TypeCheck.hs revision 5a13581acc5a76d392c1dec01657bb3efd4dcf2d
{- |
Module : $Header$
Copyright : (c) Christian Maeder and Uni Bremen 2003
License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt
Maintainer : maeder@tzi.de
Stability : experimental
Portability : portable
type inference based on
Principal Type Schemes for Functional Programs with Overloading and
Subtyping, Geoffrey S. Smith, Science of Computer Programming 23(2-3),
pp. 197-226, December 1994
-}
module HasCASL.TypeCheck where
import HasCASL.Unify
import HasCASL.AsUtils
import HasCASL.Merge
import HasCASL.VarDecl
import HasCASL.As
import HasCASL.Le
import HasCASL.MixAna
import HasCASL.TypeAna
import HasCASL.MapTerm
import HasCASL.Constrain
import HasCASL.ProgEq
import HasCASL.MinType
import qualified Common.Lib.Map as Map
import qualified Common.Lib.Set as Set
import qualified Common.Lib.Rel as Rel
import Common.Id
import Common.Result
import Common.GlobalAnnotations
import Common.Lib.State
import Data.List as List
import Control.Exception(assert)
substTerm :: Subst -> Term -> Term
substTerm s = mapTerm (id, subst s)
resolveTerm :: GlobalAnnos -> Maybe Type -> Term -> State Env (Maybe Term)
resolveTerm ga mt trm = do
mtrm <- resolve ga trm
case mtrm of
Nothing -> return Nothing
Just t -> typeCheck mt t
instantiate :: TypeScheme -> State Env (Type, [Type], Constraints)
instantiate (TypeScheme tArgs t _) =
do let ls = leaves (< 0) t -- generic vars
vs = map snd ls
ts <- toEnvState $ mkSubst vs
let s = Map.fromList $ zip (map fst ls) ts
(ats, cs) = unzip $ mapArgs s (zip (map fst vs) ts) tArgs
return (subst s t, ats, Set.fromList cs)
mapArgs :: Subst -> [(Id, Type)] -> [TypeArg] -> [(Type, Constrain)]
mapArgs s ts = foldr ( \ (TypeArg i _ vk _ _ _ _) l ->
maybe l ( \ (_, t) -> (t, case vk of
MissingKind -> error "mapArgs"
VarKind k -> Kinding t k
Downset super -> Subtyping t $ subst s super) : l) $
find ( \ (j, _) -> i == j) ts) []
instOpInfo :: OpInfo -> State Env (Type, [Type], Constraints, OpInfo)
instOpInfo oi = do
(ty, inst, cs) <- instantiate $ opType oi
return (ty, inst, cs, oi)
lookupError :: Type -> [OpInfo] -> String
lookupError ty ois =
" with (maximal) type: " ++ showPretty ty "\n"
++ " known types:\n " ++
showSepList ("\n "++) (showPretty . opType) ois ""
checkList :: [Maybe Type] -> [Term]
-> State Env [(Subst, Constraints, [Type], [Term])]
checkList [] [] = return [(eps, noC, [], [])]
checkList (ty : rty) (trm : rt) = do
fts <- infer ty trm >>= reduce False
combs <- mapM ( \ (sf, cs, tyf, tf) -> do
vs <- gets localVars
putLocalVars $ substVarTypes sf vs
rts <- checkList (map (fmap (subst sf)) rty) rt
putLocalVars vs
return $ map ( \ (sr, cr, tys, tts) ->
(compSubst sf sr,
substC sr cs `joinC` cr,
subst sr tyf : tys,
tf : tts)) rts) fts
return $ concat combs
checkList _ _ = error "checkList"
-- | reduce a substitution, if true try to find a monomorphic substitution
reduce :: Bool -> [(Subst, Constraints, Type, Term)]
-> State Env [(Subst, Constraints, Type, Term)]
reduce b alts = do
te <- get
combs <- mapM ( \ (s, cr, ty, tr) -> do
Result ds mc <- toEnvState $ shapeRel te cr
addDiags $ map (improveDiag tr) ds
return $ case mc of
Nothing -> []
Just (cs, qs, trel) -> let
s1 = compSubst s cs
ms = if b then monoSubsts te
(Rel.transClosure $ Rel.union (fromTypeMap $ typeMap te)
$ trel) (subst cs ty)
else eps
