A => .gitignore +5 -0
@@ 1,5 @@
+dist*
+out
+stack.yaml.lock
+.stack-work
+.ccls-cache
A => LICENSE +674 -0
@@ 1,674 @@
+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
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+ If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+ END OF TERMS AND CONDITIONS
+
+ How to Apply These Terms to Your New Programs
+
+ If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+ To do so, attach the following notices to the program. It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+ <one line to give the program's name and a brief idea of what it does.>
+ Copyright (C) <year> <name of author>
+
+ This program is free software: you can redistribute it and/or modify
+ it under the terms of the GNU General Public License as published by
+ the Free Software Foundation, either version 3 of the License, or
+ (at your option) any later version.
+
+ This program is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ GNU General Public License for more details.
+
+ You should have received a copy of the GNU General Public License
+ along with this program. If not, see <https://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+ If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+ <program> Copyright (C) <year> <name of author>
+ This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+ This is free software, and you are welcome to redistribute it
+ under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License. Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+ You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<https://www.gnu.org/licenses/>.
+
+ The GNU General Public License does not permit incorporating your program
+into proprietary programs. If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library. If this is what you want to do, use the GNU Lesser General
+Public License instead of this License. But first, please read
+<https://www.gnu.org/licenses/why-not-lgpl.html>.
A => README.md +64 -0
@@ 1,64 @@
+# 羊歯 Shida
+
+Shida is an experimental SMT solver for Bit Vectors written in Haskell that has
+been developed alongside a paper on the same topic (available in [doc](doc))
+for the seminar [Automated Reasoning](https://www21.in.tum.de/teaching/sar/SS20/) at TUM.
+
+**Disclaimer**: If you are looking for an efficient, production quality solver,
+do not use this. Use something like [Z3](https://github.com/Z3Prover/z3) instead.
+
+## Usage
+
+Build:
+```
+stack build
+```
+
+Run all tests:
+```
+stack test
+```
+
+The solver can be used conveniently in ghci, for example:
+```Haskell
+$ stack repl
+λ> f = Atom $ (uVar 8 "a" :-: uConst (13::Word8)) :==: uConst (29::Word8)
+λ> f
+((a - 0b00001101) = 0b00011101)
+λ> solve f
+Solution (fromList [("a",0b00101010)])
+```
+
+More examples for formulas can be found in [test/SolveTest.hs](test/SolveTest.hs).
+
+The most important solving functions are:
+
+```Haskell
+-- |Solve to a single solution
+solve :: Formula -> SolveResult Solution
+
+-- |Solve to all solutions as a lazy list
+solveAll :: Formula -> SolveResult [Solution]
+
+-- |Solve incrementally to a single solution
+-- This can be significantly faster or slower than solve depending on the
+-- formula, see the paper for more info.
+solveIncremental :: Int -> Formula -> SolveResult Solution
+```
+
+## About
+
+Created by Florian Märkl.
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <https://www.gnu.org/licenses/>.
A => Setup.hs +2 -0
@@ 1,2 @@
+import Distribution.Simple
+main = defaultMain
A => app/Main.hs +117 -0
@@ 1,117 @@
+module Main where
+
+import Data.Word
+import Data.Int
+--import Data.Maybe
+import Data.Bits
+import Data.Either
+
+import qualified BitVectorValue as BV
+import Common
+import Formula
+import Flattening
+import Solve
+
+example0 = (Atom $ uConst (42::Word8) :==: uVar 8 "a")
+ :&&:
+ (Atom $ uVar 8 "b" :==: (uVar 8 "a" :^: uConst (123::Word8)))
+
+example1 = Atom $ uVar 8 "a" :==: (uConst (13::Word8) :+: uConst (29::Word8))
+
+bconjunction :: [Formula] -> Formula
+bconjunction [x, y] = And x y
+bconjunction (x : xs) = And x $ bconjunction xs
+bconjunction [] = undefined
+
+example2 :: Word8 -> Formula
+example2 x = bconjunction $ map (\i ->
+ if ((x `shiftR` i) .&. 1) /= 0 then
+ Atom $ Pick (fromIntegral i) (uVar 8 "a")
+ else
+ Not $ Atom $ Pick (fromIntegral i) (uVar 8 "a")
+ ) [0..7]
+
+example3 :: Int8 -> Formula
+example3 x = bconjunction $
+ (if x == -128 then [] else [
+ Atom $ sConst (x-1) :<: sVar 8 "a"
+ ]) ++ (if x == 127 then [] else [
+ Atom $ sVar 8 "a" :<: sConst (x+1)
+ ])
+
+exampleShift :: Word8 -> Word8 -> Formula
+exampleShift x s =
+ Atom $ uVar 8 "a" :==: (uConst x :>>: Const Unsigned (BV.slice (BV.toBitVector s) 0 3))
+
+exampleMult :: Word8 -> Word8 -> Formula
+exampleMult l r =
+ Atom $ uVar 8 "a" :==: (uConst l :*: uConst r)
+
+exampleDiv :: Int8 -> Int8 -> Formula
+exampleDiv l r =
+ Atom $ sVar 8 "a" :==: (sConst l :/: sConst r)
+
+exampleMod :: Int8 -> Int8 -> Formula
+exampleMod l r =
+ Atom $ sVar 8 "a" :==: (sConst l :%: sConst r)
+
+exampleConcat :: Word8 -> Word8 -> Formula
+exampleConcat l r =
+ Atom $ sVar 16 "a" :==: Concat Signed (uConst l) (uConst r)
+
+exampleTernary :: Bool -> Word8 -> Word8 -> Formula
+exampleTernary c a b = Atom $ uVar 8 "a" :==: Ternary (BConst c) (uConst a) (uConst b)
+
+exampleHardUnsat0 :: Size -> Formula
+exampleHardUnsat0 sz = Atom ((uVar sz "a" :*: uVar sz "b") :==: uVar sz "c")
+ :&&: Not (Atom ((uVar sz "b" :*: uVar sz "a") :==: uVar sz "c"))
+ :&&: Atom (uVar sz "x" :<: uVar sz "y")
+ :&&: Atom (uVar sz "y" :<: uVar sz "x")
+
+exampleHardUnsat1 :: Size -> Formula
+exampleHardUnsat1 sz = Atom ((uVar sz "a" :*: uVar sz "b") :==: uVar sz "c")
+ :&&: Atom ((uVar sz "b" :*: uVar sz "a") :==: uVar sz "c")
+ :&&: Atom (uVar sz "x" :<: uVar sz "y")
+ :&&: Atom (uVar sz "y" :<: uVar sz "x")
+
+exampleSat1 :: Size -> Formula
+exampleSat1 sz = Atom (uVar sz "a" :==: Const Unsigned (BV.replicate sz False))
+ :&&: Not ( Not (Atom $ (uVar sz "b" :*: uVar sz "c") :<: uVar sz "d")
+ :&&: Not (Atom $ uVar sz "d" :<: (uVar sz "b" :*: uVar sz "c")))
+
+main :: IO ()
+main = do
+ let x = 1::Int8
+ let y = -1::Int8
+ let f = Atom $ sVar 8 "a" :==: (sConst x :*: sConst y)
+ putStrLn $ "Solve: " ++ show f
+ putStrLn "-- Flattened:"
+ let flat = fromRight undefined $ flatten f
+ print flat
+ putStrLn "-- Final Result:"
+ print $ solve f
+
+--main :: IO ()
+--main = do
+-- let x = -1::Int8
+-- let y = 2::Int8
+-- --print $ flatten $ exampleDiv x y
+-- putStrLn $ "Solve: " ++ show x ++ " / " ++ show y
+-- putStrLn $ "Result: " ++ show (solve $ exampleDiv x y)
+-- putStrLn $ "Remain: " ++ show (solve $ exampleMod x y)
+
+--main :: IO ()
+--main = do
+-- let x = 1
+-- let f = exampleHardUnsat1 64 -- example1
+-- putStrLn $ "Solve: " ++ show f
+-- --putStrLn ""
+-- --putStrLn "-- Flattened:"
+-- --let flat = fromRight undefined $ flatten f
+-- --print flat
+-- --putStrLn "-- Propositional:"
+-- --print $ propositional flat
+-- putStrLn ""
+-- putStrLn "-- Final Result:"
+-- print $ solveIncremental 1 f
+-- --print $ solve f
A => doc/crackme/.gitignore +2 -0
A => doc/crackme/crackme +0 -0
A => doc/crackme/solve.hs +54 -0
@@ 1,54 @@
+import Common
+import Formula
+import Solve
+import qualified BitVectorValue as BV
+
+import Data.Maybe
+import Data.Word
+import qualified Data.Map as Map
+import qualified Data.ByteString as B
+
+import Control.Monad
