----------------------------------------------------------------------------- -- | -- Module : Data.SBV.BitVectors.Data -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- Portability : portable -- -- Internal data-structures for the sbv library ----------------------------------------------------------------------------- {-# LANGUAGE Rank2Types #-} {-# LANGUAGE PatternGuards #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE TypeSynonymInstances #-} {-# LANGUAGE TypeOperators #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE ScopedTypeVariables #-} module Data.SBV.BitVectors.Data ( SBool, SWord8, SWord16, SWord32, SWord64 , SInt8, SInt16, SInt32, SInt64 , SymWord(..) , CW(..) , mkConstCW, liftCW2, mapCW, mapCW2 , SW(..), trueSW, falseSW , SBV(..), NodeId(..), mkSymSBV , ArrayContext(..), ArrayInfo, SymArray(..), SFunArray(..), SArray(..) , sbvToSW , SBVExpr(..), newExpr , cache, uncache, HasSignAndSize(..) , Op(..), NamedSymVar, getTableIndex, Pgm, Symbolic, runSymbolic, State, Size, output, Result(..) , SBVType(..), newUninterpreted ) where import Control.DeepSeq (NFData(..)) import Control.Monad.Reader (MonadReader, ReaderT, ask, runReaderT) import Control.Monad.Trans (MonadIO, liftIO) import Data.Bits (Bits(..)) import Data.Char (isAlpha, isAlphaNum) 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 qualified Data.IntMap as IMap (IntMap, empty, size, toAscList, insert) 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.IO.Unsafe (unsafePerformIO) -- see the note at the bottom of the file import Test.QuickCheck (Testable(..)) import Data.SBV.BitVectors.Bit -- | 'CW' represents a concrete word of a fixed size: -- The unsigned variants are: 'W1', 'W8', 'W16', 'W32', and 'W64' -- The signed variants are : 'I8', 'I16', 'I32', I64' -- Endianness is mostly irrelevant (see the 'FromBits' class). -- For signed words, the most significant digit is considered to be the sign data CW = W1 { wcToW1 :: Bit } | W8 { wcToW8 :: Word8 } | W16 { wcToW16 :: Word16} | W32 { wcToW32 :: Word32} | W64 { wcToW64 :: Word64 } | I8 { wcToI8 :: Int8 } | I16 { wcToI16 :: Int16 } | I32 { wcToI32 :: Int32 } | I64 { wcToI64 :: Int64 } deriving (Eq, Ord) type Size = Int newtype NodeId = NodeId Int deriving (Eq, Ord) data SW = SW (Bool, Size) NodeId deriving (Eq, Ord) falseSW, trueSW :: SW falseSW = SW (False, 1) $ NodeId (-2) trueSW = SW (False, 1) $ NodeId (-1) newtype SBVType = SBVType [(Bool, Size)] deriving (Eq, Ord) instance Show SBVType where show (SBVType []) = error "SBV: internal error, empty SBVType" show (SBVType xs) = intercalate " -> " $ map sh xs where sh (False, 1) = "SBool" sh (s, sz) = (if s then "SInt" else "SWord") ++ show sz data Op = Plus | Times | Minus | Quot | Rem -- quot and rem are unsigned only | Equal | NotEqual | LessThan | GreaterThan | LessEq | GreaterEq | Ite | And | Or | XOr | Not | Shl Int | Shr Int | Rol Int | Ror Int | Extract Int Int -- Extract i j: extract bits i to j. Least significant bit is 0 (big-endian) | Join -- Concat two words to form a bigger one, in the order given | LkUp (Int, Int, Int, Int) !SW !SW -- (table-index, arg-type, res-type, length of the table) index out-of-bounds-value | ArrEq Int Int | ArrRead Int | Uninterpreted String deriving (Eq, Ord) data SBVExpr = SBVApp {-# UNPACK #-} !Op {-# UNPACK #-} ![SW] deriving (Eq, Ord) class HasSignAndSize a where sizeOf :: a -> Size hasSign :: a -> Bool showType :: a -> String showType a | not (hasSign a) && sizeOf a == 1 = "SBool" | True = if hasSign a then "SInt" else "SWord" ++ show (sizeOf a) instance HasSignAndSize Bit where {sizeOf _ = 1; hasSign _ = False} instance HasSignAndSize Int8 where {sizeOf _ = 8; hasSign _ = True } instance HasSignAndSize Word8 where {sizeOf _ = 8; hasSign _ = False} instance HasSignAndSize Int16 where {sizeOf _ = 16; hasSign _ = True } instance HasSignAndSize Word16 where {sizeOf _ = 16; hasSign _ = False} instance HasSignAndSize Int32 where {sizeOf _ = 32; hasSign _ = True } instance HasSignAndSize Word32 where {sizeOf _ = 32; hasSign _ = False} instance HasSignAndSize Int64 where {sizeOf _ = 64; hasSign _ = True } instance HasSignAndSize Word64 where {sizeOf _ = 64; hasSign _ = False} liftCW :: (forall a. (Ord a, Bits a) => a -> b) -> CW -> b liftCW f (W1 w) = f w liftCW f (W8 w) = f w liftCW f (W16 w) = f w liftCW f (W32 w) = f w liftCW f (W64 w) = f w liftCW f (I8 w) = f w liftCW f (I16 w) = f w liftCW f (I32 w) = f w liftCW f (I64 w) = f w liftCW2 :: (forall a. (Ord a, Bits a) => a -> a -> b) -> CW -> CW -> b liftCW2 f (W1 a) (W1 b) = a `f` b liftCW2 f (W8 a) (W8 b) = a `f` b liftCW2 f (W16 a) (W16 b) = a `f` b liftCW2 f (W32 a) (W32 b) = a `f` b liftCW2 f (W64 a) (W64 b) = a `f` b liftCW2 f (I8 a) (I8 b) = a `f` b liftCW2 f (I16 a) (I16 b) = a `f` b liftCW2 f (I32 a) (I32 b) = a `f` b liftCW2 f (I64 a) (I64 b) = a `f` b liftCW2 _ a b = error $ "SBV.liftCW2: impossible, incompatible args received: " ++ show (a, b) mapCW :: (forall a. (Ord a, Bits a) => a -> a) -> CW -> CW mapCW f (W1 w) = W1 $ f w mapCW f (W8 w) = W8 $ f w mapCW f (W16 w) = W16 $ f w mapCW f (W32 w) = W32 $ f w mapCW f (W64 w) = W64 $ f w mapCW f (I8 w) = I8 $ f w mapCW f (I16 w) = I16 $ f w mapCW f (I32 w) = I32 $ f w mapCW f (I64 w) = I64 $ f w mapCW2 :: (forall a. (Ord a, Bits a) => a -> a -> a) -> CW -> CW -> CW mapCW2 f (W1 a) (W1 b) = W1 $ a `f` b mapCW2 f (W8 a) (W8 b) = W8 $ a `f` b mapCW2 f (W16 a) (W16 b) = W16 $ a `f` b mapCW2 f (W32 a) (W32 b) = W32 $ a `f` b mapCW2 f (W64 a) (W64 b) = W64 $ a `f` b mapCW2 f (I8 a) (I8 b) = I8 $ a `f` b mapCW2 f (I16 a) (I16 b) = I16 $ a `f` b mapCW2 f (I32 a) (I32 b) = I32 $ a `f` b mapCW2 f (I64 a) (I64 b) = I64 $ a `f` b mapCW2 _ a b = error $ "SBV.mapCW2: impossible, incompatible args received: " ++ show (a, b) instance HasSignAndSize CW where sizeOf = liftCW bitSize hasSign = liftCW isSigned instance HasSignAndSize SW where sizeOf (SW (_, s) _) = s hasSign (SW (b, _) _) = b instance Show CW where show (W1 b) = show (bit2Bool b) show w = liftCW show 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) = "ui_" ++ 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) -- | A program is a sequence of assignments type Pgm = S.Seq (SW, SBVExpr) -- | 'NamedSymVar' pairs symbolic words and user given/automatically generated names type NamedSymVar = (SW, String) -- | Result of running a symbolic computation data Result = Result [NamedSymVar] -- inputs [(SW, CW)] -- constants [((Int, Int, Int), [SW])] -- tables (automatically constructed) [(Int, ArrayInfo)] -- arrays (user specified) [(String, SBVType)] -- uninterpreted constants Pgm -- assignments [SW] -- outputs instance Show Result where show (Result _ cs _ _ [] _ [r]) | Just c <- r `lookup` cs = show c show (Result is cs ts as uis xs os) = intercalate "\n" $ ["INPUTS"] ++ map shn is ++ ["CONSTANTS"] ++ map shc cs ++ ["TABLES"] ++ map sht ts ++ ["ARRAYS"] ++ map sha as ++ ["UNINTERPRETED CONSTANTS"] ++ map shui uis ++ ["DEFINE"] ++ map (\(s, e) -> " " ++ shs s ++ " = " ++ show e) (F.toList xs) ++ ["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 shn (sw, nm) = " " ++ ni ++ " :: " ++ showType sw ++ alias where ni = show sw alias | ni == nm = "" | True = ", aliasing " ++ show nm sha (i, (nm, (ai, bi), ctx)) = " " ++ ni ++ " :: " ++ mkT ai ++ " -> " ++ mkT bi ++ alias ++ "\n Context: " ++ show ctx where mkT (b, s) | s == 1 = "SBool" | True = if b then "SInt" else "SWord" ++ show s ni = "array" ++ show i alias | ni == nm = "" | True = ", aliasing " ++ show nm shui (nm, t) = " ui_" ++ nm ++ " :: " ++ show t data ArrayContext = ArrayFree | ArrayInit SW | ArrayMutate Int SW SW | ArrayMerge SW Int Int instance Show ArrayContext where show ArrayFree = " initialized with random elements" show (ArrayInit s) = " initialized 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, Int, Int) type ArrayInfo = (String, ((Bool, Size), (Bool, Size)), ArrayContext) type ArrayMap = IMap.IntMap ArrayInfo type UIMap = Map.Map String SBVType data State = State { rctr :: IORef Int , rinps :: IORef [NamedSymVar] , routs :: IORef [SW] , rtblMap :: IORef TableMap , spgm :: IORef Pgm , rconstMap :: IORef CnstMap , rexprMap :: IORef ExprMap , rArrayMap :: IORef ArrayMap , rUIMap :: IORef UIMap } -- | The "Symbolic" value. Either a constant (@Left@) or a symbolic -- value (@Right Cached@). Note that caching is essential for making -- sure sharing is preserved. The parameter 'a' is phantom, but is -- extremely important in keeping the user interface strongly typed. data SBV a = SBV !(Bool, Size) !(Either CW (Cached SW)) -- | 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 -- Needed to satisfy the Num hierarchy instance Show (SBV a) where show (SBV _ (Left c)) = show c show (SBV (sgn, sz) (Right _)) = " :: " ++ t where t | not sgn && sz == 1 = "SBool" | True = (if sgn then "SInt" else "SWord") ++ show sz 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 HasSignAndSize (SBV a) where sizeOf (SBV (_, s) _) = s hasSign (SBV (b, _) _) = b incCtr :: State -> IO Int incCtr s = do ctr <- readIORef (rctr s) let i = ctr + 1 i `seq` writeIORef (rctr s) i return ctr newUninterpreted :: State -> String -> SBVType -> IO () newUninterpreted st nm t | null nm || not (isAlpha (head nm)) || not (all isAlphaNum (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 -> modifyIORef (rUIMap st) (Map.insert nm t) -- Create a new constant; hash-cons as necessary 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 sw = SW (hasSign c, sizeOf c) (NodeId ctr) modifyIORef (rconstMap st) (Map.insert c sw) return sw -- Create a new table; hash-cons as necessary getTableIndex :: State -> Int -> Int -> [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 => (Bool, Size) -> a -> CW mkConstCW (False, 1) 0 = W1 Zero mkConstCW (False, 1) 1 = W1 One mkConstCW (False, 8) i = W8 (fromIntegral i) mkConstCW (True, 8) i = I8 (fromIntegral i) mkConstCW (False, 16) i = W16 (fromIntegral i) mkConstCW (True, 16) i = I16 (fromIntegral i) mkConstCW (False, 32) i = W32 (fromIntegral i) mkConstCW (True, 32) i = I32 (fromIntegral i) mkConstCW (False, 64) i = W64 (fromIntegral i) mkConstCW (True, 64) i = I64 (fromIntegral i) mkConstCW sgnsz i = error $ "SBV.mkConstCW: Received unexpected input: " ++ show (sgnsz, i) -- Create a new expression; hash-cons as necessary newExpr :: State -> (Bool, Size) -> SBVExpr -> IO SW newExpr st sgnsz 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 sgnsz (NodeId ctr) modifyIORef (spgm st) (flip (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 ------------------------------------------------------------------------- -- * Symbolic Computations ------------------------------------------------------------------------- -- | A Symbolic computation. Represented by a reader monad carrying the -- state of the computation, layered on top of IO for creating unique -- references to hold onto intermediate results. newtype Symbolic a = Symbolic (ReaderT State IO a) deriving (Monad, MonadIO, MonadReader State) mkSymSBV :: (Bool, Size) -> Maybe String -> Symbolic (SBV a) mkSymSBV sgnsz mbNm = do st <- ask ctr <- liftIO $ incCtr st let nm = maybe ('s':show ctr) id mbNm sw = SW sgnsz (NodeId ctr) liftIO $ modifyIORef (rinps st) ((sw, nm):) return $ SBV sgnsz $ Right $ cache (const (return sw)) -- | Mark an interim result as an output. Useful when constructing Symbolic programs -- that return multiple values, or when the result is programmatically computed. output :: SBV a -> Symbolic (SBV a) 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 -- | Run a symbolic computation and return a 'Result' runSymbolic :: Symbolic a -> IO Result runSymbolic (Symbolic c) = do ctr <- newIORef (-2) -- start from -2; False and True will always occupy the first two elements pgm <- newIORef 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 let st = State { rctr = ctr , rinps = inps , routs = outs , rtblMap = tables , spgm = pgm , rconstMap = cmap , rArrayMap = arrays , rexprMap = emap , rUIMap = uis } _ <- newConst st $ W1 Zero -- s(-2) == falseSW _ <- newConst st $ W1 One -- s(-1) == trueSW _ <- runReaderT c st rpgm <- readIORef pgm inpsR <- readIORef inps outsR <- 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 return $ Result (reverse inpsR) cnsts tbls arrs unint rpgm (reverse outsR) ------------------------------------------------------------------------------- -- * 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 Ord a => SymWord a where -- | Create a user named input free :: String -> Symbolic (SBV a) -- | Create an automatically named input free_ :: 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 -- | minimal complete definiton: free, free_, literal, fromCW unliteral (SBV _ (Left c)) = Just $ fromCW c unliteral _ = Nothing isConcrete (SBV _ (Left _)) = True isConcrete _ = False isSymbolic = not . isConcrete --------------------------------------------------------------------------------- -- * 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 an initial value is not provided in 'newArray_' and 'newArray' methods, then the elements -- are left unspecified, i.e., the solver is free to choose any value. This is the right thing -- to do if arrays are used as inputs to functions to be verified, typically. Reading an -- uninitilized entry is an error. -- 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. -- -- Minimal complete definition: All methods are required, no defaults. class SymArray array where -- | Create a new array, with an optional initial value newArray_ :: (HasSignAndSize a, HasSignAndSize b) => Maybe (SBV b) -> Symbolic (array a b) -- | Create a named new array with, with an optional initial value newArray :: (HasSignAndSize a, HasSignAndSize b) => String -> Maybe (SBV b) -> Symbolic (array a b) -- | Read the array element at @a@ readArray :: array a b -> SBV a -> SBV b -- | Reset all the elements of the array to the value @b@ resetArray :: SymWord b => array a b -> SBV b -> array a 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 -- | Arrays implemented in terms of SMT-arrays: data SArray a b = SArray ((Bool, Size), (Bool, Size)) (Cached ArrayIndex) type ArrayIndex = Int instance (HasSignAndSize a, HasSignAndSize 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 (_, bsgnsz) f) a = SBV bsgnsz $ Right $ cache r where r st = do arr <- uncache f st i <- sbvToSW st a newExpr st bsgnsz (SBVApp (ArrRead arr) [i]) resetArray (SArray ainfo _) b = SArray ainfo $ cache g where g st = do amap <- readIORef (rArrayMap st) val <- sbvToSW st b let j = IMap.size amap j `seq` modifyIORef (rArrayMap st) (IMap.insert j ("array" ++ show j, ainfo, ArrayInit val)) return j writeArray (SArray ainfo f) a b = SArray ainfo $ cache g where g st = do arr <- uncache 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 <- uncache a st bi <- uncache 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. (HasSignAndSize a, HasSignAndSize b) => (Int -> String) -> Maybe (SBV b) -> Symbolic (SArray a b) declNewSArray mkNm mbInit = do let asgnsz = (hasSign (undefined :: a), sizeOf (undefined :: a)) bsgnsz = (hasSign (undefined :: b), sizeOf (undefined :: b)) st <- ask amap <- liftIO $ readIORef $ rArrayMap st let i = IMap.size amap nm = mkNm i actx <- case mbInit of Nothing -> return ArrayFree Just ival -> liftIO $ ArrayInit `fmap` sbvToSW st ival liftIO $ modifyIORef (rArrayMap st) (IMap.insert i (nm, (asgnsz, bsgnsz), actx)) return $ SArray (asgnsz, bsgnsz) $ cache $ const $ return i -- | Arrays implemented internally as functions, and rendered as SMT-Lib functions data SFunArray a b = SFunArray (SBV a -> SBV b) instance (HasSignAndSize a, HasSignAndSize b) => Show (SFunArray a b) where show (SFunArray _) = "SFunArray<" ++ showType (undefined :: a) ++ ":" ++ showType (undefined :: b) ++ ">" --------------------------------------------------------------------------------- -- * Cached values --------------------------------------------------------------------------------- -- We implement a peculiar caching mechanism, applicable to the use case in -- implementation of SBV's. Whenever an SBV is used, we do not want to keep on -- evaluating it in the then-current state. That will produce essentially a -- semantically equivalent value. Thus, we want to run it only once, and reuse -- that result. -- -- Note that this is *not* a general memo utility! newtype Cached a = Cached { uncache :: (State -> IO a) } {-# NOINLINE cache #-} cache :: (State -> IO a) -> Cached a cache f = unsafePerformIO $ do storage <- newIORef Nothing return $ Cached (g storage) where g storage s = do mbb <- readIORef storage case mbb of Just x -> return x Nothing -> do r <- f s writeIORef storage (Just r) return r {- The following would be a perfectly good definition of cache, except for performance: cache = Cached -} -- Technicalities.. instance NFData CW where rnf (W1 w) = rnf w `seq` () rnf (W8 w) = rnf w `seq` () rnf (W16 w) = rnf w `seq` () rnf (W32 w) = rnf w `seq` () rnf (W64 w) = rnf w `seq` () rnf (I8 w) = rnf w `seq` () rnf (I16 w) = rnf w `seq` () rnf (I32 w) = rnf w `seq` () rnf (I64 w) = rnf w `seq` () instance NFData Result where rnf (Result inps consts tbls arrs uis pgm outs) = rnf inps `seq` rnf consts `seq` rnf tbls `seq` rnf arrs `seq` rnf uis `seq` rnf pgm `seq` rnf outs instance NFData ArrayContext instance NFData Pgm instance NFData SW instance NFData SBVType -- Quickcheck interface on symbolic-booleans.. instance Testable SBool where property (SBV _ (Left (W1 b))) = property . bit2Bool $ b property s = error $ "Cannot quick-check in the presence of uninterpreted constants! (" ++ show s ++ ")"