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CTIGAR.hs
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CTIGAR.hs
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{-# LANGUAGE ExistentialQuantification,FlexibleContexts,RankNTypes,
ScopedTypeVariables,PackageImports,GADTs,DeriveDataTypeable,
ViewPatterns,MultiParamTypeClasses #-}
{-# LANGUAGE DeriveGeneric#-}
module CTIGAR where
import qualified Realization as TR
import qualified Domain as Dom
import Consecution
import Args
import PartialArgs
import SMTPool
import LitOrder
import BackendOptions
import Simplify
import Language.SMTLib2 hiding (simplify)
import Language.SMTLib2.Pipe (createPipe)
import Language.SMTLib2.Debug
import Language.SMTLib2.Timing
import Language.SMTLib2.Internals.Backend (LVar)
import qualified Language.SMTLib2.Internals.Backend as B
import qualified Language.SMTLib2.Internals.Expression as E
import qualified Language.SMTLib2.Internals.Type.List as List
import Language.SMTLib2.Internals.Embed
import qualified Data.Map as Map
import qualified Data.Vector as Vec
import qualified Data.IntSet as IntSet
import qualified Data.Yaml as Y
import Data.IORef
import Control.Monad (when)
import Data.Functor.Identity
import "mtl" Control.Monad.Trans (MonadIO,liftIO)
import "mtl" Control.Monad.Reader (MonadReader(..),ask,asks)
import "mtl" Control.Monad.State (MonadState,gets,get,put,modify)
import Data.List (sort,sortBy,intercalate)
import Data.PQueue.Min (MinQueue)
import qualified Data.PQueue.Min as Queue
import Data.Graph.Inductive (Node)
import Data.Foldable
import Data.Traversable
import Prelude hiding (sequence_,concat,mapM_,or,and,mapM,foldl)
import Data.Typeable
import Data.Bits (shiftL)
import Data.Maybe (catMaybes)
import Data.Either (partitionEithers)
import Data.Time.Clock
import Control.Exception (Exception,SomeException,catch,throw)
import System.IO
import System.Exit
import Data.Dependent.Map (DMap)
import qualified Data.Dependent.Map as DMap
import Control.Monad.Reader (runReader)
import Stats
data AnyBackend m = forall b. (Backend b,SMTMonad b ~ m) => AnyBackend { anyBackend :: m b }
withAnyBackend :: AnyBackend m -> (forall b. Backend b => SMT b r) -> m r
withAnyBackend (AnyBackend constr) act
= withBackend constr act
data IC3Config mdl
= IC3Cfg { ic3Model :: mdl
, ic3ConsecutionBackend :: AnyBackend IO
, ic3LiftingBackend :: AnyBackend IO
, ic3DomainBackend :: AnyBackend IO
, ic3BaseBackend :: AnyBackend IO
, ic3InitBackend :: AnyBackend IO
, ic3InterpolationBackend :: AnyBackend IO
, ic3DebugLevel :: Int
, ic3MaxSpurious :: Int
, ic3MicAttempts :: Int
, ic3MaxDepth :: Int
, ic3MaxJoins :: Int
, ic3MaxCTGs :: Int
, ic3CollectStats :: Bool
, ic3DumpDomainFile :: Maybe String
, ic3DumpStatsFile :: Maybe String
, ic3DumpStatesFile :: Maybe String
}
data IC3Env mdl
= IC3Env { ic3Domain :: Dom.Domain (TR.State mdl) -- The domain talks about the outputs
, ic3InitialProperty :: Node
, ic3Consecution :: Consecution (TR.Input mdl) (TR.State mdl)
, ic3Lifting :: Lifting mdl
, ic3Initiation :: SMTPool (PoolVars (TR.State mdl))
, ic3Interpolation :: SMTPool (InterpolationState mdl)
, ic3LitOrder :: LitOrder
, ic3CexState :: Maybe (IORef (State (TR.Input mdl) (TR.State mdl)))
, ic3Earliest :: Int
, ic3PredicateExtractor :: TR.PredicateExtractor mdl
, ic3Stats :: Maybe IC3Stats
}
type Lifting mdl = SMTPool (LiftingState mdl)
data InterpolationState mdl b
= InterpolationState { interpCur :: TR.State mdl (Expr b)
, interpNxt :: TR.State mdl (Expr b)
, interpInputs :: TR.Input mdl (Expr b)
, interpNxtInputs :: TR.Input mdl (Expr b)
, interpAsserts :: [Expr b BoolType]
, interpReverse :: DMap (B.Var b) (RevComp (TR.State mdl))
}
data LiftingState mdl b
= LiftingState { liftCur :: TR.State mdl (Expr b)
, liftInputs :: TR.Input mdl (Expr b)
, liftNxt :: TR.State mdl (Expr b)
, liftNxtInputs :: TR.Input mdl (Expr b)
, liftNxtAsserts :: [Expr b BoolType]
}
data Obligation inp st = Obligation { oblState :: IORef (State inp st)
, oblLevel :: Int
, oblDepth :: Int
} deriving Eq
instance Ord (Obligation inp st) where
compare o1 o2 = case compare (oblLevel o1) (oblLevel o2) of
EQ -> compare (oblDepth o1) (oblDepth o2)
r -> r
type Queue inp st = MinQueue (Obligation inp st)
-- | In order to deal with exceptions, this is a custom monad.
