diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
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+ GNU GENERAL PUBLIC LICENSE
+ Version 3, 29 June 2007
+
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+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.
+
+
+ Copyright (C)
+
+ 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 .
+
+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:
+
+ Copyright (C)
+ 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
+.
+
+ 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
+.
diff --git a/Language/SMTLib2/Pipe.hs b/Language/SMTLib2/Pipe.hs
new file mode 100644
--- /dev/null
+++ b/Language/SMTLib2/Pipe.hs
@@ -0,0 +1,13 @@
+module Language.SMTLib2.Pipe
+ (SMTPipe(),
+ createPipe,
+ createPipeFromHandle,
+ withPipe
+ ) where
+
+import Language.SMTLib2.Pipe.Internals
+import Language.SMTLib2 (SMT,withBackendExitCleanly)
+
+withPipe :: String -> [String] -> SMT SMTPipe a -> IO a
+withPipe solver args act
+ = withBackendExitCleanly (createPipe solver args) act
diff --git a/Language/SMTLib2/Pipe/Internals.hs b/Language/SMTLib2/Pipe/Internals.hs
new file mode 100644
--- /dev/null
+++ b/Language/SMTLib2/Pipe/Internals.hs
@@ -0,0 +1,1785 @@
+module Language.SMTLib2.Pipe.Internals where
+
+import Language.SMTLib2.Internals.Backend as B
+import Language.SMTLib2.Internals.Type --hiding (Constr,Field,Datatype)
+import qualified Language.SMTLib2.Internals.Type as Type
+import Language.SMTLib2.Internals.Type.Nat as Type
+import Language.SMTLib2.Internals.Type.List (List(..))
+import qualified Language.SMTLib2.Internals.Type.List as List
+import Language.SMTLib2.Internals.Expression hiding (Fun,Field,Var,QVar,LVar)
+import qualified Language.SMTLib2.Internals.Expression as Expr
+import qualified Language.SMTLib2.Internals.Proof as P
+import Language.SMTLib2.Strategy as Strat
+
+import qualified Data.Text as T
+import qualified Data.Text.Read as T
+import Data.Map (Map)
+import qualified Data.Map.Strict as Map
+import Data.Set (Set)
+import qualified Data.Set as Set
+import Data.IntMap (IntMap)
+import qualified Data.IntMap as IMap
+import Data.Proxy
+import Data.Typeable
+import Data.GADT.Compare
+import Data.GADT.Show
+#if !MIN_VERSION_base(4,8,0)
+import Data.Monoid
+#endif
+import Data.Foldable (foldlM)
+import Control.Monad.Except
+import Data.Traversable
+import qualified GHC.TypeLits as TL
+
+import System.Process
+import System.IO
+import qualified Data.ByteString as BS hiding (reverse)
+import qualified Data.ByteString.Char8 as BS8
+import Blaze.ByteString.Builder
+import Data.Attoparsec.ByteString
+
+import qualified Data.AttoLisp as L
+import qualified Data.Attoparsec.Number as L
+import Data.Ratio
+
+import Control.Monad.Identity
+import Control.Monad.Trans.Except
+import Control.Monad.State
+
+data PipeDatatype = forall a. IsDatatype a => PipeDatatype (Proxy a)
+
+data SMTPipe = SMTPipe { channelIn :: Handle
+ , channelOut :: Handle
+ , processHandle :: Maybe ProcessHandle
+ , names :: Map String Int
+ , vars :: Map T.Text RevVar
+ , datatypes :: TypeRegistry T.Text T.Text T.Text
+ , interpolationMode :: InterpolationMode }
+ deriving Typeable
+
+data RevVar = forall (t::Type). Var !(Repr t)
+ | forall (t::Type). QVar !(Repr t)
+ | forall (arg::[Type]) (t::Type). Fun !(List Repr arg) !(Repr t)
+ | forall (t::Type). FunArg !(Repr t)
+ | forall (t::Type). LVar !(Repr t)
+
+data InterpolationMode = Z3Interpolation [T.Text] [T.Text]
+ | MathSATInterpolation
+
+type PipeVar = UntypedVar T.Text
+type PipeFun = UntypedFun T.Text
+
+newtype PipeClauseId = PipeClauseId T.Text deriving (Show,Eq,Ord,Typeable)
+
+type PipeProofNode = P.Proof L.Lisp (Expr SMTPipe) Int
+
+data PipeProof = PipeProof { proofNodes :: Map Int PipeProofNode
+ , proofNode :: Int }
+
+instance Eq PipeProof where
+ (==) (PipeProof _ x) (PipeProof _ y) = x == y
+
+instance Ord PipeProof where
+ compare (PipeProof _ x) (PipeProof _ y) = compare x y
+
+instance Show PipeProof where
+ showsPrec p pr = showParen (p>10) $ showsPrec 0 (proofNode pr)
+
+instance GEq (Expr SMTPipe) where
+ geq (PipeExpr e1) (PipeExpr e2) = geq e1 e2
+
+instance GCompare (Expr SMTPipe) where
+ gcompare (PipeExpr e1) (PipeExpr e2) = gcompare e1 e2
+
+instance GShow (Expr SMTPipe) where
+ gshowsPrec = showsPrec
+
+instance GetType (Expr SMTPipe) where
+ getType (PipeExpr e) = getType e
+
+instance Backend SMTPipe where
+ type SMTMonad SMTPipe = IO
+ newtype Expr SMTPipe t = PipeExpr (Expression PipeVar PipeVar PipeFun PipeVar PipeVar (Expr SMTPipe) t) deriving (Show,Typeable)
+ type Var SMTPipe = PipeVar
+ type QVar SMTPipe = PipeVar
+ type Fun SMTPipe = PipeFun
+ type FunArg SMTPipe = PipeVar
+ type LVar SMTPipe = PipeVar
+ type ClauseId SMTPipe = PipeClauseId
+ type Model SMTPipe = AssignmentModel SMTPipe
+ type Proof SMTPipe = PipeProof
+ setOption opt b = do
+ putRequest b $ renderSetOption opt
+ return ((),b)
+ getInfo info b = do
+ putRequest b (renderGetInfo info)
+ resp <- parseResponse b
+ case info of
+ SMTSolverName -> case resp of
+ L.List [L.Symbol ":name",L.String name] -> return (T.unpack name,b)
+ _ -> error $ "Invalid response to 'get-info' query: "++show resp
+ SMTSolverVersion -> case resp of
+ L.List [L.Symbol ":version",L.String name] -> return (T.unpack name,b)
+ _ -> error $ "Invalid response to 'get-info' query: "++show resp
+ declareVar tp name b = do
+ let (sym,req,nnames) = renderDeclareVar (names b) tp name
+ nb = b { names = nnames
+ , vars = Map.insert sym (Var tp) (vars b) }
+ putRequest nb req
+ return (UntypedVar sym tp,nb)
+ createQVar tp name b = do
+ let name' = case name of
+ Just n -> n
+ Nothing -> "qv"
+ (name'',nb) = genName b name'
+ return (UntypedVar name'' tp,nb { vars = Map.insert name'' (QVar tp) (vars nb) })
+ createFunArg tp name b = do
+ let name' = case name of
+ Just n -> n
+ Nothing -> "fv"
+ (name'',nb) = genName b name'
+ return (UntypedVar name'' tp,nb { vars = Map.insert name'' (FunArg tp) (vars nb) })
+ defineVar name (PipeExpr expr) b = do
+ let tp = getType expr
+ (sym,req,nnames) = renderDefineVar (names b) tp name (exprToLisp (datatypes b) expr)
+ nb = b { names = nnames
+ , vars = Map.insert sym (Var tp) (vars b) }
+ putRequest nb req
+ return (UntypedVar sym tp,nb)
+ declareFun arg res name b = do
+ let (sym,req,nnames) = renderDeclareFun (names b) arg res name
+ nb = b { names = nnames
+ , vars = Map.insert sym (Fun arg res) (vars b) }
+ putRequest nb req
+ return (UntypedFun sym arg res,nb)
+ defineFun name arg body b = do
+ let argTp = runIdentity $ List.mapM (return . getType) arg
+ bodyTp = getType body
+ (name',req,nnames) = renderDefineFun (\(UntypedVar n _) -> L.Symbol n)
+ (\(PipeExpr e) -> exprToLisp (datatypes b) e) (names b) name arg body
+ nb = b { names = nnames }
+ putRequest nb req
+ return (UntypedFun name' argTp bodyTp,nb)
+ assert (PipeExpr expr) b = do
+ putRequest b (L.List [L.Symbol "assert"
+ ,exprToLisp (datatypes b) expr])
+ return ((),b)
+ assertId (PipeExpr expr) b = do
+ let (name,b1) = genName b "cl"
+ putRequest b1 (L.List [L.Symbol "assert"
+ ,L.List [L.Symbol "!"
+ ,exprToLisp (datatypes b) expr
+ ,L.Symbol ":named"
+ ,L.Symbol name]])
+ return (PipeClauseId name,b1)
+ assertPartition (PipeExpr expr) part b = case interpolationMode b of
+ Z3Interpolation grpA grpB -> do
+ let (name,b1) = genName b "grp"
+ putRequest b1 (L.List [L.Symbol "assert"
+ ,L.List [L.Symbol "!"
+ ,exprToLisp (datatypes b) expr
+ ,L.Symbol ":named"
+ ,L.Symbol name]])
+ return ((),b1 { interpolationMode = case part of
+ PartitionA -> Z3Interpolation (name:grpA) grpB
+ PartitionB -> Z3Interpolation grpA (name:grpB) })
+ MathSATInterpolation -> do
+ putRequest b (L.List [L.Symbol "assert"
+ ,L.List [L.Symbol "!"
