hevm-0.58.0: src/EVM/SMT.hs
{- |
Module: EVM.SMT
Description: Utilities for building and executing SMT queries from Expr instances
-}
module EVM.SMT
(
module EVM.SMT.Types,
module EVM.SMT.SMTLIB,
collapse,
getVar,
formatSMT2,
declareIntermediates,
assertProps,
exprToSMT,
encodeConcreteStore,
zero,
one,
propToSMT,
parseVar,
parseEAddr,
parseBlockCtx,
parseTxCtx,
getAddrs,
getVars,
queryMaxReads,
getBufs,
getStore
) where
import Prelude hiding (LT, GT, Foldable(..))
import Control.Monad
import Control.Monad.Trans.Maybe (MaybeT(..))
import Data.Containers.ListUtils (nubOrd, nubInt)
import Data.ByteString (ByteString)
import Data.ByteString qualified as BS
import Data.Foldable (Foldable(..))
import Data.List qualified as List
import Data.List.NonEmpty (NonEmpty((:|)))
import Data.List.NonEmpty qualified as NonEmpty
import Data.Maybe (fromJust, fromMaybe, isJust, listToMaybe)
import Data.Either.Extra (fromRight')
import Data.Map.Strict (Map)
import Data.Map.Strict qualified as Map
import Data.Set (Set)
import Data.Set qualified as Set
import Data.Word (Word8)
import Data.Text.Lazy (Text)
import Data.Text qualified as TS
import Data.Text.Lazy qualified as T
import Data.Text.Lazy.Builder
import qualified Data.Text.Lazy.Builder.Int (decimal)
import Language.SMT2.Parser (getValueRes, parseCommentFreeFileMsg, parseString, specConstant)
import Language.SMT2.Syntax (Symbol, SpecConstant(..), GeneralRes(..), Term(..), QualIdentifier(..), Identifier(..), Sort(..), Index(..), VarBinding(..))
import Numeric (readHex, readBin)
import Witch (into, unsafeInto)
import EVM.Format (formatProp)
import EVM.CSE
import EVM.Expr (writeByte, bufLengthEnv, bufLength, minLength, inRange)
import EVM.Expr qualified as Expr
import EVM.Keccak (keccakAssumptions, concreteKeccaks, findKeccakPropsExprs)
import EVM.Traversals
import EVM.Types
import EVM.Effects
import EVM.SMT.Types
import EVM.SMT.SMTLIB
-- ** Encoding ** ----------------------------------------------------------------------------------
-- | Attempts to collapse a compressed buffer representation down to a flattened one
collapse :: BufModel -> Maybe BufModel
collapse model = case toBuf model of
Just (ConcreteBuf b) -> Just $ Flat b
_ -> Nothing
where
toBuf (Comp (Base b sz)) | sz <= 120_000_000 = Just . ConcreteBuf $ BS.replicate (unsafeInto sz) b
toBuf (Comp (Write b idx next)) = fmap (writeByte (Lit idx) (LitByte b)) (toBuf $ Comp next)
toBuf (Flat b) = Just . ConcreteBuf $ b
toBuf _ = Nothing
getVar :: SMTCex -> TS.Text -> W256
getVar cex name = fromJust $ Map.lookup (Var name) cex.vars
formatSMT2 :: SMT2 -> Text
formatSMT2 (SMT2 (SMTScript entries) _ ps) = expr <> smt2
where
expr = T.concat [T.singleton ';', T.replace "\n" "\n;" $ T.pack . TS.unpack $ TS.unlines (fmap formatProp ps)]
smt2 = T.unlines (fmap toText entries)
-- | Reads all intermediate variables from the builder state and produces SMT declaring them as constants
declareIntermediates :: BufEnv -> StoreEnv -> Err [SMTEntry]
declareIntermediates bufs stores = do
let encSs = Map.mapWithKey encodeStore stores
encBs = Map.mapWithKey encodeBuf bufs
snippets <- sequence $ Map.elems $ encSs <> encBs
let decls = concat snippets
pure $ (SMTComment "intermediate buffers & stores") : decls
where
encodeBuf n expr = do
buf <- exprToSMT expr
bufLen <- encodeBufLen n expr
pure [SMTCommand ("(define-fun buf" <> (Data.Text.Lazy.Builder.Int.decimal n) <> "() Buf " <> buf <> ")\n"), bufLen]
encodeBufLen n expr = do
bufLen <- exprToSMT (bufLengthEnv bufs True expr)
pure $ SMTCommand ("(define-fun buf" <> (Data.Text.Lazy.Builder.Int.decimal n) <>"_length () (_ BitVec 256) " <> bufLen <> ")")
encodeStore n expr = do
storage <- exprToSMT expr
pure [SMTCommand ("(define-fun store" <> (Data.Text.Lazy.Builder.Int.decimal n) <> " () Storage " <> storage <> ")")]
-- simplify to rewrite sload/sstore combos
-- notice: it is VERY important not to concretize early, because Keccak assumptions
-- need unconcretized Props
assertProps :: Config -> [Prop] -> Err SMT2
assertProps conf ps =
if not conf.simp then assertPropsHelper False ps
else assertPropsHelper True (decompose ps)
where
decompose :: [Prop] -> [Prop]
decompose props = if conf.decomposeStorage && safeExprs && safeProps
then fromMaybe props (mapM (mapPropM Expr.decomposeStorage) props)
else props
where
-- All in these lists must be a `Just ()` or we cannot decompose
safeExprs = all (isJust . mapPropM_ Expr.safeToDecompose) props
safeProps = all Expr.safeToDecomposeProp props
-- Note: we need a version that does NOT call simplify,
-- because we make use of it to verify the correctness of our simplification
-- passes through property-based testing.