newtype IC3 mdl a = IC3 { evalIC3 :: IC3Config mdl -> IORef (IC3Env mdl) -> IO a }
data State inp st = State { stateSuccessor :: Maybe (IORef (State inp st))
, stateLiftedAst :: Maybe (Dom.AbstractState st)
, stateFullAst :: Maybe (Dom.AbstractState st)
, stateFull :: Unpacked st
, stateInputs :: Unpacked inp
, stateNxtInputs :: Unpacked inp
, stateLifted :: Partial st
, stateLiftedInputs :: Partial inp
, stateSpuriousLevel :: Int
, stateNSpurious :: Int
, stateSpuriousSucc :: Bool
, stateDomainHash :: Int
}
instance Applicative (IC3 mdl) where
pure x = IC3 (\_ _ -> return x)
x <*> y = IC3 (\cfg env -> do
f <- evalIC3 x cfg env
v <- evalIC3 y cfg env
return (f v))
instance Monad (IC3 mdl) where
(>>=) ic3 f = IC3 $ \cfg ref -> do
r1 <- evalIC3 ic3 cfg ref
evalIC3 (f r1) cfg ref
return x = IC3 $ \_ _ -> return x
instance MonadIO (IC3 mdl) where
liftIO f = IC3 $ \_ _ -> f
instance Functor (IC3 mdl) where
fmap f act = IC3 $ \cfg ref -> do
res <- evalIC3 act cfg ref
return (f res)
instance MonadState (IC3Env mdl) (IC3 mdl) where
get = IC3 $ \_ ref -> readIORef ref
put x = IC3 $ \_ ref -> writeIORef ref x
instance MonadReader (IC3Config mdl) (IC3 mdl) where
ask = IC3 $ \cfg _ -> return cfg
local f act = IC3 $ \cfg ref -> evalIC3 act (f cfg) ref
reader f = IC3 $ \cfg _ -> return $ f cfg
ic3Catch :: Exception e => IC3 mdl a -> (e -> IC3 mdl a) -> IC3 mdl a
ic3Catch act handle = IC3 $ \cfg ref -> evalIC3 act cfg ref `catch`
(\ex -> evalIC3 (handle ex) cfg ref)
bestAbstraction :: State inp st -> Dom.AbstractState st
bestAbstraction st = case stateLiftedAst st of
Just abs -> abs
Nothing -> case stateFullAst st of
Just abs -> abs
Nothing -> error "State doesn't have an abstraction."
k :: IC3 mdl Int
k = do
cons <- gets ic3Consecution
return $ frontier cons
ic3Debug :: Int -> String -> IC3 mdl ()
ic3Debug lvl txt = ic3DebugAct lvl (liftIO $ hPutStrLn stderr txt)
ic3DebugAct :: Int -> IC3 mdl () -> IC3 mdl ()
ic3DebugAct lvl act = do
dbgLevel <- asks ic3DebugLevel
if dbgLevel >= lvl
then act
else return ()
splitLast :: [a] -> ([a],a)
splitLast [x] = ([],x)
splitLast (x:xs) = let (rest,last) = splitLast xs
in (x:rest,last)
mkIC3Config :: mdl -> BackendOptions
-> Int -- ^ Verbosity
-> Bool -- ^ Dump stats?
-> Maybe String -- ^ Dump domain?
-> Maybe String -- ^ Dump stats?
-> Maybe String -- ^ Dump states?
-> IC3Config mdl
mkIC3Config mdl opts verb stats dumpDomain dumpStats dumpStates
= IC3Cfg { ic3Model = mdl
, ic3ConsecutionBackend = mkPipe (optBackend opts Map.! ConsecutionBackend)
(fmap (\t -> ("cons",t)) $ Map.lookup ConsecutionBackend (optDebugBackend opts))
, ic3LiftingBackend = mkPipe (optBackend opts Map.! Lifting)
(fmap (\t -> ("lift",t)) $ Map.lookup Lifting (optDebugBackend opts))
, ic3DomainBackend = mkPipe (optBackend opts Map.! Domain)
(fmap (\t -> ("domain",t)) $ Map.lookup Domain (optDebugBackend opts))
, ic3BaseBackend = mkPipe (optBackend opts Map.! Base)
(fmap (\t -> ("base",t)) $ Map.lookup Base (optDebugBackend opts))
, ic3InitBackend = mkPipe (optBackend opts Map.! Initiation)
(fmap (\t -> ("init",t)) $ Map.lookup Initiation (optDebugBackend opts))
, ic3InterpolationBackend = mkPipe (optBackend opts Map.! Interpolation)
(fmap (\t -> ("interp",t)) $ Map.lookup Interpolation (optDebugBackend opts))
, ic3DebugLevel = verb
, ic3MaxSpurious = 0
, ic3MicAttempts = 1 `shiftL` 20
, ic3MaxDepth = 1
, ic3MaxJoins = 1 `shiftL` 20
, ic3MaxCTGs = 3
, ic3CollectStats = stats
, ic3DumpDomainFile = dumpDomain
, ic3DumpStatsFile = dumpStats
, ic3DumpStatesFile = dumpStates
}
where
mkPipe :: BackendUse -> Maybe (String,BackendDebug) -> AnyBackend IO
mkPipe cmd debug = createBackend cmd (\b -> case debug of
Nothing -> AnyBackend b
Just (name,tp) -> AnyBackend $ do
b' <- b
createDebugBackend name tp b')