+ ,exprToLisp (datatypes b) expr
+ ,L.Symbol ":interpolation-group"
+ ,L.Symbol (case part of
+ PartitionA -> "partA"
+ PartitionB -> "partB")]])
+ return ((),b)
+ getUnsatCore b = do
+ putRequest b (L.List [L.Symbol "get-unsat-core"])
+ resp <- parseResponse b
+ case resp of
+ L.List names -> do
+ cids <- mapM (\name -> case name of
+ L.Symbol name' -> return $ PipeClauseId name'
+ _ -> error $ "smtlib2: Invalid clause when getting unsatisfiable core: "++show name
+ ) names
+ return (cids,b)
+ _ -> error $ "smtlib2: Invalid response to query for unsatisfiable core: "++show resp
+ checkSat tactic limits b = do
+ putRequest b $ renderCheckSat tactic limits
+ res <- BS.hGetLine (channelOut b)
+ return (case res of
+ "sat" -> Sat
+ "sat\r" -> Sat
+ "unsat" -> Unsat
+ "unsat\r" -> Unsat
+ "unknown" -> Unknown
+ "unknown\r" -> Unknown
+ _ -> error $ "smtlib2: unknown check-sat response: "++show res,b)
+ getValue expr b = do
+ putRequest b (renderGetValue b expr)
+ l <- parseResponse b
+ return (parseGetValue b (getType expr) l,b)
+ getProof b = do
+ putRequest b renderGetProof
+ l <- parseResponse b
+ return (parseGetProof b l,b)
+ analyzeProof b pr = case Map.lookup (proofNode pr) (proofNodes pr) of
+ Just nd -> case nd of
+ P.Rule r args res -> P.Rule (show r) (fmap (\arg -> PipeProof (proofNodes pr) arg) args) res
+ push b = do
+ putRequest b (L.List [L.Symbol "push",L.Number $ L.I 1])
+ return ((),b)
+ pop b = do
+ putRequest b (L.List [L.Symbol "pop",L.Number $ L.I 1])
+ return ((),b)
+ getModel b = do
+ putRequest b (L.List [L.Symbol "get-model"])
+ mdl <- parseResponse b
+ case runExcept $ parseGetModel b mdl of
+ Right mdl' -> return (mdl',b)
+ Left err -> error $ "smtlib2: Unknown get-model response: "++err
+ simplify (PipeExpr expr) b = do
+ putRequest b (L.List [L.Symbol "simplify"
+ ,exprToLisp (datatypes b) expr])
+ resp <- parseResponse b
+ case runExcept $ lispToExprTyped b (getType expr) resp of
+ Right res -> return (res,b)
+ Left err -> error $ "smtlib2: Unknown simplify response: "++show resp++" ["++err++"]"
+ toBackend expr b = return (PipeExpr expr,b)
+ fromBackend b (PipeExpr expr) = expr
+ interpolate b = do
+ case interpolationMode b of
+ Z3Interpolation grpA grpB -> do
+ putRequest b (L.List [L.Symbol "get-interpolant",getAnd grpA,getAnd grpB])
+ MathSATInterpolation -> do
+ putRequest b (L.List [L.Symbol "get-interpolant",L.List [L.Symbol "partA"]])
+ resp <- parseResponse b
+ case runExcept $ lispToExprTyped b BoolRepr resp of
+ Right res -> return (res,b)
+ Left err -> error $ "smtlib2: Unknown get-interpolant response: "++show resp++" ["++err++"]"
+ where
+ getAnd [] = L.Symbol "true"
+ getAnd [x] = L.Symbol x
+ getAnd xs = L.List $ (L.Symbol "and"):fmap L.Symbol xs
+ declareDatatypes coll b = do
+ let (req,nnames,nreg) = renderDeclareDatatype (names b) (datatypes b) coll
+ nb = b { names = nnames
+ , datatypes = nreg }
+ putRequest nb req
+ return ((),nb)
+ exit b = do
+ putRequest b (L.List [L.Symbol "exit"])
+ hClose (channelIn b)
+ hClose (channelOut b)
+ case processHandle b of
+ Nothing -> return ()
+ Just ph -> do
+ terminateProcess ph
+ _ <- waitForProcess ph
+ return ()
+ return ((),b)
+ comment msg b = do
+ hPutStrLn (channelIn b) ("; "++msg)
+ return ((),b)
+
+renderDeclareFun :: Map String Int -> List Repr arg -> Repr ret -> Maybe String
+ -> (T.Text,L.Lisp,Map String Int)
+renderDeclareFun names args ret name
+ = (name'',L.List [L.Symbol "declare-fun"
+ ,L.Symbol name''
+ ,typeList args
+ ,typeSymbol Set.empty ret],nnames)
+ where
+ name' = case name of
+ Just n -> n
+ Nothing -> "fun"
+ (name'',nnames) = genName' names name'
+
+renderDefineFun :: (GetType e,GetType fv)
+ => (forall t. fv t -> L.Lisp)
+ -> (forall t. e t -> L.Lisp)
+ -> Map String Int -> Maybe String
+ -> List fv arg
+ -> e ret
+ -> (T.Text,L.Lisp,Map String Int)
+renderDefineFun renderFV renderE names name args body
+ = (name'',L.List [L.Symbol "define-fun"
+ ,L.Symbol name''
+ ,L.List $ mkList renderFV args
+ ,typeSymbol Set.empty (getType body)
+ ,renderE body],nnames)
+ where
+ name' = case name of
+ Just n -> n
+ Nothing -> "fun"
+ (name'',nnames) = genName' names name'
+ mkList :: GetType fv => (forall t. fv t -> L.Lisp) -> List fv ts -> [L.Lisp]
+ mkList _ Nil = []
+ mkList renderFV (v ::: xs)
+ = (L.List [renderFV v,typeSymbol Set.empty (getType v)]):
+ mkList renderFV xs
+
+renderCheckSat :: Maybe Tactic -> CheckSatLimits -> L.Lisp
+renderCheckSat tactic limits
+ = L.List (if extendedCheckSat
+ then [L.Symbol "check-sat-using"
+ ,case tactic of
+ Just t -> tacticToLisp t
+ Nothing -> L.Symbol "smt"]++
+ (case limitTime limits of
+ Just t -> [L.Symbol ":timeout"
+ ,L.Number (L.I t)]
+ Nothing -> [])++
+ (case limitMemory limits of
+ Just m -> [L.Symbol ":max-memory"
+ ,L.Number (L.I m)]
+ Nothing -> [])
+ else [L.Symbol "check-sat"])
+ where
+ extendedCheckSat = case tactic of
+ Just _ -> True
+ _ -> case limitTime limits of
+ Just _ -> True
+ _ -> case limitMemory limits of
+ Just _ -> True
+ _ -> False
+
+renderDeclareDatatype' :: Integer
+ -> [(T.Text,[(T.Text,[(T.Text,L.Lisp)])])]
+ -> L.Lisp
+renderDeclareDatatype' npar coll
+ = L.List [L.Symbol "declare-datatypes"
+ ,case npar of
+ 0 -> L.Symbol "()"
+ _ -> L.List [L.Symbol $ T.pack $ "a"++show i
+ | i <- [0..npar-1]]
+ ,L.List [ L.List ((L.Symbol name):
+ [L.List ((L.Symbol con):
+ [ L.List [L.Symbol field
+ ,tp]
+ | (field,tp) <- fields ])
+ | (con,fields) <- cons ])
+ | (name,cons) <- coll]]
+
+renderDeclareDatatype :: Map String Int -> TypeRegistry T.Text T.Text T.Text -> [AnyDatatype]
+ -> (L.Lisp,Map String Int,TypeRegistry T.Text T.Text T.Text)
+renderDeclareDatatype names reg dts
+ = (renderDeclareDatatype' (case dts of
+ AnyDatatype dt : _ -> naturalToInteger (parameters dt)
+ [] -> 0)
+ str,nnames,nreg)
+ where
+ ((nnames,nreg),str) = mapAccumL mkDt (names,reg) dts
+ mkDt (names,reg) dt'@(AnyDatatype dt)
+ = let (name,names1) = genName' names (datatypeName dt)
+ reg1 = reg { allDatatypes = Map.insert name dt' (allDatatypes reg)
+ , revDatatypes = Map.insert dt' name (revDatatypes reg) }
+ (cons,(names2,reg2)) = runState (List.toList (mkCon dt)
+ (constructors dt)) (names1,reg1)
+ in ((names2,reg2),(name,cons))
+ mkCon dt con = do
+ (names,reg) <- get
+ let (name,names1) = genName' names (constrName con)
+ reg1 = reg { allConstructors = Map.insert name (AnyConstr dt con) (allConstructors reg)
+ , revConstructors = Map.insert (AnyConstr dt con) name (revConstructors reg) }
+ put (names1,reg1)
+ fs <- List.toList (mkField dt) (fields con)
+ return (name,fs)
+ mkField dt field = do
+ (names,reg) <- get
+ let (name,names1) = genName' names (fieldName field)
+ reg1 = reg { allFields = Map.insert name (AnyField dt field) (allFields reg)
+ , revFields = Map.insert (AnyField dt field) name (revFields reg) }
+ put (names1,reg1)
+ return (name,typeSymbol allTypes (fieldType field))
+
+ allParameters :: (forall n. Natural n -> a) -> a
+ allParameters f = case dts of
+ AnyDatatype dt : dts'
+ | all (\(AnyDatatype dt') -> case geq (parameters dt') (parameters dt) of
+ Just Refl -> True
+ Nothing -> False) dts' -> f (parameters dt)
+ _ -> error "Not all datatypes in a cycle share the same parameters."
+
+ isRecType :: IsDatatype dt => Datatype dt -> Bool
+ isRecType dt = Set.member (datatypeName dt) allTypes
+
+ allTypes :: Set String
+ allTypes = Set.fromList [ datatypeName dt
+ | AnyDatatype dt <- dts ]
+
+renderSetOption :: SMTOption -> L.Lisp
+renderSetOption (SMTLogic name) = L.List [L.Symbol "set-logic",L.Symbol $ T.pack name]
+renderSetOption opt
+ = L.List $ [L.Symbol "set-option"]++
+ (case opt of
+ PrintSuccess v -> [L.Symbol ":print-success"
+ ,L.Symbol $ if v then "true" else "false"]
+ ProduceModels v -> [L.Symbol ":produce-models"
+ ,L.Symbol $ if v then "true" else "false"]
+ B.ProduceProofs v -> [L.Symbol ":produce-proofs"
+ ,L.Symbol $ if v then "true" else "false"]
+ B.ProduceUnsatCores v -> [L.Symbol ":produce-unsat-cores"
+ ,L.Symbol $ if v then "true" else "false"]
+ ProduceInterpolants v -> [L.Symbol ":produce-interpolants"
+ ,L.Symbol $ if v then "true" else "false"])
+
+renderGetInfo :: SMTInfo i -> L.Lisp
+renderGetInfo SMTSolverName
+ = L.List [L.Symbol "get-info"
+ ,L.Symbol ":name"]
+renderGetInfo SMTSolverVersion
+ = L.List [L.Symbol "get-info"
+ ,L.Symbol ":version"]
+
+renderDeclareVar :: Map String Int -> Repr tp -> Maybe String
+ -> (T.Text,L.Lisp,Map String Int)
+renderDeclareVar names tp name
+ = (name'',L.List [L.Symbol "declare-fun"
+ ,L.Symbol name''
+ ,L.Symbol "()"
+ ,typeSymbol Set.empty tp
+ ],nnames)
+ where
+ name' = case name of
+ Just n -> n
+ Nothing -> "var"
+ (name'',nnames) = genName' names name'
+
+renderDefineVar :: Map String Int -> Repr t -> Maybe String -> L.Lisp
+ -> (T.Text,L.Lisp,Map String Int)
+renderDefineVar names tp name lexpr
+ = (name'',
+ L.List [L.Symbol "define-fun"
+ ,L.Symbol name''
+ ,L.Symbol "()"
+ ,typeSymbol Set.empty tp
+ ,lexpr],
+ nnames)
+ where
+ name' = case name of
+ Just n -> n
+ Nothing -> "var"
+ (name'',nnames) = genName' names name'
+
+renderGetValue :: SMTPipe -> Expr SMTPipe t -> L.Lisp
+renderGetValue b (PipeExpr e) = L.List [L.Symbol "get-value"
+ ,L.List [exprToLisp (datatypes b) e]]
+
+parseGetValue :: SMTPipe -> Repr t -> L.Lisp -> Value t
+parseGetValue b repr (L.List [L.List [_,val]])
+ = case runExcept $ lispToValue b (Just $ Sort repr) val of
+ Right (AnyValue v) -> case geq repr (valueType v) of
+ Just Refl -> v
+ Nothing -> error $ "smtlib2: Wrong type of returned value."
