{-# LANGUAGE TypeSynonymInstances, FlexibleInstances #-} {-| This module exposes a DSL for writing symbolic computations atop the Boolector SMT solver. The monadic interface manages the interface to Boolector, caches already created sorts and variables, etc. A Boolector computation should not be shared between threads. Consider, the simple example from the Z3 tutorial written in SMT LIB format: @ (declare-fun f (Int) Int) (declare-fun a () Int) ; a is a constant (declare-const b Int) ; syntax sugar for (declare-fun b () Int) (assert (> a 20)) (assert (> b a)) (assert (= (f 10) 1)) (check-sat) (get-model) @ With this library you can write the same program in Haskell: @ main :: IO () main = do bs <- B.'newBoolectorState' Nothing B.'evalBoolector' bs $ do -- Create sorts: u32 <- B.'bitvecSort' 32 fSort <- B.'funSort' [u32] u32 -- Create variables f, a, and b: f <- B.'uf' fSort "f" a <- B.'var' u32 "a" b <- B.'var' u32 "b" -- Create several constants: c20 <- B.'unsignedInt' 20 u32 c10 <- B.'unsignedInt' 10 u32 c1 <- B.'one' u32 -- Make assertions: B.'assert' =<< B.'ugt' a c20 B.'assert' =<< B.'ugt' b a res <- B.'apply' [c10] f B.'assert' =<< B.'eq' res c1 -- Check satisfiability: B.'Sat' <- B.'sat' -- Get model: ma <- B.'unsignedBvAssignment' a mb <- B.'unsignedBvAssignment' b -- Check model: assert (ma == 21) $ return () assert (mb == 22) $ return () @ The API is inspired by the Z3 Haskell API . -} {-# language CPP #-} {-# language GeneralizedNewtypeDeriving #-} {-# language NoMonomorphismRestriction #-} {-# language FlexibleContexts #-} module Boolector ( -- * Boolector monadic computations Boolector , MonadBoolector(..) , evalBoolector , runBoolector -- ** Boolector state , BoolectorState , newBoolectorState , createDefaultSorts -- ** Options and configurations , Option(..) , setOpt , getOpt , SatSolver(..) , setSatSolver -- * SAT/SMT queries , Node , sat , limitedSat , simplify , Status(..) -- ** Assert and assume , assert , assume , failed , fixateAssumptions , resetAssumptions , push , pop -- ** Variables and constants , var , const , constd , consth -- *** Booleans , bool , true , false -- *** Bit-vectors , zero , one , ones , unsignedInt , signedInt -- *** Arrays , array -- *** Functions , fun , uf -- **** Parameters , param -- *** Quantified terms , forall , exists -- ** Operations -- *** Implications and conditionals , implies , iff , cond -- *** Equality checking , eq , ne -- *** Bit flipping, extraction, extension, and reduction , not , neg , redor , redxor , redand , slice , uext , sext , concat , repeat -- *** Bit-wise operations , xor , xnor , and , nand , or , nor , sll , srl , sra , rol , ror -- *** Arithmetic operations , add , inc , sub , dec , mul , udiv , sdiv , urem , srem , smod -- **** Overflow detection , uaddo , saddo , usubo , ssubo , umulo , smulo , sdivo -- *** Comparison operations , ult , slt , ulte , slte , ugt , sgt , ugte , sgte -- *** Array operations , read , write -- *** Function operations , apply -- ** Accessors , getSort , funGetDomainSort , funGetCodomainSort , funGetArity , getSymbol , setSymbol , getWidth , getIndexWidth , isConst , isVar , isArray , isArrayVar , isParam , isBoundParam , isUf , isFun -- ** Models , bvAssignment , unsignedBvAssignment , signedBvAssignment , boolAssignment -- ** Constant nodes , boolConst , signedBvConst , unsignedBvConst -- ** Sorts , Sort , SortTy, sortTy , boolSort , bitvecSort , funSort , arraySort -- *** Accessors , isEqualSort , isArraySort , isBoolSort , isBitvecSort , isFunSort , funSortCheck -- * Debug dumping , dump , dumpNode , dumpToString , dumpNodeToString , DumpFormat(..) ) where import Boolector.Foreign (Option(..), Status(..)) import qualified Boolector.Foreign as B import qualified Control.Monad.Fail as Fail import Data.Char (isDigit) import Data.IORef import Data.Maybe (listToMaybe) import Data.Map (Map) import qualified Data.Map as Map import Data.IntMap (IntMap) import qualified Data.IntMap as IntMap import Data.Word import Control.Applicative ((<$>)) import Control.Monad.State.Strict import Control.Exception hiding (assert) import Data.Time.Clock import Data.Time.Clock.TAI import Data.Time.Clock.System import Prelude hiding (read, not, and, or, const, concat, repeat) import qualified Prelude as Prelude -- -- Boolector monad -- -- | Type class for Monads that wish to perform symbolic computations. class MonadIO m => MonadBoolector m where -- | Get the Boolector state. getBoolectorState :: m BoolectorState -- | Put the Boolector state. putBoolectorState :: BoolectorState -> m () instance MonadBoolector Boolector where getBoolectorState = get putBoolectorState = put -- | Solver state, cache, and start time. data BoolectorState = BoolectorState { unBoolectorState :: B.Btor , unBoolectorCache :: BoolectorCache , unBoolectorStartTime :: Maybe (IORef (Maybe AbsoluteTime)) } -- | Bolector monad, keeping track of underlying solver state. newtype Boolector a = Boolector { unBoolector :: StateT BoolectorState IO a } deriving (Functor, Applicative, Monad, MonadState BoolectorState, MonadIO, Fail.MonadFail) -- | Evaluate a Boolector action with a given configurations. evalBoolector :: BoolectorState -> Boolector a -> IO a