----------------------------------------------------------------------------- -- | -- Module : Data.SBV.SMT.SMT -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- -- Abstraction of SMT solvers ----------------------------------------------------------------------------- {-# LANGUAGE ScopedTypeVariables #-} module Data.SBV.SMT.SMT where import qualified Control.Exception as C import Control.Concurrent (newEmptyMVar, takeMVar, putMVar, forkIO) import Control.DeepSeq (NFData(..)) import Control.Monad (when, zipWithM) import Data.Char (isSpace) import Data.Int (Int8, Int16, Int32, Int64) import Data.List (intercalate, isPrefixOf, isInfixOf) import Data.Maybe (isNothing, fromJust) import Data.Word (Word8, Word16, Word32, Word64) import System.Directory (findExecutable) import System.Process (readProcessWithExitCode, runInteractiveProcess, waitForProcess) import System.Exit (ExitCode(..)) import System.IO (hClose, hFlush, hPutStr, hGetContents, hGetLine) import Data.SBV.BitVectors.AlgReals import Data.SBV.BitVectors.Data import Data.SBV.BitVectors.PrettyNum import Data.SBV.Utils.TDiff -- | Solver configuration. See also 'z3' and 'yices', which are instantiations of this type for those solvers, with -- reasonable defaults. In particular, custom configuration can be created by varying those values. (Such as @z3{verbose=True}@.) -- -- Most fields are self explanatory. The notion of precision for printing algebraic reals stems from the fact that such values does -- not necessarily have finite decimal representations, and hence we have to stop printing at some depth. It is important to -- emphasize that such values always have infinite precision internally. The issue is merely with how we print such an infinite -- precision value on the screen. The field 'printRealPrec' controls the printing precision, by specifying the number of digits after -- the decimal point. The default value is 16, but it can be set to any positive integer. -- -- When printing, SBV will add the suffix @...@ at the and of a real-value, if the given bound is not sufficient to represent the real-value -- exactly. Otherwise, the number will be written out in standard decimal notation. Note that SBV will always print the whole value if it -- is precise (i.e., if it fits in a finite number of digits), regardless of the precision limit. The limit only applies if the representation -- of the real value is not finite, i.e., if it is not rational. data SMTConfig = SMTConfig { verbose :: Bool -- ^ Debug mode , timing :: Bool -- ^ Print timing information on how long different phases took (construction, solving, etc.) , timeOut :: Maybe Int -- ^ How much time to give to the solver. (In seconds) , printBase :: Int -- ^ Print integral literals in this base (2, 8, and 10, and 16 are supported.) , printRealPrec :: Int -- ^ Print algebraic real values with this precision. (SReal, default: 16) , solverTweaks :: [String] -- ^ Additional lines of script to give to the solver (user specified) , satCmd :: String -- ^ Usually "(check-sat)". However, users might tweak it based on solver characteristics. , smtFile :: Maybe FilePath -- ^ If Just, the generated SMT script will be put in this file (for debugging purposes mostly) , useSMTLib2 :: Bool -- ^ If True, we'll treat the solver as using SMTLib2 input format. Otherwise, SMTLib1 , solver :: SMTSolver -- ^ The actual SMT solver. } -- | An SMT engine type SMTEngine = SMTConfig -> Bool -> [(Quantifier, NamedSymVar)] -> [(String, UnintKind)] -> [Either SW (SW, [SW])] -> String -> IO SMTResult -- | An SMT solver data SMTSolver = SMTSolver { name :: String -- ^ Printable name of the solver , executable :: String -- ^ The path to its executable , options :: [String] -- ^ Options to provide to the solver , engine :: SMTEngine -- ^ The solver engine, responsible for interpreting solver output } -- | A model, as returned by a solver