+ Left err -> error $ "smtlib2: Failed to parse get-value entry: "++show val++" ["++err++"]"
+parseGetValue _ _ expr = error $ "smtlib2: Failed to parse get-value result: "++show expr
+
+renderGetProof :: L.Lisp
+renderGetProof = L.List [L.Symbol "get-proof"]
+
+parseGetProof :: SMTPipe -> L.Lisp -> PipeProof
+parseGetProof b resp = case runExcept $ parseProof b Map.empty Map.empty Map.empty proof of
+ Right res -> res
+ Left err -> error $ "smtlib2: Failed to parse proof: "++show resp++" ["++err++"]"
+ where
+ proof = case resp of
+ L.List items -> case findProof items of
+ Nothing -> resp
+ Just p -> p
+ _ -> resp
+ findProof [] = Nothing
+ findProof ((L.List [L.Symbol "proof",p]):_) = Just p
+ findProof (x:xs) = findProof xs
+
+parseProof :: SMTPipe
+ -> Map T.Text (Expr SMTPipe BoolType)
+ -> Map T.Text Int
+ -> Map Int PipeProofNode
+ -> L.Lisp
+ -> LispParse PipeProof
+parseProof pipe exprs proofs nodes l = case l of
+ L.List [L.Symbol "let",L.List defs,body] -> do
+ (nexprs,nproofs,nnodes)
+ <- foldlM (\(exprs,proofs,nodes) def
+ -> case def of
+ L.List [L.Symbol name,def'] -> do
+ res <- parseDef exprs proofs nodes def'
+ case res of
+ Left expr -> return (Map.insert name expr exprs,proofs,nodes)
+ Right (proof,nnodes)
+ -> return (exprs,Map.insert name proof proofs,nnodes)
+ ) (exprs,proofs,nodes) defs
+ parseProof pipe nexprs nproofs nnodes body
+ _ -> do
+ (res,nnodes) <- parseDefProof exprs proofs nodes l
+ return (PipeProof nnodes res)
+ where
+ exprParser = pipeParser pipe
+ exprParser' exprs = exprParser { parseRecursive = \_ -> parseDefExpr' exprs
+ }
+ parseDefExpr' :: Map T.Text (Expr SMTPipe BoolType) -> Maybe Sort -> L.Lisp
+ -> (forall tp. Expr SMTPipe tp -> LispParse a)
+ -> LispParse a
+ parseDefExpr' exprs srt l@(L.Symbol name) res = case Map.lookup name exprs of
+ Just def -> res def
+ Nothing -> lispToExprWith (exprParser' exprs) srt l $
+ \e -> res (PipeExpr e)
+ parseDefExpr' exprs srt l res = lispToExprWith (exprParser' exprs) srt l
+ (res.PipeExpr)
+ parseDefExpr :: Map T.Text (Expr SMTPipe BoolType) -> L.Lisp
+ -> LispParse (Expr SMTPipe BoolType)
+ parseDefExpr exprs l = parseDefExpr' exprs (Just $ Sort BoolRepr) l $
+ \e -> case getType e of
+ BoolRepr -> return e
+ _ -> throwError "let expression in proof is not bool"
+ parseDefProof exprs proofs nodes (L.List (rule:args)) = do
+ (args',res,nnodes) <- parseArgs nodes args
+ let sz = Map.size nnodes
+ return (sz,Map.insert sz (P.Rule rule args' res) nnodes)
+ where
+ parseArgs nodes [x] = case x of
+ L.List [L.Symbol "~",lhs,rhs] -> do
+ lhs' <- parseDefExpr exprs lhs
+ rhs' <- parseDefExpr exprs rhs
+ return ([],P.EquivSat lhs' rhs',nodes)
+ _ -> do
+ e <- parseDefExpr exprs x
+ return ([],P.ProofExpr e,nodes)
+ parseArgs nodes (x:xs) = do
+ (nd,nodes1) <- parseDefProof exprs proofs nodes x
+ (nds,res,nodes2) <- parseArgs nodes1 xs
+ return (nd:nds,res,nodes2)
+ parseDefProof exprs proofs nodes (L.Symbol sym) = case Map.lookup sym proofs of
+ Just pr -> return (pr,nodes)
+ parseDef exprs proofs nodes l
+ = (fmap Left $ parseDefExpr exprs l) `catchError`
+ (\_ -> fmap Right $ parseDefProof exprs proofs nodes l)
+
+parseGetModel :: SMTPipe -> L.Lisp -> LispParse (Model SMTPipe)
+parseGetModel b (L.List ((L.Symbol "model"):mdl)) = do
+ nb <- foldlM adapt b mdl
+ assign <- mapM (parseAssignment nb) mdl
+ return $ AssignmentModel assign
+ where
+ adapt b (L.List [L.Symbol "define-fun",L.Symbol fname,L.List args,rtp,body])
+ = case args of
+ [] -> do
+ srt@(Sort tp) <- lispToSort (pipeParser b) rtp
+ return $ b { vars = Map.insert fname (Var tp) (vars b) }
+ _ -> do
+ srt@(Sort tp) <- lispToSort (pipeParser b) rtp
+ withFunList b args $
+ \b' tps args'
+ -> return $ b { vars = Map.insert fname (Fun tps tp) (vars b) }
+ parseAssignment b (L.List [L.Symbol "define-fun",L.Symbol fname,L.List args,rtp,body])
+ = case args of
+ [] -> do
+ srt@(Sort tp) <- lispToSort (pipeParser b) rtp
+ expr <- lispToExprTyped b tp body
+ return $ VarAssignment (UntypedVar fname tp) expr
+ _ -> do
+ srt@(Sort tp) <- lispToSort (pipeParser b) rtp
+ withFunList b args $
+ \b' tps args' -> do
+ body' <- lispToExprTyped b' tp body
+ return $ FunAssignment (UntypedFun fname tps tp) args' body'
+ parseAssignment _ lsp = throwE $ "Invalid model entry: "++show lsp
+ withFunList :: SMTPipe -> [L.Lisp]
+ -> (forall arg. SMTPipe -> List Repr arg -> List PipeVar arg -> LispParse a) -> LispParse a
+ withFunList b [] f = f b Nil Nil
+ withFunList b ((L.List [L.Symbol v,tp]):ls) f = do
+ Sort tp <- lispToSort (pipeParser b) tp
+ withFunList (b { vars = Map.insert v (FunArg tp) (vars b) }) ls $
+ \b' tps args -> f b' (tp ::: tps) ((UntypedVar v tp) ::: args)
+ withFunList _ lsp _ = throwE $ "Invalid fun args: "++show lsp
+parseGetModel _ lsp = throwE $ "Invalid model: "++show lsp
+
+data Sort = forall (t :: Type). Sort (Repr t)
+data Sorts = forall (t :: [Type]). Sorts (List Repr t)
+
+data ParsedFunction fun
+ = ParsedFunction { argumentTypeRequired :: Integer -> Bool
+ , getParsedFunction :: [Maybe Sort] -> LispParse (AnyFunction fun)
+ }
+
+data AnyExpr e = forall (t :: Type). AnyExpr (e t)
+
+instance GShow e => Show (AnyExpr e) where
+ showsPrec p (AnyExpr x) = gshowsPrec p x
+
+data LispParser (v :: Type -> *) (qv :: Type -> *) (fun :: ([Type],Type) -> *) (fv :: Type -> *) (lv :: Type -> *) (e :: Type -> *)
+ = LispParser { parseFunction :: forall a. Maybe Sort -> T.Text
+ -> (forall args res. fun '(args,res) -> LispParse a)
+ -> (forall args res. (IsDatatype res) => Type.Datatype res -> Type.Constr res args -> LispParse a) -- constructor
+ -> (forall args res. (IsDatatype res) => Type.Datatype res -> Type.Constr res args -> LispParse a) -- constructor test
+ -> (forall t args res. (IsDatatype t) => Type.Datatype t -> Type.Field t res -> LispParse a)
+ -> LispParse a
+ , parseDatatype :: forall a. T.Text
+ -> (forall dt. IsDatatype dt
+ => Type.Datatype dt -> LispParse a)
+ -> LispParse a
+ , parseVar :: forall a. Maybe Sort -> T.Text
+ -> (forall t. v t -> LispParse a)
+ -> (forall t. qv t -> LispParse a)
+ -> (forall t. fv t -> LispParse a)
+ -> (forall t. lv t -> LispParse a)
+ -> LispParse a
+ , parseRecursive :: forall a. LispParser v qv fun fv lv e
+ -> Maybe Sort -> L.Lisp
+ -> (forall t. e t -> LispParse a)
+ -> LispParse a
+ , registerQVar :: forall (t :: Type). T.Text -> Repr t
+ -> (qv t,LispParser v qv fun fv lv e)
+ , registerLetVar :: forall (t :: Type). T.Text -> Repr t
+ -> (lv t,LispParser v qv fun fv lv e)
+ }
+
+type LispParse = Except String
+
+-- | Spawn a new SMT solver process and create a pipe to communicate with it.
+createPipe :: String -- ^ Path to the binary of the SMT solver
+ -> [String] -- ^ Command line arguments to be passed to the SMT solver
+ -> IO SMTPipe
+createPipe solver args = do
+ let cmd = (proc solver args) { std_in = CreatePipe
+ , std_out = CreatePipe
+ , std_err = Inherit
+ , close_fds = False }
+ (Just hin,Just hout,_,handle) <- createProcess cmd
+ let p0 = SMTPipe { channelIn = hin
+ , channelOut = hout
+ , processHandle = Just handle
+ , names = Map.empty
+ , vars = Map.empty
+ , datatypes = emptyTypeRegistry
+ , interpolationMode = MathSATInterpolation }
+ putRequest p0 (L.List [L.Symbol "get-info"
+ ,L.Symbol ":name"])
+ resp <- parseResponse p0
+ case resp of
+ L.List [L.Symbol ":name",L.String name] -> case name of
+ "Z3" -> return $ p0 { interpolationMode = Z3Interpolation [] [] }
+ _ -> return p0
+ _ -> return p0
+
+-- | Create a SMT pipe by giving the input and output handle.
+createPipeFromHandle :: Handle -- ^ Input handle
+ -> Handle -- ^ Output handle
+ -> IO SMTPipe
+createPipeFromHandle hin hout = do
+ return SMTPipe { channelIn = hin
+ , channelOut = hout
+ , processHandle = Nothing
+ , names = Map.empty
+ , vars = Map.empty
+ , datatypes = emptyTypeRegistry
+ , interpolationMode = MathSATInterpolation }
+
+lispToExprUntyped :: SMTPipe -> L.Lisp
+ -> (forall (t::Type). Expr SMTPipe t -> LispParse a)
+ -> LispParse a
+lispToExprUntyped st l res = lispToExprWith (pipeParser st) Nothing l $
+ \e -> res (PipeExpr e)
+
+lispToExprTyped :: SMTPipe -> Repr t -> L.Lisp -> LispParse (Expr SMTPipe t)
+lispToExprTyped st tp l = lispToExprWith (pipeParser st) (Just (Sort tp)) l $
+ \e -> case geq tp (getType e) of
+ Just Refl -> return (PipeExpr e)
+ Nothing -> throwE $ show l++" has type "++show (getType e)++", but "++show tp++" was expected."
+
+pipeParser :: SMTPipe
+ -> LispParser PipeVar PipeVar PipeFun PipeVar PipeVar (Expr SMTPipe)
+pipeParser st = parse
+ where
+ parse = LispParser { parseFunction = \srt name fun con test field
+ -> case T.stripPrefix "is-" name of
+ Just con -> case Map.lookup name (allConstructors $ datatypes st) of
+ Just (AnyConstr dt con) -> test dt con
+ _ -> throwE $ "Unknown constructor: "++show name
+ Nothing -> case Map.lookup name (allConstructors $ datatypes st) of
+ Just (AnyConstr dt c) -> con dt c
+ Nothing -> case Map.lookup name (allFields $ datatypes st) of
+ Just (AnyField dt f) -> field dt f
+ Nothing -> case Map.lookup name (vars st) of
+ Just (Fun arg tp)
+ -> fun (UntypedFun name arg tp)
+ _ -> throwE $ "Unknown symbol "++show name
+ , parseDatatype = \name res -> case Map.lookup name (allDatatypes $ datatypes st) of
+ Just (AnyDatatype p) -> res p
+ _ -> throwE $ "Unknown datatype "++show name
+ , parseVar = \srt name v qv fv lv -> case Map.lookup name (vars st) of
+ Just (Var tp)
+ -> v (UntypedVar name tp)
+ Just (QVar tp)
+ -> qv (UntypedVar name tp)
+ Just (FunArg tp)
+ -> fv (UntypedVar name tp)
+ Just (LVar tp)
+ -> lv (UntypedVar name tp)
+ _ -> throwE $ "Unknown variable "++show name
+ , parseRecursive = \parse srt l res -> lispToExprWith parse srt l $
+ \e -> res (PipeExpr e)
+ , registerQVar = \name tp
+ -> (UntypedVar name tp,
+ pipeParser (st { vars = Map.insert name (QVar tp)
+ (vars st) }))
+ , registerLetVar = \name tp
+ -> (UntypedVar name tp,
+ pipeParser (st { vars = Map.insert name (LVar tp)
+ (vars st) }))
+ }
+
+lispToExprWith :: (GShow fun,GShow e,GetFunType fun,GetType e)
+ => LispParser v qv fun fv lv e
+ -> Maybe Sort
+ -> L.Lisp
+ -> (forall (t :: Type).