evalBoolector bState act = evalStateT (unBoolector $ createDefaultSorts >> act) bState -- | Like 'evalBoolector', but take an explicit starting BoolectorState, and -- return the final BoolectorState runBoolector :: BoolectorState -> Boolector a -> IO (a, BoolectorState) runBoolector bState act = runStateT (unBoolector $ createDefaultSorts >> act) bState -- | Create new Boolector state with optional timeout for `sat`. By default, we enable -- support for model generation and incremental solving. newBoolectorState :: Maybe Integer -> IO BoolectorState newBoolectorState Nothing = do b <- B.new B.setOpt b OPT_MODEL_GEN 2 B.setOpt b OPT_AUTO_CLEANUP 1 B.setOpt b OPT_INCREMENTAL 1 return $ BoolectorState b emptyBoolectorCache Nothing newBoolectorState (Just time) = do btorState@(BoolectorState b _ _) <- newBoolectorState Nothing ref <- newIORef Nothing B.setTerm b $ \_ -> do mt0 <- readIORef ref case mt0 of Nothing -> return 0 Just t0 -> do t1 <- systemToTAITime `liftM` getSystemTime let shouldTerminate = diffAbsoluteTime t1 t0 > secondsToDiffTime time return $ if shouldTerminate then 1 else 0 return $ btorState { unBoolectorStartTime = Just ref } -- | Start the timer if we're running this instance with a timeout. To ensure -- we only set the timer once, we remove the reference from the state. maybeStartTimer :: MonadBoolector m => m () maybeStartTimer = do s0 <- getBoolectorState let mref = unBoolectorStartTime s0 case mref of Nothing -> return () Just ref -> do putBoolectorState $ s0 { unBoolectorStartTime = Nothing } t0 <- liftIO $ systemToTAITime `liftM` getSystemTime liftIO $ writeIORef ref (Just t0) -- | Set option. setOpt :: MonadBoolector m => Option -> Word32 -> m () setOpt o w = liftBoolector2 B.setOpt o (fromIntegral w) -- | Get option. getOpt :: MonadBoolector m => Option -> m Word32 getOpt o = fromIntegral `liftM` liftBoolector1 B.getOpt o -- | Which sat solver to use. data SatSolver = Lingeling | PicoSAT | MiniSAT deriving Show -- | Set the SAT solver to use. Returns 'True' if sucessfull. setSatSolver :: MonadBoolector m => SatSolver -> m () setSatSolver solver = liftBoolector1 B.setSatSolver (show solver) -- | Add a constraint. assert :: MonadBoolector m => Node -> m () assert = liftBoolector1 B.assert . _node -- | Add an assumption. assume :: MonadBoolector m => Node -> m () assume = liftBoolector1 B.assume . _node -- | Determine if assumption node is a failed assumption. failed :: MonadBoolector m => Node -> m Bool failed = liftBoolector1 B.failed . _node -- | Add all assumptions as assertions. fixateAssumptions :: MonadBoolector m => m () fixateAssumptions = liftBoolector0 B.fixateAssumptions -- | Resets all added assumptions. resetAssumptions :: MonadBoolector m => m () resetAssumptions = liftBoolector0 B.resetAssumptions -- | Solve an input formula (or time out). sat :: MonadBoolector m => m Status sat = maybeStartTimer >> liftBoolector0 B.sat -- | Push new context levels. push :: MonadBoolector m => Word32 -> m () push w = liftBoolector1 B.push (fromIntegral w) -- | Pop context levels. pop :: MonadBoolector m => Word32 -> m () pop w = liftBoolector1 B.pop (fromIntegral w) -- | Solve an input formula and limit the search by the number of lemmas -- generated and the number of conflicts encountered by the underlying -- SAT solver. limitedSat :: MonadBoolector m => Int -- ^ Limit for lemmas on demand (-1 unlimited). -> Int -- ^ Conflict limit for SAT solver (-1 unlimited). -> m Status limitedSat = liftBoolector2 B.limitedSat -- | Simplify current input formula. simplify :: MonadBoolector m => m Status simplify = liftBoolector0 B.sat -- -- Expressions -- -- | Node data type wrapping the underlying Boolector node with a show string. data Node = Node { _node :: B.Node , _showNode :: String } deriving (Eq, Ord) instance Show Node where show = _showNode -- | Like true and false bool :: MonadBoolector m => Bool -> m Node bool True = true bool False = false -- | Create constant true. This is represented by the bit vector constant one -- with bit width one. true :: MonadBoolector m => m Node true = mkNode "true" $ liftBoolector0 B.true -- | Create bit vector constant zero with bit width one. false :: MonadBoolector m => m Node false = mkNode "false" $ liftBoolector0 B.false -- | Create bit vector constant representing the bit vector @bits@. const :: MonadBoolector m => String -> m Node const str = mkNode ("0b" ++ str) $ liftBoolector1 B.const str -- | Create bit vector constant representing the decimal number @str@. constd :: MonadBoolector m => Sort -> String -> m Node constd srt str = mkNode str $ liftBoolector2 B.constd (_sort srt) str -- | Create bit vector constant representing the hexadecimal number @str@. consth :: MonadBoolector m => Sort -> String -> m Node consth srt str = mkNode ("0x" ++ str) $ liftBoolector2 B.consth (_sort srt) str -- | Create bit vector constant zero of sort @sort@. zero :: MonadBoolector m => Sort -> m Node zero = mkNode "zero" . liftBoolector1 B.zero . _sort -- | Create bit vector constant of sort @sort@, where each bit is set to one. ones :: MonadBoolector m => Sort -> m Node ones srt = mkNode onesStr $ liftBoolector1 B.ones $ _sort srt where onesStr = "0b" ++ replicate nr '1' nr = case sortTy srt of BoolSort -> 1 BitVecSort wNr -> fromIntegral wNr _ -> error "invalid sort" -- | Create bit vector constant one of sort @sort@. one :: MonadBoolector m => Sort -> m Node one = mkNode "1" . liftBoolector1 B.one . _sort -- | Create bit vector constant representing the unsigned integer @u@ of -- sort @sort@. -- -- The constant is obtained by either truncating bits or by unsigned extension -- (padding with zeroes). unsignedInt :: MonadBoolector m => Integer -> Sort -> m Node unsignedInt i srt = constd srt (show i) -- | Create bit vector constant representing the signed integer @i@ of sort -- @sort@. -- -- The constant is obtained by either truncating bits or by -- signed extension (padding with ones). signedInt :: MonadBoolector m => Integer -> Sort -> m Node signedInt i srt = constd srt (show i) -- | Create a bit vector variable of sort @sort@. var :: MonadBoolector m => Sort -> String -> m Node var srt str = mkNamedNode "var" B.var srt str -- | Create the one's complement of bit vector @node@. not :: MonadBoolector m => Node -> m Node not n1 = mkNode ["not", show n1] $ liftBoolector1 B.not (_node n1) -- | Create the two's complement of bit vector @node@. neg :: MonadBoolector m => Node -> m Node neg n1 = mkNode ["neg", show n1] $ liftBoolector1 B.neg (_node n1) -- | Create *or* reduction of node @node@. -- -- All bits of node @node@ are combined by a Boolean *or*. redor :: MonadBoolector m => Node -> m Node redor n1 = mkNode ["redor", show n1] $ liftBoolector1 B.redor (_node n1) -- | Create *xor* reduction of node @node@. -- -- All bits of @node@ are combined by a Boolean *xor*. redxor :: MonadBoolector m => Node -> m Node redxor n1 = mkNode ["redxor", show n1] $ liftBoolector1 B.redxor (_node n1) -- | Create *and* reduction of node @node@. -- -- All bits of @node@ are combined by a Boolean *and*. redand :: MonadBoolector m => Node -> m Node redand n = mkNode ["redand", show n] $ liftBoolector1 B.redand (_node n) -- | Create a bit vector slice of @node@ from index @upper@ to index @lower@. slice :: MonadBoolector m => Node -- ^ Bit vector node. -> Word32 -- ^ Upper index which must be greater than or equal to zero, and less than the bit width of @node@. -> Word32 -- ^ Lower index which must be greater than or equal to zero, and less than or equal to @upper@. -> m Node slice n u l = do -- Create sort if not already in cache void $ bitvecSort (fromIntegral $ u - l + 1) -- mkNode ["slice", show n, show u, show l] $ liftBoolector3 B.slice (_node n) (fromIntegral u) (fromIntegral l) -- | Create unsigned extension. -- -- The bit vector @node@ is padded with @width@ * zeroes. uext :: MonadBoolector m => Node -> Word32 -> m Node uext n w = do -- Create sort if not already in cache nw <- getWidth n void $ bitvecSort (fromIntegral $ nw + w) -- mkNode ["uext", show n, show w] $ liftBoolector2 B.uext (_node n) (fromIntegral w) -- | Create signed extension. -- -- The bit vector @node@ is padded with @width@ bits where the value -- depends on the value of the most significant bit of node @n@. sext :: MonadBoolector m => Node -> Word32 -> m Node sext n w = do -- Create sort if not already in cache nw <- getWidth n void $ bitvecSort (fromIntegral $ nw + w) -- mkNode ["sext", show n, show w] $ liftBoolector2 B.sext (_node n) (fromIntegral w) -- | Create the concatenation of two bit vectors. concat :: MonadBoolector m => Node -> Node -> m Node concat n1 n2 = do -- Create sort if not already in cache nw1 <- getWidth n1 nw2 <- getWidth n2 void $ bitvecSort (fromIntegral $ nw1 + nw2) -- mkNode ["concat", show n1, show n2] $ liftBoolector2 B.concat (_node n1) (_node n2) -- | Create @n@ concatenations of a given node @node@. repeat :: MonadBoolector m => Node -> Word32 -> m Node repeat n w = do -- Create sort if not already in cache nw <- getWidth n void $ bitvecSort (fromIntegral $ nw * w) -- mkNode ["repeat", show n, show w] $ liftBoolector2 B.repeat (_node n) (fromIntegral w) -- | Create boolean implication. implies :: MonadBoolector m => Node -> Node -> m Node implies n1 n2 = mkNode ["implies", show n1, show n2] $ liftBoolector2 B.implies (_node n1) (_node n2) -- | Create Boolean equivalence. iff :: MonadBoolector m => Node -> Node -> m Node iff n1 n2 = mkNode ["iff", show n1, show n2] $ liftBoolector2 B.iff (_node n1) (_node n2) -- | Create bit vector or array equality. -- -- Both operands are either bit vectors with the same bit width or arrays -- of the same type. eq :: MonadBoolector m => Node -> Node -> m Node eq n1 n2 = mkNode ["eq", show n1, show n2] $ liftBoolector2 B.eq (_node n1) (_node n2) -- | Create bit vector or array inequality. -- -- Both operands are either bit vectors with the same bit width or arrays -- of the same type. ne :: MonadBoolector m => Node -> Node -> m Node ne n1 n2 = mkNode ["ne", show n1, show n2] $ liftBoolector2 B.ne (_node n1) (_node n2) -- | Create an if-then-else. -- -- If condition @n_cond@ is true, then @n_then@ is returned, else @n_else@ -- is returned. -- Nodes @n_then@ and @n_else@ must be either both arrays or both bit vectors. cond :: MonadBoolector m => Node -- ^ Condition -> Node -- ^ Then node -> Node -- ^ Else node -> m Node cond n1 n2 n3 = mkNode ["cond", show