assertPropsHelper :: Bool -> [Prop] -> Err SMT2
assertPropsHelper simp psPreConc = do
encs <- mapM propToSMT psElim
intermediates <- declareIntermediates bufs stores
readAssumes' <- readAssumes
keccakAssertions' <- keccakAssertions
frameCtxs <- (declareFrameContext . nubOrd $ foldl' (<>) [] frameCtx)
blockCtxs <- (declareBlockContext . nubOrd $ foldl' (<>) [] blockCtx)
pure $ prelude
<> SMT2 (SMTScript (declareAbstractStores abstractStores)) mempty mempty
<> declareConstrainAddrs addresses
<> (declareBufs toDeclarePsElim bufs stores)
<> (declareVars . nubOrd $ foldl' (<>) [] allVars)
<> frameCtxs
<> blockCtxs
<> SMT2 (SMTScript intermediates) mempty mempty
<> SMT2 (SMTScript keccakAssertions') mempty mempty
<> SMT2 (SMTScript readAssumes') mempty mempty
<> SMT2 (SMTScript gasOrder) mempty mempty
<> SMT2 (SMTScript (fmap (\p -> SMTCommand("(assert " <> p <> ")")) encs)) (cexInfo storageReads) ps
where
ps = if simp then Expr.concKeccakSimpProps psPreConc else Expr.concKeccakProps psPreConc
(psElim, bufs, stores) = eliminateProps ps
-- Props storing info that need declaration(s)
toDeclarePs = ps <> keccAssump <> keccComp
toDeclarePsElim = psElim <> keccAssump <> keccComp
-- vars, frames, and block contexts in need of declaration
allVars = fmap referencedVars toDeclarePsElim <> fmap referencedVars bufVals <> fmap referencedVars storeVals
frameCtx = fmap referencedFrameContext toDeclarePsElim <> fmap referencedFrameContext bufVals <> fmap referencedFrameContext storeVals
blockCtx = fmap referencedBlockContext toDeclarePsElim <> fmap referencedBlockContext bufVals <> fmap referencedBlockContext storeVals
gasOrder = enforceGasOrder psPreConc
-- Buf, Storage, etc. declarations needed
bufVals = Map.elems bufs
storeVals = Map.elems stores
storageReads = mconcat $ fmap findStorageReads toDeclarePs
abstractStores = Set.toList $ Set.unions (fmap referencedAbstractStores toDeclarePs)
addresses = Set.toList $ Set.unions (fmap referencedAddrs toDeclarePs)
-- Keccak assertions: concrete values, distance between pairs, injectivity, etc.
-- This will make sure concrete values of Keccak are asserted, if they can be computed (i.e. can be concretized)
concreteKecc = concreteKeccaks psPreConc
allKeccaks = (findKeccakPropsExprs psElim bufVals storeVals) <> Set.map (Keccak . fst) concreteKecc
keccAssump = keccakAssumptions $ Set.toList allKeccaks
keccComp = [(PEq (Lit l) (Keccak buf)) | (buf, l) <- Set.toList concreteKecc]
keccakAssertions = do
assumps <- mapM assertSMT keccAssump
comps <- mapM assertSMT keccComp
pure $ ((SMTComment "keccak assumptions") : assumps) <> ((SMTComment "keccak computations") : comps)
-- assert that reads beyond size of buffer & storage is zero
readAssumes = do
assumps <- mapM assertSMT $ assertReads psElim bufs stores
pure (SMTComment "read assumptions" : assumps)
cexInfo :: StorageReads -> CexVars
cexInfo a = mempty { storeReads = a }
referencedAbstractStores :: TraversableTerm a => a -> Set Builder
referencedAbstractStores term = foldTerm go mempty term
where
go = \case
AbstractStore s idx -> Set.singleton (storeName s idx)
_ -> mempty
referencedAddrs :: TraversableTerm a => a -> Set Builder
referencedAddrs term = foldTerm go mempty term
where
go = \case
SymAddr a -> Set.singleton (formatEAddr (SymAddr a))
_ -> mempty
referencedBufs :: TraversableTerm a => a -> [Builder]
referencedBufs expr = nubOrd $ foldTerm go [] expr
where
go :: Expr a -> [Builder]
go = \case
AbstractBuf s -> [fromText s]
_ -> []
referencedVars :: TraversableTerm a => a -> [Builder]
referencedVars expr = nubOrd $ foldTerm go [] expr
where
go :: Expr a -> [Builder]
go = \case
Var s -> [fromText s]
_ -> []
referencedFrameContext :: TraversableTerm a => a -> [(Builder, [Prop])]
referencedFrameContext expr = nubOrd $ foldTerm go [] expr
where
go :: Expr a -> [(Builder, [Prop])]
go = \case
o@TxValue -> [(fromRight' $ exprToSMT o, [])]
o@(Balance _) -> [(fromRight' $ exprToSMT o, [PLT o (Lit $ 2 ^ (96 :: Int))])]
o@(Gas _ _) -> [(fromRight' $ exprToSMT o, [])]
o@(CodeHash (LitAddr _)) -> [(fromRight' $ exprToSMT o, [])]
_ -> []
referencedBlockContext :: TraversableTerm a => a -> [(Builder, [Prop])]
referencedBlockContext expr = nubOrd $ foldTerm go [] expr
where
go :: Expr a -> [(Builder, [Prop])]
go = \case
Origin -> [("origin", [inRange 160 Origin])]
Coinbase -> [("coinbase", [inRange 160 Coinbase])]
Timestamp -> [("timestamp", [])]
BlockNumber -> [("blocknumber", [])]
PrevRandao -> [("prevrandao", [])]
GasLimit -> [("gaslimit", [])]
ChainId -> [("chainid", [])]
BaseFee -> [("basefee", [])]
_ -> []
-- | This function overapproximates the reads from the abstract
-- storage. Potentially, it can return locations that do not read a
-- slot directly from the abstract store but from subsequent writes on
-- the store (e.g, SLoad addr idx (SStore addr idx val AbstractStore)).