runIC3 :: TR.TransitionRelation mdl => IC3Config mdl -> IC3 mdl a -> IO a
runIC3 cfg act = do
let mdl = ic3Model cfg
stats <- if ic3CollectStats cfg
then fmap Just newIC3Stats
else return Nothing
-- MathSAT is really annoying, we have to take care of it like a baby
interpolationIsMathSAT <- do
withAnyBackend (ic3InterpolationBackend cfg) $ do
name <- getInfo SMTSolverName
return $ name=="MathSAT5"
let consBackend = case stats of
Nothing -> ic3ConsecutionBackend cfg
Just stats -> addTiming (consecutionTime stats) (consecutionNum stats)
(ic3ConsecutionBackend cfg)
liftingBackend = case stats of
Nothing -> ic3LiftingBackend cfg -- >>= namedDebugBackend "lift"
Just stats -> addTiming (liftingTime stats) (liftingNum stats)
(ic3LiftingBackend cfg)
initiationBackend = case stats of
Nothing -> ic3InitBackend cfg -- >>= namedDebugBackend "init"
Just stats -> addTiming (initiationTime stats) (initiationNum stats)
(ic3InitBackend cfg)
--initiationBackend = initiationBackend' >>= namedDebugBackend "init"
domainBackend = case stats of
Nothing -> ic3DomainBackend cfg
Just stats -> addTiming (domainTime stats) (domainNum stats)
(ic3DomainBackend cfg)
--domainBackend = domainBackend' >>= namedDebugBackend "domain"
interpBackend' = case stats of
Nothing -> ic3InterpolationBackend cfg -- >>= namedDebugBackend "interp"
Just stats -> addTiming (interpolationTime stats) (interpolationNum stats)
(ic3InterpolationBackend cfg)
cons <- case consBackend of
AnyBackend cr
-> consecutionNew cr
(do
cur <- TR.createState mdl
inp <- TR.createInput mdl
TR.stateInvariant mdl cur inp >>= assert
(nxt,real1) <- TR.createNextState mdl cur inp
(TR.startingProgress mdl)
--assert (blockConstraint nxtBlks)
(asserts1,real2) <- TR.declareAssertions (\_ -> defineVar) mdl cur inp real1
(assumps1,real3) <- TR.declareAssumptions (\_ -> defineVar) mdl cur inp real2
mapM_ assert asserts1
mapM_ assert assumps1
nxtInp <- TR.createInput mdl
(asserts2,real1') <- TR.declareAssertions (\_ -> defineVar) mdl nxt nxtInp
(TR.startingProgress mdl)
(assumps2,real2') <- TR.declareAssumptions (\_ -> defineVar) mdl nxt nxtInp real1'
TR.stateInvariant mdl nxt nxtInp >>= assert
mapM_ assert assumps2
return $ ConsecutionVars { consecutionInput = inp
, consecutionNxtInput = nxtInp
, consecutionState = cur
, consecutionNxtState = nxt
, consecutionNxtAsserts = asserts2 })
(mkCompExpr (TR.initialState mdl) (TR.stateAnnotation mdl))
lifting <- case liftingBackend of
AnyBackend cr
-> createSMTPool cr $ do
setOption (ProduceUnsatCores True)
cur <- TR.createStateVars (\tp rev -> declareVar tp) mdl
inp <- TR.createInputVars (\tp rev -> declareVar tp) mdl
TR.stateInvariant mdl cur inp >>= assert
(nxt,real1) <- TR.declareNextState (\_ -> defineVar) mdl cur inp
(TR.startingProgress mdl)
(assumps,real2) <- TR.declareAssumptions (\_ -> defineVar) mdl cur inp real1
mapM_ assert assumps
inp' <- TR.createInputVars (\tp rev -> declareVar tp) mdl
(asserts,real1') <- TR.declareAssertions (\_ -> defineVar) mdl nxt inp'
(TR.startingProgress mdl)
(assumps2,real2') <- TR.declareAssumptions (\_ -> defineVar) mdl nxt inp' real1'
TR.stateInvariant mdl nxt inp' >>= assert
mapM_ assert assumps2
return $ LiftingState cur inp nxt inp' asserts
initiation <- case initiationBackend of
AnyBackend cr -> createSMTPool cr $ do
cur <- TR.createStateVars (\tp rev -> declareVar tp) mdl
TR.initialState mdl cur >>= assert
--assert $ TR.stateInvariant mdl inp cur
return (PoolVars cur)
interpolation <- case interpBackend' of
AnyBackend cr -> createSMTPool cr $ do
setOption (SMTLogic "QF_AUFLIA")
setOption (ProduceInterpolants True)
setOption (ProduceModels True)
cur <- TR.createState mdl
inp <- TR.createInput mdl
nxtInp <- TR.createInput mdl
(nxt,real1) <- TR.createNextState mdl cur inp (TR.startingProgress mdl)