n1, show n2, show n3] $ liftBoolector3 B.cond (_node n1) (_node n2) (_node n3) -- -- Bit-wise operations. -- -- | Create a bit vector *xor*. xor :: MonadBoolector m => Node -> Node -> m Node xor n1 n2 = mkNode ["xor", show n1, show n2] $ liftBoolector2 B.xor (_node n1) (_node n2) -- | Create a bit vector *xnor*. xnor :: MonadBoolector m => Node -> Node -> m Node xnor n1 n2 = mkNode ["xnor", show n1, show n2] $ liftBoolector2 B.xnor (_node n1) (_node n2) -- | Create a bit vector *and*. and :: MonadBoolector m => Node -> Node -> m Node and n1 n2 = mkNode ["and", show n1, show n2] $ liftBoolector2 B.and (_node n1) (_node n2) -- | Create a bit vector *nand*. nand :: MonadBoolector m => Node -> Node -> m Node nand n1 n2 = mkNode ["nand", show n1, show n2] $ liftBoolector2 B.nand (_node n1) (_node n2) -- | Create a bit vector *or*. or :: MonadBoolector m => Node -> Node -> m Node or n1 n2 = mkNode ["or", show n1, show n2] $ liftBoolector2 B.or (_node n1) (_node n2) -- | Create a bit vector *nor*. nor :: MonadBoolector m => Node -> Node -> m Node nor n1 n2 = mkNode ["nor", show n1, show n2] $ liftBoolector2 B.nor (_node n1) (_node n2) -- | Create a logical shift left. -- -- Given node @n1@, the value it represents is the number of zeroes shifted -- into node @n0@ from the right. sll :: MonadBoolector m => Node -- ^ First bit vector operand where the bit width is a power of two and greater than 1. -> Node -- ^ Second bit vector operand with bit width log2 of the bit width of @n0@. -> m Node sll n1 n2 = mkNode ["sll", show n1, show n2] $ liftBoolector2 B.sll (_node n1) (_node n2) -- | Create a logical shift right. -- -- Given node @n1@, the value it represents is the number of zeroes shifted -- into node @n0@ from the left. srl :: MonadBoolector m => Node -- ^ First bit vector operand where the bit width is a power of two and greater than 1. -> Node -- ^ Second bit vector operand with bit width log2 of the bit width of @n0@. -> m Node srl n1 n2 = mkNode ["srl", show n1, show n2] $ liftBoolector2 B.srl (_node n1) (_node n2) -- | Create an arithmetic shift right. -- -- Analogously to 'srl', but whether zeroes or ones are shifted in depends on -- the most significant bit of @n0@. sra :: MonadBoolector m => Node -- ^ First bit vector operand where the bit width is a power of two and greater than 1. -> Node -- ^ Second bit vector operand with bit width log2 of the bit width of @n0@. -> m Node sra n1 n2 = mkNode ["sra", show n1, show n2] $ liftBoolector2 B.sra (_node n1) (_node n2) -- | Create a rotate left. -- -- Given bit vector node @n1@, the value it represents is the number of bits -- by which node @n0@ is rotated to the left. rol :: MonadBoolector m => Node -- ^ First bit vector operand where the bit width is a power of two and greater than 1. -> Node -- ^ Second bit vector operand with bit width log2 of the bit width of @n0@. -> m Node rol n1 n2 = mkNode ["rol", show n1, show n2] $ liftBoolector2 B.rol (_node n1) (_node n2) -- | Create a rotate right. -- -- Given bit vector node @n1@, the value it represents is the number of bits by -- which node @n0@ is rotated to the right. ror :: MonadBoolector m => Node -- ^ First bit vector operand where the bit width is a power of two and greater than 1. -> Node -- ^ Second bit vector operand with bit width log2 of the bit width of @n0@. -> m Node ror n1 n2 = mkNode ["ror", show n1, show n2] $ liftBoolector2 B.ror (_node n1) (_node n2) -- -- Arithmetic operations. -- -- | Create bit vector addition. add :: MonadBoolector m => Node -> Node -> m Node add n1 n2 = mkNode ["add", show n1, show n2] $ liftBoolector2 B.add (_node n1) (_node n2) -- | Create bit vector expression that increments bit vector @node@ by one. inc :: Node -> Boolector Node inc n = mkNode ["inc", show n] $ liftBoolector1 B.inc (_node n) -- | Create a bit vector subtraction. sub :: MonadBoolector m => Node -> Node -> m Node sub n1 n2 = mkNode ["sub", show n1, show n2] $ liftBoolector2 B.sub (_node n1) (_node n2) -- | Create bit vector expression that decrements bit vector @node@ by one. dec :: MonadBoolector m => Node -> m Node dec n = mkNode ["dec", show n] $ liftBoolector1 B.dec (_node n) -- | Create a bitvector multiplication. mul :: MonadBoolector m => Node -> Node -> m Node mul n1 n2 = mkNode ["mul", show n1, show n2] $ liftBoolector2 B.mul (_node n1) (_node n2) -- | Create unsigned division. udiv :: MonadBoolector m => Node -> Node -> m Node udiv n1 n2 = mkNode ["udiv", show n1, show n2] $ liftBoolector2 B.udiv (_node n1) (_node n2) -- | Create signed division. sdiv :: MonadBoolector m => Node -> Node -> m Node sdiv n1 n2 = mkNode ["sdiv", show n1, show n2] $ liftBoolector2 B.sdiv (_node n1) (_node n2) -- | Create an unsigned remainder. urem :: MonadBoolector m => Node -> Node -> m Node urem n1 n2 = mkNode ["urem", show n1, show n2] $ liftBoolector2 B.urem (_node n1) (_node n2) -- | Create a signed remainder. srem :: MonadBoolector m => Node -> Node -> m Node srem n1 n2 = mkNode ["srem", show n1, show n2] $ liftBoolector2 B.srem (_node n1) (_node n2) -- | Create a, signed remainder where its sign matches the sign of the divisor. smod :: MonadBoolector m => Node -> Node -> m Node smod n1 n2 = mkNode ["smod", show n1, show n2] $ liftBoolector2 B.smod (_node n1) (_node n2) -- -- Overflow detection -- -- | Create an unsigned bit vector subtraction overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. usubo :: MonadBoolector m => Node -> Node -> m Node usubo n1 n2 = mkNode ["usubo", show n1, show n2] $ liftBoolector2 B.usubo (_node n1) (_node n2) -- | Create a signed bit vector subtraction overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. ssubo :: MonadBoolector m => Node -> Node -> m Node ssubo n1 n2 = mkNode ["ssubo", show n1, show n2] $ liftBoolector2 B.ssubo (_node n1) (_node n2) -- | Create an unsigned bit vector addition overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. uaddo :: MonadBoolector m => Node -> Node -> m Node uaddo n1 n2 = mkNode ["uaddo", show n1, show n2] $ liftBoolector2 B.uaddo (_node n1) (_node n2) -- | Create a signed bit vector addition overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. saddo :: MonadBoolector m => Node -> Node -> m Node saddo n1 n2 = mkNode ["saddo", show n1, show n2] $ liftBoolector2 B.saddo (_node n1) (_node n2) -- | Create an unsigned bit vector multiplication overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. umulo :: MonadBoolector m => Node -> Node -> m Node umulo n1 n2 = mkNode ["umulo", show n1, show n2] $ liftBoolector2 B.umulo (_node n1) (_node n2) -- | Create signed multiplication overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. smulo :: MonadBoolector m => Node -> Node -> m Node smulo n1 n2 = mkNode ["smulo", show n1, show n2] $ liftBoolector2 B.smulo (_node n1) (_node n2) -- | Create a signed bit vector division overflow detection. -- Returns bit vector with bit-width one, which indicates if the operation -- overflows. sdivo :: MonadBoolector m => Node -> Node -> m Node sdivo n1 n2 = mkNode ["sdivo", show n1, show n2] $ liftBoolector2 B.sdivo (_node n1) (_node n2) -- -- Comparison operations. -- -- | Create an unsigned less than. ult :: MonadBoolector m => Node -> Node -> m Node ult n1 n2 = mkNode ["ult", show n1, show n2] $ liftBoolector2 B.ult (_node n1) (_node n2) -- | Create a signed less than. slt :: MonadBoolector m => Node -> Node -> m Node slt n1 n2 = mkNode ["slt", show n1, show n2] $ liftBoolector2 B.slt (_node n1) (_node n2) -- | Create an unsigned less than or equal. ulte :: MonadBoolector m => Node -> Node -> m Node ulte n1 n2 = mkNode ["ulte", show n1, show n2] $ liftBoolector2 B.ulte (_node n1) (_node n2) -- | Create a signed less than or equal. slte :: MonadBoolector m => Node -> Node -> m Node slte n1 n2 = mkNode ["slte", show n1, show n2] $ liftBoolector2 B.slte (_node n1) (_node n2) -- | Create an unsigned greater than. ugt :: MonadBoolector m => Node -> Node -> m Node ugt n1 n2 = mkNode ["ugt", show n1, show n2] $ liftBoolector2 B.ugt (_node n1) (_node n2) -- | Create a signed greater than. sgt :: MonadBoolector m => Node -> Node -> m Node sgt n1 n2 = mkNode ["sgt", show n1, show n2] $ liftBoolector2 B.sgt (_node n1) (_node n2) -- | Create an unsigned greater than or equal. ugte :: MonadBoolector m => Node -> Node -> m Node ugte n1 n2 = mkNode ["ugte", show n1, show n2] $ liftBoolector2 B.ugte (_node n1) (_node n2) -- | Create a signed greater than or equal. sgte :: MonadBoolector m => Node -> Node -> m Node sgte n1 n2 = mkNode ["sgte", show n1, show n2] $ liftBoolector2 B.sgte (_node n1) (_node n2) -- -- Array operations -- -- | Create a one-dimensional bit vector array with sort @sort@. -- -- The name must be unique. array :: MonadBoolector m => Sort -> String -> m Node array srt str = mkNamedNode "array" B.array srt str -- | Create a read on array @n_array@ at position @n_index@. read :: MonadBoolector m => Node -- ^ Array operand. -> Node -- ^ Bit vector index. The bit width of @n_index@ must have the same bit width as the indices of @n_array@. -> m Node read n1 n2 = mkNode ["read", show n1, show n2] $ liftBoolector2 B.read (_node n1) (_node n2) -- | Create a write on array @n_array@ at position @n_index@ with value -- @n_value@. -- -- The array is updated at exactly one position, all other elements remain -- unchanged. The bit width of @n_index@ must be the same as the bit width of -- the indices of @n_array@. The bit width of @n_value@ must be the same as -- the bit width of the elements of @n_array@. write :: MonadBoolector m => Node -- ^ Array operand. -> Node -- ^ Bit vector index. -> Node -- ^ Bit vector value. -> m Node write n1 n2 n3 = mkNode ["write", show n1, show n2, show n3] $ liftBoolector3 B.write (_node n1) (_node n2) (_node n3) -- -- Functions -- -- | Create an uninterpreted function with sort @sort@. -- -- The name must be unique. uf :: MonadBoolector m => Sort -> String -> m Node uf srt str = mkNamedNode "uf" B.uf srt str -- | Create function parameter of sort @sort@. -- -- This kind of node is used to create parameterized expressions, which are -- used to create functions. Once a parameter is bound to a function, it -- cannot be re-used in other functions. param :: MonadBoolector m => Sort -> String -> m Node param srt str = mkNode ["param", show srt, str] $ liftBoolector2 B.param (_sort srt) str -- | Create a function with body @node@ parameterized over