----------------------------------------------------------------------------- -- | -- Module : Data.SBV.SMT.SMT -- Copyright : (c) Levent Erkok -- License : BSD3 -- Maintainer : erkokl@gmail.com -- Stability : experimental -- Portability : portable -- -- Abstraction of SMT solvers ----------------------------------------------------------------------------- {-# LANGUAGE ScopedTypeVariables #-} module Data.SBV.SMT.SMT where import Control.DeepSeq (NFData(..)) import Control.Monad (when, zipWithM) import Data.Char (isSpace) import Data.Int (Int8, Int16, Int32, Int64) import Data.List (intercalate) import Data.Word (Word8, Word16, Word32, Word64) import System.Directory (findExecutable) import System.Process (readProcessWithExitCode) import System.Exit (ExitCode(..)) import Data.SBV.BitVectors.Data import Data.SBV.BitVectors.PrettyNum import Data.SBV.Utils.TDiff -- | Solver configuration data SMTConfig = SMTConfig { verbose :: Bool -- ^ Debug mode , timing :: Bool -- ^ Print timing information on how long different phases took (construction, solving, etc.) , printBase :: Int -- ^ Print literals in this base , solver :: SMTSolver -- ^ The actual SMT solver } type SMTEngine = SMTConfig -> [NamedSymVar] -> [(String, UnintKind)] -> 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) 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' newtype AllSatResult = AllSatResult [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 instance Show AllSatResult where show (AllSatResult []) = "No solutions found" show (AllSatResult [s]) = "Only one solution found:\n" ++ shUnique s where shUnique = showSMTResult "Unsatisfiable" ("Unknown (No assignment to variables returned)") "Unknown. Potential assignment:\n" "" "" show (AllSatResult ss) = "Multiple solutions found:\n" -- shouldn't display how-many; would be too slow/leak-space to compute everything.. ++ unlines (zipWith sh [(1::Int)..] ss) ++ "Done." where sh i = showSMTResult "Unsatisfiable" ("Unknown #" ++ show i ++ "(No assignment to variables returned)") "Unknown. Potential assignment:\n" ("Solution #" ++ show i ++ " (No assignment to variables returned)") ("Solution #" ++ show i ++ ":\n") -- | 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) genParse :: Integral a => (Bool,Size) -> [CW] -> Maybe (a,[CW]) genParse (signed,size) (x:r) | hasSign x == signed && sizeOf x == size = Just (fromIntegral (cwVal x),r) genParse _ _ = Nothing instance SatModel Bool where parseCWs xs = do (x,r) <- genParse (False,1) xs return ((x :: Integer) /= 0, r) instance SatModel Word8 where parseCWs = genParse (False,8) instance SatModel Int8 where parseCWs = genParse (True,8) instance SatModel Word16 where parseCWs = genParse (False,16) instance SatModel Int16 where parseCWs = genParse (True,16) instance SatModel Word32 where parseCWs = genParse (False,32) instance SatModel Int32 where parseCWs = genParse (True,32) instance SatModel Word64 where parseCWs = genParse (False,64) instance SatModel Int64 where parseCWs = genParse (True,64) -- 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) -- | Given an 'SMTResult', extract an arbitrarily typed model from it, given a 'SatModel' instance getModel :: SatModel a => SMTResult -> a getModel (Unsatisfiable _) = error "SatModel.getModel: Unsatisfiable result" getModel (Unknown _ _) = error "Impossible! Backend solver returned unknown for Bit-vector problem!" getModel (ProofError _ s) = error $ unlines $ "An error happened: " : s getModel (TimeOut _) = error $ "Timeout" getModel (Satisfiable _ 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. displayModels :: SatModel a => (Int -> a -> IO ()) -> AllSatResult -> IO Int displayModels disp (AllSatResult ms) = do inds <- zipWithM display (map getModel ms) [(1::Int)..] return $ last (0:inds) where display r i = disp i r >> return i 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 showModel :: SMTConfig -> SMTModel -> String showModel cfg m = intercalate "\n" (map (shM cfg) assocs ++ concatMap shUI uninterps ++ concatMap shUA arrs) where assocs = modelAssocs m uninterps = modelUninterps m arrs = modelArrays m shCW :: SMTConfig -> CW -> String shCW cfg v = sh (printBase cfg) v 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." shM :: SMTConfig -> (String, CW) -> String shM cfg (s, v) = " " ++ s ++ " = " ++ shCW cfg v -- very crude.. printing uninterpreted functions 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 -- very crude.. printing array values shUA :: (String, [String]) -> [String] shUA (f, cases) = (" -- array: " ++ f) : map shC cases where shC s = " " ++ s pipeProcess :: String -> String -> [String] -> String -> IO (Either String [String]) pipeProcess nm execName opts script = 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, errors) <- readProcessWithExitCode execPath opts script 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 (dropWhile isSpace 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 = take 78 $ repeat '=' standardSolver :: SMTConfig -> String -> ([String] -> a) -> ([String] -> a) -> IO a standardSolver config script 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)) contents <- timeIf isTiming nmSolver $ pipeProcess nmSolver exec opts script msg $ nmSolver ++ " output:\n" ++ either id (intercalate "\n") contents case contents of Left e -> return $ failure (lines e) Right xs -> return $ success xs