(asserts,real2) <- TR.declareAssertions (const defineVar) mdl cur inp real1
(assumps,real3) <- TR.declareAssumptions (const defineVar) mdl cur inp real2
(nxt',rev) <- TR.createRevState mdl
mapM_ (\assump -> assertPartition assump PartitionA
) assumps
mapM_ (\ass -> assertPartition ass PartitionA
) asserts
inv1 <- TR.stateInvariant mdl cur inp
inv2 <- TR.stateInvariant mdl nxt' nxtInp
eq <- eqComposite nxt' nxt
assertPartition inv1 PartitionA
assertPartition inv2 PartitionB
assertPartition eq PartitionA
return $ InterpolationState { interpCur = cur
, interpNxt = nxt'
, interpInputs = inp
, interpNxtInputs = nxtInp
, interpAsserts = asserts
, interpReverse = rev
}
dom <- case domainBackend of
AnyBackend cr -> Dom.initialDomain (ic3DebugLevel cfg) cr
(TR.stateAnnotation mdl)
(initNode,_,dom') <- Dom.domainAdd (mkCompExpr (TR.initialState mdl) (TR.stateAnnotation mdl)) dom
extractor <- TR.defaultPredicateExtractor mdl
ref <- newIORef (IC3Env { ic3Domain = dom'
, ic3InitialProperty = initNode
, ic3Consecution = cons
, ic3Lifting = lifting
, ic3Initiation = initiation
, ic3Interpolation = interpolation
, ic3CexState = Nothing
, ic3LitOrder = Map.empty
, ic3Earliest = 0
, ic3PredicateExtractor = extractor
, ic3Stats = stats
})
evalIC3 act cfg ref
extractState :: (Backend b,PartialComp inp,PartialComp st)
=> Maybe (IORef (State inp st))
-> ConsecutionVars inp st (Expr b)
-> SMT b (State inp st)
extractState (succ::Maybe (IORef (State inp st))) vars = do
inps <- unliftComp getValue (consecutionInput vars)
nxtInps <- unliftComp getValue (consecutionNxtInput vars)
full <- unliftComp getValue (consecutionState vars)
return $ State { stateSuccessor = succ
, stateLiftedAst = Nothing
, stateFullAst = Nothing
, stateFull = full
, stateInputs = inps
, stateNxtInputs = nxtInps
, stateLifted = unmaskValue (Proxy::Proxy st) full
, stateLiftedInputs = unmaskValue (Proxy::Proxy inp) inps
, stateSpuriousLevel = 0
, stateNSpurious = 0
, stateSpuriousSucc = False
, stateDomainHash = 0 }
liftState :: (TR.TransitionRelation mdl)
=> Lifting mdl -> State (TR.Input mdl) (TR.State mdl)
-> IO (State (TR.Input mdl) (TR.State mdl))
liftState lifting st = do
rsuc <- case stateSuccessor st of
Nothing -> return Nothing
Just succ -> do
succ' <- readIORef succ
return $ Just succ'
(part,partInp) <- withSMTPool lifting $
\vars' -> do
next <- case rsuc of
Nothing -> and' (liftNxtAsserts vars')
Just succ -> do
conj <- fmap catMaybes $
assignPartial assignEq
(liftNxt vars') (stateLifted succ)
not' $ and' conj
lift' (liftCur vars')
(liftInputs vars')
(liftNxtInputs vars')
(stateFull st)
(stateInputs st)
(stateNxtInputs st)
next
return $ st { stateLifted = part
, stateLiftedInputs = partInp }
lift' :: (Backend b,PartialComp st,PartialComp inp)
=> st (Expr b)
-> inp (Expr b)
-> inp (Expr b)
-> Unpacked st
-> Unpacked inp
-> Unpacked inp
-> Expr b BoolType
-> SMT b (Partial st,Partial inp)
lift' (cur::st (Expr b)) (inp::inp (Expr b)) inp' vcur vinp vinp' vnxt = stack $ do
assignedCur <- assignUnpacked cur vcur
assignedInp <- assignUnpacked inp vinp
--comment "State:"
(cmp1,len_st) <- foldlM (\(mp,n) cond -> case cond of
Nothing -> return (mp,n+1)
Just cond' -> do
cid <- assertId cond'
return (Map.insert cid (Left n) mp,n+1)
) (Map.empty,0) assignedCur
--comment "Input:"
(cmp2,len_inp) <- foldlM (\(mp,n) cond -> case cond of
Nothing -> return (mp,n+1)
Just cond' -> do
cid <- assertId cond'
return (Map.insert cid (Right n) mp,n+1)
) (cmp1,0) assignedInp
--assert $ argEq inp (liftArgs vinp (extractArgAnnotation inp))
--assert $ argEq inp' (liftArgs vinp' (extractArgAnnotation inp'))
--comment "Next state:"
assert vnxt
res <- checkSat
when (res/=Unsat) $ error $ "The model appears to be non-deterministic."
