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|
-----------------------------------------------------------------------------
-- |
-- 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 #-}
{-# OPTIONS_GHC -Wall -Werror #-}
module Data.SBV.Utils.SExpr (SExpr(..), parenDeficit, parseSExpr, parseSExprFunction, makeHaskellFunction) where
import Data.Bits (setBit, testBit)
import Data.Char (isDigit, ord, isSpace)
import Data.Either (partitionEithers)
import Data.List (isPrefixOf, nubBy, intercalate)
import Data.Maybe (fromMaybe, listToMaybe)
import Data.Word (Word32, Word64)
import Control.Monad (foldM)
import Numeric (readInt, readSigned, readDec, readHex, fromRat)
import Data.SBV.Core.AlgReals
import Data.SBV.Core.SizedFloats
import Data.SBV.Core.Data (nan, infinity, RoundingMode(..))
import Data.SBV.Utils.Numeric (fpIsEqualObjectH, 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
| EFloatingPoint FP
| 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 = Left $ "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 | possiblyNum n = if all intChar n then mkNum Nothing $ readSigned readDec n else getReal n
pTok n = return $ ECon (constantMap n)
-- crude, but effective!
possiblyNum s = case s of
"" -> False
('-':c:_) -> isDigit c
(c:_) -> isDigit c
intChar c = c == '-' || isDigit c
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
-- Deal with CVC4's approximate reals
cvt x@(EApp [ECon "witness", EApp [EApp [ECon v, ECon "Real"]]
, EApp [ECon "or", EApp [ECon "=", ECon v', val], _]]) | v == v' = do
approx <- cvt val
case approx of
ENum (s, _) -> return $ EReal $ mkPolyReal (Left (False, show s))
EReal aval -> case aval of
AlgRational _ r -> return $ EReal $ AlgRational False r
_ -> return $ EReal aval
_ -> die $ "Cannot parse a CVC4 approximate value from: " ++ show x
-- Deal with CVC5's algebraic reals. This is very crude!
cvt x@(EApp (ECon "_" : ECon "real_algebraic_number" : rest)) =
let isComma (ECon ",") = True
isComma _ = False
get (ENum (n, _)) = return $ fromIntegral n
get (EReal (AlgRational True r)) = return r
get (EFloat f) = return $ toRational f
get (EDouble d) = return $ toRational d
get t = die $ "Cannot get a CVC5 real-algebraic bound from: " ++ show t
in case drop 1 (dropWhile (not . isComma) rest) of
[EApp [n1, n2], _] -> do low <- get n1
high <- get n2
return $ EReal $ AlgInterval (OpenPoint low) (OpenPoint high)
_ -> die $ "Cannot parse a CVC5 real-algebraic number from: " ++ show x
-- 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 "fp", ENum (s, Just 1), ENum ( e, Just eb), ENum (m, Just sb)]) = return $ EFloatingPoint $ fpFromRawRep (s == 1) (e, eb) (m, sb+1)
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 "NaN", ENum (eb, _), ENum (sb, _)]) = return $ EFloatingPoint $ fpNaN (fromIntegral eb) (fromIntegral sb)
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 (eb, _), ENum (sb, _)]) = return $ EFloatingPoint $ fpInf False (fromIntegral eb) (fromIntegral sb)
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 (eb, _), ENum (sb, _)]) = return $ EFloatingPoint $ fpInf True (fromIntegral eb) (fromIntegral sb)
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 (eb, _), ENum (sb, _)]) = return $ EFloatingPoint $ fpZero False (fromIntegral eb) (fromIntegral sb)
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 (eb, _), ENum (sb, _)]) = return $ EFloatingPoint $ fpZero True (fromIntegral eb) (fromIntegral sb)
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 <- parseSetLambda 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 set-lambda expression, which is literally a lambda function, that might look like this:
-- (lambda ((x!1 String))
-- (or (not (or (= x!1 "o") (= x!1 "l") (= x!1 "e") (= x!1 "h")))
-- (= x!1 "o")
-- (= x!1 "l")
-- (= x!1 "e")
-- (= x!1 "h")))
-- For this, we do a little bit of an interpretative dance to see if we can "construct" the necesary expression.