+ Expression v qv fun fv lv e t
+ -> LispParse a)
+ -> LispParse a
+lispToExprWith p hint (runExcept . lispToConstant -> Right (AnyValue val)) res
+ = res (Const val)
+lispToExprWith p hint (L.Symbol sym) res
+ = parseVar p hint sym (res . Expr.Var) (res . Expr.QVar) (res . Expr.FVar) (res . Expr.LVar) `catchError`
+ (\_ -> do
+ parsed <- lispToFunction p hint (L.Symbol sym)
+ AnyFunction f <- getParsedFunction parsed []
+ case getFunType f of
+ (Nil,_) -> res $ App f Nil
+ _ -> throwError $ "Arguments expected for function "++show sym)
+lispToExprWith p hint (L.List [L.Symbol "_",L.Symbol "as-array",fsym]) res = do
+ parsed <- lispToFunction p el_hint fsym
+ AnyFunction fun <- getParsedFunction parsed idx_hint
+ res (AsArray fun)
+ where
+ (idx_hint,el_hint) = case hint of
+ Nothing -> ([],Nothing)
+ Just (Sort tp) -> case tp of
+ ArrayRepr args el
+ -> (runIdentity $ List.toList (\t -> return (Just $ Sort t)) args,
+ Just $ Sort el)
+lispToExprWith p hint (L.List [L.Symbol "forall",L.List args,body]) res
+ = mkQuant p args $
+ \np args' -> parseRecursive np np (Just (Sort BoolRepr)) body $
+ \body' -> case getType body' of
+ BoolRepr -> res (Quantification Forall args' body')
+lispToExprWith p hint (L.List [L.Symbol "exists",L.List args,body]) res
+ = mkQuant p args $
+ \np args' -> parseRecursive np np (Just (Sort BoolRepr)) body $
+ \body' -> case getType body' of
+ BoolRepr -> res (Quantification Exists args' body')
+lispToExprWith p hint (L.List [L.Symbol "let",L.List args,body]) res
+ = mkLet p args $
+ \np args' -> parseRecursive np np hint body $
+ \body' -> res (Let args' body')
+lispToExprWith p hint (L.List [L.Symbol "as",expr,tp]) res = do
+ srt <- lispToSort p tp
+ lispToExprWith p (Just srt) expr res
+lispToExprWith p hint (L.List (fun:args)) res = do
+ parsed <- lispToFunction p hint fun
+ args' <- matchList (argumentTypeRequired parsed) 0 args
+ let hints = fmap (\arg -> case arg of
+ Left _ -> Nothing
+ Right (AnyExpr e) -> Just $ Sort (getType e)
+ ) args'
+ AnyFunction fun' <- getParsedFunction parsed hints
+ let (argTps,ret) = getFunType fun'
+ args'' <- catchE (makeList p argTps args') $
+ \err -> throwE $ "While parsing arguments of function: "++
+ show fun'++": "++err
+ res $ App fun' args''
+ where
+ matchList _ _ [] = return []
+ matchList f i (e:es) = if f i
+ then parseRecursive p p Nothing e
+ (\e' -> do
+ rest <- matchList f (i+1) es
+ return $ (Right (AnyExpr e')):rest)
+ else do
+ rest <- matchList f (i+1) es
+ return $ (Left e):rest
+ makeList :: (GShow e,GetType e) => LispParser v qv fun fv lv e
+ -> List Repr arg -> [Either L.Lisp (AnyExpr e)] -> LispParse (List e arg)
+ makeList _ Nil [] = return Nil
+ makeList _ Nil _ = throwE $ "Too many arguments to function."
+ makeList p (tp ::: args) (e:es) = case e of
+ Right (AnyExpr e') -> do
+ r <- case geq tp (getType e') of
+ Just Refl -> return e'
+ Nothing -> throwE $ "Argument "++gshowsPrec 11 e' ""++" has wrong type."
+ rs <- makeList p args es
+ return (r ::: rs)
+ Left l -> parseRecursive p p (Just $ Sort tp) l $
+ \e' -> do
+ r <- case geq tp (getType e') of
+ Just Refl -> return e'
+ Nothing -> throwE $ "Argument "++gshowsPrec 11 e' ""++" has wrong type."
+ rs <- makeList p args es
+ return (r ::: rs)
+ makeList _ (_ ::: _) [] = throwE $ "Not enough arguments to function."
+lispToExprWith _ _ lsp _ = throwE $ "Invalid SMT expression: "++show lsp
+
+mkQuant :: LispParser v qv fun fv lv e -> [L.Lisp]
+ -> (forall arg. LispParser v qv fun fv lv e -> List qv arg -> LispParse a)
+ -> LispParse a
+mkQuant p [] f = f p Nil
+mkQuant p ((L.List [L.Symbol name,sort]):args) f = do
+ Sort srt <- lispToSort p sort
+ let (qvar,np) = registerQVar p name srt
+ mkQuant np args $ \p args -> f p (qvar ::: args)
+mkQuant _ lsp _ = throwE $ "Invalid forall/exists parameter: "++show lsp
+
+mkLet :: GetType e
+ => LispParser v qv fun fv lv e -> [L.Lisp]
+ -> (forall arg. LispParser v qv fun fv lv e
+ -> List (LetBinding lv e) arg -> LispParse a)
+ -> LispParse a
+mkLet p [] f = f p Nil
+mkLet p ((L.List [L.Symbol name,expr]):args) f
+ = parseRecursive p p Nothing expr $
+ \expr' -> do
+ let (lvar,np) = registerLetVar p name (getType expr')
+ mkLet np args $ \p args -> f p ((LetBinding lvar expr') ::: args)
+mkLet _ lsp _ = throwE $ "Invalid let parameter: "++show lsp
+
+withEq :: Repr t -> [b]
+ -> (forall n. Natural n -> List Repr (AllEq t n) -> a)
+ -> a
+withEq tp [] f = f Zero Nil
+withEq tp (_:xs) f = withEq tp xs $
+ \n args -> f (Succ n) (tp ::: args)
+
+lispToFunction :: LispParser v qv fun fv lv e
+ -> Maybe Sort -> L.Lisp -> LispParse (ParsedFunction fun)
+lispToFunction _ _ (L.Symbol "=")
+ = return $ ParsedFunction (==0)
+ (\args -> case args of
+ Just (Sort tp):_ -> withEq tp args $
+ \n args
+ -> return $ AnyFunction (Eq tp n)
+ _ -> throwE $ "Cannot derive type of = parameters.")
+lispToFunction _ _ (L.Symbol "distinct")
+ = return $ ParsedFunction (==0)
+ (\args -> case args of
+ Just (Sort tp):_ -> withEq tp args $
+ \n args' -> return $ AnyFunction (Distinct tp n)
+ _ -> throwE $ "Cannot derive type of \"distinct\" parameters.")
+lispToFunction rf sort (L.List [L.Symbol "_",L.Symbol "map",sym]) = do
+ f <- lispToFunction rf sort' sym
+ let reqList 0 = case idx' of
+ Nothing -> True
+ Just _ -> argumentTypeRequired f 0
+ reqList n = argumentTypeRequired f n
+ fun args = do
+ Sorts pidx <- case idx' of
+ Just srts -> return srts
+ Nothing -> case args of
+ Just srt:_ -> case asArraySort srt of
+ Just (idx,_) -> return idx
+ Nothing -> throwE $ "Could not derive type of the array index in map function."
+ _ -> throwE $ "Could not derive type of the array index in map function."
+ argSorts <- mapM (\prx -> case prx of
+ Nothing -> return Nothing
+ Just srt -> do
+ (_,elsrt) <- case asArraySort srt of
+ Just srt' -> return srt'
+ Nothing -> throwE $ "Argument to map function isn't an array."
+ return (Just elsrt)
+ ) args
+ fun' <- getParsedFunction f argSorts
+ return $ mkMap pidx fun'
+ return (ParsedFunction reqList fun)
+ where
+ (sort',idx') = case sort of
+ Just (Sort tp) -> case tp of
+ ArrayRepr idx el
+ -> (Just (Sort el),
+ Just (Sorts idx))
+ _ -> (Nothing,Nothing)
+ _ -> (Nothing,Nothing)
+lispToFunction _ _ (L.Symbol ">=") = lispToOrdFunction Ge
+lispToFunction _ _ (L.Symbol ">") = lispToOrdFunction Gt
+lispToFunction _ _ (L.Symbol "<=") = lispToOrdFunction Le
+lispToFunction _ _ (L.Symbol "<") = lispToOrdFunction Lt
+lispToFunction _ sort (L.Symbol "+") = lispToArithFunction sort Plus
+lispToFunction _ sort (L.Symbol "*") = lispToArithFunction sort Mult
+lispToFunction _ sort (L.Symbol "-") = lispToArithFunction sort Minus
+lispToFunction _ _ (L.Symbol "div") = return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction (ArithIntBin Div))
+lispToFunction _ _ (L.Symbol "mod") = return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction (ArithIntBin Mod))
+lispToFunction _ _ (L.Symbol "rem") = return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction (ArithIntBin Rem))
+lispToFunction _ _ (L.Symbol "/") = return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction Divide)
+lispToFunction _ sort (L.Symbol "abs") = case sort of
+ Just (Sort tp) -> case tp of
+ IntRepr -> return $ ParsedFunction (const False) (\_ -> return $ AnyFunction (Abs NumInt))
+ RealRepr -> return $ ParsedFunction (const False) (\_ -> return $ AnyFunction (Abs NumReal))
+ exp -> throwE $ "abs function can't have type "++show exp
+ Nothing -> return $ ParsedFunction (==0) $
+ \args -> case args of
+ [Just (Sort tp)] -> case tp of
+ IntRepr -> return $ AnyFunction (Abs NumInt)
+ RealRepr -> return $ AnyFunction (Abs NumReal)
+ srt -> throwE $ "abs can't take argument of type "++show srt
+ _ -> throwE $ "abs function takes exactly one argument."
+lispToFunction _ _ (L.Symbol "not")
+ = return $ ParsedFunction (const False) (\_ -> return $ AnyFunction Not)
+lispToFunction _ _ (L.Symbol "and") = return $ lispToLogicFunction And
+lispToFunction _ _ (L.Symbol "or") = return $ lispToLogicFunction Or
+lispToFunction _ _ (L.Symbol "xor") = return $ lispToLogicFunction XOr
+lispToFunction _ _ (L.Symbol "=>") = return $ lispToLogicFunction Implies
+lispToFunction _ _ (L.Symbol "to_real")
+ = return $ ParsedFunction (const False) (\_ -> return $ AnyFunction ToReal)
+lispToFunction _ _ (L.Symbol "to_int")
+ = return$ ParsedFunction (const False) (\_ -> return $ AnyFunction ToInt)
+lispToFunction _ sort (L.Symbol "ite") = case sort of
+ Just (Sort tp)
+ -> return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction (ITE tp))
+ Nothing -> return $ ParsedFunction (==1) $
+ \args -> case args of
+ [_,Just (Sort tp),_]
+ -> return $ AnyFunction (ITE tp)
+ _ -> throwE $ "Invalid arguments to ite function."
