hevm-0.50.0: src/EVM/SMT.hs
{-# Language DataKinds #-}
{-# Language GADTs #-}
{-# Language PolyKinds #-}
{-# Language ScopedTypeVariables #-}
{-# Language TypeApplications #-}
{-# Language QuasiQuotes #-}
{- |
Module: EVM.SMT
Description: Utilities for building and executing SMT queries from Expr instances
-}
module EVM.SMT where
import Prelude hiding (LT, GT)
import GHC.Natural
import Control.Monad
import GHC.IO.Handle (Handle, hFlush, hSetBuffering, BufferMode(..))
import Control.Concurrent.Chan (Chan, newChan, writeChan, readChan)
import Control.Concurrent (forkIO, killThread)
import Data.Char (isSpace)
import Data.Containers.ListUtils (nubOrd)
import Language.SMT2.Parser (getValueRes, parseCommentFreeFileMsg)
import Language.SMT2.Syntax (SpecConstant(..), GeneralRes(..), Term(..), QualIdentifier(..), Identifier(..), Sort(..), Index(..), VarBinding(..))
import Data.Word
import Numeric (readHex)
import Data.ByteString (ByteString)
import Data.Maybe (fromMaybe)
import qualified Data.ByteString as BS
import qualified Data.List as List
import Data.List.NonEmpty (NonEmpty((:|)))
import Data.String.Here
import Data.Maybe
import Data.Map (Map)
import qualified Data.Map as Map
import Data.Text.Lazy (Text)
import qualified Data.Text as TS
import qualified Data.Text.Lazy as T
import qualified Data.Text.Lazy.IO as T
import Data.Text.Lazy.Builder
import Data.Bifunctor (second)
import System.Process (createProcess, cleanupProcess, proc, ProcessHandle, std_in, std_out, std_err, StdStream(..))
import EVM.Types
import EVM.Traversals
import EVM.CSE
import EVM.Keccak
import EVM.Expr hiding (copySlice, writeWord, op1, op2, op3, drop)
-- ** Encoding ** ----------------------------------------------------------------------------------
-- variable names in SMT that we want to get values for
data CexVars = CexVars
{ calldataV :: [Text]
, buffersV :: [Text]
, blockContextV :: [Text]
, txContextV :: [Text]
}
deriving (Eq, Show)
instance Semigroup CexVars where
(CexVars a b c d) <> (CexVars a2 b2 c2 d2) = CexVars (a <> a2) (b <> b2) (c <> c2) (d <> d2)
instance Monoid CexVars where
mempty = CexVars
{ calldataV = mempty
, buffersV = mempty
, blockContextV = mempty
, txContextV = mempty
}
data SMTCex = SMTCex
{ vars :: Map (Expr EWord) W256
, buffers :: Map (Expr Buf) ByteString
, blockContext :: Map (Expr EWord) W256
, txContext :: Map (Expr EWord) W256
}
deriving (Eq, Show)
getVar :: EVM.SMT.SMTCex -> TS.Text -> W256
getVar cex name = fromJust $ Map.lookup (Var name) (vars cex)
data SMT2 = SMT2 [Builder] CexVars
deriving (Eq, Show)
instance Semigroup SMT2 where
(SMT2 a b) <> (SMT2 a2 b2) = SMT2 (a <> a2) (b <> b2)
instance Monoid SMT2 where
mempty = SMT2 mempty mempty
formatSMT2 :: SMT2 -> Text
formatSMT2 (SMT2 ls _) = T.unlines (fmap toLazyText ls)
-- | Reads all intermediate variables from the builder state and produces SMT declaring them as constants
declareIntermediates :: BufEnv -> StoreEnv -> SMT2
declareIntermediates bufs stores =
let encSs = Map.mapWithKey encodeStore stores
encBs = Map.mapWithKey encodeBuf bufs
sorted = List.sortBy compareFst $ Map.toList $ encSs <> encBs
decls = fmap snd sorted
in SMT2 ([fromText "; intermediate buffers & stores"] <> decls) mempty
where
compareFst (l, _) (r, _) = compare l r
encodeBuf n expr =
fromLazyText ("(define-const buf" <> (T.pack . show $ n) <> " Buf ") <> exprToSMT expr <> ")"
encodeStore n expr =
fromLazyText ("(define-const store" <> (T.pack . show $ n) <> " Storage ") <> exprToSMT expr <> ")"
assertProps :: [Prop] -> SMT2
assertProps ps =
let encs = map propToSMT ps_elim
intermediates = declareIntermediates bufs stores in
prelude
<> (declareBufs . nubOrd $ foldl (<>) [] allBufs)
<> SMT2 [""] mempty
<> (declareVars . nubOrd $ foldl (<>) [] allVars)
<> SMT2 [""] mempty
<> (declareFrameContext . nubOrd $ foldl (<>) [] frameCtx)
<> SMT2 [""] mempty
<> (declareBlockContext . nubOrd $ foldl (<>) [] blockCtx)
<> SMT2 [""] mempty
<> intermediates
<> SMT2 [""] mempty
<> keccakAssumes
<> SMT2 [""] mempty
<> SMT2 (fmap (\p -> "(assert " <> p <> ")") encs) mempty
where
(ps_elim, bufs, stores) = eliminateProps ps
allBufs = fmap referencedBufs' ps_elim <> fmap referencedBufs bufVals <> fmap referencedBufs storeVals
allVars = fmap referencedVars' ps_elim <> fmap referencedVars bufVals <> fmap referencedVars storeVals
frameCtx = fmap referencedFrameContext' ps_elim <> fmap referencedFrameContext bufVals <> fmap referencedFrameContext storeVals
blockCtx = fmap referencedBlockContext' ps_elim <> fmap referencedBlockContext bufVals <> fmap referencedBlockContext storeVals
bufVals = Map.elems bufs
storeVals = Map.elems stores
keccakAssumes
= SMT2 ["; keccak assumptions"] mempty
<> SMT2 (fmap (\p -> "(assert " <> propToSMT p <> ")") (keccakAssumptions ps_elim bufVals storeVals)) mempty
prelude :: SMT2
prelude = (flip SMT2) mempty $ fmap (fromLazyText . T.drop 2) . T.lines $ [i|
; logic
; TODO: this creates an error when used with z3?
