----------------------------------------------------------------------------- -- | -- Module : Data.SBV.Utils.SExpr -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer: erkokl@gmail.com -- Stability : experimental -- -- Parsing of S-expressions (mainly used for parsing SMT-Lib get-value output) ----------------------------------------------------------------------------- {-# LANGUAGE BangPatterns #-} module Data.SBV.Utils.SExpr (SExpr(..), parenDeficit, parseSExpr, parseSExprFunction) where import Data.Bits (setBit, testBit) import Data.Char (isDigit, ord, isSpace) import Data.Either (partitionEithers) import Data.List (isPrefixOf) import Data.Maybe (fromMaybe, listToMaybe) import Data.Word (Word32, Word64) import Numeric (readInt, readDec, readHex, fromRat) import Data.SBV.Core.AlgReals import Data.SBV.Core.Data (nan, infinity, RoundingMode(..)) import Data.SBV.Utils.Numeric (fpIsEqualObjectH) import Data.Numbers.CrackNum (wordToFloat, wordToDouble) -- | ADT S-Expression format, suitable for representing get-model output of SMT-Lib data SExpr = ECon String | ENum (Integer, Maybe Int) -- Second argument is how wide the field was in bits, if known. Useful in FP parsing. | EReal AlgReal | EFloat Float | EDouble Double | EApp [SExpr] deriving Show -- | Extremely simple minded tokenizer, good for our use model. tokenize :: String -> [String] tokenize inp = go inp [] where go "" sofar = reverse sofar go (c:cs) sofar | isSpace c = go (dropWhile isSpace cs) sofar go ('(':cs) sofar = go cs ("(" : sofar) go (')':cs) sofar = go cs (")" : sofar) go (':':':':cs) sofar = go cs ("::" : sofar) go (':':cs) sofar = case break (`elem` stopper) cs of (pre, rest) -> go rest ((':':pre) : sofar) go ('|':r) sofar = case span (/= '|') r of (pre, '|':rest) -> go rest (pre : sofar) (pre, rest) -> go rest (pre : sofar) go ('"':r) sofar = go rest (finalStr : sofar) where grabString [] acc = (reverse acc, []) -- Strictly speaking, this is the unterminated string case; but let's ignore grabString ('"' :'"':cs) acc = grabString cs ('"' :acc) grabString ('"':cs) acc = (reverse acc, cs) grabString (c:cs) acc = grabString cs (c:acc) (str, rest) = grabString r [] finalStr = '"' : str ++ "\"" go cs sofar = case span (`notElem` stopper) cs of (pre, post) -> go post (pre : sofar) -- characters that can stop the current token -- it is *crucial* that this list contains every character -- we can match in one of the previous cases! stopper = " \t\n():|\"" -- | The balance of parens in this string. If 0, this means it's a legit line! parenDeficit :: String -> Int parenDeficit = go 0 . tokenize where go :: Int -> [String] -> Int go !balance [] = balance go !balance ("(" : rest) = go (balance+1) rest go !balance (")" : rest) = go (balance-1) rest go !balance (_ : rest) = go balance rest -- | Parse a string into an SExpr, potentially failing with an error message parseSExpr :: String -> Either String SExpr parseSExpr inp = do (sexp, extras) <- parse inpToks if null extras then case sexp of EApp [ECon "error", ECon er] -> Left $ "Solver returned an error: " ++ er _ -> return sexp else die "Extra tokens after valid input" where inpToks = tokenize inp die w = fail $ "SBV.Provers.SExpr: Failed to parse S-Expr: " ++ w ++ "\n*** Input : <" ++ inp ++ ">" parse [] = die "ran out of tokens" parse ("(":toks) = do (f, r) <- parseApp toks [] f' <- cvt (EApp f) return (f', r) parse (")":_) = die "extra tokens after