s2 = compSubst s1 ms
in [(s2, substC ms $ foldr ( \ (a, t) -> insertC
(Subtyping a t))
qs $ Rel.toList trel, subst s2 ty,
substTerm s2 tr)]) alts
return $ concat combs
typeCheck :: Maybe Type -> Term -> State Env (Maybe Term)
typeCheck mt trm =
do alts <- infer mt trm >>= reduce True
te <- get
let p = getRange trm
if null alts then
do addDiags [mkDiag Error "no typing for" trm]
return Nothing
else if null $ tail alts then do
let (_, cs, ty, t) = head alts
(ds, rcs) = simplify te cs
es = map ( \ d -> d {diagKind = Hint, diagPos = p}) ds
addDiags es
if Set.null rcs then return ()
else addDiags [(mkDiag Error ("in term '"
++ showPretty t "' of type '"
++ showPretty ty "'\n unresolved constraints")
rcs){diagPos = p}]
return $ Just t
else let alts3 = filter ( \ (_, cs, _, _) ->
Set.null $ snd $ simplify te cs) alts
falts = typeNub te q2p alts3 in
if null falts then do
addDiags [mkDiag Error "no constraint resolution for" trm]
addDiags $ map (\ (_, cs, _, _) -> (mkDiag Hint
"simplification failed for" cs){diagPos = p}) alts
return Nothing
else if null $ tail falts then
let (_, _, _, t) = head falts in
return $ Just t
else
do addDiags [Diag Error
("ambiguous typings \n " ++
showSepList ("\n " ++)
( \ (n, t) -> shows n . (". " ++) . showPretty t)
(zip [1..(5::Int)] $ map ( \ (_,_,_,t) ->
t) falts) "")
p]
return Nothing
freshTypeVar :: Range -> State Env Type
freshTypeVar p =
do (var, c) <- toEnvState $ freshVar p
return $ TypeName var rStar c
freshVars :: [Term] -> State Env [Type]
freshVars l = mapM (freshTypeVar . getRange) l
substVarTypes s = Map.map ( \ (VarDefn t) -> VarDefn $ subst s t)
-- | infer type of application, if true consider lifting for lazy types
inferAppl :: Range -> Maybe Type -> Term -> Term
-> State Env [(Subst, Constraints, Type, Term)]
inferAppl ps mt t1 t2 = do
let origAppl = ApplTerm t1 t2 ps
aty <- freshTypeVar $ getRange t2
rty <- case mt of
Nothing -> freshTypeVar $ getRange t1
Just ty -> return ty
ops <- infer (Just $ mkFunArrType aty PFunArr rty) t1
>>= reduce False
te <- get
combs <- mapM ( \ (sf, cf, funty, tf) -> do
let (sfty, frty) = case getTypeAppl funty of
(topTy, [paty, prty]) |
lesserType te topTy (toType $ arrowId PFunArr) ->
(paty, prty)
_ -> (subst sf aty, subst sf rty)
vs <- gets localVars
putLocalVars $ substVarTypes sf vs
args <- infer (Just sfty) t2 >>= reduce False
putLocalVars vs
let combs2 = map ( \ (sa, ca, _, ta) ->
let sr = compSubst sf sa
nTy = subst sa frty in
[(sr, joinC ca $ substC sa cf, nTy,
TypedTerm (ApplTerm tf ta ps)
Inferred nTy ps)]) args
return $ concat combs2) ops
let res = concat combs
if null res then
addDiags [case mt of
Nothing -> mkDiag Hint
"untypable application" origAppl
Just ty -> mkDiag Hint
("untypable application (with result type: "
++ showPretty ty ")\n")
origAppl]
else return ()
return res
getTypeOf :: Term -> Type
getTypeOf trm = case trm of
TypedTerm _ q t _ -> case q of InType -> unitType
_ -> t
QualVar (VarDecl _ t _ _) -> t
QualOp _ _ (TypeScheme [] t _) _ -> t
TupleTerm ts _ -> if null ts then unitType
else mkProductType (map getTypeOf ts)
QuantifiedTerm _ _ t _ -> getTypeOf t
LetTerm _ _ t _ -> getTypeOf t
AsPattern _ p _ -> getTypeOf p
_ -> error "getTypeOf"
-- | infer type of term, if true consider lifting for lazy types
infer :: Maybe Type -> Term
-> State Env [(Subst, Constraints, Type, Term)]
infer mt trm = do