;(set-logic QF_AUFBV)
(set-logic ALL)
; types
(define-sort Byte () (_ BitVec 8))
(define-sort Word () (_ BitVec 256))
(define-sort Buf () (Array Word Byte))
; address -> slot -> value
(define-sort Storage () (Array Word (Array Word Word)))
; hash functions
(declare-fun keccak (Buf) Word)
(declare-fun sha256 (Buf) Word)
; word indexing
(define-fun indexWord31 ((w Word)) Byte ((_ extract 7 0) w))
(define-fun indexWord30 ((w Word)) Byte ((_ extract 15 8) w))
(define-fun indexWord29 ((w Word)) Byte ((_ extract 23 16) w))
(define-fun indexWord28 ((w Word)) Byte ((_ extract 31 24) w))
(define-fun indexWord27 ((w Word)) Byte ((_ extract 39 32) w))
(define-fun indexWord26 ((w Word)) Byte ((_ extract 47 40) w))
(define-fun indexWord25 ((w Word)) Byte ((_ extract 55 48) w))
(define-fun indexWord24 ((w Word)) Byte ((_ extract 63 56) w))
(define-fun indexWord23 ((w Word)) Byte ((_ extract 71 64) w))
(define-fun indexWord22 ((w Word)) Byte ((_ extract 79 72) w))
(define-fun indexWord21 ((w Word)) Byte ((_ extract 87 80) w))
(define-fun indexWord20 ((w Word)) Byte ((_ extract 95 88) w))
(define-fun indexWord19 ((w Word)) Byte ((_ extract 103 96) w))
(define-fun indexWord18 ((w Word)) Byte ((_ extract 111 104) w))
(define-fun indexWord17 ((w Word)) Byte ((_ extract 119 112) w))
(define-fun indexWord16 ((w Word)) Byte ((_ extract 127 120) w))
(define-fun indexWord15 ((w Word)) Byte ((_ extract 135 128) w))
(define-fun indexWord14 ((w Word)) Byte ((_ extract 143 136) w))
(define-fun indexWord13 ((w Word)) Byte ((_ extract 151 144) w))
(define-fun indexWord12 ((w Word)) Byte ((_ extract 159 152) w))
(define-fun indexWord11 ((w Word)) Byte ((_ extract 167 160) w))
(define-fun indexWord10 ((w Word)) Byte ((_ extract 175 168) w))
(define-fun indexWord9 ((w Word)) Byte ((_ extract 183 176) w))
(define-fun indexWord8 ((w Word)) Byte ((_ extract 191 184) w))
(define-fun indexWord7 ((w Word)) Byte ((_ extract 199 192) w))
(define-fun indexWord6 ((w Word)) Byte ((_ extract 207 200) w))
(define-fun indexWord5 ((w Word)) Byte ((_ extract 215 208) w))
(define-fun indexWord4 ((w Word)) Byte ((_ extract 223 216) w))
(define-fun indexWord3 ((w Word)) Byte ((_ extract 231 224) w))
(define-fun indexWord2 ((w Word)) Byte ((_ extract 239 232) w))
(define-fun indexWord1 ((w Word)) Byte ((_ extract 247 240) w))
(define-fun indexWord0 ((w Word)) Byte ((_ extract 255 248) w))
; symbolic word indexing
; a bitshift based version might be more performant here...
(define-fun indexWord ((idx Word) (w Word)) Byte
(ite (bvuge idx (_ bv32 256)) (_ bv0 8)
(ite (= idx (_ bv31 256)) (indexWord31 w)
(ite (= idx (_ bv30 256)) (indexWord30 w)
(ite (= idx (_ bv29 256)) (indexWord29 w)
(ite (= idx (_ bv28 256)) (indexWord28 w)
(ite (= idx (_ bv27 256)) (indexWord27 w)
(ite (= idx (_ bv26 256)) (indexWord26 w)
(ite (= idx (_ bv25 256)) (indexWord25 w)
(ite (= idx (_ bv24 256)) (indexWord24 w)
(ite (= idx (_ bv23 256)) (indexWord23 w)
(ite (= idx (_ bv22 256)) (indexWord22 w)
(ite (= idx (_ bv21 256)) (indexWord21 w)
(ite (= idx (_ bv20 256)) (indexWord20 w)
(ite (= idx (_ bv19 256)) (indexWord19 w)
(ite (= idx (_ bv18 256)) (indexWord18 w)
(ite (= idx (_ bv17 256)) (indexWord17 w)
(ite (= idx (_ bv16 256)) (indexWord16 w)
(ite (= idx (_ bv15 256)) (indexWord15 w)
(ite (= idx (_ bv14 256)) (indexWord14 w)
(ite (= idx (_ bv13 256)) (indexWord13 w)
(ite (= idx (_ bv12 256)) (indexWord12 w)
(ite (= idx (_ bv11 256)) (indexWord11 w)
(ite (= idx (_ bv10 256)) (indexWord10 w)
(ite (= idx (_ bv9 256)) (indexWord9 w)
(ite (= idx (_ bv8 256)) (indexWord8 w)
(ite (= idx (_ bv7 256)) (indexWord7 w)
(ite (= idx (_ bv6 256)) (indexWord6 w)
(ite (= idx (_ bv5 256)) (indexWord5 w)
(ite (= idx (_ bv4 256)) (indexWord4 w)
(ite (= idx (_ bv3 256)) (indexWord3 w)
(ite (= idx (_ bv2 256)) (indexWord2 w)
(ite (= idx (_ bv1 256)) (indexWord1 w)
(indexWord0 w)
))))))))))))))))))))))))))))))))
)
; buffers
(declare-fun bufLength (Buf) Word)
(define-const emptyBuf Buf ((as const Buf) #b00000000))
(define-fun readWord ((idx Word) (buf Buf)) Word
(concat
(select buf idx)