+
+hash :: [Word8]
+hash = [0xa2, 0x35, 0xa3, 0x0f, 0x1c, 0xd0, 0x0e, 0x9e]
+
+-- |Combine a list of formulas into a single formula one using And
+conjunction :: [Formula] -> Formula
+conjunction [a] = a
+conjunction (a : as) = And a (conjunction as)
+conjunction _ = undefined
+
+-- |Variable name for the i-th character in the password
+pwCharVarName :: Int -> String
+pwCharVarName i = "pw[" ++ show i ++ "]"
+
+-- |Term for the i-th character in the password
+pwChar :: Int -> Term
+pwChar = uVar 8 . pwCharVarName
+
+formula :: Formula
+formula =
+ conjunction $
+ map (\i ->
+ let a = pwChar $ i
+ b = pwChar $ (i + 1) `rem` 8
+ c = pwChar $ (i + 2) `rem` 8
+ d = pwChar $ (i + 3) `rem` 8
+ shiftPlus = Slice Unsigned 0 3 (b :+: c)
+ shiftMinus = Slice Unsigned 0 3 (b :-: c)
+ eight = Const Unsigned $ BV.pack [False, False, False] -- Only 3 bits, overflow on purpose for 8 - x
+ term = ((a :<<: shiftPlus) :|: (a :>>: (eight :-: shiftMinus))) :-: d
+ in (Atom $ term :==: uConst (hash!!i)) :&&: (Not $ Atom $ Pick 7 a)
+ ) [0..7]
+
+main :: IO ()
+main =
+ case solveAll formula of
+ Solution s ->
+ forM_ s (\s ->
+ putStrLn $ toEnum <$> fromIntegral <$> map (\i ->
+ let bv = s Map.! (pwCharVarName i) in
+ (fromJust (BV.fromBitVector bv))::Word8) [0..7]
+ )
+ res -> print res
A => doc/paper.pdf +0 -0
A => doc/slides.pdf +0 -0
A => shida.cabal +62 -0
@@ 1,62 @@
+cabal-version: 1.12
+
+name: shida
+version: 0.1.0.0
+author: Florian Märkl
+license: GPL-3
+license-file: LICENSE
+build-type: Simple
+extra-source-files:
+ README.md
+
+source-repository head
+ type: git
+ location: https://github.com/thestr4ng3r/shida
+
+library
+ exposed-modules:
+ Common,
+ BitVectorValue
+ Formula
+ Propositional
+ Flattening
+ Solve
+ MiniSat
+ hs-source-dirs:
+ src
+ build-depends:
+ base >=4.7 && <5,
+ bytestring,
+ containers,
+ mtl,
+ transformers,
+ minisat-solver
+ default-language: Haskell2010
+ ghc-options: -W
+
+executable shida-exe
+ main-is: Main.hs
+ hs-source-dirs:
+ app
+ ghc-options: -threaded -rtsopts -with-rtsopts=-N
+ build-depends:
+ base >=4.7 && <5,
+ shida,
+ minisat-solver
+ default-language: Haskell2010
+
+test-suite shida-test
+ type: exitcode-stdio-1.0
+ main-is: Spec.hs
+ other-modules:
+ BitVectorValueTest
+ SolveTest
+ hs-source-dirs:
+ test
+ ghc-options: -threaded -rtsopts -with-rtsopts=-N
+ build-depends:
+ base >=4.7 && <5,
+ QuickCheck,
+ shida,
+ containers
+ default-language: Haskell2010
A => src/BitVectorValue.hs +135 -0
@@ 1,135 @@
+module BitVectorValue (
+ Size,
+ BoundsException,
+ BitVectorValue,
+ index,
+ replicate,
+ length,
+ unpack,
+ pack,
+ ToBitVector,
+ toBitVector,
+ FromBitVector,
+ fromBitVector,
+ slice
+) where
+
+
+import qualified Prelude as P
+import Prelude hiding (length,replicate)
+
+import Data.Word
+import Data.Int
+import Data.Bits
+import qualified Data.ByteString as B
+
+import Control.Exception
+import Data.Function ((&))
+
+import Common
+
+data BoundsException = BoundsException deriving (Show)
+instance Exception BoundsException
+
+data BitVectorValue = BitVectorValue Size B.ByteString
+
+instance Eq BitVectorValue where
+ (==) (BitVectorValue lsz ldat) (BitVectorValue rsz rdat) =
+ lsz == rsz && foldl (\acc i -> acc && (index (BitVectorValue lsz ldat) i == index (BitVectorValue rsz rdat) i)) True [0..lsz-1]
+
+compareBits :: Size -> BitVectorValue -> BitVectorValue -> Ordering
+compareBits 0 a b = compare (index a 0) (index b 0)
+compareBits i a b =
+ let r = compare (index a i) (index b i) in
+ if r == EQ then
+ compareBits (i-1) a b
+ else
+ r
+
+instance Ord BitVectorValue where
+ compare a b =
+ let szc = compare (length a) (length b) in
+ if szc == EQ then
+ compareBits (length a - 1) a b
+ else
+ szc
+
+instance Show BitVectorValue where
+ show (BitVectorValue sz dat) =
+ foldl (\acc i -> acc ++ (if index (BitVectorValue sz dat) i then "1" else "0")) "0b" $ reverse [0..sz-1]
+
+index :: BitVectorValue -> Size -> Bool
+index (BitVectorValue sz dat) i =
+ if i >= sz then
+ throw BoundsException
+ else
+ let byte = B.index dat $ fromIntegral $ i `shiftR` 3
+ biti = i .&. 0x7 in
+ ((byte `shiftR` fromIntegral biti) .&. 1) == 1
+
+replicate :: Size -> Bool -> BitVectorValue
+replicate sz v = BitVectorValue sz $ B.replicate (fromIntegral ((sz + 7) `shiftR` 3)) $ if v then 0xff else 0
+
+length :: BitVectorValue -> Size
+length (BitVectorValue sz _) = sz
+
+unpack :: BitVectorValue -> [Bool]
+unpack bv = map (index bv) [0..length bv - 1]
+
+packByte :: Bool -> Bool -> Bool -> Bool -> Bool -> Bool -> Bool -> Bool -> Word8
+packByte b0 b1 b2 b3 b4 b5 b6 b7 = foldr (\b acc -> (acc `shiftL` 1) .|. (if b then 1 else 0)) 0 [b0, b1, b2, b3, b4, b5, b6, b7]
+
+packBytes :: [Bool] -> [Word8]
+packBytes (b0 : b1 : b2 : b3 : b4 : b5 : b6 : b7 : bs) = packByte b0 b1 b2 b3 b4 b5 b6 b7 : packBytes bs
+packBytes [b0, b1, b2, b3, b4, b5, b6] = [packByte b0 b1 b2 b3 b4 b5 b6 False]
+packBytes [b0, b1, b2, b3, b4, b5] = [packByte b0 b1 b2 b3 b4 b5 False False]
+packBytes [b0, b1, b2, b3, b4] = [packByte b0 b1 b2 b3 b4 False False False]
+packBytes [b0, b1, b2, b3] = [packByte b0 b1 b2 b3 False False False False]
+packBytes [b0, b1, b2] = [packByte b0 b1 b2 False False False False False]
+packBytes [b0, b1] = [packByte b0 b1 False False False False False False]
+packBytes [b0] = [packByte b0 False False False False False False False]
+packBytes [] = []
+
+pack :: [Bool] -> BitVectorValue
+pack bits = BitVectorValue (fromIntegral $ P.length bits) $ B.pack $ packBytes bits
+
+class ToBitVector a where
+ toBitVector :: a -> BitVectorValue
+
+instance ToBitVector Word8 where
+ toBitVector w = BitVectorValue 8 $ B.singleton w
+
+instance ToBitVector Word16 where
+ toBitVector w = BitVectorValue 16 $ B.pack $ map fromIntegral [w .&. 0xff,
+ (w `shiftR` 8) .&. 0xff]
+
+instance ToBitVector Word32 where
+ toBitVector w = BitVectorValue 32 $ B.pack $ map fromIntegral [w .&. 0xff,
+ (w `shiftR` 8) .&. 0xff,
+ (w `shiftR` 0x10) .&. 0xff,
+ (w `shiftR` 0x18) .&. 0xff]
+instance ToBitVector Word64 where
+ toBitVector w = BitVectorValue 64 $ B.pack $ map fromIntegral [w .&. 0xff,
+ (w `shiftR` 8) .&. 0xff,
+ (w `shiftR` 0x10) .&. 0xff,
+ (w `shiftR` 0x18) .&. 0xff,
+ (w `shiftR` 0x20) .&. 0xff,
+ (w `shiftR` 0x28) .&. 0xff,
+ (w `shiftR` 0x30) .&. 0xff,
+ (w `shiftR` 0x38) .&. 0xff]
+
+instance ToBitVector Int8 where toBitVector v = toBitVector (fromIntegral v :: Word8)
+instance ToBitVector Int16 where toBitVector v = toBitVector (fromIntegral v :: Word16)
+instance ToBitVector Int32 where toBitVector v = toBitVector (fromIntegral v :: Word32)
+instance ToBitVector Int64 where toBitVector v = toBitVector (fromIntegral v :: Word64)
+
+class FromBitVector a where
+ fromBitVector :: BitVectorValue -> Maybe a
+
+instance FromBitVector Word8 where
+ fromBitVector (BitVectorValue 8 v) = Just $ B.head v
+ fromBitVector _ = Nothing
+
+slice :: BitVectorValue -> Size -> Size -> BitVectorValue
+slice v start sz =
+ unpack v & drop (fromIntegral start) & take (fromIntegral sz) & pack<
\ No newline at end of file
A => src/Common.hs +13 -0
@@ 1,13 @@
+module Common where
+
+type Size = Word
+data BitVectorSign = Unsigned | Signed deriving (Eq, Ord)
+data BitVectorType = BitVectorType BitVectorSign Size deriving (Eq, Ord)
+
+instance Show BitVectorType where
+ show (BitVectorType sign sz) = (if sign == Signed then "s" else "u") ++ show sz
+
+fixedPoint :: Eq a => (a -> a) -> a -> a