-- However, we expect that most of such reads will have been
-- simplified away.
findStorageReads :: Prop -> StorageReads
findStorageReads p = foldProp go mempty p
where
go :: Expr a -> StorageReads
go = \case
SLoad slot store | baseIsAbstractStore store -> case Expr.getAddr store of
Nothing -> internalError $ "could not extract address from: " <> show store
Just address -> StorageReads $ Map.singleton (address, Expr.getLogicalIdx store) (Set.singleton slot)
_ -> mempty
baseIsAbstractStore :: Expr 'Storage -> Bool
baseIsAbstractStore (AbstractStore _ _) = True
baseIsAbstractStore (ConcreteStore _) = False
baseIsAbstractStore (SStore _ _ base) = baseIsAbstractStore base
baseIsAbstractStore (GVar _) = internalError "Unexpected GVar"
findBufferAccess :: TraversableTerm a => [a] -> [(Expr EWord, Expr EWord, Expr Buf)]
findBufferAccess = foldl' (foldTerm go) mempty
where
go :: Expr a -> [(Expr EWord, Expr EWord, Expr Buf)]
go = \case
ReadWord idx buf -> [(idx, Lit 32, buf)]
ReadByte idx buf -> [(idx, Lit 1, buf)]
CopySlice srcOff _ size src _ -> [(srcOff, size, src)]
_ -> mempty
-- | Asserts that buffer reads beyond the size of the buffer are equal
-- to zero. Looks for buffer reads in the a list of given predicates
-- and the buffer and storage environments.
assertReads :: [Prop] -> BufEnv -> StoreEnv -> [Prop]
assertReads props benv senv = nubOrd $ concatMap assertRead allReads
where
assertRead :: (Expr EWord, Expr EWord, Expr Buf) -> [Prop]
assertRead (_, Lit 0, _) = []
assertRead (idx, Lit sz, buf) = [PImpl (PGEq (Expr.add idx $ Lit offset) (bufLength buf)) (PEq (ReadByte (Expr.add idx $ Lit offset) buf) (LitByte 0)) | offset <- [(0::W256).. sz-1]]
assertRead (_, _, _) = internalError "Cannot generate assertions for accesses of symbolic size"
allReads = filter keepRead $ nubOrd $ findBufferAccess props <> findBufferAccess (Map.elems benv) <> findBufferAccess (Map.elems senv)
-- discard constraints if we can statically determine that read is less than the buffer length
keepRead (Lit idx, Lit size, buf) =
case minLength benv buf of
Just l | into (idx + size) <= l -> False
_ -> True
keepRead _ = True
-- | Finds the maximum read index for each abstract buffer in the input props
discoverMaxReads :: [Prop] -> BufEnv -> StoreEnv -> Map Text (Expr EWord)
discoverMaxReads props benv senv = bufMap
where
allReads = nubOrd $ findBufferAccess props <> findBufferAccess (Map.elems benv) <> findBufferAccess (Map.elems senv)
-- we can have buffers that are not read from but are still mentioned via BufLength in some branch condition
-- we assign a default read hint of 4 to start with in these cases (since in most cases we will need at least 4 bytes to produce a counterexample)
allBufs = Map.fromList . fmap (, Lit 4) . fmap toLazyText . nubOrd . concat $ fmap referencedBufs props <> fmap referencedBufs (Map.elems benv) <> fmap referencedBufs (Map.elems senv)
bufMap = Map.unionWith Expr.max (foldl' addBound mempty allReads) allBufs
addBound m (idx, size, buf) =
case baseBuf buf of
AbstractBuf b -> Map.insertWith Expr.max (T.fromStrict b) (Expr.add idx size) m
_ -> m
baseBuf :: Expr Buf -> Expr Buf
baseBuf (AbstractBuf b) = AbstractBuf b
baseBuf (ConcreteBuf b) = ConcreteBuf b
baseBuf (GVar (BufVar a)) =
case Map.lookup a benv of
Just b -> baseBuf b
Nothing -> internalError "could not find buffer variable"
baseBuf (WriteByte _ _ b) = baseBuf b
baseBuf (WriteWord _ _ b) = baseBuf b
baseBuf (CopySlice _ _ _ _ dst)= baseBuf dst
-- | Returns an SMT2 object with all buffers referenced from the input props declared, and with the appropriate cex extraction metadata attached
declareBufs :: [Prop] -> BufEnv -> StoreEnv -> SMT2
declareBufs props bufEnv storeEnv = SMT2 (SMTScript ((SMTComment "buffers") : fmap declareBuf allBufs <> ((SMTComment "buffer lengths") : fmap declareLength allBufs))) cexvars mempty
where
cexvars = (mempty :: CexVars){ buffers = discoverMaxReads props bufEnv storeEnv }
allBufs = fmap fromLazyText $ Map.keys cexvars.buffers
declareBuf n = SMTCommand $ "(declare-fun " <> n <> " () (Array (_ BitVec 256) (_ BitVec 8)))"
declareLength n = SMTCommand $ "(declare-fun " <> n <> "_length" <> " () (_ BitVec 256))"
-- Given a list of variable names, create an SMT2 object with the variables declared
declareVars :: [Builder] -> SMT2
declareVars names = SMT2 (SMTScript ([SMTComment "variables"] <> fmap declare names)) cexvars mempty