parameters -- @param_nodes@. -- -- This kind of node is similar to macros in the SMT-LIB standard 2.0. -- Note that as soon as a parameter is bound to a function, it can not be -- reused in other functions. -- Call a function via 'apply'. fun :: MonadBoolector m => [Node] -- ^ Parameters of function. -> Node -- ^ Function body parameterized over @param_nodes@. -> m Node fun n1 n2 = mkNode ["fun", show n1, show n2] $ liftBoolector2 B.fun (map _node n1) (_node n2) -- | Create a function application on function @n_fun@ with arguments -- @arg_nodes@. apply :: MonadBoolector m => [Node] -- ^ Arguments to be applied. -> Node -- ^ Number of arguments to be applied. -> m Node apply n1 n2 = mkNode ["apply", show n1, show n2] $ liftBoolector2 B.apply (map _node n1) (_node n2) -- -- Quantified terms -- -- | Create a universally quantified term. forall :: MonadBoolector m => [Node] -- ^ Quantified variables (create with 'param') -> Node -- ^ Term where variables may occur. (Cannot contain functions.) -> m Node forall n1 n2 = mkNode ["forall", show n1, show n2] $ liftBoolector2 B.forall (map _node n1) (_node n2) -- | Create an existentially quantifed term. exists :: MonadBoolector m => [Node] -- ^ Quantified variables (create with 'param') -> Node -- ^ Term where variables may occur. (Cannot contain functions.) -> m Node exists n1 n2 = mkNode ["exists", show n1, show n2] $ liftBoolector2 B.exists (map _node n1) (_node n2) -- -- Accessors -- -- | Get the sort of given @node@. The result does not have to be released. getSort :: MonadBoolector m => Node -> m Sort getSort n = liftBoolector1 B.getSort (_node n) >>= lookupSort -- | Get the domain sort of given function node @node@. -- -- The result does not have to be released. funGetDomainSort :: MonadBoolector m => Node -> m Sort funGetDomainSort n = liftBoolector1 B.funGetDomainSort (_node n) >>= lookupSort -- | Get the codomain sort of given function node @node@. -- -- The result does not have to be released. funGetCodomainSort :: MonadBoolector m => Node -> m Sort funGetCodomainSort n = liftBoolector1 B.funGetCodomainSort (_node n) >>= lookupSort -- | Get the arity of function node. funGetArity :: MonadBoolector m => Node -> m Word funGetArity n = fromIntegral `liftM` liftBoolector1 B.getFunArity (_node n) -- | Get the symbol of an expression. getSymbol :: MonadBoolector m => Node -> m (Maybe String) getSymbol = liftBoolector1 B.getSymbol . _node -- | Set the symbol of an expression. setSymbol :: MonadBoolector m => Node -> String -> m () setSymbol n str = liftBoolector2 B.setSymbol (_node n) str -- | Get the bit vector of a constant node as a bit string. getBits :: MonadBoolector m => Node -> m String getBits = liftBoolector1 B.getBits . _node -- | Get the bit width of an expression. -- -- If the expression is an array, it returns the bit width of the array -- elements. -- If the expression is a function, it returns the bit width of the function's -- return value. getWidth :: MonadBoolector m => Node -> m Word32 getWidth n = fromIntegral `liftM` liftBoolector1 B.getWidth (_node n) -- | Get the bit width of indices of @n_array@. getIndexWidth :: MonadBoolector m => Node -> m Word32 getIndexWidth n = fromIntegral `liftM` liftBoolector1 B.getIndexWidth (_node n) -- | Determine if given node is a constant node. isConst :: MonadBoolector m => Node -> m Bool isConst = liftBoolector1 B.isConst . _node -- | Determine if given node is a bit vector variable. isVar :: MonadBoolector m => Node -> m Bool isVar = liftBoolector1 B.isVar . _node -- | Determine if given node is an array node. isArray :: MonadBoolector m => Node -> m Bool isArray = liftBoolector1 B.isArray . _node -- | Determine if given node is an array node. isArrayVar :: MonadBoolector m => Node -> m Bool isArrayVar = liftBoolector1 B.isArrayVar . _node -- | Determine if given node is a parameter node. isParam :: MonadBoolector m => Node -> m Bool isParam = liftBoolector1 B.isParam . _node -- | Determine if given parameter node is bound by a function. isBoundParam :: MonadBoolector m => Node -> m Bool isBoundParam = liftBoolector1 B.isBoundParam . _node -- | Determine if given node is an uninterpreted function node. isUf :: MonadBoolector m => Node -> m Bool isUf = liftBoolector1 B.isUf . _node -- | Determine if given node is a function node. isFun :: MonadBoolector m => Node -> m Bool isFun = liftBoolector1 B.isFun . _node -- -- Models. -- -- | Get the bool value of a constant node if it is constant. boolConst :: MonadBoolector m => Node -> m (Maybe Bool) boolConst node = do cnst <- isConst node if cnst then do str <- getBits node Just `liftM` bitsToBool str else return Nothing -- | Get the unsigned integer value of a constant node if it is constant. unsignedBvConst :: MonadBoolector m => Node -> m (Maybe Integer) unsignedBvConst node = do cnst <- isConst node if cnst then do str <- getBits node Just `liftM` bitsToUnsignedInteger str else return Nothing -- | Get the signed integer value of a constant node if it is constant. signedBvConst :: MonadBoolector m => Node -> m (Maybe Integer) signedBvConst node = do cnst <- isConst node if cnst then do str <- getBits node val <- bitsToUnsignedInteger str w <- getWidth node let