+fixedPoint f v =
+ if r == v then v else fixedPoint f r
+ where r = f v<
\ No newline at end of file
A => src/Flattening.hs +418 -0
@@ 1,418 @@
+module Flattening where
+
+import Text.Printf
+import Data.Map (Map)
+import qualified Data.Map as Map
+import qualified Data.Set as Set
+import Control.Monad
+import Data.Maybe
+
+import Control.Monad.Except
+import Control.Monad.State
+
+import qualified BitVectorValue as BV
+import Common
+import Formula
+import qualified Propositional as P
+import Propositional ((<->), (&&&), (|||), (^^^))
+
+newtype FlattenState = FlattenState P.Identifier
+data FlattenError =
+ TermTypeError Term |
+ AtomTypeMismatch Atom |
+ AtomPickBoundsError Atom
+ deriving (Eq, Show)
+
+type Flattening a = StateT FlattenState (Except FlattenError) a
+
+runFlattening :: Flattening a -> FlattenState -> Either FlattenError a
+runFlattening m = runExcept . evalStateT m
+
+type PropVector = Size -> P.Formula
+data PropVectorVariable = PropVectorVariable P.Identifier Size
+
+instance Show PropVectorVariable where
+ show (PropVectorVariable base sz) = "(" ++ show base ++ ":" ++ show sz ++ ")"
+
+variableVector :: PropVectorVariable -> PropVector
+variableVector (PropVectorVariable base sz) i =
+ if i < sz then
+ P.Var $ base + fromIntegral i
+ else
+ error "overflow in reserved prop vector"
+
+reserveProps :: Size -> Flattening PropVectorVariable
+reserveProps sz = do
+ FlattenState nextPropId <- get
+ put $ FlattenState (nextPropId + fromIntegral sz)
+ return $ PropVectorVariable nextPropId sz
+
+class Reservable a where
+ requiredProps :: a -> Flattening Size
+
+
+reserveVarFor :: (Reservable a) => a -> Flattening PropVectorVariable
+reserveVarFor x = requiredProps x >>= reserveProps
+
+reserveVarsForAll :: (Reservable a, Ord a, Foldable t) => t a -> Flattening (Map a PropVectorVariable)
+reserveVarsForAll =
+ foldM (\map x -> do
+ var <- reserveVarFor x
+ return $ Map.insert x var map
+ ) Map.empty
+
+curPropsCount :: Flattening P.Identifier
+curPropsCount = do
+ FlattenState nextPropId <- get
+ return nextPropId
+
+maybeToFlattening :: FlattenError -> Maybe a -> Flattening a
+maybeToFlattening _ (Just v) = return v
+maybeToFlattening e Nothing = throwError e
+
+getTermType :: Term -> Flattening BitVectorType
+getTermType t = maybeToFlattening (TermTypeError t) $ termType t
+
+skeleton :: (Atom -> PropVectorVariable) -> Formula -> P.Formula
+skeleton atomProps (Atom atom) = variableVector (atomProps atom) 0 -- This is simply using the atom's reserved variable
+skeleton atomProps (Not f) = P.Not $ skeleton atomProps f
+skeleton atomProps (And l r) = skeleton atomProps l &&& skeleton atomProps r
+
+bitwiseConstraintIff :: (Size -> P.Formula) -> (Term -> PropVectorVariable) -> Term -> Flattening P.Formula
+bitwiseConstraintIff op termProps t = do
+ (BitVectorType _ sz) <- getTermType t
+ let tProp = variableVector $ termProps t
+ return $ P.conjunction $ map (\i -> P.Iff (tProp i) $ op i) [0..sz - 1]
+
+bitwiseConstraintBinary :: (P.Formula -> P.Formula -> P.Formula) -> (Term -> PropVectorVariable) -> Term -> Term -> Term -> Flattening P.Formula
+bitwiseConstraintBinary op termProps l r =
+ let lProp = variableVector $ termProps l
+ rProp = variableVector $ termProps r in
+ bitwiseConstraintIff (\i -> op (lProp i) (rProp i)) termProps
+
+fullAdderSum :: P.Formula -> P.Formula -> P.Formula -> P.Formula
+fullAdderSum a b cin = (a ^^^ b) ^^^ cin -- (6.37)
+
+fullAdderCarry :: P.Formula -> P.Formula -> P.Formula -> P.Formula
+fullAdderCarry a b cin = (a &&& b) ||| ((a ^^^ b) &&& cin) -- (6.38)
+
+-- (6.39) and (6.42)
+adderCarry :: PropVector -> PropVector -> P.Formula -> PropVector
+adderCarry _ _ cin 0 = cin
+adderCarry l r cin i = fullAdderCarry (l (i-1)) (r (i-1)) cin
+
+adderCarryRec :: PropVector -> PropVector -> Bool -> PropVector
+adderCarryRec _ _ cin 0 = P.Const cin
+adderCarryRec l r cin i = adderCarry l r (adderCarryRec l r cin (i - 1)) i
+
+adder :: PropVector -> PropVector -> Bool -> Size -> Flattening ([P.Formula], PropVector)
+adder l r cin sz = do
+ carriesPropVector <- reserveProps (sz-1)
+ let carryProp = (\i ->
+ if i == 0 then
+ P.Const cin
+ else
+ variableVector carriesPropVector (i-1)
+ ) :: PropVector
+ adderCarryConstraints = map (\i -> carryProp i <-> adderCarry l r (carryProp $ i-1) i) [1..sz-1]
+ return (adderCarryConstraints, \i -> fullAdderSum (l i) (r i) (carryProp i))
+
+doubleIf :: P.Formula -> P.Formula -> P.Formula -> P.Formula -> P.Formula -> P.Formula
+doubleIf ifa resa ifb resb els =
+ (ifa &&& resa) ||| (P.Not ifa &&& ifb &&& resb) ||| (P.Not ifa &&& P.Not ifb &&& els)
+
+singleIf :: P.Formula -> P.Formula -> P.Formula -> P.Formula
+singleIf ifa resa els =
+ (ifa &&& resa) ||| (P.Not ifa &&& els)
+
+shift :: (Size -> Size -> Size) -> (Int -> Size -> Bool) -> PropVector -> PropVector -> Int -> PropVector
+shift _ _ l _ (-1) i = l i -- (6.48)
+shift dir cond l r s i | cond s i =
+ doubleIf (r $ fromIntegral s)
+ (shift dir cond l r (s - 1) (i `dir` (2^s)))
+ (P.Not (r $ fromIntegral s))
+ (shift dir cond l r (s - 1) i)
+ -- else
+ (P.Const False)
+shift dir cond l r s i = -- (6.49)
+ singleIf (P.Not (r $ fromIntegral s))
+ (shift dir cond l r (s - 1) i)
+ -- else
+ (P.Const False)
+
+shiftLStatic :: PropVector -> Size -> PropVector
+shiftLStatic x s i = if i < s then P.Const False else x (i - s)
+
+lessThanUnsigned :: PropVector -> PropVector -> Size -> P.Formula
+lessThanUnsigned l r sz =
+ P.Not $ adderCarryRec l (P.Not . r) True (fromIntegral sz) -- (6.46)
+
+lessThanSigned :: PropVector -> PropVector -> PropVector
+lessThanSigned l r sz =
+ l (fromIntegral (sz-1)) <-> r (fromIntegral (sz-1))
+ ^^^
+ adderCarryRec l (P.Not . r) True (fromIntegral sz) -- (6.47) but there is a mistake in the book, see "Errata For 2nd Edition"
+
+mult :: PropVector -> PropVector -> Size -> Int -> Flattening ([P.Formula], PropVector)
+mult _ _ _ (-1) = return ([], \_ -> P.Const False) -- (6.50)
+mult l r sz s = do
+ (prevMultConstraints, prevMultBits) <- mult l r sz (s - 1)
+ (adderConstraints, addedBits) <- adder prevMultBits (\i -> r (fromIntegral s) &&& shiftLStatic l (fromIntegral s) i) False sz
+ return (adderConstraints ++ prevMultConstraints, addedBits) -- (6.51)
+
+multiplication :: PropVector -> PropVector -> Size -> Flattening ([P.Formula], PropVector)
+multiplication l r sz = mult l r sz (fromIntegral sz - 1)
+
+extendUnsigned :: PropVector -> Size -> PropVector
+extendUnsigned bv oldsz i
+ | i < oldsz = bv i
+ | otherwise = P.Const False
+
+extendSigned :: PropVector -> Size -> PropVector
+extendSigned bv oldsz i
+ | i < oldsz - 1 = bv i
+ | otherwise = bv (oldsz - 1)
+
+extend :: BitVectorSign -> PropVector -> Size -> PropVector
+extend Signed = extendSigned
+extend Unsigned = extendUnsigned
+
+increment :: PropVector -> Size -> Flattening ([P.Formula], PropVector)
+increment v sz = do
+ carries <- reserveProps (sz - 1)
+ let carryProp = (\i ->
+ if i == 0 then
+ P.Const True
+ else
+ variableVector carries (i-1)
+ ) :: PropVector
+ carryConstraints = map (\i -> carryProp i <-> if i == 0 then P.Const True else v (i-1) &&& carryProp (i-1)) [1..sz-1]
+ return (carryConstraints, \i -> v i ^^^ carryProp i)
+
+absolute :: PropVector -> Size -> Flattening ([P.Formula], PropVector)
+absolute v sz = do
+ let inverted i = P.Not (v i)
+ (tcConstraints, tcVec) <- increment inverted sz
+ let signProp = v (sz-1)
+ return (tcConstraints, \i -> (signProp &&& tcVec i) ||| (P.Not signProp &&& v i))