core <- getUnsatCore
let (coreSt,coreInp) = partitionEithers $ fmap (cmp2 Map.!) core
partSt = toTruthValues len_st 0 (sort coreSt)
partInp = toTruthValues len_inp 0 (sort coreInp)
vcur' = unmaskValue (Proxy::Proxy st) vcur
vinp' = unmaskValue (Proxy::Proxy inp) vinp
(vcur'',[]) = maskValue (Proxy::Proxy st) vcur' partSt
(vinp'',[]) = maskValue (Proxy::Proxy inp) vinp' partInp
return (vcur'',vinp'')
where
toTruthValues len n []
| n==len = []
| otherwise = False:toTruthValues len (n+1) []
toTruthValues len n (x:xs)
= if n==x
then True:toTruthValues len (n+1) xs
else False:toTruthValues len (n+1) (x:xs)
assignUnpacked :: (PartialComp a,Backend b) => a (Expr b) -> Unpacked a
-> SMT b [Maybe (Expr b BoolType)]
assignUnpacked (var::a (Expr b)) val
= assignPartial assignEq var (unmaskValue (Proxy::Proxy a) val)
-- | Check if the abstract state intersects with the initial condition
initiationAbstract :: TR.TransitionRelation mdl => Dom.AbstractState (TR.State mdl) -> IC3 mdl Bool
initiationAbstract state = do
env <- get
liftIO $ withSMTPool (ic3Initiation env) $
\(PoolVars vars) -> stack $ do
--comment $ "initiation abstract: "++show state
Dom.toDomainTerm state (ic3Domain env) vars >>= assert
fmap (==Unsat) checkSat
initiationConcrete :: TR.TransitionRelation mdl => Partial (TR.State mdl) -> IC3 mdl Bool
initiationConcrete vals = do
env <- get
liftIO $ withSMTPool (ic3Initiation env) $
\(PoolVars vars) -> stack $ do
eqs <- assignPartial assignEq vars vals
mapM_ assert (catMaybes eqs)
fmap (==Unsat) checkSat
-- From ConsRefConcrPred
-- XXX: Henning: Use full state to abstract domain
updateAbstraction :: TR.TransitionRelation mdl
=> IORef (State (TR.Input mdl) (TR.State mdl)) -> IC3 mdl Bool
updateAbstraction ref = do
st <- liftIO $ readIORef ref
dom <- gets ic3Domain
mdl <- asks ic3Model
initialPred <- gets ic3InitialProperty
succUpdated <- case stateSuccessor st of
Nothing -> return False
Just succ -> updateAbstraction succ
if (not succUpdated) &&
(stateDomainHash st == Dom.domainHash dom)
then return False
else (do
let {-concr = mkCompExpr (\x -> do
eqs <- fmap catMaybes $
assignPartial assignEq x (stateLifted st)
and' eqs
) (TR.stateAnnotation mdl)-}
concrFull = mkCompExpr (\x -> do
rst <- liftComp (stateFull st)
eqComposite x rst
) (TR.stateAnnotation mdl)
full <- liftIO $ Dom.domainAbstract concrFull
initialPred
dom
lifted <- case stateSuccessor st of
Nothing -> lift full (stateInputs st) (stateNxtInputs st) Nothing
Just succ -> do
succ' <- liftIO $ readIORef succ
lift full (stateInputs st) (stateNxtInputs st) (Just $ bestAbstraction succ')
liftIO $ writeIORef ref $ st { stateDomainHash = Dom.domainHash dom
, stateFullAst = Just full
, stateLiftedAst = lifted
}
return True)
lift :: (TR.TransitionRelation mdl,
LiftComp (TR.Input mdl))
=> Dom.AbstractState (TR.State mdl)
-> Unpacked (TR.Input mdl)
-> Unpacked (TR.Input mdl)
-> Maybe (Dom.AbstractState (TR.State mdl))
-> IC3 mdl (Maybe (Dom.AbstractState (TR.State mdl)))
lift toLift inps nxtInps succ = do
lifting <- gets ic3Lifting
domain <- gets ic3Domain
initProp <- gets ic3InitialProperty
mdl <- asks ic3Model
liftAbs <- liftIO $ withSMTPool lifting $ \st -> stack $ do
trms <- Dom.toDomainTerms toLift domain (liftCur st)
(_,rev) <- foldlM (\(i,mp) (nd,e,act) -> do
cond <- if act
then return e
else not' e
cid <- assertId cond
return (i+1,Map.insert cid i mp)
) (0,Map.empty) trms
liftedInps <- liftComp inps
eqComposite (liftInputs st) liftedInps >>= assert
--assert $ argEq (liftNxtInputs st) (liftArgs nxtInps (TR.annotationInput mdl))
case succ of
Nothing -> and' (liftNxtAsserts st) >>= assert
Just succ_abstr -> do
trm <- Dom.toDomainTerm succ_abstr domain (liftNxt st)
not' trm >>= assert
res <- checkSat
if res==Sat
then return Nothing
else (do
core <- getUnsatCore
return $ Just $ Vec.fromList [ toLift Vec.! (rev Map.! cid)
| cid <- core ])
case liftAbs of
Nothing -> return Nothing
Just lift_abs' -> do
init_res <- initiationAbstract lift_abs'
let nlift_abs = if init_res
then lift_abs'
else Vec.cons (initProp,False) lift_abs'
--init_res2 <- initiationAbstract nlift_abs
--return $ error ("Init res2: "++show init_res2)
return $ Just nlift_abs
{- | Checks if an abstract state is inductive at a given level.
This is done by searching for a solution for F_i and (not s) and T and next(s).
If the formula is unsatisfiable, we return a possible smaller state that is still inductive
by extracting the unsatisfiable core of the formula. This state 't' is returned as
'Left t'.
If the formula is satisfiable, we can extract a counter-example state by extracting
a valuation of 's'. This counter-example state is returned via the 'Right' constructor.