max_signed_w = 2 ^ pred w return . Just $ if val >= max_signed_w then val - (2*max_signed_w) else val else return Nothing -- | Helper for converting bit-string to an unsigned integer. bitsToUnsignedInteger :: MonadBoolector m => String -> m Integer bitsToUnsignedInteger str = do when (Prelude.not $ all isDigit str) $ error $ "getModelVal: not numeric: " ++ str liftIO $ evaluate $ foldl (\ n c -> 2 * n + Prelude.read [c]) 0 str -- | Helper for converting bit-string to a boolean. bitsToBool :: MonadBoolector m => String -> m Bool bitsToBool str = liftIO $ evaluate $ case str of "0" -> False "1" -> True _ -> error $ "bitsToBool: not boolean: " ++ str -- | Generate an assignment string for bit vector expression if -- boolector_sat has returned BOOLECTOR_SAT and model generation has been -- enabled. -- -- The expression can be an arbitrary bit vector expression which -- occurs in an assertion or current assumption. The assignment string has to -- be freed by 'freeBvAssignment'. bvAssignment :: MonadBoolector m => Node -> m String bvAssignment = liftBoolector1 B.bvAssignment . _node -- | Get unsigned integer value from model. unsignedBvAssignment :: MonadBoolector m => Node -> m Integer unsignedBvAssignment node = do str <- bvAssignment node bitsToUnsignedInteger str -- | Get signed integer value from model. signedBvAssignment :: MonadBoolector m => Node -> m Integer signedBvAssignment node = do val <- unsignedBvAssignment node w <- getWidth node let max_signed_w = 2 ^ pred w return $ if val >= max_signed_w then val - (2*max_signed_w) else val -- | Get Boolean value from model. boolAssignment :: MonadBoolector m => Node -> m Bool boolAssignment node = do str <- bvAssignment node bitsToBool str -- -- Sorts -- -- | Type of sorts, used to keep track of sorts without having to go back into C-land. data SortTy = BoolSort | BitVecSort Word | FunSort [SortTy] SortTy | ArraySort SortTy SortTy deriving (Eq, Ord, Show) -- | Sort wraps the udnerlying Boolector sort with a showable type. data Sort = Sort { sortTy :: SortTy -- ^ Get sort type , _sort :: B.Sort } deriving (Eq, Ord) instance Show Sort where show = show . sortTy -- | Create some default, sane sorts. createDefaultSorts :: Boolector () createDefaultSorts = do void $ boolSort void $ bitvecSort 1 void $ bitvecSort 2 void $ bitvecSort 4 void $ bitvecSort 8 void $ bitvecSort 16 void $ bitvecSort 32 void $ bitvecSort 64 void $ bitvecSort 128 -- | Create Boolean sort. boolSort :: Boolector Sort boolSort = do sc <- getSortCache case scBool sc of Just srt -> return srt _ -> do srt <- Sort BoolSort <$> liftBoolector0 B.boolSort setSortCache $ sc { scBool = Just srt } return srt -- | Create bit vector sort of bit width @width@. bitvecSort :: MonadBoolector m => Word -> m Sort bitvecSort wnr = do sc <- getSortCache let bvMap = scBitVec sc case IntMap.lookup nr bvMap of Just srt -> return srt _ -> do srt <- Sort (BitVecSort nr) <$> liftBoolector1 B.bitvecSort nr setSortCache $ sc { scBitVec = IntMap.insert nr srt bvMap } return srt where nr = fromIntegral wnr -- | Create function sort. funSort :: MonadBoolector m => [Sort] -> Sort -> m Sort funSort args ret = do sc <- getSortCache let funMap = scFun sc case Map.lookup (ret, args) funMap of Just srt -> return srt _ -> do srt <- Sort (FunSort (map sortTy args) (sortTy ret)) <$> liftBoolector2 B.funSort (map _sort args) (_sort ret) setSortCache $ sc { scFun = Map.insert (ret, args) srt funMap } return srt -- | Create array sort. arraySort :: MonadBoolector m => Sort -> Sort -> m Sort arraySort dom rng = do sc <- getSortCache let arrMap = scArray sc case Map.lookup (dom, rng) arrMap of Just srt -> return srt _ -> do srt <- Sort (ArraySort (sortTy dom) (sortTy rng)) <$> liftBoolector2 B.arraySort (_sort dom) (_sort rng) setSortCache $ sc { scArray = Map.insert (dom, rng) srt arrMap } return srt -- | Determine if @n0@ and @n1@ have the same sort or not. isEqualSort :: MonadBoolector m => Node -> Node -> m Bool isEqualSort n1 n2 = liftBoolector2 B.isEqualSort (_node n1) (_node n2) -- | Determine if @sort@ is an array sort. isArraySort :: Sort -> Bool isArraySort srt = case sortTy srt of ArraySort _ _ -> True _ -> False -- | Determine if @sort@ is a bool sort. isBoolSort :: Sort -> Bool isBoolSort srt = case sortTy srt of BoolSort -> True _ -> False -- | Determine if @sort@ is a bit-vector sort. isBitvecSort :: Sort -> Bool isBitvecSort srt = case sortTy srt of BitVecSort _ -> True _ -> False -- | Determine if @sort@ is a function sort. isFunSort :: Sort -> Bool isFunSort srt = case sortTy srt of FunSort _ _ -> True _ -> False -- | Check if sorts of given arguments matches the function signature. -- Returns 'Nothing' if all sorts are correct; otherwise it returns the -- position of the incorrect argument. funSortCheck :: MonadBoolector m => [Node] -> Node -> m (Maybe Int) funSortCheck n1 n2 = liftBoolector2 B.funSortCheck (map _node n1) (_node n2) -- -- Dumping -- -- | Output dump format. data DumpFormat = DumpBtor | DumpSMT2 deriving (Eq, Show) -- | Recursively dump @node@ to file in BTOR or SMT-LIB v2 format. dumpNode :: MonadBoolector m => DumpFormat -> FilePath -> Node -> m () dumpNode fmt path node = do btor <- unBoolectorState `liftM` getBoolectorState liftIO $ B.withDumpFile path $ \file -> dumper btor file (_node node) where dumper = case fmt of DumpBtor -> B.dumpBtorNode _ -> B.dumpSmt2Node -- | Dump formula to file in BTOR or SMT-LIB v2 format. dump :: MonadBoolector m => DumpFormat -> FilePath -> m () dump fmt path = do btor <- unBoolectorState `liftM` getBoolectorState liftIO $ B.withDumpFile path (dumper btor) where dumper = case fmt of DumpBtor -> B.dumpBtor _ -> B.dumpSmt2 -- | Same as 'dumpNode', but returns string. -- TODO: this is super slow, we should request feature from boolector. dumpNodeToString :: MonadBoolector m => DumpFormat -> Node -> m String dumpNodeToString fmt node = do btor <- unBoolectorState `liftM` getBoolectorState liftIO $ B.withTempDumpFile (\file -> dumper btor file (_node node)) where dumper = case fmt of DumpBtor -> B.dumpBtorNode _ -> B.dumpSmt2Node -- | Same as 'dump', but returns string. -- TODO: this is super slow, we should request feature from boolector. dumpToString :: MonadBoolector m => DumpFormat -> m String dumpToString fmt = do btor <- unBoolectorState `liftM` getBoolectorState liftIO $ B.withTempDumpFile (dumper btor) where dumper = case fmt of DumpBtor -> B.dumpBtor _ -> B.dumpSmt2 -- -- Helpers -- liftBoolector0 :: MonadBoolector m => (B.Btor -> IO a) -> m a liftBoolector0 f = do s <- getBoolectorState liftIO $ f (unBoolectorState s) liftBoolector1 :: MonadBoolector m => (B.Btor -> a -> IO b) -> a -> m b liftBoolector1 f x1 = do s <- getBoolectorState liftIO $ f (unBoolectorState s) x1 liftBoolector2 :: MonadBoolector m => (B.Btor -> a -> b -> IO c) -> a -> b -> m c liftBoolector2 f x1 x2 = do s <- getBoolectorState liftIO $ f (unBoolectorState s) x1 x2 liftBoolector3 :: MonadBoolector m => (B.Btor -> a -> b -> c -> IO d) -> a -> b -> c -> m d liftBoolector3 f x1 x2 x3 = do s <- getBoolectorState liftIO $ f (unBoolectorState s) x1 x2 x3 -- -- Solver cache -- -- | Cache sorts and variables. data BoolectorCache = BoolectorCache { sortCache :: SortCache , varCache :: VarCache } -- | Empty boolector cache. emptyBoolectorCache :: BoolectorCache emptyBoolectorCache = BoolectorCache emptySortCache Map.empty -- | Cache sorts. data SortCache = SortCache { scBool :: Maybe Sort -- ^ Bool sort , scBitVec :: IntMap Sort -- ^ BitVector sorts , scFun :: Map (Sort, [Sort]) Sort -- ^ Function sorts , scArray :: Map (Sort, Sort) Sort -- ^ Array sorts } -- | Empty sort cache. emptySortCache :: SortCache emptySortCache = SortCache Nothing IntMap.empty Map.empty Map.empty -- | Get the sort cache from the underlying state. getSortCache :: MonadBoolector m => m SortCache getSortCache = (sortCache . unBoolectorCache) `liftM` getBoolectorState -- | Set the sort cache into the underlying state. setSortCache :: MonadBoolector m => SortCache -> m () setSortCache sc = do s0 <- getBoolectorState putBoolectorState $ s0 { unBoolectorCache = (unBoolectorCache s0) { sortCache = sc } } -- | Variable and uninterpreted function cache. type VarCache = Map (String, Sort) Node -- | Get the variable cache from the underlying state. getVarCache :: MonadBoolector m => m VarCache getVarCache = (varCache . unBoolectorCache) `liftM` getBoolectorState -- | Set the variable cache from into underlying state. setVarCache :: MonadBoolector m => VarCache -> m () setVarCache vc = do s0 <- getBoolectorState putBoolectorState $ s0 { unBoolectorCache = (unBoolectorCache s0) { varCache = vc } } -- -- Internal helpers -- -- | Class used to create nodes from boolector nodes, given a stringification class Show s => MkNode s where mkNode :: MonadBoolector m => s -> m B.Node -> m Node instance MkNode String where mkNode str act = do node <- act return $ Node node str instance MkNode [String] where mkNode str act = do node <- act return $ Node node $ "(" ++ unwords str ++ ")" -- | Create a new named node given a constructor or return it from variable -- cache. The name must be unique. mkNamedNode :: MonadBoolector m => String -- ^ Kind of node -> (B.Btor -> B.Sort -> String -> IO B.Node) -- ^ Underlying constructor -> Sort -- ^ Sort of node -> String -- ^ Name of node -> m Node mkNamedNode kind ctor sort name = do vc <- getVarCache case Map.lookup (name, sort) vc of Just srt -> return srt _ -> do node <- mkNode [kind, name, "::", show sort] $ liftBoolector2 ctor (_sort sort) name setVarCache $ Map.insert (name, sort) node vc return node -- | Get the high level sort from cache that corresponds to boolector sort lookupSort :: MonadBoolector m => B.Sort -> m Sort lookupSort bSort = do sc <- getSortCache case () of _ | Just srt <- lookupBoolSort sc -> return srt _ | Just srt <- lookupBitVecSort sc -> return srt _ | Just srt <- lookupFunSort sc -> return srt _ | Just srt <- lookupArraySort sc -> return srt _ -> fail "BUG: should really have the sort in the cache" where lookupBoolSort sc = case scBool sc of Just srt | _sort srt == bSort -> Just srt _ -> Nothing lookupBitVecSort sc = listToMaybe $ IntMap.elems $ IntMap.filter (\s -> _sort s == bSort) $ scBitVec sc lookupFunSort sc = listToMaybe $ Map.elems $ Map.filter (\s -> _sort s == bSort) $ scFun sc lookupArraySort sc = listToMaybe $ Map.elems $ Map.filter (\s -> _sort s == bSort) $ scArray sc