close paren" parse [tok] = do t <- pTok tok return (t, []) parse _ = die "ill-formed s-expr" parseApp [] _ = die "failed to grab s-expr application" parseApp (")":toks) sofar = return (reverse sofar, toks) parseApp ("(":toks) sofar = do (f, r) <- parse ("(":toks) parseApp r (f : sofar) parseApp (tok:toks) sofar = do t <- pTok tok parseApp toks (t : sofar) pTok "false" = return $ ENum (0, Nothing) pTok "true" = return $ ENum (1, Nothing) pTok ('0':'b':r) = mkNum (Just (length r)) $ readInt 2 (`elem` "01") (\c -> ord c - ord '0') r pTok ('b':'v':r) | not (null r) && all isDigit r = mkNum Nothing $ readDec (takeWhile (/= '[') r) pTok ('#':'b':r) = mkNum (Just (length r)) $ readInt 2 (`elem` "01") (\c -> ord c - ord '0') r pTok ('#':'x':r) = mkNum (Just (4 * length r)) $ readHex r pTok n | not (null n) && isDigit (head n) = if '.' `elem` n then getReal n else mkNum Nothing $ readDec n pTok n = return $ ECon (constantMap n) mkNum l [(n, "")] = return $ ENum (n, l) mkNum _ _ = die "cannot read number" getReal n = return $ EReal $ mkPolyReal (Left (exact, n')) where exact = not ("?" `isPrefixOf` reverse n) n' | exact = n | True = init n -- simplify numbers and root-obj values cvt (EApp [ECon "to_int", EReal a]) = return $ EReal a -- ignore the "casting" cvt (EApp [ECon "to_real", EReal a]) = return $ EReal a -- ignore the "casting" cvt (EApp [ECon "/", EReal a, EReal b]) = return $ EReal (a / b) cvt (EApp [ECon "/", EReal a, ENum b]) = return $ EReal (a / fromInteger (fst b)) cvt (EApp [ECon "/", ENum a, EReal b]) = return $ EReal (fromInteger (fst a) / b ) cvt (EApp [ECon "/", ENum a, ENum b]) = return $ EReal (fromInteger (fst a) / fromInteger (fst b)) cvt (EApp [ECon "-", EReal a]) = return $ EReal (-a) cvt (EApp [ECon "-", ENum a]) = return $ ENum (-(fst a), snd a) -- bit-vector value as CVC4 prints: (_ bv0 16) for instance cvt (EApp [ECon "_", ENum a, ENum _b]) = return $ ENum a cvt (EApp [ECon "root-obj", EApp (ECon "+":trms), ENum k]) = do ts <- mapM getCoeff trms return $ EReal $ mkPolyReal (Right (fst k, ts)) cvt (EApp [ECon "as", n, EApp [ECon "_", ECon "FloatingPoint", ENum (11, _), ENum (53, _)]]) = getDouble n cvt (EApp [ECon "as", n, EApp [ECon "_", ECon "FloatingPoint", ENum ( 8, _), ENum (24, _)]]) = getFloat n cvt (EApp [ECon "as", n, ECon "Float64"]) = getDouble n cvt (EApp [ECon "as", n, ECon "Float32"]) = getFloat n -- NB. Note the lengths on the mantissa for the following two are 23/52; not 24/53! cvt (EApp [ECon "fp", ENum (s, Just 1), ENum ( e, Just 8), ENum (m, Just 23)]) = return $ EFloat $ getTripleFloat s e m cvt (EApp [ECon "fp", ENum (s, Just 1), ENum ( e, Just 11), ENum (m, Just 52)]) = return $ EDouble $ getTripleDouble s e m cvt (EApp [ECon "_", ECon "NaN", ENum ( 8, _), ENum (24, _)]) = return $ EFloat nan cvt (EApp [ECon "_", ECon "NaN", ENum (11, _), ENum (53, _)]) = return $ EDouble nan cvt (EApp [ECon "_", ECon "+oo", ENum ( 8, _), ENum (24, _)]) = return $ EFloat infinity cvt (EApp [ECon "_", ECon "+oo", ENum (11, _), ENum (53, _)]) = return $ EDouble infinity cvt (EApp [ECon "_", ECon "-oo", ENum ( 8, _), ENum (24, _)]) = return $ EFloat (-infinity) cvt (EApp [ECon "_", ECon "-oo", ENum (11, _), ENum (53, _)]) = return $ EDouble (-infinity) cvt (EApp [ECon "_", ECon "+zero", ENum ( 8, _), ENum (24, _)]) = return $ EFloat 0 cvt (EApp [ECon "_", ECon "+zero", ENum (11, _), ENum (53, _)]) = return $ EDouble 0 cvt (EApp [ECon "_", ECon "-zero", ENum ( 8, _), ENum (24, _)]) = return $ EFloat (-0) cvt (EApp [ECon "_", ECon "-zero", ENum (11, _), ENum (53, _)]) = return $ EDouble (-0) cvt x = return x getCoeff (EApp [ECon "*", ENum k, EApp [ECon "^", ECon "x", ENum p]]) = return (fst k, fst p) -- kx^p getCoeff (EApp [ECon "*", ENum k, ECon "x" ] ) = return (fst k, 1) -- kx getCoeff ( EApp [ECon "^", ECon "x", ENum p] ) = return ( 1, fst p) -- x^p getCoeff ( ECon "x" ) = return ( 1, 1) -- x getCoeff ( ENum k ) = return (fst k, 0) -- k getCoeff x = die $ "Cannot parse a root-obj,\nProcessing term: " ++ show x getDouble (ECon s) = case (s, rdFP (dropWhile (== '+') s)) of ("plusInfinity", _ ) -> return $ EDouble infinity ("minusInfinity", _ ) -> return $ EDouble (-infinity) ("oo", _ ) -> return $ EDouble infinity ("-oo", _ ) -> return $ EDouble (-infinity) ("zero", _ ) -> return $ EDouble 0 ("-zero", _ ) -> return $ EDouble (-0) ("NaN", _ ) -> return $ EDouble nan (_, Just v) -> return $ EDouble v _ -> die $ "Cannot parse a double value from: " ++ s getDouble (EApp [_, s, _, _]) = getDouble s getDouble (EReal r) = return $ EDouble $ fromRat $ toRational r getDouble x = die $ "Cannot parse a double value from: " ++ show x getFloat (ECon s) = case (s, rdFP (dropWhile (== '+') s)) of ("plusInfinity", _ ) -> return $ EFloat infinity ("minusInfinity", _ ) -> return $ EFloat (-infinity) ("oo", _ ) -> return $ EFloat infinity ("-oo", _ ) -> return $ EFloat (-infinity) ("zero", _ ) -> return $ EFloat 0 ("-zero", _ ) -> return $ EFloat (-0) ("NaN", _ ) -> return $ EFloat nan (_, Just v) -> return $ EFloat v _ -> die $ "Cannot parse a float value from: " ++ s getFloat (EReal r) = return $ EFloat $ fromRat $ toRational r getFloat (EApp [_, s, _, _]) = getFloat s getFloat x = die $ "Cannot parse a float value from: " ++ show x -- | Parses the Z3 floating point formatted numbers like so: 1.321p5/1.2123e9 etc. rdFP :: (Read a, RealFloat a) => String -> Maybe a rdFP s = case break (`elem` "pe") s of (m, 'p':e) -> rd m >>= \m' -> rd e >>= \e' -> return $ m' * ( 2 ** e') (m, 'e':e) -> rd m >>= \m' -> rd e >>= \e' -> return $ m' * (10 ** e') (m, "") -> rd m _ -> Nothing where rd v = case reads v of [(n, "")] -> Just n _ -> Nothing -- | Convert an (s, e, m) triple to a float value getTripleFloat :: Integer -> Integer -> Integer -> Float getTripleFloat s e m = wordToFloat w32 where sign = [s == 1] expt = [e `testBit` i | i <- [ 7, 6 .. 0]] mantissa = [m `testBit` i | i <- [22, 21 .. 0]] positions = [i | (i, b) <- zip [31, 30 .. 0] (sign ++ expt ++ mantissa), b] w32 = foldr (flip setBit) (0::Word32) positions -- | Convert an (s, e, m) triple to a float value getTripleDouble :: Integer -> Integer -> Integer -> Double getTripleDouble s e m = wordToDouble w64 where sign = [s == 1] expt = [e `testBit` i | i <- [10, 9 .. 0]] mantissa = [m `testBit` i | i <- [51, 50 .. 0]] positions = [i | (i, b) <- zip [63, 62 .. 0] (sign ++ expt ++ mantissa), b] w64 = foldr (flip setBit) (0::Word64) positions -- | Special constants of SMTLib2 and their internal translation. Mainly -- rounding modes for now. constantMap :: String -> String constantMap n = fromMaybe n (listToMaybe [to | (from, to) <- special, n `elem` from]) where special = [ (["RNE", "roundNearestTiesToEven"], show RoundNearestTiesToEven) , (["RNA", "roundNearestTiesToAway"], show RoundNearestTiesToAway) , (["RTP", "roundTowardPositive"], show RoundTowardPositive) , (["RTN", "roundTowardNegative"], show