data SMTModel = SMTModel { modelAssocs :: [(String, CW)] , modelArrays :: [(String, [String])] -- very crude! , modelUninterps :: [(String, [String])] -- very crude! } deriving Show -- | The result of an SMT solver call. Each constructor is tagged with -- the 'SMTConfig' that created it so that further tools can inspect it -- and build layers of results, if needed. For ordinary uses of the library, -- this type should not be needed, instead use the accessor functions on -- it. (Custom Show instances and model extractors.) data SMTResult = Unsatisfiable SMTConfig -- ^ Unsatisfiable | Satisfiable SMTConfig SMTModel -- ^ Satisfiable with model | Unknown SMTConfig SMTModel -- ^ Prover returned unknown, with a potential (possibly bogus) model | ProofError SMTConfig [String] -- ^ Prover errored out | TimeOut SMTConfig -- ^ Computation timed out (see the 'timeout' combinator) -- | A script, to be passed to the solver. data SMTScript = SMTScript { scriptBody :: String -- ^ Initial feed , scriptModel :: Maybe String -- ^ Optional continuation script, if the result is sat } -- | Extract the final configuration from a result resultConfig :: SMTResult -> SMTConfig resultConfig (Unsatisfiable c) = c resultConfig (Satisfiable c _) = c resultConfig (Unknown c _) = c resultConfig (ProofError c _) = c resultConfig (TimeOut c) = c instance NFData SMTResult where rnf (Unsatisfiable _) = () rnf (Satisfiable _ xs) = rnf xs `seq` () rnf (Unknown _ xs) = rnf xs `seq` () rnf (ProofError _ xs) = rnf xs `seq` () rnf (TimeOut _) = () instance NFData SMTModel where rnf (SMTModel assocs unints uarrs) = rnf assocs `seq` rnf unints `seq` rnf uarrs `seq` () -- | A 'prove' call results in a 'ThmResult' newtype ThmResult = ThmResult SMTResult -- | A 'sat' call results in a 'SatResult' -- The reason for having a separate 'SatResult' is to have a more meaningful 'Show' instance. newtype SatResult = SatResult SMTResult -- | An 'allSat' call results in a 'AllSatResult'. The boolean says whether -- we should warn the user about prefix-existentials. newtype AllSatResult = AllSatResult (Bool, [SMTResult]) instance Show ThmResult where show (ThmResult r) = showSMTResult "Q.E.D." "Unknown" "Unknown. Potential counter-example:\n" "Falsifiable" "Falsifiable. Counter-example:\n" r instance Show SatResult where show (SatResult r) = showSMTResult "Unsatisfiable" "Unknown" "Unknown. Potential model:\n" "Satisfiable" "Satisfiable. Model:\n" r -- NB. The Show instance of AllSatResults have to be careful in being lazy enough -- as the typical use case is to pull results out as they become available. instance Show AllSatResult where show (AllSatResult (e, xs)) = go (0::Int) xs where uniqueWarn | e = " (Unique up to prefix existentials.)" | True = "" go c (s:ss) = let c' = c+1 (ok, o) = sh c' s in c' `seq` if ok then o ++ "\n" ++ go c' ss else o go c [] = case c of 0 -> "No solutions found." 1 -> "This is the only solution." ++ uniqueWarn _ -> "Found " ++ show c ++ " different solutions." ++ uniqueWarn sh i c = (ok, showSMTResult "Unsatisfiable" "Unknown" "Unknown. Potential model:\n" ("Solution #" ++ show i ++ ":\n[Backend solver returned no assignment to variables.]") ("Solution #" ++ show i ++ ":\n") c) where ok = case c of Satisfiable{} -> True _ -> False -- | Instances of 'SatModel' can be automatically extracted from models returned by the -- solvers. The idea is that the sbv infrastructure provides a stream of 'CW''s (constant-words) -- coming from the solver, and the type @a@ is interpreted based on these constants. Many typical -- instances are already provided, so new instances can be declared with relative ease. -- -- Minimum complete definition: 'parseCWs' class SatModel a where -- | Given a sequence of constant-words, extract one instance of the type @a@, returning -- the remaining elements untouched. If the next element is not what's expected for this -- type you should return 'Nothing' parseCWs :: [CW] -> Maybe (a, [CW]) -- | Given a parsed model instance, transform it using @f@, and return the result. -- The default definition for this method should be sufficient in most use cases. cvtModel :: (a -> Maybe b) -> Maybe (a, [CW]) -> Maybe (b, [CW]) cvtModel f x = x >>= \(a, r) -> f a >>= \b -> return (b, r) -- | Parse a signed/sized value from a sequence of CWs genParse :: Integral a => Kind -> [CW] -> Maybe (a, [CW]) genParse k (x@(CW _ (CWInteger i)):r) | kindOf x == k = Just (fromIntegral i, r) genParse _ _ = Nothing -- Base case, that comes in handy if there are no real variables instance SatModel () where parseCWs xs = return ((), xs) instance SatModel Bool where parseCWs xs = do (x, r) <- genParse (KBounded False 1) xs return ((x :: Integer) /= 0, r) instance SatModel Word8 where parseCWs = genParse (KBounded False 8) instance SatModel Int8 where parseCWs = genParse (KBounded True 8) instance SatModel Word16 where parseCWs = genParse (KBounded False 16) instance SatModel Int16 where parseCWs = genParse (KBounded True 16) instance SatModel Word32 where parseCWs = genParse (KBounded False 32) instance SatModel Int32 where parseCWs = genParse (KBounded True 32) instance SatModel Word64 where parseCWs = genParse (KBounded False 64) instance SatModel Int64 where parseCWs = genParse (KBounded True 64) instance SatModel Integer where parseCWs = genParse KUnbounded instance SatModel AlgReal where parseCWs (CW KReal (CWAlgReal i) : r) = Just (i, r) parseCWs _ = Nothing -- when reading a list; go as long as we can (maximal-munch) -- note that this never fails.. instance SatModel a => SatModel [a] where parseCWs [] = Just ([], []) parseCWs xs = case parseCWs xs of Just (a, ys) -> case parseCWs ys of Just (as, zs) -> Just (a:as, zs) Nothing -> Just ([], ys) Nothing -> Just ([], xs) instance (SatModel a, SatModel b) => SatModel (a, b) where parseCWs as = do (a, bs) <- parseCWs as (b, cs) <- parseCWs bs return ((a, b), cs) instance (SatModel a, SatModel b, SatModel c) => SatModel (a, b, c) where parseCWs as = do (a, bs) <- parseCWs as ((b, c), ds) <- parseCWs bs return ((a, b, c), ds) instance (SatModel a, SatModel b, SatModel c, SatModel d) => SatModel (a, b, c, d) where parseCWs as = do (a, bs) <- parseCWs as ((b, c, d), es) <- parseCWs bs return ((a, b, c, d), es) instance (SatModel a, SatModel b, SatModel c, SatModel d, SatModel e) => SatModel (a, b, c, d, e) where parseCWs as = do (a, bs) <- parseCWs as ((b, c, d, e), fs) <- parseCWs bs return ((a, b, c, d, e), fs) instance (SatModel a, SatModel b, SatModel c, SatModel d, SatModel e, SatModel f) => SatModel (a, b, c, d, e, f) where parseCWs as = do (a, bs) <- parseCWs as ((b, c, d, e, f), gs) <- parseCWs bs return ((a, b, c, d, e, f), gs) instance (SatModel a, SatModel b, SatModel c, SatModel d, SatModel e, SatModel f, SatModel g) => SatModel (a, b, c, d, e, f, g) where parseCWs as = do (a, bs) <- parseCWs as ((b, c, d, e, f, g), hs) <- parseCWs bs return ((a, b, c, d, e, f, g), hs) -- | Various SMT results that we can extract models out of. class Modelable a where -- | Is there a model? modelExists :: a -> Bool -- | Extract a model, the result is a tuple where the first argument (if True) -- indicates whether the model was "probable". (i.e., if the solver returned unknown.) getModel :: SatModel b => a -> Either String (Bool, b) -- | A simpler variant of 'getModel' to get a model out without the fuss. extractModel :: SatModel b => a -> Maybe b extractModel a = case getModel a of Right (_, b) -> Just b _ -> Nothing -- | Return all the models from an 'allSat' call, similar to 'extractModel' but -- is suitable for the case of multiple results. extractModels :: SatModel a => AllSatResult -> [a] extractModels (AllSatResult (_, xs)) = [ms | Right (_, ms) <- map getModel xs] instance Modelable ThmResult where getModel (ThmResult