--
-- In parsed form:
-- EApp [ECon "lambda",EApp [EApp [ECon "x!1",ECon "String"]],EApp [ECon "not",EApp [ECon "or",EApp [ECon "=",ECon "x!1",ECon "\"e\""],EApp [ECon "=",ECon "x!1",ECon "\"l\""]]]]
--
-- This is by no means comprehensive, and is quite crude, but hopefully covers the cases we see in practice.
parseSetLambda :: SExpr -> Maybe ([([SExpr], SExpr)], SExpr)
parseSetLambda funExpr = case funExpr of
EApp [l@(ECon "lambda"), bv@(EApp [EApp [ECon _, _]]), body] -> go (\bd -> EApp [l, bv, bd]) body
_ -> Nothing
where go mkLambda = build
where build (EApp [ECon "not", rest ]) = neg =<< build rest
build (EApp (ECon "or" : rest@(_:_))) = foldM1 disj =<< mapM build rest
build (EApp (ECon "and" : rest@(_:_))) = foldM1 conj =<< mapM build rest
build other = parseLambdaExpression (mkLambda other)
-- We're guaranteed by above construction that foldM1 will never take an empty list (due to rest@(_:_) pattern match.)
foldM1 _ [] = error "Data.SBV.parseSetLambda: Impossible happened; empty arg to foldM1"
foldM1 f (x:xs) = foldM f x xs
checkBool (ENum (1, Nothing)) = True
checkBool (ENum (0, Nothing)) = True
checkBool _ = False
negBool (ENum (1, Nothing)) = ENum (0, Nothing)
negBool _ = ENum (1, Nothing)
orBool t@(ENum (1, Nothing)) _ = t
orBool _ t@(ENum (1, Nothing)) = t
orBool _ _ = ENum (0, Nothing)
andBool f@(ENum (0, Nothing)) _ = f
andBool _ f@(ENum (0, Nothing)) = f
andBool _ _ = ENum (1, Nothing)
neg :: ([([SExpr], SExpr)], SExpr) -> Maybe ([([SExpr], SExpr)], SExpr)
neg (rows, dflt)
| all checkBool (dflt : map snd rows) = Just ([(e, negBool r) | (e, r) <- rows], negBool dflt)
| True = Nothing
disj, conj :: ([([SExpr], SExpr)], SExpr) -> ([([SExpr], SExpr)], SExpr) -> Maybe ([([SExpr], SExpr)], SExpr)
disj = bin orBool
conj = bin andBool
bin f rd1@(rows1, dflt1) rd2@(rows2, dflt2)
| all checkBool (dflt1 : dflt2 : map snd rows1 ++ map snd rows2) = Just (combine f rd1 rd2)
| True = Nothing
-- Since we don't have equality over SExprs (can of worms!), we use "show" equality here. The ice is thin, but it works!
combine f (rows1, dflt1) (rows2, dflt2) = (rows, f dflt1 dflt2)
where rows = map calc $ nubBy (\x y -> show x == show y) (map fst rows1 ++ map fst rows2)
calc :: [SExpr] -> ([SExpr], SExpr)
calc args = (args, f (find rows1 dflt1 args) (find rows2 dflt2 args))
find rs d a = case [r | (v, r) <- rs, show v == show a] of
[] -> d
[x] -> x
x -> error $ unlines [ "Data.SBV.parseSetLambda: Impossible happened while combining rows."