+lispToFunction _ _ (L.Symbol "bvule") = return $ lispToBVCompFunction BVULE
+lispToFunction _ _ (L.Symbol "bvult") = return $ lispToBVCompFunction BVULT
+lispToFunction _ _ (L.Symbol "bvuge") = return $ lispToBVCompFunction BVUGE
+lispToFunction _ _ (L.Symbol "bvugt") = return $ lispToBVCompFunction BVUGT
+lispToFunction _ _ (L.Symbol "bvsle") = return $ lispToBVCompFunction BVSLE
+lispToFunction _ _ (L.Symbol "bvslt") = return $ lispToBVCompFunction BVSLT
+lispToFunction _ _ (L.Symbol "bvsge") = return $ lispToBVCompFunction BVSGE
+lispToFunction _ _ (L.Symbol "bvsgt") = return $ lispToBVCompFunction BVSGT
+lispToFunction _ sort (L.Symbol "bvadd") = lispToBVBinFunction sort BVAdd
+lispToFunction _ sort (L.Symbol "bvsub") = lispToBVBinFunction sort BVSub
+lispToFunction _ sort (L.Symbol "bvmul") = lispToBVBinFunction sort BVMul
+lispToFunction _ sort (L.Symbol "bvurem") = lispToBVBinFunction sort BVURem
+lispToFunction _ sort (L.Symbol "bvsrem") = lispToBVBinFunction sort BVSRem
+lispToFunction _ sort (L.Symbol "bvudiv") = lispToBVBinFunction sort BVUDiv
+lispToFunction _ sort (L.Symbol "bvsdiv") = lispToBVBinFunction sort BVSDiv
+lispToFunction _ sort (L.Symbol "bvshl") = lispToBVBinFunction sort BVSHL
+lispToFunction _ sort (L.Symbol "bvlshr") = lispToBVBinFunction sort BVLSHR
+lispToFunction _ sort (L.Symbol "bvashr") = lispToBVBinFunction sort BVASHR
+lispToFunction _ sort (L.Symbol "bvxor") = lispToBVBinFunction sort BVXor
+lispToFunction _ sort (L.Symbol "bvand") = lispToBVBinFunction sort BVAnd
+lispToFunction _ sort (L.Symbol "bvor") = lispToBVBinFunction sort BVOr
+lispToFunction _ sort (L.Symbol "bvnot") = lispToBVUnFunction sort BVNot
+lispToFunction _ sort (L.Symbol "bvneg") = lispToBVUnFunction sort BVNeg
+lispToFunction _ _ (L.Symbol "select")
+ = return $ ParsedFunction (==0)
+ (\args -> case args of
+ Just (Sort arr):_ -> case arr of
+ ArrayRepr idx el
+ -> return $ AnyFunction (Select idx el)
+ srt -> throwE $ "Invalid argument type to select function: "++show srt
+ _ -> throwE $ "Invalid arguments to select function.")
+lispToFunction _ sort (L.Symbol "store") = case sort of
+ Just (Sort srt) -> case srt of
+ ArrayRepr idx el
+ -> return (ParsedFunction (const False)
+ (\_ -> return $ AnyFunction
+ (Store idx el)))
+ srt' -> throwE $ "Invalid argument types to store function: "++show srt'
+ Nothing -> return $ ParsedFunction (==0)
+ (\args -> case args of
+ Just (Sort arr):_ -> case arr of
+ ArrayRepr idx el
+ -> return $ AnyFunction
+ (Store idx el)
+ srt -> throwE $ "Invalid first argument type to store function: "++show srt
+ _ -> throwE $ "Invalid arguments to store function.")
+lispToFunction r sort (L.List [L.Symbol "as",L.Symbol "const",sig]) = do
+ Sort rsig <- case sort of
+ Just srt -> return srt
+ Nothing -> lispToSort r sig
+ case rsig of
+ ArrayRepr idx el
+ -> return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction (ConstArray idx el))
+ _ -> throwE $ "Invalid signature for (as const ...) function."
+lispToFunction _ sort (L.Symbol "concat")
+ = return $ ParsedFunction (const True)
+ (\args -> case args of
+ [Just (Sort tp1),Just (Sort tp2)]
+ -> case (tp1,tp2) of
+ (BitVecRepr sz1,BitVecRepr sz2)
+ -> return $ AnyFunction (Concat sz1 sz2)
+ _ -> throwE $ "Invalid argument types to concat function."
+ _ -> throwE $ "Wrong number of arguments to concat function.")
+lispToFunction _ sort (L.List [L.Symbol "_",L.Symbol "extract",L.Number (L.I end),L.Number (L.I start)])
+ = return $ ParsedFunction (==0)
+ (\args -> case args of
+ [Just (Sort srt)] -> case srt of
+ BitVecRepr size
+ | start <= end &&
+ end <= bwSize size
+ -> case TL.someNatVal start of
+ Just (TL.SomeNat start')
+ -> case TL.someNatVal (end-start+1) of
+ Just (TL.SomeNat len')
+ -> return $ AnyFunction
+ (Extract size (bw start')
+ (bw len'))
+ | otherwise -> throwE $ "Invalid extract parameters."
+ srt -> throwE $ "Invalid type of extract argument: "++show srt
+ _ -> throwE $ "Wrong number of arguments to extract function.")
+lispToFunction _ sort (L.List [L.Symbol "_",L.Symbol "divisible",L.Number (L.I div)])
+ = return $ ParsedFunction (const False)
+ (\_ -> return $ AnyFunction (Divisible div))
+lispToFunction rf sort (L.List [sym,lispToList -> Just sig,tp]) = do
+ nsort <- lispToSort rf tp
+ fun <- lispToFunction rf (Just nsort) sym
+ rsig <- lispToSorts rf sig $
+ \sig' -> return $ runIdentity $ List.toList (\tp -> return $ Just (Sort tp)) sig'
+ return $ ParsedFunction (const False) (\_ -> getParsedFunction fun rsig)
+lispToFunction rf sort (L.Symbol name)
+ = parseFunction rf sort name
+ (p . Expr.Fun)
+ getCon
+ getTest
+ getField
+ where
+ p f = return $ ParsedFunction (const False) (const (return $ AnyFunction f))
+
+ getCon :: IsDatatype dt
+ => Datatype dt -> Constr dt csig
+ -> LispParse (ParsedFunction fun)
+ getCon (dt :: Datatype dt) con
+ = return $
+ ParsedFunction (case sort of
+ Just _ -> const False
+ Nothing -> \i -> List.indexDyn (fields con) i $
+ \f -> not $ Set.null $
+ containedParameter
+ (fieldType f) Set.empty)
+ (\argSorts -> case sort of
+ Just (Sort (DataRepr (dt'::Datatype dt') par)) -> case eqT :: Maybe (dt :~: dt') of
+ Nothing -> throwError "Type mismatch"
+ Just Refl -> return $ AnyFunction $ Expr.Constructor dt par con
+ Nothing -> case inferArgs argSorts (fields con) IMap.empty of
+ Nothing -> throwError "Cannot infer parameter type"
+ Just mp -> case fullArgs 0 (IMap.toList mp) (parameters dt) $
+ \par -> AnyFunction $ Expr.Constructor
+ dt par con of
+ Nothing -> throwError "Cannot infer parameter type"
+ Just res -> return res)
+
+ getTest :: IsDatatype dt => Datatype dt -> Constr dt csig
+ -> LispParse (ParsedFunction fun)
+ getTest (dt :: Datatype dt) con
+ = return $
+ ParsedFunction (\i -> i==0 && (case parameters dt of
+ Zero -> False
+ _ -> True))
+ (\argSorts -> case parameters dt of
+ Zero -> return $ AnyFunction $ Expr.Test dt Nil con
+ _ -> case argSorts of
+ [Just (Sort (DataRepr (dt'::Datatype dt') par))] -> case eqT :: Maybe (dt :~: dt') of
+ Nothing -> throwError "Type mismatch"
+ Just Refl -> return $ AnyFunction $ Expr.Test dt par con)
+
+ getField :: IsDatatype dt => Datatype dt -> Field dt tp
+ -> LispParse (ParsedFunction fun)
+ getField (dt::Datatype dt) f
+ = return $
+ ParsedFunction (\i -> i==0 && (case parameters dt of
+ Zero -> False
+ _ -> True))
+ (\argSorts -> case parameters dt of
+ Zero -> return $ AnyFunction $ Expr.Field dt Nil f
+ _ -> case argSorts of
+ [Just (Sort (DataRepr (dt'::Datatype dt') par))] -> case eqT :: Maybe (dt :~: dt') of
+ Nothing -> throwError "Type mismatch"
+ Just Refl -> return $ AnyFunction $ Expr.Field dt par f
+ _ -> throwError "Cannot infer field type")
+
+ inferArgs :: IsDatatype dt => [Maybe Sort] -> List (Field dt) tps -> IntMap Sort -> Maybe (IntMap Sort)
+ inferArgs [] Nil mp = Just mp
+ inferArgs (Nothing : args) (_ ::: fs) mp = inferArgs args fs mp
+ inferArgs (Just (Sort arg) : args) (f ::: fs) mp = do
+ mp1 <- typeInference arg (fieldType f)
+ (\p tp cmp -> let p' = fromInteger $ naturalToInteger p
+ in case IMap.lookup p' cmp of
+ Nothing -> Just $ IMap.insert p' (Sort tp) cmp
+ Just (Sort tp') -> do
+ Refl <- geq tp tp'
+ return cmp) mp
+ inferArgs args fs mp1
+lispToFunction _ _ lsp = throwE $ "Unknown function: "++show lsp
+
+fullArgs :: Int -> [(Int,Sort)] -> Natural len -> (forall tps. (List.Length tps ~ len) => List Repr tps -> a) -> Maybe a
+fullArgs cpos [] Zero f = Just $ f Nil
+fullArgs cpos ((pos,Sort srt):srts) (Succ n) f
+ = if cpos==pos
+ then fullArgs (cpos+1) srts n $ \lst -> f (srt ::: lst)
+ else Nothing
+fullArgs _ _ _ _ = Nothing
+
+lispToOrdFunction :: OrdOp -> LispParse (ParsedFunction fun)
+lispToOrdFunction op
+ = return (ParsedFunction (==0)
+ (\argSrt -> case argSrt of
+ (Just (Sort srt)):_ -> case srt of
+ IntRepr -> return $ AnyFunction (Ord NumInt op)
+ RealRepr -> return $ AnyFunction (Ord NumReal op)
+ srt' -> throwE $ "Invalid argument to "++show op++" function: "++show srt'
+ _ -> throwE $ "Wrong number of arguments to "++show op++" function."))
+
+lispToArithFunction :: Maybe Sort -> ArithOp -> LispParse (ParsedFunction fun)
+lispToArithFunction sort op = case sort of
+ Just (Sort tp) -> case tp of
+ IntRepr -> return (ParsedFunction (const False)
+ (\args -> withEq IntRepr args $
+ \n _ -> return $ AnyFunction (Arith NumInt op n)))
+ RealRepr -> return (ParsedFunction (const False)
+ (\args -> withEq RealRepr args $
+ \n _ -> return $ AnyFunction (Arith NumReal op n)))
+ srt -> throwE $ "Invalid type of "++show op++" function: "++show srt
+ Nothing -> return (ParsedFunction (==0)
+ (\argSrt -> case argSrt of
+ (Just (Sort srt)):_ -> case srt of
+ IntRepr -> withEq IntRepr argSrt $
+ \n args
+ -> return $ AnyFunction (Arith NumInt op n)
+ RealRepr -> withEq RealRepr argSrt $
+ \n args
+ -> return $ AnyFunction (Arith NumReal op n)
+ srt' -> throwE $ "Wrong argument type to "++show op++" function: "++show srt'
+ _ -> throwE $ "Wrong number of arguments to "++show op++" function."))
+
+lispToLogicFunction :: LogicOp -> ParsedFunction fun
+lispToLogicFunction op
+ = ParsedFunction (const False)
+ (\args -> withEq BoolRepr args $
+ \n args
+ -> return $ AnyFunction (Logic op n))
+
+lispToBVCompFunction :: BVCompOp -> ParsedFunction fun
+lispToBVCompFunction op
+ = ParsedFunction (==0)
+ (\args -> case args of
+ [Just (Sort srt),_] -> case srt of
+ BitVecRepr bw -> return $ AnyFunction (BVComp op bw)
+ srt -> throwE $ "Invalid argument type to "++show op++" function: "++show srt
+ _ -> throwE $ "Wrong number of arguments to "++show op++" function.")