+
+lessThanAbsolute :: PropVector -> PropVector -> Size -> Flattening ([P.Formula], P.Formula)
+lessThanAbsolute l r sz = do
+ (absLConstraints, absLVec) <- absolute l sz
+ (absRConstraints, absRVec) <- absolute r sz
+ return (absLConstraints ++ absRConstraints, lessThanUnsigned absLVec absRVec sz)
+
+divisionConstraint :: BitVectorSign -> PropVector -> PropVector -> PropVector -> PropVector -> Size -> Flattening P.Formula
+divisionConstraint sign res l r rem sz = do
+ let extsz = sz + sz
+ ext = extend sign
+ extl = ext l sz
+ extr = ext r sz
+ extres = ext res sz
+ extrem = ext rem sz
+ (multConstraints, multBit) <- multiplication extres extr extsz -- term * r
+ (addConstraints, addedBit) <- adder multBit extrem False extsz -- (term * r) + rem
+ let multAddConstraints = map (\i -> extl i <-> addedBit i) [0..extsz - 1] -- (6.52)
+ remainderConstraints <-
+ if sign == Signed then do -- extr
+ (extraConstraints, constraint) <- lessThanAbsolute extrem extr extsz
+ let signConstraint = (l (sz - 1) <-> rem (sz - 1)) ||| P.conjunction (map (P.Not . rem) [0..sz-1]) -- (sign l == sign rem) || (rem == 0)
+ return $ signConstraint : constraint : extraConstraints
+ else
+ return [lessThanUnsigned extrem extr extsz] -- (6.53)
+ return $ P.conjunction $ remainderConstraints ++ multAddConstraints ++ addConstraints ++ multConstraints
+
+termPropVector :: (Term -> PropVectorVariable) -> Term -> PropVector
+termPropVector termProps t = variableVector $ termProps t
+
+notTermPropVector :: (Term -> PropVectorVariable) -> Term -> PropVector
+notTermPropVector termProps t i = P.Not $ variableVector (termProps t) i
+
+termConstraint :: (Atom -> PropVectorVariable) -> (Term -> PropVectorVariable) -> Term -> Flattening P.Formula
+termConstraint atomProps termProps term =
+ let termBit = termPropVector termProps
+ notTermBit = notTermPropVector termProps in
+ case term of
+ (Var _ _) -> return $ P.Const True
+ (Const _ bv) -> return $ P.conjunction $ map (\i ->
+ if BV.index bv i then
+ termBit term i
+ else
+ notTermBit term i
+ ) [0..BV.length bv - 1] -- (6.35)
+ (BinAnd l r) -> bitwiseConstraintBinary (&&&) termProps l r term
+ (BinOr l r) -> bitwiseConstraintBinary (|||) termProps l r term
+ --(BinXor l r) -> bitwiseConstraintBinary P.Xor termProps l r term
+ (BinXor l r) -> do
+ (BitVectorType _ sz) <- getTermType term
+ return $ P.And $ map (\i ->
+ -- Constraint for the i-th bit, bringing the output in relation to the inputs:
+ termBit term i <-> (termBit l i ^^^ termBit r i)
+ ) [0..sz - 1]
+ (Complement t) -> bitwiseConstraintIff (notTermBit t) termProps term
+ (Inc t) -> do
+ (BitVectorType _ sz) <- getTermType term
+ (incConstraints, incVec) <- increment (termBit t) sz
+ return $ P.conjunction $ map (\i -> termBit term i <-> incVec i) [0..sz-1] ++ incConstraints
+ (Abs t) -> do
+ (BitVectorType sign sz) <- getTermType t
+ if sign == Signed then do
+ (absConstraints, absVec) <- absolute (termBit t) sz
+ return $ P.conjunction $ map (\i -> termBit term i <-> absVec i) [0..sz-1] ++ absConstraints
+ else
+ return $ P.conjunction $ map (\i -> termBit term i <-> termBit t i) [0..sz-1]
+ (Plus l r) -> do
+ let (BitVectorType _ sz) = fromJust $ termType term
+ (adderConstraints, addedBit) <- adder (termBit l) (termBit r) False sz
+ return $ P.conjunction $ adderConstraints ++ map (\i ->
+ termBit term i <-> addedBit i -- (6.41), (6.43)
+ ) [0..sz - 1]
+ (Minus l r) -> do
+ (BitVectorType _ sz) <- getTermType term
+ (adderConstraints, addedBit) <- adder (termBit l) (notTermBit r) True sz
+ return $ P.conjunction $ adderConstraints ++ map (\i ->
+ termBit term i <-> addedBit i -- (6.44)
+ ) [0..sz - 1] -- (6.41)
+ (ShL l r) -> do
+ (BitVectorType _ sz) <- getTermType l -- Term type checking ensures sz == 2^ssz
+ (BitVectorType _ ssz) <- getTermType r
+ return $ P.conjunction $ map (\i ->
+ termBit term i <-> shift (-) (\s i -> i >= 2^s) (termBit l) (termBit r) (fromIntegral ssz - 1) i
+ ) [0..fromIntegral sz - 1]
+ (ShR l r) -> do
+ (BitVectorType _ sz) <- getTermType l -- Term type checking ensures sz == 2^ssz
+ (BitVectorType _ ssz) <- getTermType r
+ return $ P.conjunction $ map (\i ->
+ termBit term i <-> shift (+) (\s i -> i + (2^s) < sz) (termBit l) (termBit r) (fromIntegral ssz - 1) i
+ ) [0..fromIntegral sz - 1]
+ (Mult l r) -> do
+ let (BitVectorType _ sz) = fromJust $ termType term
+ (multConstraints, multBit) <- multiplication (termBit l) (termBit r) sz
+ return $ P.conjunction $ multConstraints ++ map (\i ->
+ termBit term i <-> multBit i
+ ) [0..fromIntegral sz - 1]
+ (Div l r) -> do
+ BitVectorType sign sz <- getTermType l
+ remPV <- reserveProps sz
+ divisionConstraint sign (termBit term) (termBit l) (termBit r) (variableVector remPV) sz
+ (Remainder l r) -> do
+ BitVectorType sign sz <- getTermType l
+ resPV <- reserveProps sz
+ divisionConstraint sign (variableVector resPV) (termBit l) (termBit r) (termBit term) sz
+ (Concat _ l r) -> do
+ (BitVectorType _ lsz) <- getTermType l
+ bitwiseConstraintIff (\i -> if i < lsz then termBit l i else termBit r (i-lsz)) termProps term
+ (Ext _ t) -> do
+ (BitVectorType sign sz) <- getTermType t
+ bitwiseConstraintIff (extend sign (termBit t) sz) termProps term
+ (Slice _ off _ t) ->
+ bitwiseConstraintIff (\i -> termBit t (off + i)) termProps term
+ (Ternary c a b) ->
+ let atomProp = variableVector (atomProps c) 0 in
+ bitwiseConstraintIff (\i -> (atomProp &&& termBit a i) ||| (P.Not atomProp &&& termBit b i)) termProps term
+
+atomConstraint :: (Atom -> PropVectorVariable) -> (Term -> PropVectorVariable) -> Atom -> Flattening P.Formula
+atomConstraint atomProps termProps atom =
+ let atomProp = variableVector (atomProps atom) 0
+ termBit = termPropVector termProps in
+ case atom of
+ (BConst True) -> return $ variableVector (atomProps atom) 0
+ (BConst False) -> return $ P.Not $ variableVector (atomProps atom) 0
+ (Equals l r) -> do
+ lt <- getTermType l
+ rt <- getTermType r
+ when (lt /= rt) $ throwError $ AtomTypeMismatch atom
+ (atomProp <->) <$> bitwiseConstraintIff (variableVector (termProps r)) termProps l
+ (Pick i t) -> do
+ (BitVectorType _ sz) <- getTermType t
+ when (i >= sz) $ throwError $ AtomPickBoundsError atom
+ return $ atomProp <-> termBit t i
+ (LessThan l r) -> do
+ lt <- getTermType l
+ rt <- getTermType r
+ when (lt /= rt) $ throwError $ AtomTypeMismatch atom
+ let (BitVectorType sign sz) = lt
+ return $ atomProp <->
+ if sign == Signed then
+ lessThanSigned (termBit l) (termBit r) sz
+ else
+ lessThanUnsigned (termBit l) (termBit r) sz
+
+
+-- |reserves one propositional variable for each bit in each term
+termVars :: Foldable a => a Term -> Flattening (Map Term PropVectorVariable)
+termVars =
+ foldM (\map term -> do
+ (BitVectorType _ sz) <- getTermType term
+ baseProp <- reserveProps sz
+ return $ Map.insert term baseProp map
+ ) Map.empty
+
+instance Reservable Term where
+ requiredProps term = (\(BitVectorType _ sz) -> sz) <$> getTermType term
+
+instance Reservable Atom where
+ requiredProps _ = return 1
+
+data FlattenedFormula = FlattenedFormula {
+ atomProps :: Map Atom PropVectorVariable,
+ termProps :: Map Term PropVectorVariable,
+ skeletonFormula :: P.Formula,
+ termConstraints :: Map Term P.Formula,
+ atomConstraints :: Map Atom P.Formula,
+ propsCount :: Int
+}
+
+-- |Helper function that applies a function in m to each set member and constructs a
+-- Map containing the results.