-}
abstractConsecution :: TR.TransitionRelation mdl
=> Int -- ^ The level 'i'
-> Dom.AbstractState (TR.State mdl) -- ^ The possibly inductive abstract state 's'
-> Maybe (IORef (State (TR.Input mdl) (TR.State mdl)))
-> IC3 mdl (Either (Dom.AbstractState (TR.State mdl))
(State (TR.Input mdl) (TR.State mdl))
)
abstractConsecution fi abs_st succ = do
--rebuildConsecution
--modify (\env -> env { ic3ConsecutionCount = (ic3ConsecutionCount env)+1 })
ic3DebugAct 3 $ do
abs_st_str <- renderAbstractState abs_st
liftIO $ hPutStrLn stderr ("Original abstract state: "++abs_st_str)
env <- get
res <- liftIO $ consecutionPerform (ic3Domain env) (ic3Consecution env) fi $ \vars -> do
trm <- Dom.toDomainTerm abs_st (ic3Domain env) (consecutionState vars)
not' trm >>= assert
trms <- Dom.toDomainTerms abs_st (ic3Domain env)
(consecutionNxtState vars)
(_,rev) <- foldlM (\(i,mp) (nd,e,act) -> do
e' <- if act
then return e
else not' e
cid <- assertId e'
return (i+1,Map.insert cid i mp)
) (0,Map.empty) trms
-- Henning: This tries to take the lifted inputs of the successor into account (doesn't do anything yet)
{-case succ of
Nothing -> return ()
Just s -> do
succ' <- liftIO $ readIORef s
assert $ app and' $ assignPartial' (consecutionNxtInput vars)
(stateLiftedInputs succ')-}
res <- checkSat
if res==Sat
then (do
st <- extractState succ vars
return $ Right st)
else (do
core <- getUnsatCore
let absCore = Vec.fromList [ abs_st Vec.! (rev Map.! cid)
| cid <- core ]
return $ Left absCore)
case res of
Right st -> return $ Right st
Left absCore -> do
absInit <- initiationAbstract absCore
let absCore' = if absInit
then absCore
else Vec.cons (ic3InitialProperty env,False) absCore
ic3DebugAct 3 $ do
abs_st_str <- renderAbstractState absCore'
liftIO $ hPutStrLn stderr ("Reduced abstract state: "++abs_st_str)
--absInit' <- initiationAbstract absCore'
--error $ "abstractConsecution core: "++show absCore'++" "++show absInit'
return $ Left absCore'
concreteConsecution :: TR.TransitionRelation mdl
=> Int -> Partial (TR.State mdl)
-> IORef (State (TR.Input mdl) (TR.State mdl))
-> IC3 mdl (Maybe (IORef (State (TR.Input mdl) (TR.State mdl))))
concreteConsecution fi st succ = do
env <- get
res <- liftIO $ consecutionPerform (ic3Domain env) (ic3Consecution env) fi $ \vars -> do
eqs <- fmap catMaybes $ assignPartial assignEq (consecutionState vars) st
not' (and' eqs) >>= assert
{-do
succ' <- liftIO $ readIORef succ
assert $ app and' $ assignPartial' (consecutionNxtInput vars)
(stateLiftedInputs succ')-}
eqs' <- assignPartial assignEq (consecutionNxtState vars) st
mapM_ assert (catMaybes eqs')
sat <- checkSat
if sat==Sat
then (do
rst <- extractState (Just succ) vars
return $ Just rst)
else return Nothing
case res of
Nothing -> return Nothing
Just st -> do
res' <- liftIO $ liftState (ic3Lifting env) st >>= newIORef
return $ Just res'
handleObligations :: TR.TransitionRelation mdl
=> Queue (TR.Input mdl) (TR.State mdl) -> IC3 mdl Bool
handleObligations queue = case Queue.minView queue of
Nothing -> do
ic3Debug 3 $ "All obligations handled."
return True
Just (obl,queue') -> do
ic3Debug 3 $ "Obligation level: "++show (oblLevel obl)
if oblLevel obl==0
then (do
st <- liftIO $ readIORef (oblState obl)
init <- initiationConcrete (stateLifted st)
if init
then handleRest obl queue'
else (if stateNSpurious st==0
then (do
modify $ \env -> env { ic3CexState = Just (oblState obl) }
return False)
else error "backtrackRefine..."))
else handleRest obl queue'
where
handleRest obl obls = do
updateAbstraction (oblState obl)
rst <- liftIO $ readIORef (oblState obl)
init <- initiationAbstract (bestAbstraction rst)
if init
then return ()
else error "Initiation failed on abstract state"
ic3Debug 1 $
"Trying to prove abstract consecution at level "++(show $ oblLevel obl)
consRes <- abstractConsecution (oblLevel obl) (bestAbstraction rst) (Just (oblState obl))
case consRes of
Right abstractPred -> do
ic3Debug 4 "Abstract counter-example found."
concConsRes <- concreteConsecution (oblLevel obl) (stateLifted rst) (oblState obl)
case concConsRes of
Nothing -> do
ic3Debug 4 "No corresponding concrete counter-example found."
absPred <- case stateLiftedAst rst of
Nothing -> return $ Right abstractPred
Just _ -> case stateFullAst rst of
Just full -> abstractConsecution (oblLevel obl) full (Just (oblState obl))
maxSpur <- asks ic3MaxSpurious
case absPred of
Right abstractPred
| stateNSpurious rst >= maxSpur -> elim
| oblLevel obl==0 -> elim
| otherwise -> do
init <- initiationConcrete (stateLifted abstractPred)
if init
then spurious
else elim
where
elim = do
ic3Debug 4 "Eliminating spurious counter-example."