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000001))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000002))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000003))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000004))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000005))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000006))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000007))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000008))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000009))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000000a))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000000b))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000000c))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000000d))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000000e))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000000f))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000010))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000011))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000012))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000013))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000014))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000015))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000016))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000017))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000018))
(select buf (bvadd idx #x0000000000000000000000000000000000000000000000000000000000000019))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000001a))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000001b))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000001c))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000001d))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000001e))
(select buf (bvadd idx #x000000000000000000000000000000000000000000000000000000000000001f))
)
)
(define-fun writeWord ((idx Word) (val Word) (buf Buf)) Buf
(store (store (store (store (store (store (store (store (store (store (store (store (store (store (store (store (store
(store (store (store (store (store (store (store (store (store (store (store (store (store (store (store buf
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000001f) (indexWord31 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000001e) (indexWord30 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000001d) (indexWord29 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000001c) (indexWord28 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000001b) (indexWord27 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000001a) (indexWord26 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000019) (indexWord25 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000018) (indexWord24 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000017) (indexWord23 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000016) (indexWord22 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000015) (indexWord21 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000014) (indexWord20 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000013) (indexWord19 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000012) (indexWord18 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000011) (indexWord17 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000010) (indexWord16 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000000f) (indexWord15 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000000e) (indexWord14 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000000d) (indexWord13 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000000c) (indexWord12 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000000b) (indexWord11 val))
(bvadd idx #x000000000000000000000000000000000000000000000000000000000000000a) (indexWord10 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000009) (indexWord9 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000008) (indexWord8 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000007) (indexWord7 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000006) (indexWord6 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000005) (indexWord5 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000004) (indexWord4 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000003) (indexWord3 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000002) (indexWord2 val))
(bvadd idx #x0000000000000000000000000000000000000000000000000000000000000001) (indexWord1 val))
idx (indexWord0 val))
)
; block context
(declare-fun blockhash (Word) Word)
; macros
(define-fun signext ( (b Word) (val Word)) Word
(ite (= b (_ bv0 256)) ((_ sign_extend 248) ((_ extract 7 0) val))
(ite (= b (_ bv1 256)) ((_ sign_extend 240) ((_ extract 15 0) val))
(ite (= b (_ bv2 256)) ((_ sign_extend 232) ((_ extract 23 0) val))
(ite (= b (_ bv3 256)) ((_ sign_extend 224) ((_ extract 31 0) val))
(ite (= b (_ bv4 256)) ((_ sign_extend 216) ((_ extract 39 0) val))
(ite (= b (_ bv5 256)) ((_ sign_extend 208) ((_ extract 47 0) val))
(ite (= b (_ bv6 256)) ((_ sign_extend 200) ((_ extract 55 0) val))
(ite (= b (_ bv7 256)) ((_ sign_extend 192) ((_ extract 63 0) val))
