-----------------------------------------------------------------------------
-- |
-- 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 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.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.)
       , timeOut    :: Maybe Int      -- ^ How much time to give to the solver. (In seconds)
       , printBase  :: Int            -- ^ Print literals in this base
       , solver     :: SMTSolver      -- ^ The actual SMT solver
       , 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
       }

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
        }

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 #" ++ show i ++ "(No assignment to variables returned)") "Unknown. Potential assignment:\n"
                                      ("Solution #" ++ show i ++ " (No assignment to variables returned)") ("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)

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

-- 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 (False, Size (Just 1)) xs
                   return ((x :: Integer) /= 0, r)

instance SatModel Word8 where
  parseCWs = genParse (False, Size (Just 8))

instance SatModel Int8 where
  parseCWs = genParse (True, Size (Just 8))

instance SatModel Word16 where
  parseCWs = genParse (False, Size (Just 16))

instance SatModel Int16 where
  parseCWs = genParse (True, Size (Just 16))

instance SatModel Word32 where
  parseCWs = genParse (False, Size (Just 32))

instance SatModel Int32 where
  parseCWs = genParse (True, Size (Just 32))

instance SatModel Word64 where
  parseCWs = genParse (False, Size (Just 64))

instance SatModel Int64 where
  parseCWs = genParse (True, Size (Just 64))

instance SatModel Integer where
  parseCWs = genParse (True, Size 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

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

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

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 = 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."

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 :: Bool -> String -> String -> [String] -> SMTScript -> (String -> String) -> IO (Either String [String])
pipeProcess verb 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 verb 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 '='

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 (verbose 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 xs

-- A variant of readProcessWithExitCode; except it knows about continuation strings
-- and can speak SMT-Lib2 (just a little)
runSolver :: Bool -> FilePath -> [String] -> SMTScript -> IO (ExitCode, String, String)
runSolver verb 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 "(check-sat)"
      when (any (`isPrefixOf` r) ["sat", "unknown"]) $ do
        let mls = lines (fromJust (scriptModel script))
        when verb $ do putStrLn "** Sending the following model extraction commands:"
                       mapM_ putStrLn mls
        mapM_ send mls
      cleanUp r