e <- get
tm <- gets typeMap
as <- gets assumps
vs <- gets localVars
case trm of
qv@(QualVar (VarDecl _ t _ _)) -> return $
case mt of
Nothing -> [(eps, noC, t, qv)]
Just ty -> [(eps, insertC (Subtyping t ty) noC, t, qv)]
QualOp br (InstOpId i ts qs) sc ps -> do
(ty, inst, cs) <- instantiate sc
let Result ds ms = mguList tm (if null ts then inst else ts) inst
addDiags $ map (improveDiag trm) ds
return $ case ms of
Nothing -> []
Just s ->
let nTy = subst s ty
ncs = substC s cs
qv = TypedTerm (QualOp br
(InstOpId i (map (subst s) inst) qs) sc ps)
Inferred nTy ps
in case mt of
Nothing -> [(s, ncs, nTy, qv)]
Just inTy -> [(s, insertC (Subtyping nTy $ subst s inTy)
ncs, nTy, qv)]
ResolvedMixTerm i ts ps ->
if null ts then case Map.lookup i vs of
Just (VarDefn t) -> infer mt $ QualVar $ VarDecl i t Other ps
Nothing -> do
let ois = opInfos $ Map.findWithDefault (OpInfos []) i as
insts <- mapM instOpInfo ois
let ls = map ( \ (ty, is, cs, oi) ->
(eps, ty, is, case mt of
Just inTy -> insertC (Subtyping ty inTy) cs
Nothing -> cs, oi)) insts
if null ls then addDiags
[Diag Hint
("no type match for: " ++ showId i "" ++ case mt of
Nothing -> ""
Just inTy -> '\n' : lookupError inTy ois) (posOfId i)]
else return ()
return $ typeNub e q2p $ map
( \ (s, ty, is, cs, oi) ->
let od = opDefn oi
br = case od of
NoOpDefn v -> v
Definition v _ -> v
_ -> Op
in (s, cs, ty, case opType oi of
sc@(TypeScheme [] sTy _) -> assert (sTy == ty) $
QualOp br (InstOpId i [] nullRange) sc ps
sc -> TypedTerm (QualOp br
(InstOpId i is nullRange) sc ps)
Inferred ty ps)) ls
else inferAppl ps mt (ResolvedMixTerm i [] ps)
$ mkTupleTerm ts ps
ApplTerm t1 t2 ps -> inferAppl ps mt t1 t2
TupleTerm ts ps -> if null ts then return
[(eps, case mt of
Nothing -> noC
Just ty -> insertC (Subtyping unitType ty) noC,
unitType, trm)]
else do
ls <- checkList (map (const Nothing) ts) ts
return $ map ( \ (su, cs, tys, trms) ->
let nTy = mkProductType tys in
(su, case mt of
Nothing -> cs
Just ty -> insertC (Subtyping nTy
$ subst su ty) cs, nTy,
assert (and $ zipWith (==) tys
$ map (subst su . getTypeOf) trms) $
mkTupleTerm trms ps)) ls
TypedTerm t qual ty ps -> do
case qual of
InType -> do
vTy <- freshTypeVar ps
rs <- infer Nothing t
return $ map ( \ (s, cs, typ, tr) ->
let sTy = subst s ty in
(s, insertC (Subtyping sTy vTy)
$ insertC (Subtyping typ vTy)
$ case mt of
Nothing -> cs
Just jTy -> insertC (Subtyping (subst s jTy)
unitType) cs,
unitType,
TypedTerm tr qual sTy ps)) rs
AsType -> do
vTy <- freshTypeVar ps
rs <- infer Nothing t
return $ map ( \ (s, cs, typ, tr) ->
let sTy = subst s ty in
(s, insertC (Subtyping sTy vTy)
$ insertC (Subtyping typ vTy)
$ case mt of
Nothing -> cs
Just jTy -> insertC (Subtyping sTy
$ subst s jTy) cs,
sTy, TypedTerm tr qual sTy ps)) rs
_ -> do
rs <- infer (Just ty) t
return $ map ( \ (s, cs, _, tr) ->
let sTy = subst s ty in
(s, case mt of
Nothing -> cs
Just jTy -> insertC (Subtyping sTy
$ subst s jTy) cs,
sTy, if getTypeOf tr == sTy then tr
else TypedTerm tr qual sTy ps)) rs
QuantifiedTerm quant decls t ps -> do
mapM_ addGenVarDecl decls
rs <- infer (Just unitType) t
putLocalVars vs
putTypeMap tm
return $ map ( \ (s, cs, typ, tr) ->
(s, case mt of
Nothing -> cs
Just ty -> insertC (Subtyping (subst s ty)
unitType) cs,
typ, QuantifiedTerm quant decls tr ps)) rs
LambdaTerm pats part resTrm ps -> do
pvs <- freshVars pats