(ite (= b (_ bv8 256)) ((_ sign_extend 184) ((_ extract 71 0) val))
(ite (= b (_ bv9 256)) ((_ sign_extend 176) ((_ extract 79 0) val))
(ite (= b (_ bv10 256)) ((_ sign_extend 168) ((_ extract 87 0) val))
(ite (= b (_ bv11 256)) ((_ sign_extend 160) ((_ extract 95 0) val))
(ite (= b (_ bv12 256)) ((_ sign_extend 152) ((_ extract 103 0) val))
(ite (= b (_ bv13 256)) ((_ sign_extend 144) ((_ extract 111 0) val))
(ite (= b (_ bv14 256)) ((_ sign_extend 136) ((_ extract 119 0) val))
(ite (= b (_ bv15 256)) ((_ sign_extend 128) ((_ extract 127 0) val))
(ite (= b (_ bv16 256)) ((_ sign_extend 120) ((_ extract 135 0) val))
(ite (= b (_ bv17 256)) ((_ sign_extend 112) ((_ extract 143 0) val))
(ite (= b (_ bv18 256)) ((_ sign_extend 104) ((_ extract 151 0) val))
(ite (= b (_ bv19 256)) ((_ sign_extend 96 ) ((_ extract 159 0) val))
(ite (= b (_ bv20 256)) ((_ sign_extend 88 ) ((_ extract 167 0) val))
(ite (= b (_ bv21 256)) ((_ sign_extend 80 ) ((_ extract 175 0) val))
(ite (= b (_ bv22 256)) ((_ sign_extend 72 ) ((_ extract 183 0) val))
(ite (= b (_ bv23 256)) ((_ sign_extend 64 ) ((_ extract 191 0) val))
(ite (= b (_ bv24 256)) ((_ sign_extend 56 ) ((_ extract 199 0) val))
(ite (= b (_ bv25 256)) ((_ sign_extend 48 ) ((_ extract 207 0) val))
(ite (= b (_ bv26 256)) ((_ sign_extend 40 ) ((_ extract 215 0) val))
(ite (= b (_ bv27 256)) ((_ sign_extend 32 ) ((_ extract 223 0) val))
(ite (= b (_ bv28 256)) ((_ sign_extend 24 ) ((_ extract 231 0) val))
(ite (= b (_ bv29 256)) ((_ sign_extend 16 ) ((_ extract 239 0) val))
(ite (= b (_ bv30 256)) ((_ sign_extend 8 ) ((_ extract 247 0) val)) val))))))))))))))))))))))))))))))))
; storage
(declare-const abstractStore Storage)
(define-const emptyStore Storage ((as const Storage) ((as const (Array (_ BitVec 256) (_ BitVec 256))) #x0000000000000000000000000000000000000000000000000000000000000000)))
(define-fun sstore ((addr Word) (key Word) (val Word) (storage Storage)) Storage (store storage addr (store (select storage addr) key val)))
(define-fun sload ((addr Word) (key Word) (storage Storage)) Word (select (select storage addr) key))
|]
declareBufs :: [Builder] -> SMT2
declareBufs names = SMT2 ("; buffers" : fmap declareBuf names <> ("; buffer lengths" : fmap declareLength names)) cexvars
where
declareBuf n = "(declare-const " <> n <> " (Array (_ BitVec 256) (_ BitVec 8)))"
declareLength n = "(define-const " <> n <> "_length" <> " (_ BitVec 256) (bufLength " <> n <> "))"
cexvars = CexVars
{ calldataV = mempty
, buffersV = (fmap toLazyText names)
, blockContextV = mempty
, txContextV = mempty
}
referencedBufs :: Expr a -> [Builder]
referencedBufs expr = nubOrd (foldExpr go [] expr)
where
go :: Expr a -> [Builder]
go = \case
AbstractBuf s -> [fromText s]
_ -> []
referencedBufs' :: Prop -> [Builder]
referencedBufs' = \case
PEq a b -> nubOrd $ referencedBufs a <> referencedBufs b
PLT a b -> nubOrd $ referencedBufs a <> referencedBufs b
PGT a b -> nubOrd $ referencedBufs a <> referencedBufs b
PLEq a b -> nubOrd $ referencedBufs a <> referencedBufs b
PGEq a b -> nubOrd $ referencedBufs a <> referencedBufs b
PAnd a b -> nubOrd $ referencedBufs' a <> referencedBufs' b
POr a b -> nubOrd $ referencedBufs' a <> referencedBufs' b
PNeg a -> referencedBufs' a
PBool _ -> []
referencedVars' :: Prop -> [Builder]
referencedVars' = \case
PEq a b -> nubOrd $ referencedVars a <> referencedVars b
PLT a b -> nubOrd $ referencedVars a <> referencedVars b
PGT a b -> nubOrd $ referencedVars a <> referencedVars b
PLEq a b -> nubOrd $ referencedVars a <> referencedVars b
PGEq a b -> nubOrd $ referencedVars a <> referencedVars b
PAnd a b -> nubOrd $ referencedVars' a <> referencedVars' b
POr a b -> nubOrd $ referencedVars' a <> referencedVars' b
PNeg a -> referencedVars' a
PBool _ -> []
referencedFrameContext' :: Prop -> [Builder]
referencedFrameContext' = \case
PEq a b -> nubOrd $ referencedFrameContext a <> referencedFrameContext b
PLT a b -> nubOrd $ referencedFrameContext a <> referencedFrameContext b
PGT a b -> nubOrd $ referencedFrameContext a <> referencedFrameContext b
PLEq a b -> nubOrd $ referencedFrameContext a <> referencedFrameContext b
PGEq a b -> nubOrd $ referencedFrameContext a <> referencedFrameContext b
PAnd a b -> nubOrd $ referencedFrameContext' a <> referencedFrameContext' b
POr a b -> nubOrd $ referencedFrameContext' a <> referencedFrameContext' b
PNeg a -> referencedFrameContext' a
PBool _ -> []
referencedBlockContext' :: Prop -> [Builder]
referencedBlockContext' = \case
PEq a b -> nubOrd $ referencedBlockContext a <> referencedBlockContext b
PLT a b -> nubOrd $ referencedBlockContext a <> referencedBlockContext b