elimSpuriousTrans (oblState obl) (oblLevel obl)
return True
spurious = error "spur"
Left core -> generalizeErase obl obls core
Just concretePred -> do
predRes <- predecessor obl obls concretePred
case predRes of
Nothing -> return False
Just nobls -> handleObligations nobls
Left core -> generalizeErase obl obls core
generalizeErase obl obls core = do
n <- abstractGeneralize (oblLevel obl) core
tk <- k
if n <= tk
then handleObligations (Queue.insert (obl { oblLevel = n }) obls)
else (do
updateStats (\stats -> stats { numErased = (numErased stats)+1 })
oblState <- liftIO $ readIORef (oblState obl)
case stateLiftedAst oblState of
Nothing -> updateStats (\stats -> stats { numUnliftedErased = (numUnliftedErased stats)+1 })
Just _ -> return ()
handleObligations obls)
removeObligations :: IORef (State inp st)
-> Int
-> Queue inp st
-> IC3 mdl (Queue inp st)
removeObligations st depth obls
= return $ Queue.filter (\obl -> oblState obl /= st ||
oblDepth obl /= depth
) obls
backtrackRefine :: TR.TransitionRelation mdl
=> Obligation (TR.Input mdl) (TR.State mdl)
-> Queue (TR.Input mdl) (TR.State mdl)
-> Bool
-> IC3 mdl (Queue (TR.Input mdl) (TR.State mdl))
backtrackRefine obl obls enforceRefinement
= backtrack' (oblState obl) (oblDepth obl) obls
where
backtrack' st depth obls = do
rst <- liftIO $ readIORef st
nobls <- removeObligations st depth obls
if stateSpuriousSucc rst && stateNSpurious rst == 1
then (case stateSuccessor rst of
Just succ -> do
if enforceRefinement
then elimSpuriousTrans succ (stateSpuriousLevel rst)
else (do
updateAbstraction succ
rsucc <- liftIO $ readIORef succ
consRes <- abstractConsecution (stateSpuriousLevel rst)
(bestAbstraction rsucc) Nothing
case consRes of
Left _ -> return ()
Right _ -> elimSpuriousTrans succ (stateSpuriousLevel rst))
return nobls)
else (case stateSuccessor rst of
Just succ -> backtrack' succ (depth-1) nobls
Nothing -> error $ "backtrackRefine: State has no successor")
abstractGeneralize :: TR.TransitionRelation mdl
=> Int -> Dom.AbstractState (TR.State mdl)
-> IC3 mdl Int
abstractGeneralize level cube = do
ic3DebugAct 3 $ do
cubeStr <- renderAbstractState cube
liftIO $ hPutStrLn stderr $ "mic: "++cubeStr
ncube <- mic level cube
ic3DebugAct 3 $ do
ncubeStr <- renderAbstractState ncube
liftIO $ hPutStrLn stderr $ "mic done: "++ncubeStr
pushForward (level+1) ncube
where
pushForward level cube = do
tk <- k
if level <= tk
then (do
consRes <- abstractConsecution level cube Nothing
case consRes of
Left ncube -> pushForward (level+1) ncube
Right _ -> addCube level cube)
else addCube level cube
addCube level cube = do
ic3DebugAct 3 $ do
cubeStr <- renderAbstractState cube
liftIO $ hPutStrLn stderr $ "Adding cube at level "++show level++": "++cubeStr
addAbstractCube level cube
return level
baseCases :: (TR.TransitionRelation mdl,Backend b)
=> mdl -> SMT b (Maybe [(Unpacked (TR.State mdl),
Unpacked (TR.Input mdl))])
baseCases st = do
--comment "State:"
cur0 <- TR.createStateVars (\tp rev -> declareVar tp) st
--comment "Inputs:"
inp0 <- TR.createInputVars (\tp rev -> declareVar tp) st
TR.initialState st cur0 >>= assert
--comment "Assumptions:"
(assumps0,real0) <- TR.declareAssumptions (const defineVar) st cur0 inp0
(TR.startingProgress st)
mapM_ assert assumps0
--comment "Invariant:"
TR.stateInvariant st cur0 inp0 >>= assert
--comment "Declare assertions:"
(asserts0,real1) <- TR.declareAssertions (const defineVar) st cur0 inp0 real0
--comment "Declare next state:"
(cur1,real2) <- TR.declareNextState (const defineVar) st cur0 inp0 real1
--comment "Inputs 2:"
inp1 <- TR.createInputVars (\tp rev -> declareVar tp) st
--comment "Assumptions 2:"
(assumps1,real0) <- TR.declareAssumptions (const defineVar) st cur1 inp1
(TR.startingProgress st)
--comment "Invariant 2:"
TR.stateInvariant st cur1 inp1 >>= assert
mapM_ assert assumps1
--comment "Declare assertions 2:"
(asserts1,_) <- TR.declareAssertions (const defineVar) st cur1 inp1 real0
not' (and' $ asserts0++asserts1) >>= assert
res <- checkSat
if res==Sat
then (do
succ0 <- mapM getValue asserts0
if not $ and [ v | BoolValue v <- succ0 ]