, " First row :" ++ show rows1
, " First dflt :" ++ show dflt1
, " Second row :" ++ show rows2
, " Second dflt:" ++ show dflt2
, " Looking for: " ++ show a
, "Multiple matches found: " ++ show x
]
-- | 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, ECon ty]) = Just (v, ty == "Bool")
getParam (EApp [ECon v, _ ]) = Just (v, False)
getParam _ = Nothing
lambda :: [(String, Bool)] -- Bool is True if this is a boolean variable. Otherwise we don't keep track of the type
-> 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) paramNames
| True = Nothing
where paramNames = map fst params
-- 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` paramNames = 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) = case v `lookup` params of
Just True -> Just (v, true) -- boolean identity, require it to be true
_ -> Nothing
-- 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 EFloatingPoint{} = 4
eRank EDouble{} = 5
eRank EApp{} = 6
-- Turn
-- "((F (lambda ((x!1 Int)) (+ 3 (* 2 x!1)))))"
--- into
-- "F x = 3 + 2 * x"
-- if we can. We try but don't push too hard! This is only used for display purposes.
--
-- This isn't very fool-proof; can be confused if there are binding constructs etc.
-- Also, the generated text isn't necessarily fully Haskell acceptable.
-- But it seems to do an OK job for most common use cases.
makeHaskellFunction :: String -> String -> Maybe [String] -> Maybe String
makeHaskellFunction resp nm mbArgs
= case parseSExpr resp of
Right (EApp [EApp [ECon o, e]]) | o == nm -> do (args, bd) <- lambda e
return $ unwords (nm : args) ++ " = " ++ bd
_ -> Nothing
where -- infinite supply of names; starting with the ones we're given
preSupply = fromMaybe [] mbArgs
extras = ["x", "y", "z"]
++ [[c] | c <- ['a' .. 'z'], c < 'x']
++ ['x' : show i | i <- [(1::Int) ..]]
mkUnique x | x `elem` preSupply = mkUnique $ x ++ "'"
| True = x
supply = preSupply ++ map mkUnique extras
lambda :: SExpr -> Maybe ([String], String)
lambda (EApp [ECon "lambda", EApp args, bd]) = do as <- mapM getArg args
let env = zip as supply
pure (map snd env, body env bd)
lambda _ = Nothing
getArg (EApp [ECon argName, _]) = Just argName
getArg _ = Nothing
body env = go
where go :: SExpr -> String
go (ECon n) | Just a <- lookup n env = a
| True = n
go (ENum (i, _)) = show i
go (EReal a) = show a
go (EFloat f) = show f
go (EFloatingPoint f) = show f
go (EDouble f) = show f
go (EApp xs) = app (map (wrap . go) xs)
parens x = '(' : x ++ ")"
wrap x | "-" `isPrefixOf` x = parens x
| any isSpace x = parens x
| True = x
mkBin o a b = wrap a ++ " " ++ o ++ " " ++ wrap b
isPlus = (`elem` ["+", "bvadd"])
isTimes = (`elem` ["*", "bvmul"])
isLT = (`elem` ["<", "bvult", "bvslt", "fp.lt" ])
isLTE = (`elem` ["<=", "bvule", "bvsle", "fp.leq"])
isGT = (`elem` [">", "bvugt", "bvsgt", "fp.gt" ])
isGTE = (`elem` [">=", "bvuge", "bvsge", "fp.gte"])
-- Make an application, with some simplifications
app :: [String] -> String
app (o : xs) | isPlus o = intercalate " + " xs
-- multiplication of arbitrary elements, with proviso for multiplication by -1
app [m, "(-1)", x] | isTimes m = '-' : x
app (m : xs) | isTimes m = intercalate " * " xs
-- binary arith ops
app ["-", a, b] = mkBin "-" a b
app ["/", a, b] = mkBin "/" a b
app [o, a, b] | isLT o = mkBin "<" a b
app [o, a, b] | isLTE o = mkBin "<=" a b
app [o, a, b] | isGT o = mkBin ">" a b
app [o, a, b] | isGTE o = mkBin ">=" a b
-- give up, and just do prefix!
app xs = unwords xs
{- HLint ignore chainAssigns "Redundant if" -}
|