PGT a b -> nubOrd $ referencedBlockContext a <> referencedBlockContext b
PLEq a b -> nubOrd $ referencedBlockContext a <> referencedBlockContext b
PGEq a b -> nubOrd $ referencedBlockContext a <> referencedBlockContext b
PAnd a b -> nubOrd $ referencedBlockContext' a <> referencedBlockContext' b
POr a b -> nubOrd $ referencedBlockContext' a <> referencedBlockContext' b
PNeg a -> referencedBlockContext' a
PBool _ -> []
-- Given a list of 256b VM variable names, create an SMT2 object with the variables declared
declareVars :: [Builder] -> SMT2
declareVars names = SMT2 (["; variables"] <> fmap declare names) cexvars
where
declare n = "(declare-const " <> n <> " (_ BitVec 256))"
cexvars = CexVars
{ calldataV = fmap toLazyText names
, buffersV = mempty
, blockContextV = mempty
, txContextV = mempty
}
referencedVars :: Expr a -> [Builder]
referencedVars expr = nubOrd (foldExpr go [] expr)
where
go :: Expr a -> [Builder]
go = \case
Var s -> [fromText s]
_ -> []
declareFrameContext :: [Builder] -> SMT2
declareFrameContext names = SMT2 (["; frame context"] <> fmap declare names) cexvars
where
declare n = "(declare-const " <> n <> " (_ BitVec 256))"
cexvars = CexVars
{ calldataV = mempty
, buffersV = mempty
, blockContextV = mempty
, txContextV = fmap toLazyText names
}
referencedFrameContext :: Expr a -> [Builder]
referencedFrameContext expr = nubOrd (foldExpr go [] expr)
where
go :: Expr a -> [Builder]
go = \case
CallValue a -> [fromLazyText $ T.append "callvalue_" (T.pack . show $ a)]
Caller a -> [fromLazyText $ T.append "caller_" (T.pack . show $ a)]
Address a -> [fromLazyText $ T.append "address_" (T.pack . show $ a)]
Balance {} -> error "TODO: BALANCE"
SelfBalance {} -> error "TODO: SELFBALANCE"
Gas {} -> error "TODO: GAS"
_ -> []
declareBlockContext :: [Builder] -> SMT2
declareBlockContext names = SMT2 (["; block context"] <> fmap declare names) cexvars
where
declare n = "(declare-const " <> n <> " (_ BitVec 256))"
cexvars = CexVars
{ calldataV = mempty
, buffersV = mempty
, blockContextV = fmap toLazyText names
, txContextV = mempty
}
referencedBlockContext :: Expr a -> [Builder]
referencedBlockContext expr = nubOrd (foldExpr go [] expr)
where
go :: Expr a -> [Builder]
go = \case
Origin -> ["origin"]
Coinbase -> ["coinbase"]
Timestamp -> ["timestamp"]
BlockNumber -> ["blocknumber"]
PrevRandao -> ["prevrandao"]
GasLimit -> ["gaslimit"]
ChainId -> ["chainid"]
BaseFee -> ["basefee"]
_ -> []
exprToSMT :: Expr a -> Builder
exprToSMT = \case
Lit w -> fromLazyText $ "(_ bv" <> (T.pack $ show (num w :: Integer)) <> " 256)"
Var s -> fromText s
GVar (BufVar n) -> fromLazyText $ "buf" <> (T.pack . show $ n)
GVar (StoreVar n) -> fromLazyText $ "store" <> (T.pack . 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 b of
Lit b' -> expandExp a b'
_ -> error "cannot encode symbolic exponentation into SMT"
Min a b ->
let aenc = exprToSMT a
benc = exprToSMT b in
"(ite (bvule " <> aenc `sp` benc <> ") " <> aenc `sp` benc <> ")"
LT a b ->
let cond = op2 "bvult" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
SLT a b ->
let cond = op2 "bvslt" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
GT a b ->
let cond = op2 "bvugt" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
LEq a b ->
let cond = op2 "bvule" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
GEq a b ->
let cond = op2 "bvuge" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
Eq a b ->
let cond = op2 "=" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
IsZero a ->
let cond = op2 "=" a (Lit 0) in
"(ite " <> cond `sp` one `sp` zero <> ")"
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
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 ->
let aExp = exprToSMT a
bExp = exprToSMT b
cExp = exprToSMT c
aLift = "(concat (_ bv0 256) " <> aExp <> ")"
bLift = "(concat (_ bv0 256) " <> bExp <> ")"
cLift = "(concat (_ bv0 256) " <> cExp <> ")"
in "((_ extract 255 0) (ite (= " <> cExp <> " (_ bv0 256)) (_ bv0 512) (bvurem (bvmul " <> aLift `sp` bLift <> ")" <> cLift <> ")))"
EqByte a b ->
let cond = op2 "=" a b in
"(ite " <> cond `sp` one `sp` zero <> ")"
Keccak a ->
let enc = exprToSMT a in
"(keccak " <> enc <> ")"
SHA256 a ->
let enc = exprToSMT a in
"(sha256 " <> enc <> ")"
CallValue a -> fromLazyText $ T.append "callvalue_" (T.pack . show $ a)
Caller a -> fromLazyText $ T.append "caller_" (T.pack . show $ a)
Address a -> fromLazyText $ T.append "address_" (T.pack . show $ a)
Origin -> "origin"
BlockHash a ->
let enc = exprToSMT a in
"(blockhash " <> enc <> ")"
Coinbase -> "coinbase"
Timestamp -> "timestamp"
BlockNumber -> "blocknumber"
PrevRandao -> "prevrandao"
GasLimit -> "gaslimit"
ChainId -> "chainid"
BaseFee -> "basefee"
-- TODO: make me binary...