+mapFromSetM :: (Ord k, Monad m) => (k -> m a) -> Set.Set k -> m (Map k a)
+mapFromSetM f ks = Map.fromList <$> mapM (\a -> f a >>= \c -> return (a, c)) (Set.toList ks)
+
+formulaFlattening :: Formula -> Flattening FlattenedFormula
+formulaFlattening f = do
+ let allTerms = Set.fromList $ terms f
+ allAtoms = Set.fromList $ atoms f
+ atomProps <- reserveVarsForAll allAtoms
+ termProps <- reserveVarsForAll allTerms
+ let skel = skeleton (atomProps Map.!) f
+ termConstraints <- mapFromSetM (termConstraint (atomProps Map.!) (termProps Map.!)) allTerms
+ atomConstraints <- mapFromSetM (atomConstraint (atomProps Map.!) (termProps Map.!)) allAtoms
+ propsCount <- curPropsCount
+ return $ FlattenedFormula {
+ atomProps = atomProps,
+ termProps = termProps,
+ skeletonFormula = skel,
+ termConstraints = termConstraints,
+ atomConstraints = atomConstraints,
+ propsCount = propsCount
+ }
+
+-- |Convenience function that calls formulaFlattening and evaluates the returned monadic value
+flatten :: Formula -> Either FlattenError FlattenedFormula
+flatten f = runFlattening (formulaFlattening f) (FlattenState 0)
+
+instance Show FlattenedFormula where
+ show (FlattenedFormula atomProps termProps skeletonFormula termConstraints atomConstraints _) =
+ printf "skeleton: %s\nterms:\n%satoms:\n%s" (show skeletonFormula) (
+ concat $
+ Map.mapWithKey (\term (prop, constraint) -> " " ++ show term ++ " = " ++ show prop ++ " => " ++ show constraint ++ "\n") $
+ Map.intersectionWith (,) termProps termConstraints
+ ) (
+ concat $
+ Map.mapWithKey (\atom (prop, constraint) -> " " ++ show atom ++ " = " ++ show prop ++ " => " ++ show constraint ++ "\n") $
+ Map.intersectionWith (,) atomProps atomConstraints
+ )
+
+propositional :: FlattenedFormula -> P.Formula
+propositional (FlattenedFormula _ _ skeletonFormula termConstraints atomConstraints _) =
+ P.conjunction $ skeletonFormula : Map.elems termConstraints ++ Map.elems atomConstraints
+
+-- |Maps the result from the SAT-solver back to the original bit vector variables
+reconstructResult :: Formula -> FlattenedFormula -> Map P.Identifier Bool -> Map Identifier BV.BitVectorValue
+reconstructResult f flat propResults =
+ let allVars = Set.fromList $ vars f in
+ Map.fromList $ map (\(BitVectorType sign sz, name) ->
+ let (PropVectorVariable baseProp _) = termProps flat Map.! Var (BitVectorType sign sz) name
+ bits = map (\i -> Map.findWithDefault False (baseProp + i) propResults) [0..fromIntegral sz - 1] in
+ (name, BV.pack bits)
+ ) $ Set.toList allVars
A => src/Formula.hs +262 -0
@@ 1,262 @@
+{-# LANGUAGE PatternSynonyms #-}
+module Formula where
+
+import Text.Printf
+
+import Common
+import qualified BitVectorValue as BV
+
+type Identifier = String
+
+data Formula =
+ And Formula Formula |
+ Not Formula |
+ Atom Atom
+ deriving (Eq, Ord)
+
+data Atom =
+ BConst Bool |
+ LessThan Term Term |
+ Equals Term Term |
+ Pick Size Term
+ deriving (Eq, Ord)
+
+data Term =
+ Plus Term Term |
+ Minus Term Term |
+ Mult Term Term |
+ Div Term Term |
+ Remainder Term Term |
+ ShL Term Term |
+ ShR Term Term |
+ BinAnd Term Term |
+ BinOr Term Term |
+ BinXor Term Term |
+ Var BitVectorType Identifier |
+ Complement Term |
+ Inc Term |
+ Abs Term |
+ Const BitVectorSign BV.BitVectorValue |
+ Ternary Atom Term Term |
+ Concat BitVectorSign Term Term |
+ Ext Size Term |
+ Slice BitVectorSign Size Size Term -- new sign -> start offset -> new size -> term
+ deriving (Eq, Ord)
+
+pattern (:&&:) a b = And a b
+pattern (:!!:) a = Not a
+
+pattern (:==:) a b = Equals a b
+pattern (:<:) a b = LessThan a b
+
+pattern (:+:) a b = Plus a b
+pattern (:-:) a b = Minus a b
+pattern (:*:) a b = Mult a b
+pattern (:/:) a b = Div a b
+pattern (:%:) a b = Remainder a b
+pattern (:<<:) a b = ShL a b
+pattern (:>>:) a b = ShR a b
+pattern (:&:) a b = BinAnd a b
+pattern (:|:) a b = BinOr a b
+pattern (:^:) a b = BinXor a b
+
+uVar :: BV.Size -> Identifier -> Term
+uVar sz = Var (BitVectorType Unsigned sz)
+
+sVar :: BV.Size -> Identifier -> Term
+sVar sz = Var (BitVectorType Signed sz)
+
+uConst :: BV.ToBitVector a => a -> Term
+uConst v = Const Unsigned $ BV.toBitVector v
+
+sConst :: BV.ToBitVector a => a -> Term
+sConst v = Const Signed $ BV.toBitVector v
+
+instance Show Formula where
+ show (And l r) = printf "(%s ∧ %s)" (show l) (show r)
+ show (Not f) = printf "¬%s" (show f)
+ show (Atom a) = show a
+
+instance Show Atom where
+ show (BConst True) = printf "True"
+ show (BConst False) = printf "False"
+ show (LessThan l r) = printf "(%s < %s)" (show l) (show r)
+ show (Equals l r) = printf "(%s = %s)" (show l) (show r)
+ show (Pick i t) = printf "%s[%s]" (show t) (show i)
+
+instance Show Term where
+ show (Plus l r) = printf "(%s + %s)" (show l) (show r)
+ show (Minus l r) = printf "(%s - %s)" (show l) (show r)
+ show (Mult l r) = printf "(%s * %s)" (show l) (show r)
+ show (Div l r) = printf "(%s / %s)" (show l) (show r)
+ show (Remainder l r) = printf "(%s %% %s)" (show l) (show r)
+ show (ShL l r) = printf "(%s << %s)" (show l) (show r)
+ show (ShR l r) = printf "(%s >> %s)" (show l) (show r)
+ show (BinAnd l r) = printf "(%s & %s)" (show l) (show r)
+ show (BinOr l r) = printf "(%s | %s)" (show l) (show r)
+ show (BinXor l r) = printf "(%s ^ %s)" (show l) (show r)
+ show (Concat _ l r) = printf "(%s ⚬ %s)" (show l) (show r)
+ show (Var _ name) = name
+ show (Complement term) = printf "~%s" (show term)
+ show (Inc term) = printf "%s+1" (show term)
+ show (Abs term) = printf "|%s|" (show term)
+ show (Const _ bv) = show bv
+ show (Ternary c a b) = printf "(%s ? %s : %s)" (show c) (show a) (show b)
+ show (Ext sz term) = printf "ext_%s %s" (show sz) (show term)
+ show (Slice _ off sz t) = printf "%s[%s:%s]" (show t) (show off) (show sz)
+
+combinedTermTypes :: Term -> Term -> Maybe BitVectorType
+combinedTermTypes l r =
+ case (termType l, termType r) of
+ (Just tl, Just tr) | tl == tr -> Just tl
+ _ -> Nothing
+
+shiftTermTypes :: Term -> Term -> Maybe BitVectorType
+shiftTermTypes l r =
+ case (termType l, termType r) of
+ (Just (BitVectorType sign sz), Just (BitVectorType Unsigned ssz)) | sz == 2 ^ ssz -> Just $ BitVectorType sign sz
+ _ -> Nothing
+
+-- |returns the term's type or Nothing if it is invalid wrt. typing
+termType :: Term -> Maybe BitVectorType
+termType (Plus l r) = combinedTermTypes l r
+termType (Minus l r) = combinedTermTypes l r
+termType (Mult l r) = combinedTermTypes l r
+termType (Div l r) = combinedTermTypes l r
+termType (Remainder l r) = combinedTermTypes l r
+termType (ShL l r) = shiftTermTypes l r
+termType (ShR l r) = shiftTermTypes l r
+termType (BinAnd l r) = combinedTermTypes l r
+termType (BinOr l r) = combinedTermTypes l r
+termType (BinXor l r) = combinedTermTypes l r
+termType (Concat sign l r) = do
+ (BitVectorType _ lsz) <- termType l
+ (BitVectorType _ rsz) <- termType r
+ return $ BitVectorType sign (lsz + rsz)
+termType (Var tp _) = Just tp
+termType (Complement term) = termType term
+termType (Inc term) = termType term
+termType (Abs term) = (\(BitVectorType _ sz) -> BitVectorType Unsigned sz) <$> termType term
+termType (Const sign bv) = Just $ BitVectorType sign (BV.length bv)
+termType (Ternary _ a b) = combinedTermTypes a b
+termType (Ext sz term) =
+ case termType term of
+ Just (BitVectorType sign tsz) | tsz <= sz -> Just $ BitVectorType sign sz
+ _ -> Nothing
+termType (Slice sign off sz term) =
+ case termType term of
+ Just (BitVectorType _ tsz) | off + sz <= tsz -> Just $ BitVectorType sign sz
+ _ -> Nothing
+
+subTerms :: Term -> [Term]
+subTerms (Plus l r) = [l, r]
+subTerms (Minus l r) = [l, r]
+subTerms (Mult l r) = [l, r]
+subTerms (Div l r) = [l, r]
+subTerms (Remainder l r) = [l, r]
+subTerms (ShL l r) = [l, r]
+subTerms (ShR l r) = [l, r]
+subTerms (BinAnd l r) = [l, r]
+subTerms (BinOr l r) = [l, r]
+subTerms (BinXor l r) = [l, r]
+subTerms (Concat _ l r) = [l, r]
+subTerms (Var _ _) = []
+subTerms (Complement term) = [term]