where
declare n = SMTCommand $ "(declare-fun " <> n <> " () (_ BitVec 256))"
cexvars = (mempty :: CexVars){ calldata = fmap toLazyText names }
-- Given a list of variable names, create an SMT2 object with the variables declared
declareConstrainAddrs :: [Builder] -> SMT2
declareConstrainAddrs names = SMT2 (SMTScript ([SMTComment "concrete and symbolic addresses"] <> fmap declare names <> fmap assume names)) cexvars mempty
where
declare n = SMTCommand $ "(declare-fun " <> n <> " () Addr)"
-- assume that symbolic addresses do not collide with the zero address or precompiles
assume n = SMTCommand $ "(assert (bvugt " <> n <> " (_ bv9 160)))"
cexvars = (mempty :: CexVars){ addrs = fmap toLazyText names }
-- The gas is a tuple of (prefix, index). Within each prefix, the gas is strictly decreasing as the
-- index increases. This function gets a map of Prefix -> [Int], and for each prefix,
-- enforces the order
enforceGasOrder :: [Prop] -> [SMTEntry]
enforceGasOrder ps = [SMTComment "gas ordering"] <> (concatMap (uncurry order) indices)
where
order :: TS.Text -> [Int] -> [SMTEntry]
order prefix n = consecutivePairs (nubInt n) >>= \(x, y)->
-- The GAS instruction itself costs gas, so it's strictly decreasing
[SMTCommand $ "(assert (bvugt " <> fromRight' (exprToSMT (Gas prefix x)) <> " " <>
fromRight' ((exprToSMT (Gas prefix y))) <> "))"]
consecutivePairs :: [Int] -> [(Int, Int)]
consecutivePairs [] = []
consecutivePairs l@(_:t) = zip l t
indices = Map.toList $ toMapOfLists $ concatMap (foldProp go mempty) ps
toMapOfLists :: [(TS.Text, Int)] -> Map.Map TS.Text [Int]
toMapOfLists = foldr (\(k, v) acc -> Map.insertWith (++) k [v] acc) Map.empty
go :: Expr a -> [(TS.Text, Int)]
go e = case e of
Gas prefix v -> [(prefix, v)]
_ -> []
declareFrameContext :: [(Builder, [Prop])] -> Err SMT2
declareFrameContext names = do
decls <- concatMapM declare names
pure $ SMT2 (SMTScript ([SMTComment "frame context"] <> decls)) cexvars mempty
where
declare (n,props) = do
asserts <- mapM assertSMT props
pure $ (SMTCommand $ "(declare-fun " <> n <> " () (_ BitVec 256))") : asserts
cexvars = (mempty :: CexVars){ txContext = fmap (toLazyText . fst) names }
declareAbstractStores :: [Builder] -> [SMTEntry]
declareAbstractStores names = [SMTComment "abstract base stores"] <> fmap declare names
where
declare n = SMTCommand $ "(declare-fun " <> n <> " () Storage)"
declareBlockContext :: [(Builder, [Prop])] -> Err SMT2
declareBlockContext names = do
decls <- concatMapM declare names
pure $ SMT2 (SMTScript ([SMTComment "block context"] <> decls)) cexvars mempty
where
declare (n, props) = do
asserts <- mapM assertSMT props
pure $ [ SMTCommand $ "(declare-fun " <> n <> " () (_ BitVec 256))" ] <> asserts
cexvars = (mempty :: CexVars){ blockContext = fmap (toLazyText . fst) names }
assertSMT :: Prop -> Either String SMTEntry
assertSMT p = do
p' <- propToSMT p
pure $ SMTCommand ("(assert " <> p' <> ")")
wordAsBV :: forall a. Integral a => a -> Builder
wordAsBV w = "(_ bv" <> Data.Text.Lazy.Builder.Int.decimal w <> " 256)"
byteAsBV :: Word8 -> Builder
byteAsBV b = "(_ bv" <> Data.Text.Lazy.Builder.Int.decimal b <> " 8)"
exprToSMT :: Expr a -> Err Builder
exprToSMT = \case
Lit w -> pure $ wordAsBV w
Var s -> pure $ fromText s
GVar (BufVar n) -> pure $ fromString $ "buf" <> (show n)
GVar (StoreVar n) -> pure $ fromString $ "store" <> (show n)
JoinBytes
z o two three four five six seven
eight nine ten eleven twelve thirteen fourteen fifteen
sixteen seventeen eighteen nineteen twenty twentyone twentytwo twentythree
twentyfour twentyfive twentysix twentyseven twentyeight twentynine thirty thirtyone
-> concatBytes [
z, o, two, three, four, five, six, seven
, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen
, sixteen, seventeen, eighteen, nineteen, twenty, twentyone, twentytwo, twentythree
, twentyfour, twentyfive, twentysix, twentyseven, twentyeight, twentynine, thirty, thirtyone]
Add a b -> op2 "bvadd" a b
Sub a b -> op2 "bvsub" a b
Mul a b -> op2 "bvmul" a b
Exp a b -> case a of
Lit 0 -> do
benc <- exprToSMT b
pure $ "(ite (= " <> benc `sp` zero <> " ) " <> one `sp` zero <> ")"
Lit 1 -> pure one
Lit 2 -> do
benc <- exprToSMT b
pure $ "(bvshl " <> one `sp` benc <> ")"
_ -> case b of
-- b is limited below, otherwise SMT query will be huge, and eventually Haskell stack overflows