RoundTowardNegative) , (["RTZ", "roundTowardZero"], show RoundTowardZero) ] -- | Parse a function like value. These come in two flavors: Either in the form of -- a store-expression or a lambda-expression. So we handle both here. parseSExprFunction :: SExpr -> Maybe (Either String ([([SExpr], SExpr)], SExpr)) parseSExprFunction e | Just r <- parseLambdaExpression e = Just (Right r) | Just r <- parseStoreAssociations e = Just r | True = Nothing -- out-of luck. NB. This is where we would add support for other solvers! -- | Parse a lambda expression, most likely z3 specific. There's some guess work -- involved here regarding how z3 produces lambda-expressions; while we try to -- be flexible, this is certainly not a full fledged parser. But hopefully it'll -- cover everything z3 will throw at it. parseLambdaExpression :: SExpr -> Maybe ([([SExpr], SExpr)], SExpr) parseLambdaExpression funExpr = case funExpr of EApp [ECon "lambda", EApp params, body] -> mapM getParam params >>= flip lambda body >>= chainAssigns _ -> Nothing where getParam (EApp [ECon v, _]) = Just v getParam _ = Nothing lambda :: [String] -> SExpr -> Maybe [Either ([SExpr], SExpr) SExpr] lambda params body = reverse <$> go [] body where true = ENum (1, Nothing) false = ENum (0, Nothing) go :: [Either ([SExpr], SExpr) SExpr] -> SExpr -> Maybe [Either ([SExpr], SExpr) SExpr] go sofar (EApp [ECon "ite", selector, thenBranch, elseBranch]) = do s <- select selector tB <- go [] thenBranch case cond s tB of Just sv -> go (Left sv : sofar) elseBranch _ -> Nothing -- Catch cases like: x = a) go sofar inner@(EApp [ECon "=", _, _]) = go sofar (EApp [ECon "ite", inner, true, false]) -- Catch cases like: not x go sofar (EApp [ECon "not", inner]) = go sofar (EApp [ECon "ite", inner, false, true]) -- Catch (or x y z..) go sofar (EApp (ECon "or" : elts)) = let xform [] = false xform [x] = x xform (x:xs) = EApp [ECon "ite", x, true, xform xs] in go sofar $ xform elts -- Catch (and x y z..) go sofar (EApp (ECon "and" : elts)) = let xform [] = true xform [x] = x xform (x:xs) = EApp [ECon "ite", x, xform xs, false] in go sofar $ xform elts -- z3 sometimes puts together a bunch of booleans as final expression, -- see if we can catch that. go sofar e | Just s <- select e = go (Left (s, true) : sofar) false -- Otherwise, just treat it as an "unknown" arbitrary expression -- as the default. It could be something arbitrary of course, but it's -- too complicated to parse; and hopefully this is good enough. go sofar e = Just $ Right e : sofar cond :: [SExpr] -> [Either ([SExpr], SExpr) SExpr] -> Maybe ([SExpr], SExpr) cond s [Right v] = Just (s, v) cond _ _ = Nothing -- select takes the condition of an ite, and returns precisely what match is done to the parameters select :: SExpr -> Maybe [SExpr] select e | Just dict <- build e [] = mapM (`lookup` dict) params | True = Nothing where -- build a dictionary of assignments from the scrutinee build :: SExpr -> [(String, SExpr)] -> Maybe [(String, SExpr)] build (EApp (ECon "and" : rest)) sofar = let next _ Nothing = Nothing next c (Just x) = build c x in foldr next (Just sofar) rest build expr sofar | Just (v, r) <- grok expr, v `elem` params = Just $ (v, r) : sofar | True = Nothing -- See if we can figure out what z3 is telling us; hopefully this -- mapping covers everything we can see: grok (EApp [ECon "=", ECon v, r]) = Just (v, r) grok (EApp [ECon "=", r, ECon v]) = Just (v, r) grok (EApp [ECon "not", ECon v]) = Just (v, false) -- boolean negation, require it to be false grok (ECon v) = Just (v, true) -- boolean identity, require it to be true -- Tough luck, we couldn't understand: grok _ = Nothing -- | Parse a series of associations in the array notation, things that look like: -- -- (store (store ((as const Array) 12) 3 5 9) 5 6 75) -- -- This is (most likely) entirely Z3 specific. So, we might have to tweak it for other -- solvers; though it isn't entirely clear how to do that as we do not know what solver -- we're using here. The trick is to handle all of possible SExpr's we see. -- We'll cross that bridge when we get to it. -- -- NB. In case there's no "constraint" on the UI, Z3 produces the self-referential model: -- -- (x (_ as-array x)) -- -- So, we specifically handle that here, by returning a Left of that name. parseStoreAssociations :: SExpr -> Maybe (Either String ([([SExpr], SExpr)], SExpr)) parseStoreAssociations (EApp [ECon "_", ECon "as-array", ECon nm]) = Just $ Left nm parseStoreAssociations e = Right <$> (chainAssigns =<< vals e) where vals :: SExpr -> Maybe [Either ([SExpr], SExpr) SExpr] vals (EApp [EApp [ECon "as", ECon "const", ECon "Array"], defVal]) = return [Right defVal] vals (EApp [EApp [ECon "as", ECon "const", EApp (ECon "Array" : _)], defVal]) = return [Right defVal] vals (EApp (ECon "store" : prev : argsVal)) | length argsVal >= 2 = do rest <- vals prev return $ Left (init argsVal, last argsVal) : rest vals _ = Nothing -- | Turn a sequence of left-right chain assignments (condition + free) into a single chain chainAssigns :: [Either ([SExpr], SExpr) SExpr] -> Maybe ([([SExpr], SExpr)], SExpr) chainAssigns chain = regroup $ partitionEithers chain where regroup (vs, [d]) = Just (checkDup vs, d) regroup _ = Nothing -- If we get into a case like this: -- -- (store (store a 1 2) 1 3) -- -- then we need to drop the 1->2 assignment! -- -- The way we parse these, the first assignment wins. checkDup :: [([SExpr], SExpr)] -> [([SExpr], SExpr)] checkDup [] = [] checkDup (a@(key, _):as) = a : checkDup [r | r@(key', _) <- as, not (key `sameKey` key')] sameKey :: [SExpr] -> [SExpr] -> Bool sameKey as bs | length as == length bs = and $ zipWith same as bs | True = error $ "Data.SBV: Differing length of key received in chainAssigns: " ++ show (as, bs) -- We don't want to derive Eq; as this is more careful on floats and such same :: SExpr -> SExpr -> Bool same x y = case (x, y) of (ECon a, ECon b) -> a == b (ENum (i, _), ENum (j, _)) -> i == j (EReal a, EReal b) -> algRealStructuralEqual a b (EFloat f1, EFloat f2) -> fpIsEqualObjectH f1 f2 (EDouble d1, EDouble d2) -> fpIsEqualObjectH d1 d2 (EApp as, EApp bs) -> length as == length bs && and (zipWith same as bs) (e1, e2) -> if eRank e1 == eRank e2 then error $ "Data.SBV: You've found a bug in SBV! Please report: SExpr(same): " ++ show (e1, e2) else False -- Defensive programming: It's too long to list all pair up, so we use this function and -- GHC's pattern-match completion warning to catch cases we might've forgotten. If -- you ever get the error line above fire, because you must've disabled the pattern-match -- completion check warning! Shame on you. eRank :: SExpr -> Int eRank ECon{} = 0 eRank ENum{} = 1 eRank EReal{} = 2 eRank EFloat{} = 3 eRank EDouble{} = 4 eRank EApp{} = 5 {-# ANN chainAssigns ("HLint: ignore Redundant if" :: String) #-}