+subTerms (Inc term) = [term]
+subTerms (Abs term) = [term]
+subTerms (Const _ _) = []
+subTerms (Ternary _ a b) = [a, b]
+subTerms (Ext _ term) = [term]
+subTerms (Slice _ _ _ t) = [t]
+
+class Terms a where
+ terms :: a -> [Term]
+
+instance Terms Term where
+ terms term =
+ term : concatMap terms at ++ concatMap terms st
+ where st = subTerms term
+ at = case term of
+ (Ternary c _ _) -> terms c
+ _ -> []
+
+instance Terms Formula where
+ terms (And l r) = terms l ++ terms r
+ terms (Not f) = terms f
+ terms (Atom a) = terms a
+
+instance Terms Atom where
+ terms (BConst _) = []
+ terms (LessThan l r) = terms l ++ terms r
+ terms (Equals l r) = terms l ++ terms r
+ terms (Pick _ t) = terms t
+
+class Atoms a where
+ atoms :: a -> [Atom]
+
+instance Atoms Formula where
+ atoms (And l r) = atoms l ++ atoms r
+ atoms (Not f) = atoms f
+ atoms (Atom a) = atoms a
+
+instance Atoms Atom where
+ atoms (BConst b) = [BConst b]
+ atoms (LessThan l r) = LessThan l r : atoms l ++ atoms r
+ atoms (Equals l r) = Equals l r : atoms l ++ atoms r
+ atoms (Pick i t) = Pick i t : atoms t
+
+instance Atoms Term where
+ atoms (Plus l r) = atoms l ++ atoms r
+ atoms (Minus l r) = atoms l ++ atoms r
+ atoms (Mult l r) = atoms l ++ atoms r
+ atoms (Div l r) = atoms l ++ atoms r
+ atoms (Remainder l r) = atoms l ++ atoms r
+ atoms (ShL l r) = atoms l ++ atoms r
+ atoms (ShR l r) = atoms l ++ atoms r
+ atoms (BinAnd l r) = atoms l ++ atoms r
+ atoms (BinOr l r) = atoms l ++ atoms r
+ atoms (BinXor l r) = atoms l ++ atoms r
+ atoms (Concat _ l r) = atoms l ++ atoms r
+ atoms (Var _ _) = []
+ atoms (Complement t) = atoms t
+ atoms (Inc t) = atoms t
+ atoms (Abs t) = atoms t
+ atoms (Const _ _) = []
+ atoms (Ternary c a b) = atoms c ++ atoms a ++ atoms b
+ atoms (Ext _ t) = atoms t
+ atoms (Slice _ _ _ t) = atoms t
+
+class Vars a where
+ vars :: a -> [(BitVectorType, Identifier)]
+
+instance Vars Formula where
+ vars (And l r) = vars l ++ vars r
+ vars (Not f) = vars f
+ vars (Atom a) = vars a
+
+instance Vars Atom where
+ vars (BConst _) = []
+ vars (LessThan l r) = vars l ++ vars r
+ vars (Equals l r) = vars l ++ vars r
+ vars (Pick _ t) = vars t
+
+instance Vars Term where
+ vars (Plus l r) = vars l ++ vars r
+ vars (Minus l r) = vars l ++ vars r
+ vars (Mult l r) = vars l ++ vars r
+ vars (Div l r) = vars l ++ vars r
+ vars (Remainder l r) = vars l ++ vars r
+ vars (ShL l r) = vars l ++ vars r
+ vars (ShR l r) = vars l ++ vars r
+ vars (BinAnd l r) = vars l ++ vars r
+ vars (BinOr l r) = vars l ++ vars r
+ vars (BinXor l r) = vars l ++ vars r
+ vars (Concat _ l r) = vars l ++ vars r
+ vars (Var tp name) = [(tp, name)]
+ vars (Complement t) = vars t
+ vars (Inc t) = vars t
+ vars (Abs t) = vars t
+ vars (Const _ _) = []
+ vars (Ternary c a b) = vars c ++ vars a ++ vars b
+ vars (Ext _ t) = vars t
+ vars (Slice _ _ _ t) = vars t<
\ No newline at end of file
A => src/MiniSat.hs +18 -0
@@ 1,18 @@
+module MiniSat where
+
+import qualified SAT.MiniSat as M
+
+import qualified Propositional as P
+
+-- |Convert our representation of propositional formulas to the one accepted by SAT.MiniSat
+miniSat :: P.Formula -> M.Formula P.Identifier
+miniSat (P.Iff l r) = miniSat l M.:<->: miniSat r
+miniSat (P.Impl l r) = miniSat l M.:->: miniSat r
+--miniSat (P.And l r) = miniSat l M.:&&: miniSat r
+--miniSat (P.Or l r) = miniSat l M.:||: miniSat r
+miniSat (P.And fs) = M.All $ map miniSat fs
+miniSat (P.Or fs) = M.Some $ map miniSat fs
+miniSat (P.Xor l r) = miniSat l M.:++: miniSat r
+miniSat (P.Not f) = M.Not $ miniSat f
+miniSat (P.Var id) = M.Var id
+miniSat (P.Const c) = if c then M.Yes else M.No<
\ No newline at end of file
A => src/Propositional.hs +98 -0
@@ 1,98 @@
+{-# LANGUAGE LambdaCase #-}
+
+module Propositional (
+ Identifier,
+ Formula (..),
+ (<->),
+ (-->),
+ (&&&),
+ (|||),
+ (^^^),
+ (Propositional.!!),
+ conjunction,
+ elimAllConsts,
+ eval
+) where
+
+import Text.Printf
+import Data.List
+
+import Common
+
+type Identifier = Int
+
+data Formula =
+ Iff Formula Formula |
+ Impl Formula Formula |
+ And [Formula] |
+ Or [Formula] |
+ Xor Formula Formula |
+ Not Formula |
+ Var Identifier |
+ Const Bool
+ deriving (Eq)
+
+instance Show Formula where
+ show (Iff l r) = printf "(%s ↔ %s)" (show l) (show r)
+ show (Impl l r) = printf "(%s → %s)" (show l) (show r)
+ show (And fs) = "(" ++ intercalate " ∧ " (map show fs) ++ ")"
+ show (Or fs) = "(" ++ intercalate " ∨ " (map show fs) ++ ")"
+ show (Xor l r) = printf "(%s ⊕ %s)" (show l) (show r)
+ show (Not f) = printf "¬%s" (show f)
+ show (Var a) = show a
+ show (Const b) = show b
+
+(<->) = Iff;
+(-->) = Impl;
+(&&&) l r = And [l, r];
+(|||) l r = Or [l, r]
+(^^^) = Xor;
+(!!) = Not
+
+conjunction :: [Formula] -> Formula
+conjunction = And
+
+elimConst :: Formula -> Formula
+elimConst (Iff l (Const True)) = elimConst l
+elimConst (Iff l (Const False)) = elimConst $ Not l
+elimConst (Iff (Const True) r) = elimConst r
+elimConst (Iff (Const False) r) = elimConst $ Not r
+elimConst (Iff l r) = Iff (elimConst l) (elimConst r)
+elimConst (Impl (Const True) r) = elimConst r
+elimConst (Impl (Const False) _) = Const True
+elimConst (Impl _ (Const True)) = Const True
+elimConst (Impl l (Const False)) = Not $ elimConst l
+elimConst (Impl l r) = Impl (elimConst l) (elimConst r)
+elimConst (And fs) =
+ if any (\case Const False -> True; _ -> False) fs then
+ Const False
+ else
+ And $ filter (\case Const True -> False; _ -> True) $ map elimConst fs
+elimConst (Or fs) =
+ if any (\case Const True -> True; _ -> False) fs then
+ Const True
+ else
+ And $ filter (\case Const False -> False; _ -> True) $ map elimConst fs
+elimConst (Xor l (Const True)) = Not $ elimConst l
+elimConst (Xor l (Const False)) = elimConst l
+elimConst (Xor (Const True) r) = Not $ elimConst r
+elimConst (Xor (Const False) r) = elimConst r
+elimConst (Xor l r) = Xor (elimConst l) (elimConst r)
+elimConst (Not (Const True)) = Const False
+elimConst (Not (Const False)) = Const True
+elimConst (Not f) = Not $ elimConst f
+elimConst (Var id) = Var id
+elimConst (Const v) = Const v
+
+elimAllConsts :: Formula -> Formula
+elimAllConsts = fixedPoint elimConst
+
+eval :: (Identifier -> Bool) -> Formula -> Bool
+eval ass (Iff l r) = eval ass l == eval ass r
+eval ass (Impl l r) = eval ass l || (eval ass l && eval ass r)
+eval ass (And fs) = foldl (\acc f -> acc && eval ass f) True fs
+eval ass (Or fs) = foldl (\acc f -> acc || eval ass f) False fs
+eval ass (Xor l r) = eval ass l /= eval ass r
+eval ass (Not f) = not $ eval ass f
+eval ass (Var id) = ass id
+eval _ (Const c) = c<
\ No newline at end of file
A => src/Solve.hs +96 -0
@@ 1,96 @@
+module Solve (
+ SolveResult (..),
+ Solution,
+ solve,
+ solveAll,
+ solveIncremental,
+ costEstimate
+) where
+
+import Data.Map (Map)
+import qualified Data.Map as Map
+import Data.List
+-- import Debug.Trace
+
+import qualified SAT.MiniSat as M
+
+import qualified BitVectorValue as BV
+import qualified Propositional as P
+import Formula
+import Flattening
+import MiniSat
+
+data SolveResult a =
+ Solution a |
+ Unsatisfiable |
+ FlattenError FlattenError
+ deriving (Eq, Show)
+
+type Solution = Map Identifier BV.BitVectorValue
+
+-- |Solve to a single solution
+solve :: Formula -> SolveResult Solution
+solve f =
+ case flatten f of
+ Left e -> FlattenError e
+ Right flat ->
+ case M.solve $ miniSat $ propositional flat of
+ Nothing -> Unsatisfiable
+ Just r -> Solution $ reconstructResult f flat r
+
+-- |Solve to all solutions as a lazy list
+solveAll :: Formula -> SolveResult [Solution]
+solveAll f =
+ case flatten f of
+ Left e -> FlattenError e
+ Right flat ->
+ case M.solve_all $ miniSat $ propositional flat of
+ [] -> Unsatisfiable
+ sols -> Solution $ map (reconstructResult f flat) sols
+
+-- |Solve incrementally to a single solution
+-- This can be significantly faster or slower than solve depending on the
+-- formula, see the paper for more info.