Lit b' | b' < 1000 -> expandExp a b'
_ -> Left $ "Cannot encode symbolic exponent into SMT. Offending symbolic value: " <> show b
Min a b -> do
aenc <- exprToSMT a
benc <- exprToSMT b
pure $ "(ite (bvule " <> aenc `sp` benc <> ") " <> aenc `sp` benc <> ")"
Max a b -> do
aenc <- exprToSMT a
benc <- exprToSMT b
pure $ "(max " <> aenc `sp` benc <> ")"
LT a b -> do
cond <- op2 "bvult" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
SLT a b -> do
cond <- op2 "bvslt" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
SGT a b -> do
cond <- op2 "bvsgt" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
GT a b -> do
cond <- op2 "bvugt" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
LEq a b -> do
cond <- op2 "bvule" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
GEq a b -> do
cond <- op2 "bvuge" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
Eq a b -> do
cond <- op2 "=" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
IsZero a -> do
cond <- op2 "=" a (Lit 0)
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
ITE c t f -> do
condEnc <- exprToSMT c
thenEnc <- exprToSMT t
elseEnc <- exprToSMT f
pure $ "(ite (distinct " <> condEnc `sp` zero <> ") " <> thenEnc `sp` elseEnc <> ")"
And a b -> op2 "bvand" a b
Or a b -> op2 "bvor" a b
Xor a b -> op2 "bvxor" a b
Not a -> op1 "bvnot" a
SHL a b -> op2 "bvshl" b a
SHR a b -> op2 "bvlshr" b a
SAR a b -> op2 "bvashr" b a
CLZ a -> op1 "clz256" a
SEx a b -> op2 "signext" a b
Div a b -> op2CheckZero "bvudiv" a b
SDiv a b -> op2CheckZero "bvsdiv" a b
Mod a b -> op2CheckZero "bvurem" a b
SMod a b -> op2CheckZero "bvsrem" a b
-- NOTE: this needs to do the MUL at a higher precision, then MOD, then downcast
MulMod a b c -> do
aExp <- exprToSMT a
bExp <- exprToSMT b
cExp <- exprToSMT c
let aLift = "((_ zero_extend 256) " <> aExp <> ")"
bLift = "((_ zero_extend 256) " <> bExp <> ")"
cLift = "((_ zero_extend 256) " <> cExp <> ")"
pure $ "(ite (= " <> cExp <> " (_ bv0 256)) (_ bv0 256) ((_ extract 255 0) (bvurem (bvmul " <> aLift `sp` bLift <> ")" <> cLift <> ")))"
AddMod a b c -> do
aExp <- exprToSMT a
bExp <- exprToSMT b
cExp <- exprToSMT c
let aLift = "((_ zero_extend 1) " <> aExp <> ")"
bLift = "((_ zero_extend 1) " <> bExp <> ")"
cLift = "((_ zero_extend 1) " <> cExp <> ")"
pure $ "(ite (= " <> cExp <> " (_ bv0 256)) (_ bv0 256) ((_ extract 255 0) (bvurem (bvadd " <> aLift `sp` bLift <> ")" <> cLift <> ")))"
EqByte a b -> do
cond <- op2 "=" a b
pure $ "(ite " <> cond `sp` one `sp` zero <> ")"
Keccak a -> do
enc <- exprToSMT a
sz <- exprToSMT $ Expr.bufLength a
pure $ "(keccak " <> enc <> " " <> sz <> ")"
TxValue -> pure $ fromString "txvalue"
Balance a -> pure $ fromString "balance_" <> formatEAddr a
Origin -> pure "origin"
BlockHash a -> do
enc <- exprToSMT a
pure $ "(blockhash " <> enc <> ")"
CodeSize a -> do
enc <- exprToSMT a
pure $ "(codesize " <> enc <> ")"
Coinbase -> pure "coinbase"
Timestamp -> pure "timestamp"
BlockNumber -> pure "blocknumber"
PrevRandao -> pure "prevrandao"
GasLimit -> pure "gaslimit"
ChainId -> pure "chainid"
BaseFee -> pure "basefee"
a@(SymAddr _) -> pure $ formatEAddr a
WAddr(a@(SymAddr _)) -> do
wa <- exprToSMT a
pure $ "((_ zero_extend 96)" `sp` wa `sp` ")"
LitByte b -> pure $ byteAsBV b
IndexWord idx w -> case idx of
Lit n -> if n >= 0 && n < 32
then do
enc <- exprToSMT w
pure $ fromLazyText ("(indexWord" <> T.pack (show (into n :: Integer))) `sp` enc <> ")"
else exprToSMT (LitByte 0)
_ -> op2 "indexWord" idx w
ReadByte idx src -> op2 "select" src idx
ConcreteBuf "" -> pure "((as const Buf) #b00000000)"
ConcreteBuf bs -> writeBytes bs mempty
AbstractBuf s -> pure $ fromText s
ReadWord idx prev -> op2 "readWord" idx prev
BufLength (AbstractBuf b) -> pure $ fromText b <> "_length"
BufLength (GVar (BufVar n)) -> pure $ fromLazyText $ "buf" <> (T.pack . show $ n) <> "_length"
BufLength b -> exprToSMT (bufLength b)
WriteByte idx val prev -> do
encIdx <- exprToSMT idx
encVal <- exprToSMT val
encPrev <- exprToSMT prev
pure $ "(store " <> encPrev `sp` encIdx `sp` encVal <> ")"
WriteWord idx val prev -> do
encIdx <- exprToSMT idx
encVal <- exprToSMT val
encPrev <- exprToSMT prev
pure $ "(writeWord " <> encIdx `sp` encVal `sp` encPrev <> ")"
CopySlice srcIdx dstIdx size src dst -> do
srcSMT <- exprToSMT src
dstSMT <- exprToSMT dst
copySlice srcIdx dstIdx size srcSMT dstSMT
-- we need to do a bit of processing here.