rty <- freshTypeVar $ getRange resTrm
let myty = getFunType rty part pvs
ls <- checkList (map Just pvs) pats
rs <- mapM ( \ ( s, cs, _, nps) -> do
mapM_ (addLocalVar True) $ concatMap extractVars nps
es <- infer (Just $ subst s rty) resTrm
putLocalVars vs
return $ map ( \ (s2, cr, _, rtm) ->
let s3 = compSubst s s2
typ = subst s3 myty in
(s3, joinC (substC s2 cs) $
case mt of
Nothing -> cr
Just ty -> insertC (Subtyping typ
$ subst s3 ty) cr,
typ, TypedTerm
(LambdaTerm nps part rtm ps)
Inferred typ ps)) es) ls
return $ concat rs
CaseTerm ofTrm eqs ps -> do
ts <- infer Nothing ofTrm
rty <- case mt of
Nothing -> freshTypeVar $ getRange trm
Just ty -> return ty
if null ts then addDiags [mkDiag Hint
"unresolved of-term in case" ofTrm]
else return ()
rs <- mapM ( \ (s1, cs, oty, otrm) -> do
es <- inferCaseEqs oty (subst s1 rty) eqs
return $ map ( \ (s2, cr, _, ty, nes) ->
(compSubst s1 s2,
substC s2 cs `joinC` cr, ty,
TypedTerm (CaseTerm otrm nes ps)
Inferred ty ps)) es) ts
return $ concat rs
LetTerm br eqs inTrm ps -> do
es <- inferLetEqs eqs
rs <- mapM ( \ (s1, cs, _, nes) -> do
mapM_ (addLocalVar True) $ concatMap
( \ (ProgEq p _ _) -> extractVars p) nes
ts <- infer mt inTrm
return $ map ( \ (s2, cr, ty, nt) ->
(compSubst s1 s2,
substC s2 cs `joinC` cr,
ty, assert (getTypeOf nt == ty) $
LetTerm br nes nt ps)) ts) es
putLocalVars vs
return $ concat rs
AsPattern (VarDecl v _ ok qs) pat ps -> do
pats <- infer mt pat
return $ map ( \ (s1, cs, t1, p1) -> (s1, cs, t1,
AsPattern (VarDecl v t1 ok qs) p1 ps)) pats
_ -> do ty <- freshTypeVar $ getRange trm
addDiags [mkDiag Error "unexpected term" trm]
return [(eps, noC, ty, trm)]
inferLetEqs :: [ProgEq] -> State Env [(Subst, Constraints, [Type], [ProgEq])]
inferLetEqs es = do
let pats = map (\ (ProgEq p _ _) -> p) es
trms = map (\ (ProgEq _ t _) -> t) es
qs = map (\ (ProgEq _ _ q) -> q) es
do vs <- gets localVars
newPats <- checkList (map (const Nothing) pats) pats
combs <- mapM ( \ (sf, pcs, tys, pps) -> do
mapM_ (addLocalVar True) $ concatMap extractVars pps
newTrms <- checkList (map Just tys) trms
return $ map ( \ (sr, tcs, tys2, tts ) ->
(compSubst sf sr,
joinC tcs $ substC sr pcs, tys2,
zipWith3 ( \ p t q -> ProgEq (substTerm sr p) t q)
pps tts qs)) newTrms) newPats
putLocalVars vs
return $ concat combs
inferCaseEq :: Type -> Type -> ProgEq
-> State Env [(Subst, Constraints, Type, Type, ProgEq)]
inferCaseEq pty tty (ProgEq pat trm ps) = do
pats1 <- infer (Just pty) pat >>= reduce False
e <- get
let pats = filter ( \ (_, _, _, p) -> isPat e p) pats1
if null pats then addDiags [mkDiag Hint "unresolved case pattern" pat]
else return ()
vs <- gets localVars
es <- mapM ( \ (s, cs, ty, p) -> do
mapM_ (addLocalVar True) $ extractVars p
ts <- infer (Just $ subst s tty) trm >>= reduce False
putLocalVars vs
return $ map ( \ (st, cr, tyt, t) ->
(compSubst s st,
substC st cs `joinC` cr,
subst st ty, tyt,
ProgEq p t ps)) ts) pats
return $ concat es
inferCaseEqs :: Type -> Type -> [ProgEq]
-> State Env [(Subst, Constraints, Type, Type, [ProgEq])]
inferCaseEqs pty tTy [] = return [(eps, noC, pty, tTy, [])]
inferCaseEqs pty tty (eq:eqs) = do
fts <- inferCaseEq pty tty eq
rs <- mapM (\ (_, cs, pty1, tty1, ne) -> do
rts <- inferCaseEqs pty1 tty1 eqs
return $ map ( \ (s2, cr, pty2, tty2, nes) ->
(s2,
substC s2 cs `joinC` cr,
pty2, tty2, ne:nes)) rts) fts
return $ concat rs