+solveIncremental :: Int -> Formula -> SolveResult Solution
+solveIncremental steps f =
+ case flatten f of
+ Left e -> FlattenError e
+ Right flat -> solveFlattenedIncremental steps f flat
+
+costEstimate :: P.Formula -> Word
+costEstimate (P.Iff l r) = 1 + costEstimate l + costEstimate r
+costEstimate (P.Impl l r) = 1 + costEstimate l + costEstimate r
+costEstimate (P.And fs) = foldl (\acc f -> acc + costEstimate f) (1 + fromIntegral (length fs)) fs
+costEstimate (P.Or fs) = foldl (\acc f -> acc + costEstimate f) (1 + fromIntegral (length fs)) fs
+costEstimate (P.Xor l r) = 1 + costEstimate l + costEstimate r
+costEstimate (P.Not f) = costEstimate f
+costEstimate (P.Var _) = 1
+costEstimate (P.Const _) = 0
+
+-- |Solve a formula incrementally, given the number of new constraints to add in each step
+solveFlattenedIncremental :: Int -> Formula -> FlattenedFormula -> SolveResult Solution
+solveFlattenedIncremental stepSize f flat =
+ let (FlattenedFormula _ _ skeletonFormula termConstraints atomConstraints _) = flat
+ initialFormulas = [skeletonFormula]
+ incrementalFormulas = sortOn costEstimate $ filter (/= P.Const True) $ Map.elems termConstraints ++ Map.elems atomConstraints
+ fullFormula = propositional flat
+ in case incrementalSAT stepSize fullFormula initialFormulas incrementalFormulas of
+ Nothing -> Unsatisfiable
+ Just r -> Solution $ reconstructResult f flat r
+
+-- |Solve a SAT problem incrementally by recursion, given the number of new constraints to add in
+-- each step, the full formula, constraints to be considered right now and constraints to be
+-- considered later.
+incrementalSAT :: Int -> P.Formula -> [P.Formula] -> [P.Formula] -> Maybe (Map P.Identifier Bool)
+incrementalSAT stepSize full current pending = -- trace ("incrementalSat " ++ show (length current) ++ "/" ++ show (length pending)) $
+ case M.solve $ miniSat $ P.conjunction current of
+ Nothing -> Nothing -- partial formula unsatisfiable => full formula unsatisfiable
+ Just r -> -- partial formula satisfiable
+ let conflicts = filter (not . P.eval (\id -> Map.findWithDefault False id r)) pending in
+ if null conflicts then
+ Just r -- no conflicts, full formula satisfied!
+ else
+ -- got conflicts, move the easiest ones into the current list
+ let new = take stepSize conflicts -- pick the easiest conflicts
+ nextPending = filter (not . (`elem` new)) pending in -- remove them from pending
+ incrementalSAT stepSize full (new ++ current) nextPending
A => stack.yaml +66 -0
@@ 1,66 @@
+# This file was automatically generated by 'stack init'
+#
+# Some commonly used options have been documented as comments in this file.
+# For advanced use and comprehensive documentation of the format, please see:
+# https://docs.haskellstack.org/en/stable/yaml_configuration/
+
+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
+# A snapshot resolver dictates the compiler version and the set of packages
+# to be used for project dependencies. For example:
+#
+# resolver: lts-3.5
+# resolver: nightly-2015-09-21
+# resolver: ghc-7.10.2
+#
+# The location of a snapshot can be provided as a file or url. Stack assumes
+# a snapshot provided as a file might change, whereas a url resource does not.
+#
+# resolver: ./custom-snapshot.yaml
+# resolver: https://example.com/snapshots/2018-01-01.yaml
+resolver: lts-12.26
+
+# User packages to be built.
+# Various formats can be used as shown in the example below.
+#
+# packages:
+# - some-directory
+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
+# subdirs:
+# - auto-update
+# - wai
+packages:
+- .
+# Dependency packages to be pulled from upstream that are not in the resolver.
+# These entries can reference officially published versions as well as
+# forks / in-progress versions pinned to a git hash. For example:
+#
+# extra-deps:
+# - acme-missiles-0.3
+# - git: https://github.com/commercialhaskell/stack.git
+# commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+#
+# extra-deps: []
+
+# Override default flag values for local packages and extra-deps
+# flags: {}
+
+# Extra package databases containing global packages
+# extra-package-dbs: []
+
+# Control whether we use the GHC we find on the path
+# system-ghc: true
+#
+# Require a specific version of stack, using version ranges
+# require-stack-version: -any # Default
+# require-stack-version: ">=2.3"
+#
+# Override the architecture used by stack, especially useful on Windows
+# arch: i386
+# arch: x86_64
+#
+# Extra directories used by stack for building
+# extra-include-dirs: [/path/to/dir]
+# extra-lib-dirs: [/path/to/dir]
+#
+# Allow a newer minor version of GHC than the snapshot specifies
+# compiler-check: newer-minor
A => test/BitVectorValueTest.hs +50 -0
@@ 1,50 @@
+{-# LANGUAGE TemplateHaskell #-}
+module BitVectorValueTest (runTests) where
+
+import Test.QuickCheck (choose, Gen, Arbitrary, arbitrary, sized)
+import Test.QuickCheck.All
+
+import Text.Printf
+import Data.Word
+import Data.Bits
+import Control.Monad
+
+import BitVectorValue as BV
+
+instance Arbitrary BV.BitVectorValue where
+ arbitrary = choose (1, 128) >>= \n -> BV.pack <$> replicateM n arbitrary
+
+prop_replicate :: Bool -> Gen Bool
+prop_replicate v = do
+ sz <- choose (1, 128) :: Gen Word
+ let bv = BV.replicate sz v
+ return $ foldl (\acc i -> acc && (BV.index bv i == v)) True [0..sz-1]
+
+checkBase :: (ToBitVector a, Bits a, Num a) => BV.Size -> a -> Bool
+checkBase sz v =
+ let bv = BV.toBitVector v in
+ BV.length bv == sz && foldl (\acc i -> acc && (BV.index bv i == (v .&. (1 `shiftL` fromIntegral i) /= 0))) True [0..sz-1]
+
+prop_base8 = checkBase 8 :: Word8 -> Bool
+prop_base16 = checkBase 16 :: Word16 -> Bool
+prop_base32 = checkBase 32 :: Word32 -> Bool
+prop_base64 = checkBase 64 :: Word64 -> Bool
+
+prop_eq :: BV.BitVectorValue -> Bool
+prop_eq bv = bv == bv
+
+prop_neq :: Gen Bool
+prop_neq = do
+ bitsa <- choose (1, 128) >>= \n -> replicateM n (arbitrary::Gen Bool)
+ bitsb <- choose (1, 128) >>= \n -> replicateM n (arbitrary::Gen Bool)
+ return $ (bitsa == bitsb) == (BV.pack bitsa == BV.pack bitsb)
+
+prop_compare_eq :: BV.BitVectorValue -> Bool
+prop_compare_eq bv = compare bv bv == EQ
+
+prop_compare :: Word64 -> Word64 -> Bool
+prop_compare a b = compare a b == compare (BV.toBitVector a) (BV.toBitVector b)
+
+return []
+runTests :: IO Bool
+runTests = $quickCheckAll<
\ No newline at end of file
A => test/SolveTest.hs +170 -0
@@ 1,170 @@
+{-# LANGUAGE TemplateHaskell #-}
+module SolveTest (runTests) where
+
+import Test.QuickCheck (choose, Gen, Arbitrary, arbitrary, sized, (===), Property, property)
+import Test.QuickCheck.All
+
+import Data.Word
+import Data.Int
+import Data.Bits
+import Data.Maybe