LitByte b -> fromLazyText $ "(_ bv" <> T.pack (show (num b :: Integer)) <> " 8)"
IndexWord idx w -> case idx of
Lit n -> if n >= 0 && n < 32
then
let enc = exprToSMT w in
fromLazyText ("(indexWord" <> T.pack (show (num n :: Integer))) `sp` enc <> ")"
else exprToSMT (LitByte 0)
_ -> op2 "indexWord" idx w
ReadByte idx src -> op2 "select" src idx
ConcreteBuf "" -> "emptyBuf"
ConcreteBuf bs -> writeBytes bs mempty
AbstractBuf s -> fromText s
ReadWord idx prev -> op2 "readWord" idx prev
BufLength b -> op1 "bufLength" b
WriteByte idx val prev ->
let encIdx = exprToSMT idx
encVal = exprToSMT val
encPrev = exprToSMT prev in
"(store " <> encPrev `sp` encIdx `sp` encVal <> ")"
WriteWord idx val prev ->
let encIdx = exprToSMT idx
encVal = exprToSMT val
encPrev = exprToSMT prev in
"(writeWord " <> encIdx `sp` encVal `sp` encPrev <> ")"
CopySlice srcIdx dstIdx size src dst ->
copySlice srcIdx dstIdx size (exprToSMT src) (exprToSMT dst)
EmptyStore -> "emptyStore"
ConcreteStore s -> encodeConcreteStore s
AbstractStore -> "abstractStore"
SStore addr idx val prev ->
let encAddr = exprToSMT addr
encIdx = exprToSMT idx
encVal = exprToSMT val
encPrev = exprToSMT prev in
"(sstore" `sp` encAddr `sp` encIdx `sp` encVal `sp` encPrev <> ")"
SLoad addr idx store -> op3 "sload" addr idx store
a -> error $ "TODO: implement: " <> show a
where
op1 op a =
let enc = exprToSMT a in
"(" <> op `sp` enc <> ")"
op2 op a b =
let aenc = exprToSMT a
benc = exprToSMT b in
"(" <> op `sp` aenc `sp` benc <> ")"
op3 op a b c =
let aenc = exprToSMT a
benc = exprToSMT b
cenc = exprToSMT c in
"(" <> op `sp` aenc `sp` benc `sp` cenc <> ")"
op2CheckZero op a b =
let aenc = exprToSMT a
benc = exprToSMT b in
"(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 -> 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 ->
let enc = propToSMT a in
"(not " <> enc <> ")"
PAnd a b ->
let aenc = propToSMT a
benc = propToSMT b in
"(and " <> aenc <> " " <> benc <> ")"
POr a b ->
let aenc = propToSMT a
benc = propToSMT b in
"(or " <> aenc <> " " <> benc <> ")"
PBool b -> if b then "true" else "false"
where
op2 op a b =
let aenc = exprToSMT a
benc = exprToSMT b in
"(" <> op <> " " <> aenc <> " " <> benc <> ")"
-- ** Execution ** -------------------------------------------------------------------------------
-- | Supported solvers
data Solver
= Z3
| CVC5
| Bitwuzla
| Custom Text
instance Show Solver where
show Z3 = "z3"
show CVC5 = "cvc5"
show Bitwuzla = "bitwuzla"
show (Custom s) = T.unpack s
-- | A running solver instance
data SolverInstance = SolverInstance
{ _type :: Solver
, _stdin :: Handle
, _stdout :: Handle
, _stderr :: Handle
, _process :: ProcessHandle
}
-- | A channel representing a group of solvers
newtype SolverGroup = SolverGroup (Chan Task)
-- | A script to be executed, a list of models to be extracted in the case of a sat result, and a channel where the result should be written
data Task = Task
{ script :: SMT2
, resultChan :: Chan CheckSatResult
}
-- | The result of a call to (check-sat)
data CheckSatResult
= Sat SMTCex
| Unsat
| Unknown
| Error TS.Text
deriving (Show, Eq)
isSat :: CheckSatResult -> Bool
isSat (Sat _) = True
isSat _ = False
isErr :: CheckSatResult -> Bool
isErr (Error _) = True
isErr _ = False
isUnsat :: CheckSatResult -> Bool
isUnsat Unsat = True
isUnsat _ = False
checkSat :: SolverGroup -> SMT2 -> IO CheckSatResult
checkSat (SolverGroup taskQueue) script = do
-- prepare result channel
resChan <- newChan
-- send task to solver group
writeChan taskQueue (Task script resChan)
-- collect result
readChan resChan
parseW256 :: SpecConstant -> W256
parseW256 = parseSC
parseInteger :: SpecConstant -> Integer
parseInteger = parseSC
parseW8 :: SpecConstant -> Word8
parseW8 = parseSC
parseErr :: (Show a) => a -> b
parseErr res = error $ "Internal Error: cannot parse solver response: " <> show res
parseVar :: TS.Text -> Expr EWord
parseVar = Var
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 t = error $ "Internal Error: cannot parse " <> (TS.unpack t) <> " into an Expr"
parseFrameCtx :: TS.Text -> Expr EWord
parseFrameCtx name = case TS.unpack name of
('c':'a':'l':'l':'v':'a':'l':'u':'e':'_':frame) -> CallValue (read frame)
('c':'a':'l':'l':'e':'r':'_':frame) -> Caller (read frame)
('a':'d':'d':'r':'e':'s':'s':'_':frame) -> Address (read frame)
t -> error $ "Internal Error: cannot parse " <> t <> " into an Expr"
getVars :: (TS.Text -> Expr EWord) -> SolverInstance -> [TS.Text] -> IO (Map (Expr EWord) W256)
getVars parseFn inst names = Map.mapKeys parseFn <$> foldM getVar mempty names
where
getVar :: Map TS.Text W256 -> TS.Text -> IO (Map TS.Text W256)
getVar acc name = do
raw <- getValue inst (T.fromStrict name)
let
parsed = case parseCommentFreeFileMsg getValueRes (T.toStrict raw) of
Right (ResSpecific (valParsed :| [])) -> valParsed
r -> parseErr r
val = case parsed of
(TermQualIdentifier (
Unqualified (IdSymbol symbol)),
TermSpecConstant sc)
-> if symbol == name
then parseW256 sc
else error "Internal Error: solver did not return model for requested value"
r -> parseErr r
pure $ Map.insert name val acc
getBufs :: SolverInstance -> [TS.Text] -> IO (Map (Expr Buf) ByteString)
getBufs inst names = foldM getBuf mempty names
where
getLength :: TS.Text -> IO Int
getLength name = do
val <- getValue inst (T.fromStrict name <> "_length")
len <- case parseCommentFreeFileMsg getValueRes (T.toStrict val) of
Right (ResSpecific (parsed :| [])) -> case parsed of
(TermQualIdentifier (Unqualified (IdSymbol symbol)), (TermSpecConstant sc))
-> if symbol == (name <> "_length")
then pure $ parseW256 sc
else error "Internal Error: solver did not return model for requested value"
res -> parseErr res
res -> parseErr res
pure $ if len <= num (maxBound :: Int)
then fromIntegral len
else error $ "Internal Error: buffer: "
<> (TS.unpack name)
<> " is too large to be represented in a ByteString. Length: "
<> show len
getBuf :: Map (Expr Buf) ByteString -> TS.Text -> IO (Map (Expr Buf) ByteString)
getBuf acc name = do
-- Sometimes the solver gives us back a model for a Buffer that has every
-- element set to some concrete value. This is impossible to represent as
-- a concrete ByteString in haskell (or in any existing computer hardware :D),
-- so we ask the solver to give us back a model for the length of
-- this buffer and then use that to produce a shorter counterexample (by
-- replicating the constant byte up to the length).
