW -> State -> IO SW
uncache = uncacheGen rSWCache
uncacheAI :: Cached ArrayIndex -> State -> IO ArrayIndex
uncacheAI = uncacheGen rAICache
uncacheGen :: (State -> IORef (Cache a)) -> Cached a -> State -> IO a
uncacheGen getCache (Cached f) st = do
let rCache = getCache st
stored <- readIORef rCache
sn <- f `seq` makeStableName f
let h = hashStableName sn
case maybe Nothing (sn `lookup`) (h `IMap.lookup` stored) of
Just r -> return r
Nothing -> do r <- f st
r `seq` modifyIORef rCache (IMap.insertWith (++) h [(sn, r)])
return r
data SMTLibVersion = SMTLib1
| SMTLib2
deriving Eq
data SMTLibPgm = SMTLibPgm SMTLibVersion ( [(String, SW)]
, [String]
, [String])
instance NFData SMTLibVersion
instance NFData SMTLibPgm
instance Show SMTLibPgm where
show (SMTLibPgm _ (_, pre, post)) = intercalate "\n" $ pre ++ post
instance NFData CW where
rnf (CW x y) = x `seq` y `seq` ()
instance NFData Result where
rnf (Result isInf sorts qcInfo cgs inps consts tbls arrs uis axs pgm cstr outs)
= rnf isInf `seq` rnf sorts `seq` rnf qcInfo `seq` rnf cgs
`seq` rnf inps `seq` rnf consts `seq` rnf tbls
`seq` rnf arrs `seq` rnf uis `seq` rnf axs
`seq` rnf pgm `seq` rnf cstr `seq` rnf outs
instance NFData Kind
instance NFData ArrayContext
instance NFData SW
instance NFData SBVExpr
instance NFData Quantifier
instance NFData SBVType
instance NFData UnintKind
instance NFData a => NFData (Cached a) where
rnf (Cached f) = f `seq` ()
instance NFData a => NFData (SBV a) where
rnf (SBV x y) = rnf x `seq` rnf y `seq` ()
instance NFData SBVPgm