ConcreteStore s -> encodeConcreteStore s
AbstractStore a idx -> pure $ storeName a idx
SStore idx val prev -> do
encIdx <- exprToSMT idx
encVal <- exprToSMT val
encPrev <- exprToSMT prev
pure $ "(store" `sp` encPrev `sp` encIdx `sp` encVal <> ")"
SLoad idx store -> op2 "select" store idx
LitAddr n -> pure $ fromLazyText $ "(_ bv" <> T.pack (show (into n :: Integer)) <> " 160)"
CodeHash a@(LitAddr _) -> pure $ fromLazyText "codehash_" <> formatEAddr a
Gas prefix var -> pure $ fromLazyText $ "gas_" <> T.pack (TS.unpack prefix) <> T.pack (show var)
a -> internalError $ "TODO: implement: " <> show a
where
op1 op a = do
enc <- exprToSMT a
pure $ "(" <> op `sp` enc <> ")"
op2 op a b = do
aenc <- exprToSMT a
benc <- exprToSMT b
pure $ "(" <> op `sp` aenc `sp` benc <> ")"
op2CheckZero op a b = do
aenc <- exprToSMT a
benc <- exprToSMT b
pure $ "(ite (= " <> benc <> " (_ bv0 256)) (_ bv0 256) " <> "(" <> op `sp` aenc `sp` benc <> "))"
sp :: Builder -> Builder -> Builder
a `sp` b = a <> (fromText " ") <> b
zero :: Builder
zero = "(_ bv0 256)"
one :: Builder
one = "(_ bv1 256)"
propToSMT :: Prop -> Err Builder
propToSMT = \case
PEq a b -> op2 "=" a b
PLT a b -> op2 "bvult" a b
PGT a b -> op2 "bvugt" a b
PLEq a b -> op2 "bvule" a b
PGEq a b -> op2 "bvuge" a b
PNeg a -> do
enc <- propToSMT a
pure $ "(not " <> enc <> ")"
PAnd a b -> do
aenc <- propToSMT a
benc <- propToSMT b
pure $ "(and " <> aenc <> " " <> benc <> ")"
POr a b -> do
aenc <- propToSMT a
benc <- propToSMT b
pure $ "(or " <> aenc <> " " <> benc <> ")"
PImpl a b -> do
aenc <- propToSMT a
benc <- propToSMT b
pure $ "(=> " <> aenc <> " " <> benc <> ")"
PBool b -> pure $ if b then "true" else "false"
where
op2 op a b = do
aenc <- exprToSMT a
benc <- exprToSMT b
pure $ "(" <> op <> " " <> aenc <> " " <> benc <> ")"
-- ** Helpers ** ---------------------------------------------------------------------------------
-- | Stores a region of src into dst
copySlice :: Expr EWord -> Expr EWord -> Expr EWord -> Builder -> Builder -> Err Builder
copySlice srcOffset dstOffset (Lit size) src dst = do
sz <- internal size
pure $ "(let ((src " <> src <> ")) " <> sz <> ")"
where
internal 0 = pure dst
internal idx = do
let idx' = idx - 1
encDstOff <- offset idx' dstOffset
encSrcOff <- offset idx' srcOffset
child <- internal idx'
pure $ "(store " <> child `sp` encDstOff `sp` "(select src " <> encSrcOff <> "))"
offset :: W256 -> Expr EWord -> Err Builder
offset o (Lit b) = pure $ wordAsBV $ o + b
offset o e = exprToSMT $ Expr.add (Lit o) e
copySlice _ _ _ _ _ = Left "CopySlice with a symbolically sized region not currently implemented, cannot execute SMT solver on this query"
-- | Unrolls an exponentiation into a series of multiplications
expandExp :: Expr EWord -> W256 -> Err Builder
expandExp base expnt
-- in EVM, anything (including 0) to the power of 0 is 1
| expnt == 0 = pure one
| expnt == 1 = exprToSMT base
| otherwise = do
b <- exprToSMT base
n <- expandExp base (expnt - 1)
pure $ "(bvmul " <> b `sp` n <> ")"
-- | Concatenates a list of bytes into a larger bitvector
concatBytes :: [Expr Byte] -> Err Builder
concatBytes bytes = do
case List.uncons $ reverse bytes of
Nothing -> Left "unexpected empty bytes"
Just (h, t) -> do
a2 <- exprToSMT h
foldM wrap a2 t
where
wrap :: Builder -> Expr a -> Err Builder
wrap inner byte = do
byteSMT <- exprToSMT byte
pure $ "(concat " <> byteSMT `sp` inner <> ")"
-- | Concatenates a list of bytes into a larger bitvector
writeBytes :: ByteString -> Expr Buf -> Err Builder
writeBytes bytes buf = do
smtText <- exprToSMT buf
let ret = BS.foldl wrap (0, smtText) bytes
pure $ snd ret
where
-- we don't need to store zeros if the base buffer is empty
skipZeros = buf == mempty
wrap :: (Int, Builder) -> Word8 -> (Int, Builder)
wrap (idx, acc) byte =
if skipZeros && byte == 0
then (idx', acc)
else (idx', "(store " <> acc `sp` (wordAsBV idx) `sp` (byteAsBV byte) <> ")")
where
!idx' = idx + 1
encodeConcreteStore :: Map W256 W256 -> Err Builder
encodeConcreteStore s = foldM encodeWrite ("((as const Storage) #x0000000000000000000000000000000000000000000000000000000000000000)") (Map.toList s)
where
encodeWrite :: Builder -> (W256, W256) -> Err Builder
encodeWrite prev (key, val) = do
encKey <- exprToSMT $ Lit key
encVal <- exprToSMT $ Lit val
pure $ "(store " <> prev `sp` encKey `sp` encVal <> ")"
storeName :: Expr EAddr -> Maybe W256 -> Builder