len <- getLength name
val <- getValue inst (T.fromStrict name)
buf <- case parseCommentFreeFileMsg getValueRes (T.toStrict val) of
Right (ResSpecific (valParsed :| [])) -> case valParsed of
(TermQualIdentifier (Unqualified (IdSymbol symbol)), term)
-> if symbol == name
then pure $ parseBuf len term
else error "Internal Error: solver did not return model for requested value"
res -> error $ "Internal Error: cannot parse solver response: " <> show res
res -> error $ "Internal Error: cannot parse solver response: " <> show res
let bs = case simplify buf of
ConcreteBuf b -> b
_ -> error "Internal Error: unable to parse solver response into a concrete buffer"
pure $ Map.insert (AbstractBuf name) bs acc
parseBuf :: Int -> Term -> Expr Buf
parseBuf len = go mempty
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 :| [])))
-> case val of
SCHexadecimal "00" -> mempty
v -> ConcreteBuf $ BS.replicate len (parseW8 v)
-- writing a byte over some array
(TermApplication
(Unqualified (IdSymbol "store"))
(base :| [TermSpecConstant idx, TermSpecConstant val])
) -> let
pbase = go env base
pidx = parseW256 idx
pval = parseW8 val
in writeByte (Lit pidx) (LitByte pval) pbase
-- binding a new name
(TermLet ((VarBinding name bound) :| []) term) -> let
pbound = go env bound
in go (Map.insert name pbound env) term
-- looking up a bound name
(TermQualIdentifier (Unqualified (IdSymbol name))) -> case Map.lookup name env of
Just t -> t
Nothing -> error $ "Internal error: could not find "
<> (TS.unpack name)
<> " in environment mapping"
p -> parseErr p
parseSC :: (Num a, Eq a) => SpecConstant -> a
parseSC (SCHexadecimal a) = fst . head . Numeric.readHex . T.unpack . T.fromStrict $ a
parseSC sc = error $ "Internal Error: cannot parse: " <> show sc
withSolvers :: Solver -> Natural -> Maybe Natural -> (SolverGroup -> IO a) -> IO a
withSolvers solver count timeout cont = do
-- spawn solvers
instances <- mapM (const $ spawnSolver solver timeout) [1..count]
-- spawn orchestration thread
taskQueue <- newChan
availableInstances <- newChan
forM_ instances (writeChan availableInstances)
orchestrateId <- forkIO $ orchestrate taskQueue availableInstances
-- run continuation with task queue
res <- cont (SolverGroup taskQueue)
-- cleanup and return results
mapM_ stopSolver instances
killThread orchestrateId
pure res
where
orchestrate queue avail = do
task <- readChan queue
inst <- readChan avail
_ <- forkIO $ runTask task inst avail
orchestrate queue avail
runTask (Task (SMT2 cmds cexvars) r) inst availableInstances = do
-- reset solver and send all lines of provided script
out <- sendScript inst (SMT2 ("(reset)" : cmds) cexvars)
case out of
-- if we got an error then return it
Left e -> writeChan r (Error ("error while writing SMT to solver: " <> T.toStrict e))
-- otherwise call (check-sat), parse the result, and send it down the result channel
Right () -> do
sat <- sendLine inst "(check-sat)"
res <- case sat of
"sat" -> do
calldatamodels <- getVars parseVar inst (fmap T.toStrict $ calldataV cexvars)
buffermodels <- getBufs inst (fmap T.toStrict $ buffersV cexvars)
blockctxmodels <- getVars parseBlockCtx inst (fmap T.toStrict $ blockContextV cexvars)
txctxmodels <- getVars parseFrameCtx inst (fmap T.toStrict $ txContextV cexvars)
pure $ Sat $ SMTCex
{ vars = calldatamodels
, buffers = buffermodels
, blockContext = blockctxmodels
, txContext = txctxmodels
}
"unsat" -> pure Unsat
"timeout" -> pure Unknown
"unknown" -> pure Unknown
_ -> pure . Error $ T.toStrict $ "Unable to parse solver output: " <> sat
writeChan r res
-- put the instance back in the list of available instances
writeChan availableInstances inst
-- | Arguments used when spawing a solver instance
solverArgs :: Solver -> Maybe (Natural) -> [Text]
solverArgs solver timeout = case solver of
Bitwuzla -> error "TODO: Bitwuzla args"
Z3 ->
[ "-in" ]
CVC5 ->
[ "--lang=smt"
, "--no-interactive"
, "--produce-models"
, "--tlimit-per=" <> T.pack (show (1000 * fromMaybe 10 timeout))
]
Custom _ -> []
-- | Spawns a solver instance, and sets the various global config options that we use for our queries
spawnSolver :: Solver -> Maybe (Natural) -> IO SolverInstance
spawnSolver solver timeout = do
let cmd = (proc (show solver) (fmap T.unpack $ solverArgs solver timeout)) { std_in = CreatePipe, std_out = CreatePipe, std_err = CreatePipe }
(Just stdin, Just stdout, Just stderr, process) <- createProcess cmd
hSetBuffering stdin (BlockBuffering (Just 1000000))
let solverInstance = SolverInstance solver stdin stdout stderr process
case timeout of
Nothing -> pure solverInstance
Just t -> case solver of
CVC5 -> pure solverInstance
_ -> do
_ <- sendLine' solverInstance $ "(set-option :timeout " <> T.pack (show t) <> ")"
pure solverInstance
-- | Cleanly shutdown a running solver instnace
stopSolver :: SolverInstance -> IO ()
stopSolver (SolverInstance _ stdin stdout stderr process) = cleanupProcess (Just stdin, Just stdout, Just stderr, process)
-- | Sends a list of commands to the solver. Returns the first error, if there was one.