then (do
rcur0 <- unliftComp getValue cur0
rinp0 <- unliftComp getValue inp0
return (Just [(rcur0,rinp0)]))
else (do
rcur0 <- unliftComp getValue cur0
rinp0 <- unliftComp getValue inp0
rcur1 <- unliftComp getValue cur1
rinp1 <- unliftComp getValue inp1
return (Just [(rcur0,rinp0),(rcur1,rinp1)])))
else return Nothing
extend :: TR.TransitionRelation mdl => IC3 mdl ()
extend = modify (\env -> env { ic3Consecution = extendFrames (ic3Consecution env) })
-- | Strengthens frontier to remove error successors
-- Returns 'Nothing' if strengthening failed
-- Returns 'Just False' if cubes were generated
-- Returns 'Just True' if no cubes were generated
strengthen :: TR.TransitionRelation mdl
=> IC3 mdl (Maybe Bool)
strengthen = strengthen' True
where
strengthen' trivial = do
tk <- k
env <- get
ic3Debug 2 $ "Trying to get from frontier at level "++show tk++" to error"
rv <- liftIO $ consecutionPerform (ic3Domain env) (ic3Consecution env) tk $ \vars -> do
not' (and' $ consecutionNxtAsserts vars) >>= assert
sat <- checkSat
if sat==Sat
then (do
sti <- extractState Nothing vars
return $ Just sti)
else return Nothing
case rv of
Just sti -> do
sti' <- liftIO $ liftState (ic3Lifting env) sti
sti'' <- liftIO $ newIORef sti'
let obl = Obligation sti'' (tk-1) 1
queue = Queue.singleton obl
updateStats (\stats -> stats { numCTI = (numCTI stats)+1 })
--ic3Debug 2 ("Enqueuing obligation "++show sti++" at level "++
-- show (tk-1)++" and depth 1")
res <- handleObligations queue
if res
then strengthen' False
else return Nothing
Nothing -> do
ic3Debug 2 $ "Can't get to error ("++
(if trivial
then "trivial"
else "not trivial")++")"
return $ Just trivial
check :: TR.TransitionRelation mdl
=> mdl
-> BackendOptions
-> Int -- ^ Verbosity
-> Bool -- ^ Dump stats?
-> Maybe String -- ^ Dump domain?
-> Maybe String -- ^ Dump stats?
-> Maybe String -- ^ Dump states?
-> IO (Either [(Unpacked (TR.State mdl),
Unpacked (TR.Input mdl))]
(CompositeExpr (TR.State mdl) BoolType))
check st opts verb stats dumpDomain dumpstats dumpstates = do
runIC3 (mkIC3Config st opts verb stats dumpDomain dumpstats dumpstates) $ do
backend <- asks ic3BaseBackend
tr <- liftIO $ withAnyBackend backend (baseCases st)
case tr of
Just tr' -> do
ic3DumpStats Nothing
return (Left tr')
Nothing -> (do
addSuggestedPredicates
extend
extend
res <- checkIt
ic3DumpStats (case res of
Left _ -> Nothing
Right fp -> Just fp)
case res of
Left tr -> return (Left tr)
Right fp -> do
dom <- gets ic3Domain
return $ Right $ renderFixpoint dom fp
) `ic3Catch` (\ex -> do
ic3DumpStats Nothing
throw (ex::SomeException))
where
checkIt :: TR.TransitionRelation mdl
=> IC3 mdl (Either [(Unpacked (TR.State mdl),
Unpacked (TR.Input mdl))]
[Dom.AbstractState (TR.State mdl)])
checkIt = do
ic3DebugAct 1 (do
lvl <- k
liftIO $ hPutStrLn stderr $ "Level "++show lvl)
extend
sres <- strengthen
case sres of
Nothing -> do
real <- asks ic3Model
cex <- gets ic3CexState
tr <- liftIO $ getWitnessTr cex
res <- liftIO $ do
withBackendExitCleanly (createPipe "z3" ["-in","-smt2"]) $ do
st0 <- TR.createStateVars (\tp rev -> declareVar tp) real
TR.initialState real st0 >>= assert
tr' <- constructTrace real st0 tr []
rv <- checkSat
if rv==Sat
then (do
tr'' <- getWitness real tr'
return (Just tr''))
else return Nothing
case res of
Nothing -> do
rtr <- mapM renderState tr
error $ "Error trace is infeasible:\n"++unlines rtr
Just res' -> return (Left res')
Just trivial -> do
pres <- propagate trivial
if pres==0
then checkIt
else (do
fp <- getAbstractFixpoint pres
checkFixpoint fp
return (Right fp))
getWitnessTr Nothing = return []
getWitnessTr (Just st) = do
rst <- readIORef st
rest <- getWitnessTr (stateSuccessor rst)
return $ (stateLifted rst):rest
constructTrace :: (TR.TransitionRelation mdl,Backend b)
=> mdl -> TR.State mdl (Expr b)
-> [Partial (TR.State mdl)]
-> [Expr b BoolType]
-> SMT b [(TR.State mdl (Expr b),TR.Input mdl (Expr b))]
constructTrace real st [] errs = do
inps <- TR.createInputVars (\tp rev -> declareVar tp) real
(assumps,real0) <- TR.declareAssumptions (const defineVar) real st inps
(TR.startingProgress real)