+
+lispToBVBinFunction :: Maybe Sort -> BVBinOp -> LispParse (ParsedFunction fun)
+lispToBVBinFunction (Just (Sort srt)) op = case srt of
+ BitVecRepr bw -> return $ ParsedFunction (const False) $
+ \_ -> return $ AnyFunction (BVBin op bw)
+ srt' -> throwE $ "Invalid argument type to "++show op++" function: "++show srt'
+lispToBVBinFunction Nothing op
+ = return $ ParsedFunction (==0) $
+ \args -> case args of
+ [Just (Sort srt),_] -> case srt of
+ BitVecRepr bw -> return $ AnyFunction (BVBin op bw)
+ srt' -> throwE $ "Invalid argument type to "++show op++" function: "++show srt'
+ _ -> throwE $ "Wrong number of arguments to "++show op++" function."
+
+lispToBVUnFunction :: Maybe Sort -> BVUnOp -> LispParse (ParsedFunction fun)
+lispToBVUnFunction (Just (Sort srt)) op = case srt of
+ BitVecRepr bw -> return $ ParsedFunction (const False) $
+ \_ -> return $ AnyFunction (BVUn op bw)
+ srt' -> throwE $ "Invalid argument type to "++show op++" function: "++show srt'
+lispToBVUnFunction Nothing op
+ = return $ ParsedFunction (==0) $
+ \args -> case args of
+ [Just (Sort srt)] -> case srt of
+ BitVecRepr bw -> return $ AnyFunction (BVUn op bw)
+ srt' -> throwE $ "Invalid argument type to "++show op++" function: "++show srt'
+ _ -> throwE $ "Wrong number of arguments to "++show op++" function."
+
+mkMap :: List Repr idx -> AnyFunction fun -> AnyFunction fun
+mkMap idx (AnyFunction f) = AnyFunction (Map idx f)
+
+asArraySort :: Sort -> Maybe (Sorts,Sort)
+asArraySort (Sort tp) = case tp of
+ ArrayRepr idx el
+ -> return (Sorts idx,Sort el)
+ _ -> Nothing
+
+lispToList :: L.Lisp -> Maybe [L.Lisp]
+lispToList (L.Symbol "()") = Just []
+lispToList (L.List lst) = Just lst
+lispToList _ = Nothing
+
+lispToSort :: LispParser v qv fun fv lv e -> L.Lisp -> LispParse Sort
+lispToSort _ (L.Symbol "Bool") = return (Sort BoolRepr)
+lispToSort _ (L.Symbol "Int") = return (Sort IntRepr)
+lispToSort _ (L.Symbol "Real") = return (Sort RealRepr)
+lispToSort r (L.List ((L.Symbol "Array"):tps)) = do
+ Sort rtp' <- lispToSort r rtp
+ lispToSorts r idx (\idx' -> return $ Sort (ArrayRepr idx' rtp'))
+ where
+ (idx,rtp) = splitLast tps
+ splitLast [x] = ([],x)
+ splitLast (x:xs) = let (xs',y') = splitLast xs
+ in (x:xs',y')
+lispToSort _ (L.List [L.Symbol "_",L.Symbol "BitVec",L.Number (L.I n)])
+ = case TL.someNatVal n of
+ Just (TL.SomeNat w) -> return (Sort (BitVecRepr (bw w)))
+lispToSort r (L.Symbol name)
+ = parseDatatype r name $ \dt -> case geq (parameters dt) Zero of
+ Just Refl -> return $ Sort (DataRepr dt Nil)
+ Nothing -> throwE $ "Wrong sort for type "++show name
+lispToSort r (L.List (L.Symbol name:args))
+ = parseDatatype r name $
+ \dt -> lispToSorts r args $
+ \args' -> case geq (List.length args') (parameters dt) of
+ Just Refl -> return $ Sort (DataRepr dt args')
+ Nothing -> throwE $ "Wrong number of arguments for type "++show name
+lispToSort _ lsp = throwE $ "Invalid SMT type: "++show lsp
+
+lispToSorts :: LispParser v qv fun fv lv e -> [L.Lisp]
+ -> (forall (arg :: [Type]). List Repr arg -> LispParse a)
+ -> LispParse a
+lispToSorts _ [] f = f Nil
+lispToSorts r (x:xs) f = do
+ Sort tp <- lispToSort r x
+ lispToSorts r xs $
+ \tps -> f (tp ::: tps)
+
+lispToValue :: SMTPipe -> Maybe Sort -> L.Lisp -> LispParse AnyValue
+lispToValue b hint l = case runExcept $ lispToConstant l of
+ Right r -> return r
+ Left e -> lispToConstrConstant b hint l
+
+lispToConstant :: L.Lisp -> LispParse AnyValue
+lispToConstant (L.Symbol "true") = return (AnyValue (BoolValue True))
+lispToConstant (L.Symbol "false") = return (AnyValue (BoolValue False))
+lispToConstant (lispToNumber -> Just n) = return (AnyValue (IntValue n))
+lispToConstant (lispToReal -> Just n) = return (AnyValue (RealValue n))
+lispToConstant (lispToBitVec -> Just (val,sz))
+ = case TL.someNatVal sz of
+ Just (TL.SomeNat w) -> return (AnyValue (BitVecValue val (bw w)))
+lispToConstant l = throwE $ "Invalid constant "++show l
+
+lispToConstrConstant :: SMTPipe -> Maybe Sort -> L.Lisp
+ -> LispParse AnyValue
+lispToConstrConstant b hint sym = do
+ (constr,args) <- case sym of
+ L.Symbol s -> return (s,[])
+ L.List ((L.Symbol s):args) -> return (s,args)
+ _ -> throwE $ "Invalid constant: "++show sym
+ case Map.lookup constr (allConstructors $ datatypes b) of
+ Just (AnyConstr (dt::Datatype dt) con)
+ -> makeList (case hint of
+ Just (Sort (DataRepr dt' par))
+ -> IMap.fromList $ runIdentity $ List.toListIndex
+ (\i srt -> return (fromInteger $ naturalToInteger i,
+ Sort srt))
+ par
+ Nothing -> IMap.empty) (fields con) args $
+ \par rargs -> case fullArgs 0 (IMap.toList par) (parameters dt) $
+ \rpar -> case instantiate
+ (runIdentity $ List.mapM
+ (return.fieldType) (fields con))
+ rpar of
+ (tsig,Refl) -> do
+ Refl <- geq tsig
+ (runIdentity $ List.mapM
+ (return.getType) rargs)
+ return $ AnyValue $ DataValue $
+ construct rpar con rargs of
+ Just (Just res) -> return res
+ _ -> throwE "Type error in constructor"
+ Nothing -> throwE $ "Invalid constructor "++show constr
+ where
+ makeList :: IsDatatype dt
+ => IntMap Sort
+ -> List (Type.Field dt) arg
+ -> [L.Lisp]
+ -> (forall narg. List.Length arg ~ List.Length narg
+ => IntMap Sort -> List Value narg -> LispParse a)
+ -> LispParse a
+ makeList par Nil [] res = res par Nil
+ makeList _ Nil _ _ = throwE $ "Too many arguments to constructor."
+ makeList par (f ::: fs) (l:ls) res
+ = partialInstantiation (fieldType f)
+ (\n g -> do
+ Sort parTp <- IMap.lookup (fromInteger $ naturalToInteger n) par
+ return $ g parTp) $
+ \ftp -> do
+ AnyValue v <- lispToValue b (Just $ Sort ftp) l
+ case typeInference ftp (valueType v)
+ (\pos ptp cpar -> let pos' = fromInteger $ naturalToInteger pos
+ in case IMap.lookup pos' cpar of
+ Just (Sort ptp') -> case geq ptp ptp' of
+ Just Refl -> return cpar
+ Nothing -> Nothing
+ Nothing -> return $ IMap.insert pos' (Sort ptp) cpar) par of
+ Nothing -> throwE "Type error in constructor arguments."
+ Just npar -> makeList npar fs ls $
+ \rpar rest -> res rpar (v ::: rest)
+ makeList _ (_ ::: _) [] _ = throwE $ "Not enough arguments to constructor."
+
+lispToNumber :: L.Lisp -> Maybe Integer
+lispToNumber (L.Number (L.I n)) = Just n
+lispToNumber (L.List [L.Symbol "-",n]) = do
+ n' <- lispToNumber n
+ return (negate n')
+lispToNumber _ = Nothing
+
+lispToReal :: L.Lisp -> Maybe Rational
+lispToReal (L.Number (L.D n)) = Just $ toRational n
+lispToReal (L.Number (L.I n)) = Just $ fromInteger n
+lispToReal (L.List [L.Symbol "/",v1,v2]) = do
+ r1 <- lispToReal v1
+ r2 <- lispToReal v2
+ return $ r1 / r2
+lispToReal (L.List [L.Symbol "-",v]) = do
+ r <- lispToReal v
+ return $ -r
+lispToReal _ = Nothing
+
+lispToBitVec :: L.Lisp -> Maybe (Integer,Integer)
+lispToBitVec (L.List [L.Symbol "_",L.Symbol (T.stripPrefix "bv" -> Just val),L.Number (L.I sz)])
+ = case T.decimal val of
+ Right (rval,"") -> Just (rval,sz)
+ _ -> Nothing
+lispToBitVec (L.Symbol (T.stripPrefix "#x" -> Just bv)) = case T.hexadecimal bv of
+ Right (rbv,"") -> Just (rbv,(fromIntegral $ T.length bv)*4)
+ _ -> Nothing
+lispToBitVec (L.Symbol (T.stripPrefix "#b" -> Just bv))
+ | T.all (\c -> c=='0' || c=='1') bv = Just (T.foldl (\v c -> case c of
+ '0' -> v*2
+ '1' -> v*2+1) 0 bv,
+ fromIntegral $ T.length bv)
+ | otherwise = Nothing
+lispToBitVec _ = Nothing
+
+exprToLisp :: TypeRegistry T.Text T.Text T.Text
+ -> Expression PipeVar PipeVar PipeFun PipeVar PipeVar (Expr SMTPipe) t
+ -> L.Lisp
+exprToLisp reg
+ = runIdentity . exprToLispWith
+ (\(UntypedVar v _) -> return $ L.Symbol v)
+ (\(UntypedVar v _) -> return $ L.Symbol v)
+ (\(UntypedFun v _ _) -> return $ L.Symbol v)
+ (\dt con -> case Map.lookup (AnyConstr dt con) (revConstructors reg) of
+ Just sym -> return $ L.Symbol sym)
+ (\dt con -> case Map.lookup (AnyConstr dt con) (revConstructors reg) of
+ Just sym -> return $ L.Symbol $ T.append "is-" sym)
+ (\dt field -> case Map.lookup (AnyField dt field) (revFields reg) of
+ Just sym -> return $ L.Symbol sym)
+ (\(UntypedVar v _) -> return $ L.Symbol v)
+ (\(UntypedVar v _) -> return $ L.Symbol v)
+ (\(PipeExpr v) -> return $ exprToLisp reg v)
+
+exprToLispWith :: (Monad m,GetType v,GetType qv,GetType fv,GetType lv,GetFunType fun,GetType e)
+ => (forall (t' :: Type).
+ v t' -> m L.Lisp) -- ^ variables
+ -> (forall (t' :: Type).
+ qv t' -> m L.Lisp) -- ^ quantified variables
+ -> (forall (arg :: [Type]) (res :: Type).
+ fun '(arg,res) -> m L.Lisp) -- ^ functions
+ -> (forall (arg :: [Type]) (dt :: [Type] -> (Type -> *) -> *).