sendScript :: SolverInstance -> SMT2 -> IO (Either Text ())
sendScript solver (SMT2 cmds _) = do
sendLine' solver (T.unlines $ fmap toLazyText cmds)
pure $ Right()
-- | Sends a single command to the solver, returns the first available line from the output buffer
sendCommand :: SolverInstance -> Text -> IO Text
sendCommand inst cmd = do
-- trim leading whitespace
let cmd' = T.dropWhile isSpace cmd
case T.unpack cmd' of
"" -> pure "success" -- ignore blank lines
';' : _ -> pure "success" -- ignore comments
_ -> sendLine inst cmd'
-- | Sends a string to the solver and appends a newline, returns the first available line from the output buffer
sendLine :: SolverInstance -> Text -> IO Text
sendLine (SolverInstance _ stdin stdout _ _) cmd = do
T.hPutStr stdin (T.append cmd "\n")
hFlush stdin
T.hGetLine stdout
-- | Sends a string to the solver and appends a newline, doesn't return stdout
sendLine' :: SolverInstance -> Text -> IO ()
sendLine' (SolverInstance _ stdin _ _ _) cmd = do
T.hPutStr stdin (T.append cmd "\n")
hFlush stdin
-- | Returns a string representation of the model for the requested variable
getValue :: SolverInstance -> Text -> IO Text
getValue (SolverInstance _ stdin stdout _ _) var = do
T.hPutStr stdin (T.append (T.append "(get-value (" var) "))\n")
hFlush stdin
fmap (T.unlines . reverse) (readSExpr stdout)
-- | Reads lines from h until we have a balanced sexpr
readSExpr :: Handle -> IO [Text]
readSExpr h = go 0 0 []
where
go 0 0 _ = do
line <- T.hGetLine h
let ls = T.length $ T.filter (== '(') line
rs = T.length $ T.filter (== ')') line
if ls == rs
then pure [line]
else go ls rs [line]
go ls rs prev = do
line <- T.hGetLine h
let ls' = T.length $ T.filter (== '(') line
rs' = T.length $ T.filter (== ')') line
if (ls + ls') == (rs + rs')
then pure $ line : prev
else go (ls + ls') (rs + rs') (line : prev)
-- ** Helpers ** ---------------------------------------------------------------------------------
-- | Stores a region of src into dst
copySlice :: Expr EWord -> Expr EWord -> Expr EWord -> Builder -> Builder -> Builder
copySlice srcOffset dstOffset size@(Lit _) src dst
| size == (Lit 0) = dst
| otherwise =
let size' = (sub size (Lit 1))
encDstOff = exprToSMT (add dstOffset size')
encSrcOff = exprToSMT (add srcOffset size')
child = copySlice srcOffset dstOffset size' src dst in
"(store " <> child `sp` encDstOff `sp` "(select " <> src `sp` encSrcOff <> "))"
copySlice _ _ _ _ _ = error "TODO: implement copySlice with a symbolically sized region"
-- | Unrolls an exponentiation into a series of multiplications
expandExp :: Expr EWord -> W256 -> Builder
expandExp base expnt
| expnt == 1 = exprToSMT base
| otherwise =
let b = exprToSMT base
n = expandExp base (expnt - 1) in
"(bvmul " <> b `sp` n <> ")"
-- | Concatenates a list of bytes into a larger bitvector
concatBytes :: [Expr Byte] -> Builder
concatBytes bytes =
let bytesRev = reverse bytes
a2 = exprToSMT (head bytesRev) in
foldl wrap a2 $ tail bytesRev
where
wrap inner byte =
let byteSMT = exprToSMT byte in
"(concat " <> byteSMT `sp` inner <> ")"
-- | Concatenates a list of bytes into a larger bitvector
writeBytes :: ByteString -> Expr Buf -> Builder
writeBytes bytes buf = snd $ BS.foldl' wrap (0, exprToSMT buf) bytes
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, inner) byte =
if skipZeros && byte == 0
then (idx + 1, inner)
else let
byteSMT = exprToSMT (LitByte byte)
idxSMT = exprToSMT . Lit . num $ idx
in (idx + 1, "(store " <> inner `sp` idxSMT `sp` byteSMT <> ")")
encodeConcreteStore :: Map W256 (Map W256 W256) -> Builder
encodeConcreteStore s = foldl encodeWrite "emptyStore" writes
where
asList = fmap (second Map.toList) $ Map.toList s
writes = concatMap (\(addr, ws) -> fmap (\(k, v) -> (addr, k, v)) ws) asList
encodeWrite prev (addr, key, val) = let
encAddr = exprToSMT (Lit addr)
encKey = exprToSMT (Lit key)
encVal = exprToSMT (Lit val)
in "(sstore " <> encAddr `sp` encKey `sp` encVal `sp` prev <> ")"