+import Data.Map (Map)
+import qualified Data.Map as Map
+
+import Common
+import Formula
+import Solve
+import qualified BitVectorValue as BV
+
+example0 x y = (Atom $ uConst x :==: uVar 8 "a")
+ :&&:
+ (Atom $ uVar 8 "b" :==: (uVar 8 "a" :^: uConst y))
+
+prop_example0 x y =
+ let f = example0 (x::Word8) (y::Word8) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector x), ("b", BV.toBitVector (x `xor` y))])
+
+prop_example0Incremental x y =
+ let f = example0 (x::Word8) (y::Word8) in
+ solveIncremental 3 f === Solution (Map.fromList [("a", BV.toBitVector x), ("b", BV.toBitVector (x `xor` y))])
+
+prop_inc x =
+ let f = Atom $ uVar 8 "a" :==: Inc (uConst (x::Word8)) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector (x+1))])
+
+prop_abs x =
+ let f = Atom $ uVar 8 "a" :==: Abs (sConst (x :: Int8))
+ in solve f == Solution (Map.fromList [("a", BV.toBitVector (fromIntegral (abs x) :: Word8))])
+
+checkOperator :: BV.ToBitVector a => (Term -> Term -> Term) -> (a -> a -> a) -> BitVectorSign -> a -> a -> Bool
+checkOperator top op sign x y =
+ let (mVar, mConst) = if sign == Signed then (sVar, sConst) else (uVar, uConst)
+ f = Atom $ mVar 8 "a" :==: (mConst x `top` mConst y) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector (x `op` y))])
+
+prop_plus x y = checkOperator (:+:) (+) Unsigned (x::Word8) (y::Word8)
+prop_plusS x y = checkOperator (:+:) (+) Signed (x::Int8) (y::Int8)
+prop_minus x y = checkOperator (:-:) (-) Unsigned (x::Word8) (y::Word8)
+prop_minusS x y = checkOperator (:-:) (-) Signed (x::Int8) (y::Int8)
+
+checkDiv :: (BV.ToBitVector a, Integral a) => BitVectorSign -> a -> a -> Bool
+checkDiv sign x y =
+ let (mVar, mConst) = if sign == Signed then (sVar, sConst) else (uVar, uConst)
+ f = Atom $ mVar 8 "a" :==: (mConst x :/: mConst y) in
+ solveAll f == if y == 0 then Unsatisfiable else Solution [Map.fromList [("a", BV.toBitVector (x `quot` y))]]
+
+prop_concat :: Word8 -> Word8 -> Bool
+prop_concat x y =
+ let f = Atom $ sVar 16 "a" :==: Concat Signed (uConst x) (uConst y)
+ v = fromIntegral ((fromIntegral x::Word16) .|. ((fromIntegral y::Word16) `shiftL` 8))::Word16 in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector v)])
+
+prop_extz :: Word8 -> Property
+prop_extz x =
+ let f = Atom $ uVar 16 "a" :==: Ext 16 (uConst x) in
+ solve f === Solution (Map.fromList [("a", BV.toBitVector (fromIntegral x :: Word16))])
+
+prop_exts :: Int8 -> Property
+prop_exts x =
+ let f = Atom $ sVar 16 "a" :==: Ext 16 (sConst x) in
+ solve f === Solution (Map.fromList [("a", BV.toBitVector (fromIntegral x :: Int16))])
+
+prop_slice :: Word64 -> Gen Property
+prop_slice x = do
+ let bv = BV.toBitVector x
+ off <- choose (0, 62)
+ sz <- choose (1, 64 - off)
+ let f = Atom $ uVar sz "a" :==: Slice Unsigned off sz (Const Signed bv)
+ return $ solve f === Solution (Map.fromList [("a", BV.slice bv off sz)])
+
+prop_complement :: Word8 -> Bool
+prop_complement x =
+ let f = Atom $ uVar 8 "a" :==: Complement (uConst x) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector (x `xor` 0xff))])
+
+prop_ternary :: Bool -> Word8 -> Word8 -> Property
+prop_ternary c a b =
+ let f = Atom $ uVar 8 "a" :==: Ternary (BConst c) (uConst a) (uConst b) in
+ solve f === Solution (Map.fromList [("a", BV.toBitVector $ if c then a else b)])
+
+prop_ternary1 :: Word8 -> Word8 -> Word8 -> Word8 -> Property
+prop_ternary1 ca cb a b =
+ let f = Atom $ uVar 8 "a" :==: Ternary (uConst ca :==: uConst cb) (uConst a) (uConst b) in
+ solve f === Solution (Map.fromList [("a", BV.toBitVector $ if ca == cb then a else b)])
+
+prop_atomEquals x =
+ let f = Atom $ uVar 8 "a" :==: uConst (x::Word8) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector x)])
+
+bconjunction :: [Formula] -> Formula
+bconjunction [x] = x
+bconjunction [x, y] = And x y
+bconjunction (x : xs) = And x $ bconjunction xs
+bconjunction [] = undefined
+
+prop_atomPick :: Word8 -> Bool
+prop_atomPick x =
+ let f = bconjunction $ map (\i ->
+ if ((x `shiftR` i) .&. 1) /= 0 then
+ Atom $ Pick (fromIntegral i) (uVar 8 "a")
+ else
+ Not $ Atom $ Pick (fromIntegral i) (uVar 8 "a")
+ ) [0..7] in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector x)])
+
+prop_atomLessThanUnsigned :: Word8 -> Bool
+prop_atomLessThanUnsigned x =
+ let f = bconjunction $
+ (if x == 0 then [] else [
+ Atom $ uConst (x-1) :<: uVar 8 "a"
+ ]) ++ (if x == 255 then [] else [
+ Atom $ uVar 8 "a" :<: uConst (x+1)
+ ]) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector x)])
+
+prop_atomLessThanSigned :: Int8 -> Bool
+prop_atomLessThanSigned x =
+ let f = bconjunction $
+ (if x == -128 then [] else [
+ Atom $ sConst (x-1) :<: sVar 8 "a"
+ ]) ++ (if x == 127 then [] else [
+ Atom $ sVar 8 "a" :<: sConst (x+1)
+ ]) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector x)])
+
+prop_shiftL :: Word8 -> Word8 -> Bool
+prop_shiftL x s =
+ let f = Atom $ uVar 8 "a" :==: (uConst x :<<: Const Unsigned (BV.slice (BV.toBitVector s) 0 3)) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector (x `shiftL` fromIntegral (s .&. 0x7)))])
+
+prop_shiftR :: Word8 -> Word8 -> Bool
+prop_shiftR x s =
+ let f = Atom $ uVar 8 "a" :==: (uConst x :>>: Const Unsigned (BV.slice (BV.toBitVector s) 0 3)) in
+ solve f == Solution (Map.fromList [("a", BV.toBitVector (x `shiftR` fromIntegral (s .&. 0x7)))])
+
+prop_incrementalUnsatisfiable :: Property
+prop_incrementalUnsatisfiable =
+ let f = Atom ((uVar 64 "a" :*: uVar 64 "b") :==: uVar 64 "c")
+ :&&: Not (Atom ((uVar 64 "b" :*: uVar 64 "a") :==: uVar 64 "c"))
+ :&&: Atom (uVar 64 "x" :<: uVar 64 "y")
+ :&&: Atom (uVar 64 "y" :<: uVar 64 "x") in
+ solveIncremental 1 f === Unsatisfiable
+
+--prop_incrementalSatisfiable :: Word64 -> Property
+--prop_incrementalSatisfiable x =
+-- let f = Atom (uVar 64 "a" :==: uConst x)
+-- :&&: Not ( Not (Atom $ (uVar 64 "b" :*: uVar 64 "c") :<: uVar 64 "d")
+-- :&&: Not (Atom $ uVar 64 "d" :<: (uVar 64 "b" :*: uVar 64 "c")))
+-- sol = solveIncremental 1 f in
+-- case sol of
+-- Solution m -> m Map.! "a" === BV.toBitVector x
+-- _ -> property False
+
+prop_mult x y = checkOperator (:*:) (*) Unsigned (x::Word8) (y::Word8)
+prop_multS x y = checkOperator (:*:) (*) Signed (x::Int8) (y::Int8)
+prop_div x y = checkDiv Unsigned (x::Word8) (y::Word8)
+prop_divS x y = checkDiv Signed (x::Int8) (y::Int8)
+
+return []
+runTests :: IO Bool
+runTests = $quickCheckAll<
\ No newline at end of file
A => test/Spec.hs +11 -0
@@ 1,11 @@
+import System.Exit
+
+import qualified BitVectorValueTest
+import qualified SolveTest
+
+main :: IO ()
+main = do
+ good <- and <$> sequence [BitVectorValueTest.runTests, SolveTest.runTests]
+ if good
+ then exitSuccess
+ else exitFailure