storeName a Nothing = fromString ("baseStore_") <> formatEAddr a
storeName a (Just idx) = fromString ("baseStore_") <> formatEAddr a <> "_" <> (fromString $ show idx)
formatEAddr :: Expr EAddr -> Builder
formatEAddr = \case
LitAddr a -> fromString ("litaddr_" <> show a)
SymAddr a -> fromText ("symaddr_" <> a)
GVar _ -> internalError "Unexpected GVar"
-- ** Cex parsing ** --------------------------------------------------------------------------------
parseAddr :: SpecConstant -> Addr
parseAddr = parseSC
parseW256 :: SpecConstant -> W256
parseW256 = parseSC
parseW8 :: SpecConstant -> Word8
parseW8 = parseSC
readOrError :: (Num a, Eq a) => ReadS a -> TS.Text -> a
readOrError reader val = fst . headErr . reader . T.unpack . T.fromStrict $ val
where
headErr x = fromMaybe (internalError "error reading empty result") $ listToMaybe x
parseSC :: (Num a, Eq a) => SpecConstant -> a
parseSC (SCHexadecimal a) = readOrError Numeric.readHex a
parseSC (SCBinary a) = readOrError Numeric.readBin a
parseSC sc = internalError $ "cannot parse: " <> show sc
parseVar :: TS.Text -> Expr EWord
parseVar = Var
parseEAddr :: TS.Text -> Expr EAddr
parseEAddr name
| Just a <- TS.stripPrefix "litaddr_" name = LitAddr (read (TS.unpack a))
| Just a <- TS.stripPrefix "symaddr_" name = SymAddr a
| otherwise = internalError $ "cannot parse: " <> show name
parseBlockCtx :: TS.Text -> Expr EWord
parseBlockCtx "origin" = Origin
parseBlockCtx "coinbase" = Coinbase
parseBlockCtx "timestamp" = Timestamp
parseBlockCtx "blocknumber" = BlockNumber
parseBlockCtx "prevrandao" = PrevRandao
parseBlockCtx "gaslimit" = GasLimit
parseBlockCtx "chainid" = ChainId
parseBlockCtx "basefee" = BaseFee
parseBlockCtx val = internalError $ "cannot parse '" <> (TS.unpack val) <> "' into an Expr"
parseTxCtx :: TS.Text -> Expr EWord
parseTxCtx name
| name == "txvalue" = TxValue
| Just a <- TS.stripPrefix "balance_" name = Balance (parseEAddr a)
| Just a <- TS.stripPrefix "codehash_" name = CodeHash (parseEAddr a)
| otherwise = internalError $ "cannot parse " <> (TS.unpack name) <> " into an Expr"
type ValGetter = Text -> MaybeIO Text
getAddrs :: (TS.Text -> Expr EAddr) -> ValGetter -> [TS.Text] -> MaybeIO (Map (Expr EAddr) Addr)
getAddrs parseName getVal names = do
m <- foldM (getOne parseAddr getVal) mempty names
pure $ Map.mapKeys parseName m
getVars :: (TS.Text -> Expr EWord) -> ValGetter -> [TS.Text] -> MaybeIO (Map (Expr EWord) W256)
getVars parseName getVal names = do
m <- foldM (getOne parseW256 getVal) mempty names
pure $ Map.mapKeys parseName m
getOne :: (SpecConstant -> a) -> ValGetter -> Map TS.Text a -> TS.Text -> MaybeIO (Map TS.Text a)
getOne parseVal getVal acc name = do
raw <- getVal (T.fromStrict name)
val <- hoistMaybe $ do
Right (ResSpecific (valParsed :| [])) <- pure $ parseCommentFreeFileMsg getValueRes (T.toStrict raw)
(TermQualIdentifier (Unqualified (IdSymbol symbol)), TermSpecConstant sc) <- pure valParsed
guard (symbol == name)
pure $ parseVal sc
pure $ Map.insert name val acc
-- | Queries the solver for models for each of the expressions representing the
-- max read index for a given buffer
queryMaxReads :: ValGetter -> Map Text (Expr EWord) -> MaybeIO (Map Text W256)
queryMaxReads getVal maxReads = mapM (queryValue getVal) maxReads
-- | Gets the initial model for each buffer, these will often be much too large for our purposes
getBufs :: ValGetter -> [Text] -> MaybeIO (Map (Expr Buf) BufModel)
getBufs getVal bufs = foldM getBuf mempty bufs
where
getLength :: Text -> MaybeIO W256
getLength name = do
val <- getVal (name <> "_length ")
hoistMaybe $ do
Right (ResSpecific (parsed :| [])) <- pure $ parseCommentFreeFileMsg getValueRes (T.toStrict val)
(TermQualIdentifier (Unqualified (IdSymbol symbol)), TermSpecConstant sc) <- pure parsed
guard (symbol == T.toStrict (name <> "_length"))
pure $ parseW256 sc
getBuf :: Map (Expr Buf) BufModel -> Text -> MaybeIO (Map (Expr Buf) BufModel)
getBuf acc name = do
len <- getLength name
val <- getVal name
buf <- hoistMaybe $ do
Right (ResSpecific (valParsed :| [])) <- pure $ parseCommentFreeFileMsg getValueRes (T.toStrict val)
(TermQualIdentifier (Unqualified (IdSymbol symbol)), term) <- pure valParsed
guard (T.fromStrict symbol == name)
parseBuf len term
pure $ Map.insert (AbstractBuf $ T.toStrict name) buf acc
parseBuf :: W256 -> Term -> Maybe BufModel