r) = getModel r modelExists (ThmResult r) = modelExists r instance Modelable SatResult where getModel (SatResult r) = getModel r modelExists (SatResult r) = modelExists r instance Modelable SMTResult where getModel (Unsatisfiable _) = Left "SBV.getModel: Unsatisfiable result" getModel (Unknown _ m) = Right (True, parseModelOut m) getModel (ProofError _ s) = error $ unlines $ "Backend solver complains: " : s getModel (TimeOut _) = Left "Timeout" getModel (Satisfiable _ m) = Right (False, parseModelOut m) modelExists (Satisfiable{}) = True modelExists (Unknown{}) = False -- don't risk it modelExists _ = False -- | Extract a model out, will throw error if parsing is unsuccessful parseModelOut :: SatModel a => SMTModel -> a parseModelOut m = case parseCWs [c | (_, c) <- modelAssocs m] of Just (x, []) -> x Just (_, ys) -> error $ "SBV.getModel: Partially constructed model; remaining elements: " ++ show ys Nothing -> error $ "SBV.getModel: Cannot construct a model from: " ++ show m -- | Given an 'allSat' call, we typically want to iterate over it and print the results in sequence. The -- 'displayModels' function automates this task by calling 'disp' on each result, consecutively. The first -- 'Int' argument to 'disp' 'is the current model number. The second argument is a tuple, where the first -- element indicates whether the model is alleged (i.e., if the solver is not sure, returing Unknown) displayModels :: SatModel a => (Int -> (Bool, a) -> IO ()) -> AllSatResult -> IO Int displayModels disp (AllSatResult (_, ms)) = do inds <- zipWithM display [a | Right a <- map (getModel . SatResult) ms] [(1::Int)..] return $ last (0:inds) where display r i = disp i r >> return i -- | Show an SMTResult; generic version showSMTResult :: String -> String -> String -> String -> String -> SMTResult -> String showSMTResult unsatMsg unkMsg unkMsgModel satMsg satMsgModel result = case result of Unsatisfiable _ -> unsatMsg Satisfiable _ (SMTModel [] [] []) -> satMsg Satisfiable _ m -> satMsgModel ++ showModel cfg m Unknown _ (SMTModel [] [] []) -> unkMsg Unknown _ m -> unkMsgModel ++ showModel cfg m ProofError _ [] -> "*** An error occurred. No additional information available. Try running in verbose mode" ProofError _ ls -> "*** An error occurred.\n" ++ intercalate "\n" (map ("*** " ++) ls) TimeOut _ -> "*** Timeout" where cfg = resultConfig result -- | Show a model in human readable form showModel :: SMTConfig -> SMTModel -> String showModel cfg m = intercalate "\n" (map shM assocs ++ concatMap shUI uninterps ++ concatMap shUA arrs) where assocs = modelAssocs m uninterps = modelUninterps m arrs = modelArrays m shM (s, v) = " " ++ s ++ " = " ++ shCW cfg v -- | Show a constant value, in the user-specified base shCW :: SMTConfig -> CW -> String shCW = sh . printBase where sh 2 = binS sh 10 = show sh 16 = hexS sh n = \w -> show w ++ " -- Ignoring unsupported printBase " ++ show n ++ ", use 2, 10, or 16." -- | Print uninterpreted function values from models. Very, very crude.. shUI :: (String, [String]) -> [String] shUI (flong, cases) = (" -- uninterpreted: " ++ f) : map shC cases where tf = dropWhile (/= '_') flong f = if null tf then flong else tail tf shC s = " " ++ s -- | Print uninterpreted array values from models. Very, very crude.. shUA :: (String, [String]) -> [String] shUA (f, cases) = (" -- array: " ++ f) : map shC cases where shC s = " " ++ s -- | Helper function to spin off to an SMT solver. pipeProcess :: SMTConfig -> String -> String -> [String] -> SMTScript -> (String -> String) -> IO (Either String [String]) pipeProcess cfg nm execName opts script cleanErrs = do mbExecPath <- findExecutable execName case mbExecPath of Nothing -> return $ Left $ "Unable to locate executable for " ++ nm ++ "\nExecutable specified: " ++ show execName Just execPath -> do (ec, contents, allErrors) <- runSolver cfg execPath opts script let errors = dropWhile isSpace (cleanErrs allErrors) case ec of ExitSuccess -> if null errors then return $ Right $ map clean (filter (not . null) (lines contents)) else return $ Left errors ExitFailure n -> let errors' = if null errors then (if null (dropWhile isSpace contents) then "(No error message printed on stderr by the executable.)" else contents) else errors in return $ Left $ "Failed to complete the call to " ++ nm ++ "\nExecutable : " ++ show execPath ++ "\nOptions : " ++ unwords opts ++ "\nExit code : " ++ show n ++ "\nSolver output: " ++ "\n" ++ line ++ "\n" ++ intercalate "\n" (filter (not . null) (lines errors')) ++ "\n" ++ line ++ "\nGiving up.." where clean = reverse . dropWhile isSpace . reverse . dropWhile isSpace line = replicate 78 '=' -- | A standard solver interface. If the solver is SMT-Lib compliant, then this function should suffice in -- communicating with it. standardSolver :: SMTConfig -> SMTScript -> (String -> String) -> ([String] -> a) -> ([String] -> a) -> IO a standardSolver config script cleanErrs failure success = do let msg = when (verbose config) . putStrLn . ("** " ++) smtSolver= solver config exec = executable smtSolver opts = options smtSolver isTiming = timing config nmSolver = name smtSolver msg $ "Calling: " ++ show (unwords (exec:opts)) case smtFile config of Nothing -> return () Just f -> do putStrLn $ "** Saving the generated script in file: " ++ show f writeFile f (scriptBody script) contents <- timeIf isTiming nmSolver $ pipeProcess config nmSolver exec opts script cleanErrs msg $ nmSolver ++ " output:\n" ++ either id (intercalate "\n") contents case contents of Left e -> return $ failure (lines e) Right xs -> return $ success (mergeSExpr xs) -- | A variant of 'readProcessWithExitCode'; except it knows about continuation strings -- and can speak SMT-Lib2 (just a little). runSolver :: SMTConfig -> FilePath -> [String] -> SMTScript -> IO (ExitCode, String, String) runSolver cfg execPath opts script | isNothing $ scriptModel script = readProcessWithExitCode execPath opts (scriptBody script) | True = do (send, ask, cleanUp) <- do (inh, outh, errh, pid) <- runInteractiveProcess execPath opts Nothing Nothing let send l = hPutStr inh (l ++ "\n") >> hFlush inh recv = hGetLine outh ask l = send l >> recv cleanUp r = do outMVar <- newEmptyMVar out <- hGetContents outh _ <- forkIO $ C.evaluate (length out) >> putMVar outMVar () err <- hGetContents errh _ <- forkIO $ C.evaluate (length err) >> putMVar outMVar () hClose inh takeMVar outMVar takeMVar outMVar hClose outh hClose errh ex <- waitForProcess pid -- if the status is unknown, prepare for the possibility of not having a model -- TBD: This is rather crude and potentially Z3 specific if "unknown" `isPrefixOf` r && "error" `isInfixOf` (out ++ err) then return (ExitSuccess, r , "") else return (ex, r ++ "\n" ++ out, err) return (send, ask, cleanUp) mapM_ send (lines (scriptBody script)) r <- ask $ satCmd cfg when (any (`isPrefixOf` r) ["sat", "unknown"]) $ do let mls = lines (fromJust (scriptModel script)) when (verbose cfg) $ do putStrLn "** Sending the following model extraction commands:" mapM_ putStrLn mls mapM_ send mls cleanUp r -- | In case the SMT-Lib solver returns a response over multiple lines, compress them so we have -- each S-Expression spanning only a single line. We'll ignore things line parentheses inside quotes -- etc., as it should not be an issue mergeSExpr :: [String] -> [String] mergeSExpr [] = [] mergeSExpr (x:xs) | d == 0 = x : mergeSExpr xs | True = let (f, r) = grab d xs in unwords (x:f) : mergeSExpr r where d = parenDiff x parenDiff :: String -> Int parenDiff = go 0 where go i "" = i go i ('(':cs) = let i'= i+1 in i' `seq` go i' cs go i (')':cs) = let i'= i-1 in i' `seq` go i' cs go i (_ :cs) = go i cs grab i ls | i <= 0 = ([], ls) grab _ [] = ([], []) grab i (l:ls) = let (a, b) = grab (i+parenDiff l) ls in (l:a, b)