+ IsDatatype dt =>
+ Datatype dt -> Type.Constr dt arg -> m L.Lisp) -- ^ constructor
+ -> (forall (arg :: [Type]) (dt :: [Type] -> (Type -> *) -> *).
+ IsDatatype dt =>
+ Datatype dt -> Type.Constr dt arg -> m L.Lisp) -- ^ constructor tests
+ -> (forall (dt :: [Type] -> (Type -> *) -> *) (res :: Type).
+ IsDatatype dt =>
+ Datatype dt -> Type.Field dt res -> m L.Lisp) -- ^ field accesses
+ -> (forall t.
+ fv t -> m L.Lisp) -- ^ function variables
+ -> (forall t.
+ lv t -> m L.Lisp) -- ^ let variables
+ -> (forall (t' :: Type).
+ e t' -> m L.Lisp) -- ^ sub expressions
+ -> Expression v qv fun fv lv e t
+ -> m L.Lisp
+exprToLispWith f _ _ _ _ _ _ _ _ (Expr.Var v) = f v
+exprToLispWith _ f _ _ _ _ _ _ _ (Expr.QVar v) = f v
+exprToLispWith _ _ _ _ _ _ f _ _ (Expr.FVar v) = f v
+exprToLispWith _ _ _ _ _ _ _ f _ (Expr.LVar v) = f v
+-- This is a special case because the argument order is different
+exprToLispWith _ _ f g h i _ _ j (Expr.App (Store _ _) (arr ::: val ::: idx)) = do
+ arr' <- j arr
+ idx' <- List.toList j idx
+ val' <- j val
+ return $ L.List ((L.Symbol "store"):arr':idx'++[val'])
+exprToLispWith _ _ f g h i _ _ j e@(Expr.App fun args) = do
+ let needAs = case fun of
+ Constructor dt par con -> not $ determines dt con
+ _ -> False
+ args' <- List.toList j args
+ sym <- functionSymbol f g h i fun
+ let c = case args' of
+ [] -> sym
+ _ -> L.List $ sym:args'
+ rc = if needAs
+ then L.List [L.Symbol "as",c,typeSymbol Set.empty (getType e)]
+ else c
+ return rc
+
+exprToLispWith _ _ _ f _ _ _ _ _ (Expr.Const val) = valueToLisp f val
+exprToLispWith _ _ f g h i _ _ _ (Expr.AsArray fun) = do
+ sym <- functionSymbolWithSig f g h i fun
+ return $ L.List [L.Symbol "_"
+ ,L.Symbol "as-array"
+ ,sym]
+exprToLispWith _ f _ _ _ _ _ _ g (Expr.Quantification q args body) = do
+ bind <- List.toList (\arg -> do
+ sym <- f arg
+ return $ L.List [sym,typeSymbol Set.empty $ getType arg]
+ ) args
+ body' <- g body
+ return $ L.List [L.Symbol (case q of
+ Expr.Forall -> "forall"
+ Expr.Exists -> "exists")
+ ,L.List bind
+ ,body']
+exprToLispWith _ _ _ _ _ _ _ f g (Expr.Let args body) = do
+ binds <- List.toList (\bind -> do
+ sym <- f (letVar bind)
+ expr <- g (letExpr bind)
+ return $ L.List [sym,expr]
+ ) args
+ body' <- g body
+ return $ L.List [L.Symbol "let"
+ ,L.List binds
+ ,body']
+
+valueToLisp :: Monad m
+ => (forall arg tp. (IsDatatype tp)
+ => Datatype tp -> Type.Constr tp arg -> m L.Lisp)
+ -> Value t -> m L.Lisp
+valueToLisp _ (BoolValue True) = return $ L.Symbol "true"
+valueToLisp _ (BoolValue False) = return $ L.Symbol "false"
+valueToLisp _ (IntValue n) = return $ numToLisp n
+valueToLisp _ (RealValue n)
+ = return $ L.List [L.Symbol "/"
+ ,numToLisp $ numerator n
+ ,numToLisp $ denominator n]
+valueToLisp _ (BitVecValue n bw)
+ = return $ L.List [L.Symbol "_"
+ ,L.Symbol (T.pack $ "bv"++show rn)
+ ,L.Number $ L.I bw']
+ where
+ bw' = bwSize bw
+ rn = n `mod` 2^bw'
+valueToLisp f v@(DataValue val) = do
+ let (dt,par) = datatypeGet val
+ case deconstruct val of
+ ConApp { constructor = con
+ , arguments = args } -> do
+ let needAs = not $ determines dt con
+ con' <- f dt con
+ args' <- List.toList (valueToLisp f) args
+ let c = case args' of
+ [] -> con'
+ xs -> L.List (con' : xs)
+ rc = if needAs
+ then L.List [L.Symbol "as",c,typeSymbol Set.empty
+ (getType v)]
+ else c
+ return rc
+
+isOverloaded :: Function fun sig -> Bool
+isOverloaded (Expr.Eq _ _) = True
+isOverloaded (Expr.Distinct _ _) = True
+isOverloaded (Expr.Map _ _) = True
+isOverloaded (Expr.Ord _ _) = True
+isOverloaded (Expr.Arith _ _ _) = True
+isOverloaded (Expr.Abs _) = True
+isOverloaded (Expr.ITE _) = True
+isOverloaded (Expr.BVComp _ _) = True
+isOverloaded (Expr.BVBin _ _) = True
+isOverloaded (Expr.BVUn _ _) = True
+isOverloaded (Expr.Select _ _) = True
+isOverloaded (Expr.Store _ _) = True
+isOverloaded (Expr.ConstArray _ _) = True
+isOverloaded (Expr.Concat _ _) = True
+isOverloaded (Expr.Extract _ _ _) = True
+isOverloaded _ = False
+
+functionSymbol :: (Monad m,GetFunType fun)
+ => (forall (arg' :: [Type]) (res' :: Type).
+ fun '(arg',res') -> m L.Lisp) -- ^ How to render user functions
+ -> (forall (arg' :: [Type]) (dt :: [Type] -> (Type -> *) -> *).
+ IsDatatype dt =>
+ Datatype dt -> Type.Constr dt arg' -> m L.Lisp) -- ^ How to render constructor applications
+ -> (forall (arg' :: [Type]) (dt :: [Type] -> (Type -> *) -> *).
+ IsDatatype dt =>
+ Datatype dt -> Type.Constr dt arg' -> m L.Lisp) -- ^ How to render constructor tests
+ -> (forall (dt :: [Type] -> (Type -> *) -> *) (res' :: Type).
+ IsDatatype dt =>
+ Datatype dt -> Type.Field dt res' -> m L.Lisp) -- ^ How to render field acceses
+ -> Function fun '(arg,res) -> m L.Lisp
+functionSymbol f _ _ _ (Expr.Fun g) = f g
+functionSymbol _ _ _ _ (Expr.Eq _ _) = return $ L.Symbol "="
+functionSymbol _ _ _ _ (Expr.Distinct _ _) = return $ L.Symbol "distinct"
+functionSymbol f g h i (Expr.Map _ j) = do
+ sym <- functionSymbolWithSig f g h i j
+ return $ L.List [L.Symbol "_"
+ ,L.Symbol "map"
+ ,sym]
+functionSymbol _ _ _ _ (Ord _ op) = return $ ordSymbol op
+functionSymbol _ _ _ _ (Arith _ op _) = return $ arithSymbol op
+functionSymbol _ _ _ _ (ArithIntBin Div) = return $ L.Symbol "div"
+functionSymbol _ _ _ _ (ArithIntBin Mod) = return $ L.Symbol "mod"
+functionSymbol _ _ _ _ (ArithIntBin Rem) = return $ L.Symbol "rem"
+functionSymbol _ _ _ _ Divide = return $ L.Symbol "/"
+functionSymbol _ _ _ _ (Abs _) = return $ L.Symbol "abs"
+functionSymbol _ _ _ _ Not = return $ L.Symbol "not"
+functionSymbol _ _ _ _ (Logic And _) = return $ L.Symbol "and"
+functionSymbol _ _ _ _ (Logic Or _) = return $ L.Symbol "or"
+functionSymbol _ _ _ _ (Logic XOr _) = return $ L.Symbol "xor"
+functionSymbol _ _ _ _ (Logic Implies _) = return $ L.Symbol "=>"
+functionSymbol _ _ _ _ ToReal = return $ L.Symbol "to_real"
+functionSymbol _ _ _ _ ToInt = return $ L.Symbol "to_int"
+functionSymbol _ _ _ _ (ITE _) = return $ L.Symbol "ite"
+functionSymbol _ _ _ _ (BVComp op _) = return $ L.Symbol $ case op of
+ BVULE -> "bvule"
+ BVULT -> "bvult"
+ BVUGE -> "bvuge"
+ BVUGT -> "bvugt"
+ BVSLE -> "bvsle"
+ BVSLT -> "bvslt"
+ BVSGE -> "bvsge"
+ BVSGT -> "bvsgt"
+functionSymbol _ _ _ _ (BVBin op _) = return $ L.Symbol $ case op of
+ BVAdd -> "bvadd"
+ BVSub -> "bvsub"
+ BVMul -> "bvmul"
+ BVURem -> "bvurem"
+ BVSRem -> "bvsrem"
+ BVUDiv -> "bvudiv"
+ BVSDiv -> "bvsdiv"
+ BVSHL -> "bvshl"
+ BVLSHR -> "bvlshr"
+ BVASHR -> "bvashr"
+ BVXor -> "bvxor"
+ BVAnd -> "bvand"
+ BVOr -> "bvor"
+functionSymbol _ _ _ _ (BVUn op _) = return $ L.Symbol $ case op of
+ BVNot -> "bvnot"
+ BVNeg -> "bvneg"
+functionSymbol _ _ _ _ (Select _ _) = return $ L.Symbol "select"
+functionSymbol _ _ _ _ (Store _ _) = return $ L.Symbol "store"
+functionSymbol _ _ _ _ (ConstArray idx el)
+ = return $ L.List [L.Symbol "as"
+ ,L.Symbol "const"
+ ,typeSymbol Set.empty (ArrayRepr idx el)]
+functionSymbol _ _ _ _ (Concat _ _) = return $ L.Symbol "concat"
+functionSymbol _ _ _ _ (Extract bw start len)
+ = return $ L.List [L.Symbol "_"
+ ,L.Symbol "extract"
+ ,L.Number $ L.I $ start'+len'-1
+ ,L.Number $ L.I start']
+ where
+ start' = bwSize start
+ len' = bwSize len
+functionSymbol _ g _ _ (Constructor dt par con) = g dt con
+functionSymbol _ _ h _ (Test dt par con) = h dt con
+functionSymbol _ _ _ i (Expr.Field dt par f) = i dt f
+functionSymbol _ _ _ _ (Divisible n) = return $ L.List [L.Symbol "_"
+ ,L.Symbol "divisible"
+ ,L.Number $ L.I n]
+
+functionSymbolWithSig :: (Monad m,GetFunType fun)
+ => (forall (arg' :: [Type]) (res' :: Type).
+ fun '(arg',res') -> m L.Lisp) -- ^ How to render user functions
+ -> (forall (arg' :: [Type])
+ (dt :: [Type] -> (Type -> *) -> *).
+ IsDatatype dt =>
+ Datatype dt -> Type.Constr dt arg' -> m L.Lisp) -- ^ How to render constructor applications
+ -> (forall (arg' :: [Type])
+ (dt :: [Type] -> (Type -> *) -> *).
+ IsDatatype dt =>
+ Datatype dt -> Type.Constr dt arg' -> m L.Lisp) -- ^ How to render constructor tests
+ -> (forall (dt :: [Type] -> (Type -> *) -> *)
+ (res' :: Type).