parseBuf len term = Comp <$> go mempty term
where
go env = \case
-- constant arrays
(TermApplication (
Qualified (IdSymbol "const") (
SortParameter (IdSymbol "Array") (
SortSymbol (IdIndexed "BitVec" (IxNumeral "256" :| []))
:| [SortSymbol (IdIndexed "BitVec" (IxNumeral "8" :| []))]
)
)) ((TermSpecConstant val :| [])))
-> Just $ Base (parseW8 val) len
-- writing a byte over some array
(TermApplication
(Unqualified (IdSymbol "store"))
(base :| [TermSpecConstant idx, TermSpecConstant val])
) -> do
pbase <- go env base
let pidx = parseW256 idx
pval = parseW8 val
Just $ Write pval pidx pbase
-- binding a new name
(TermLet ((VarBinding name' bound) :| []) term') -> do
pbound <- go env bound
go (Map.insert name' pbound env) term'
-- looking up a bound name
(TermQualIdentifier (Unqualified (IdSymbol name'))) ->
Map.lookup name' env
_ -> Nothing
-- | Takes a Map containing all reads from a store with an abstract base, as
-- well as the concrete part of the storage prestate and returns a fully
-- concretized storage
getStore
:: ValGetter
-> StorageReads
-> MaybeIO (Map (Expr EAddr) (Map W256 W256))
getStore getVal (StorageReads innerMap) = do
results <- forM (Map.toList innerMap) $ \((addr, idx), slots) -> do
let name = toLazyText (storeName addr idx)
raw <- getVal name
fun <- hoistMaybe $ do
Right (ResSpecific (valParsed :| [])) <- pure $ parseCommentFreeFileMsg getValueRes (T.toStrict raw)
(TermQualIdentifier (Unqualified (IdSymbol symbol)), term) <- pure valParsed
guard (symbol == T.toStrict name)
pure $ interpret1DArray Map.empty term
-- create a map by adding only the locations that are read by the program
store <- foldM (\m slot -> do
slot' <- queryValue getVal slot
pure $ Map.insert slot' (fun slot') m) Map.empty (Set.toList slots)
pure (addr, store)
pure $ Map.fromList results
-- | Ask the solver to give us the concrete value of an arbitrary abstract word
queryValue :: ValGetter -> Expr EWord -> MaybeIO W256
queryValue _ (Lit w) = pure w
queryValue getVal w = do
-- this exprToSMT should never fail, since we have already ran the solver
let expr = toLazyText $ fromRight' $ exprToSMT w
raw <- getVal expr
hoistMaybe $ do
valTxt <- extractValue raw
Right sc <- pure $ parseString specConstant (T.toStrict valTxt)
pure $ parseW256 sc
where
extractValue :: Text -> Maybe Text
extractValue getValResponse = (T.stripSuffix "))") $ snd $ T.breakOnEnd " " $ T.stripEnd getValResponse
-- | Interpret an N-dimensional array as a value of type a.
-- Parameterized by an interpretation function for array values.
interpretNDArray :: (Map Symbol Term -> Term -> a) -> (Map Symbol Term) -> Term -> (W256 -> a)
interpretNDArray interp env = \case
-- variable reference
TermQualIdentifier (Unqualified (IdSymbol s)) ->
case Map.lookup s env of
Just t -> interpretNDArray interp env t
Nothing -> internalError "unknown identifier, cannot parse array"
-- (let (x t') t)
TermLet (VarBinding x t' :| []) t -> interpretNDArray interp (Map.insert x t' env) t
TermLet (VarBinding x t' :| lets) t -> interpretNDArray interp (Map.insert x t' env) (TermLet (NonEmpty.fromList lets) t)
-- (as const (Array (_ BitVec 256) (_ BitVec 256))) SpecConstant
TermApplication asconst (val :| []) | isArrConst asconst ->
\_ -> interp env val
-- (store arr ind val)
TermApplication store (arr :| [TermSpecConstant ind, val]) | isStore store ->
\x -> if x == parseW256 ind then interp env val else interpretNDArray interp env arr x
t -> internalError $ "cannot parse array value. Unexpected term: " <> (show t)
where
isArrConst :: QualIdentifier -> Bool
isArrConst = \case
Qualified (IdSymbol "const") (SortParameter (IdSymbol "Array") _) -> True
_ -> False
isStore :: QualIdentifier -> Bool
isStore t = t == Unqualified (IdSymbol "store")
-- | Interpret an 1-dimensional array as a function
interpret1DArray :: (Map Symbol Term) -> Term -> (W256 -> W256)
interpret1DArray = interpretNDArray interpretW256
where
interpretW256 :: (Map Symbol Term) -> Term -> W256
interpretW256 _ (TermSpecConstant val) = parseW256 val
interpretW256 env (TermQualIdentifier (Unqualified (IdSymbol s))) =
case Map.lookup s env of
Just t -> interpretW256 env t
Nothing -> internalError "unknown identifier, cannot parse array"
interpretW256 _ t = internalError $ "cannot parse array value. Unexpected term: " <> (show t)
hoistMaybe :: Monad m => Maybe a -> MaybeT m a
hoistMaybe = MaybeT . pure