+ IsDatatype dt =>
+ Datatype dt -> Type.Field dt res' -> m L.Lisp) -- ^ How to render field acceses
+ -> Function fun '(arg,res) -> m L.Lisp
+functionSymbolWithSig f g h i j = do
+ sym <- functionSymbol f g h i j
+ if isOverloaded j
+ then return $ L.List [sym
+ ,typeList arg
+ ,typeSymbol Set.empty res]
+ else return sym
+ where
+ (arg,res) = getFunType j
+
+typeSymbol :: Set String -> Repr t -> L.Lisp
+typeSymbol _ BoolRepr = L.Symbol "Bool"
+typeSymbol _ IntRepr = L.Symbol "Int"
+typeSymbol _ RealRepr = L.Symbol "Real"
+typeSymbol _ (BitVecRepr n) = L.List [L.Symbol "_"
+ ,L.Symbol "BitVec"
+ ,L.Number (L.I $ bwSize n)]
+typeSymbol recDt (ArrayRepr idx el)
+ = L.List ((L.Symbol "Array"):
+ runIdentity (List.toList (return.typeSymbol recDt) idx) ++
+ [typeSymbol recDt el])
+typeSymbol recDt (DataRepr dt par)
+ | Set.member (datatypeName dt) recDt
+ = L.Symbol (T.pack $ datatypeName dt)
+ | otherwise = L.List $ [L.Symbol (T.pack $ datatypeName dt)]++
+ (runIdentity $ List.toList (return.typeSymbol recDt) par)
+typeSymbol _ (ParameterRepr n)
+ = L.Symbol (T.pack $ "a"++show (naturalToInteger n))
+
+
+typeList :: List Repr t -> L.Lisp
+typeList Nil = L.Symbol "()"
+typeList args = L.List (runIdentity $ List.toList
+ (return.typeSymbol Set.empty) args)
+
+ordSymbol :: OrdOp -> L.Lisp
+ordSymbol Ge = L.Symbol ">="
+ordSymbol Gt = L.Symbol ">"
+ordSymbol Le = L.Symbol "<="
+ordSymbol Lt = L.Symbol "<"
+
+arithSymbol :: ArithOp -> L.Lisp
+arithSymbol Plus = L.Symbol "+"
+arithSymbol Mult = L.Symbol "*"
+arithSymbol Minus = L.Symbol "-"
+
+numToLisp :: Integer -> L.Lisp
+numToLisp n = if n>=0
+ then L.Number $ L.I n
+ else L.List [L.Symbol "-"
+ ,L.Number $ L.I $ abs n]
+
+clearInput :: SMTPipe -> IO ()
+clearInput pipe = do
+ r <- hReady (channelOut pipe)
+ if r
+ then (do
+ _ <- BS.hGetSome (channelOut pipe) 1024
+ clearInput pipe)
+ else return ()
+
+putRequest :: SMTPipe -> L.Lisp -> IO ()
+putRequest pipe expr = do
+ clearInput pipe
+ toByteStringIO (BS.hPutStr $ channelIn pipe) (mappend (L.fromLispExpr expr) flush)
+ BS8.hPutStrLn (channelIn pipe) ""
+ hFlush (channelIn pipe)
+
+parseResponse :: SMTPipe -> IO L.Lisp
+parseResponse pipe = do
+ str <- BS.hGetLine (channelOut pipe)
+ let continue (Done _ r) = return r
+ continue res@(Partial _) = do
+ line <- BS.hGetLine (channelOut pipe)
+ continue (feed (feed res line) (BS8.singleton '\n'))
+ continue (Fail str' ctx msg) = error $ "Error parsing "++show str'++" response in "++show ctx++": "++msg
+ continue $ parse L.lisp (BS8.snoc str '\n')
+
+genName :: SMTPipe -> String -> (T.Text,SMTPipe)
+genName pipe name = (sym,pipe { names = nnames })
+ where
+ (sym,nnames) = genName' (names pipe) name
+
+genName' :: Map String Int -> String -> (T.Text,Map String Int)
+genName' names name = case Map.lookup name names of
+ Nothing -> (T.pack name',Map.insert name 0 names)
+ Just n -> (T.pack $ name' ++ "_" ++ show (n+1),
+ Map.insert name (n+1) names)
+ where
+ name' = escapeName name
+ escapeName :: String -> String
+ escapeName [] = []
+ escapeName ('_':xs) = '_':'_':escapeName xs
+ escapeName (x:xs) = x:escapeName xs
+
+tacticToLisp :: Tactic -> L.Lisp
+tacticToLisp Skip = L.Symbol "skip"
+tacticToLisp (AndThen ts) = L.List ((L.Symbol "and-then"):fmap tacticToLisp ts)
+tacticToLisp (OrElse ts) = L.List ((L.Symbol "or-else"):fmap tacticToLisp ts)
+tacticToLisp (ParOr ts) = L.List ((L.Symbol "par-or"):fmap tacticToLisp ts)
+tacticToLisp (ParThen t1 t2) = L.List [L.Symbol "par-then"
+ ,tacticToLisp t1
+ ,tacticToLisp t2]
+tacticToLisp (TryFor t n) = L.List [L.Symbol "try-for"
+ ,tacticToLisp t
+ ,L.Number $ L.I n]
+tacticToLisp (If c t1 t2) = L.List [L.Symbol "if"
+ ,probeToLisp c
+ ,tacticToLisp t1
+ ,tacticToLisp t2]
+tacticToLisp (FailIf c) = L.List [L.Symbol "fail-if"
+ ,probeToLisp c]
+tacticToLisp (UsingParams (CustomTactic name) []) = L.Symbol (T.pack name)
+tacticToLisp (UsingParams (CustomTactic name) pars)
+ = L.List ([L.Symbol "using-params"
+ ,L.Symbol $ T.pack name]++
+ concat [ [L.Symbol (T.pack $ ':':pname)
+ ,case par of
+ ParBool True -> L.Symbol "true"
+ ParBool False -> L.Symbol "false"
+ ParInt i -> L.Number $ L.I i
+ ParDouble i -> L.Number $ L.D i]
+ | (pname,par) <- pars ])
+
+probeToLisp :: Probe a -> L.Lisp
+probeToLisp (ProbeBoolConst b)
+ = L.Symbol $ if b then "true" else "false"
+probeToLisp (ProbeIntConst i)
+ = L.Number $ L.I i
+probeToLisp (ProbeAnd ps)
+ = L.List ((L.Symbol "and"):
+ fmap probeToLisp ps)
+probeToLisp (ProbeOr ps)
+ = L.List ((L.Symbol "or"):
+ fmap probeToLisp ps)
+probeToLisp (ProbeNot p)
+ = L.List [L.Symbol "not"
+ ,probeToLisp p]
+probeToLisp (ProbeEq p1 p2)
+ = L.List [L.Symbol "="
+ ,probeToLisp p1
+ ,probeToLisp p2]
+probeToLisp (ProbeGt p1 p2)
+ = L.List [L.Symbol ">"
+ ,probeToLisp p1
+ ,probeToLisp p2]
+probeToLisp (ProbeGe p1 p2)
+ = L.List [L.Symbol ">="
+ ,probeToLisp p1
+ ,probeToLisp p2]
+probeToLisp (ProbeLt p1 p2)
+ = L.List [L.Symbol "<"
+ ,probeToLisp p1
+ ,probeToLisp p2]
+probeToLisp (ProbeGe p1 p2)
+ = L.List [L.Symbol "<="
+ ,probeToLisp p1
+ ,probeToLisp p2]
+probeToLisp IsPB = L.Symbol "is-pb"
+probeToLisp ArithMaxDeg = L.Symbol "arith-max-deg"
+probeToLisp ArithAvgDeg = L.Symbol "arith-avg-deg"
+probeToLisp ArithMaxBW = L.Symbol "arith-max-bw"
+probeToLisp ArithAvgBW = L.Symbol "arith-avg-bw"
+probeToLisp IsQFLIA = L.Symbol "is-qflia"
+probeToLisp IsQFLRA = L.Symbol "is-qflra"
+probeToLisp IsQFLIRA = L.Symbol "is-qflira"
+probeToLisp IsILP = L.Symbol "is-ilp"
+probeToLisp IsQFNIA = L.Symbol "is-qfnia"
+probeToLisp IsQFNRA = L.Symbol "is-qfnra"
+probeToLisp IsNIA = L.Symbol "is-nia"
+probeToLisp IsNRA = L.Symbol "is-nra"
+probeToLisp IsUnbounded = L.Symbol "is-unbounded"
+probeToLisp Memory = L.Symbol "memory"
+probeToLisp Depth = L.Symbol "depth"
+probeToLisp Size = L.Symbol "size"
+probeToLisp NumExprs = L.Symbol "num-exprs"
+probeToLisp NumConsts = L.Symbol "num-consts"
+probeToLisp NumBoolConsts = L.Symbol "num-bool-consts"
+probeToLisp NumArithConsts = L.Symbol "num-arith-consts"
+probeToLisp NumBVConsts = L.Symbol "num-bv-consts"
+probeToLisp Strat.ProduceProofs = L.Symbol "produce-proofs"
+probeToLisp ProduceModel = L.Symbol "produce-model"
+probeToLisp Strat.ProduceUnsatCores = L.Symbol "produce-unsat-cores"
+probeToLisp HasPatterns = L.Symbol "has-patterns"
+probeToLisp IsPropositional = L.Symbol "is-propositional"
+probeToLisp IsQFBV = L.Symbol "is-qfbv"
+probeToLisp IsQFBVEQ = L.Symbol "is-qfbv-eq"
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/smtlib2-pipe.cabal b/smtlib2-pipe.cabal
new file mode 100644
--- /dev/null
+++ b/smtlib2-pipe.cabal
@@ -0,0 +1,29 @@
+Name: smtlib2-pipe
+Version: 1.0
+Author: Henning Günther
+Maintainer: guenther@forsyte.at
+Synopsis: A type-safe interface to communicate with an SMT solver.
+Stability: provisional
+Category: SMT, Formal Methods, Theorem Provers, Symbolic Computation
+License: GPL-3
+License-File: LICENSE
+Build-Type: Simple
+Cabal-Version: >=1.8
+
+Source-Repository head
+ Type: git
+ Location: https://github.com/hguenther/smtlib2.git
+
+Library
+ Build-Depends: smtlib2 >= 1.0 && < 1.1, base >=4 && <5, text, containers, process, atto-lisp >=0.2, attoparsec, mtl, bytestring, blaze-builder, dependent-sum, transformers
+ Extensions: GADTs,FlexibleContexts,FlexibleInstances,ExistentialQuantification,KindSignatures,DataKinds,TypeFamilies,AllowAmbiguousTypes,TypeOperators,MultiParamTypeClasses,OverloadedStrings,ScopedTypeVariables,RankNTypes,GeneralizedNewtypeDeriving,ViewPatterns,CPP,StandaloneDeriving,DeriveDataTypeable
+ GHC-Options: -fwarn-unused-imports
+ Exposed-Modules:
+ Language.SMTLib2.Pipe
+ Language.SMTLib2.Pipe.Internals
+
+Test-Suite test-smtlib2-pipe
+ Type: detailed-0.9
+ Test-Module: PipeTest
+ Hs-Source-Dirs: test
+ Build-Depends: base >=4 && <5, smtlib2, smtlib2-pipe==1.0, smtlib2-quickcheck >= 1.0 && < 1.1, Cabal, cabal-test-quickcheck
diff --git a/test/PipeTest.hs b/test/PipeTest.hs
new file mode 100644
--- /dev/null
+++ b/test/PipeTest.hs
@@ -0,0 +1,12 @@
+module PipeTest where
+
+import Language.SMTLib2.Pipe
+import Language.SMTLib2.QuickCheck
+
+import Distribution.TestSuite
+import Distribution.TestSuite.QuickCheck
+import Data.Either
+
+tests :: IO [Test]
+tests = return [testProperty "round-trip"
+ (roundTripTest emptyContext (createPipe "z3" ["-smt2","-in"]))]