{- |
Module : ./HasCASL/TypeCheck.hs
Description : type checking terms and program equations
Copyright : (c) Christian Maeder and Uni Bremen 2003
License : GPLv2 or higher, see LICENSE.txt
Maintainer : Christian.Maeder@dfki.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
( typeCheck
, resolveTerm
) where
import HasCASL.Unify
import HasCASL.VarDecl
import HasCASL.As
import HasCASL.Builtin
import HasCASL.FoldType
import HasCASL.Le
import HasCASL.PrintLe
import HasCASL.AsUtils
import HasCASL.MixAna
import HasCASL.TypeAna
import HasCASL.MapTerm
import HasCASL.FoldTerm
import HasCASL.Constrain
import HasCASL.ProgEq
import HasCASL.MinType
import qualified Data.Map as Map
import qualified Data.Set as Set
import Common.Id
import Common.GlobalAnnotations
import Common.Result
import Common.DocUtils
import Common.Lib.State
import Data.Maybe (catMaybes)
import Control.Monad (when, unless)
substTerm :: Subst -> Term -> Term
substTerm s = mapTerm (id, subst s)
-- | mixfix and type resolution
resolveTerm :: Type -> Term -> State Env (Maybe Term)
resolveTerm mt trm = do
mtrm <- resolve trm
case mtrm of
Nothing -> return Nothing
Just t -> typeCheck mt t
-- | get a constraint from a type argument instantiated with a type
mkConstraint :: (Type, VarKind) -> Constrain
mkConstraint (ty, vk) = case vk of
MissingKind -> error "mkConstraint"
VarKind k -> Kinding ty k
Downset super -> Subtyping ty super
instantiate :: [Type] -> TypeScheme
-> State Env (Maybe (Type, [(Type, VarKind)]))
instantiate tys sc@(TypeScheme tArgs t _) =
if null tys || length tys /= length tArgs then
if null tys then fmap Just $ toEnvState $ freshInst sc
else do
addDiags [mkDiag Hint ("for type scheme '" ++
showDoc t "' wrong length of instantiation list") tys]
return Nothing
else let s = Map.fromList $ zip [-1, -2 ..] tys
in return $ Just
(substGen s t, zip tys $ map (substTypeArg s) tArgs)
instOpInfo :: [Type] -> OpInfo
-> State Env (Maybe (Type, [Type], Constraints, OpInfo))
instOpInfo tys oi = do
m <- instantiate tys $ opType oi
return $ case m of
Just (ty, cl) ->
Just (ty, map fst cl, Set.fromList $ map mkConstraint cl, oi)
Nothing -> Nothing
{- This function has the problem that the type of an earlier component may
restrict the types of following components too much. -}
checkList :: Bool -> [Maybe Type] -> [Term]
-> State Env [(Subst, Constraints, [Type], [Term])]
checkList isP mtys trms = case (mtys, trms) of
(ty : rty, trm : rt) -> do
fts0 <- inferWithMaybeType isP ty trm
fts <- reduce True fts0
combs <- mapM ( \ (sf, cs, tyf, tf) -> do
vs <- gets localVars
putLocalVars $ substVarTypes sf vs
rts <- checkList isP (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
_ -> return [(eps, noC, [], [])]
-- | reduce a substitution
reduceR :: Bool -> Env -> (Subst, Constraints, Type, Term)
-> State Int (Result (Subst, Constraints, Type, Term))
reduceR doMono te (s, cr, ty, tr) = do
Result ds0 mc <- shapeRelAndSimplify True te cr
$ if doMono then Just ty else Nothing
let ds = map (improveDiag tr) ds0
return $ case mc of
Nothing -> Result ds Nothing
Just (s1, qs) -> let
s2 = compSubst s s1
in Result ds $ Just
(s2, qs, subst s1 ty, substTerm s2 tr)
-- | reduce a substitution
reduce :: Bool -> [(Subst, Constraints, Type, Term)]
-> State Env [(Subst, Constraints, Type, Term)]
reduce doMono alts = do
te <- get
combs <- mapM (\ alt -> do
Result ds mc <- toEnvState $ reduceR doMono te alt
addDiags ds
case mc of
Nothing -> return []
Just q -> return [q]) alts
return $ concat combs
checkForUninstantiatedVars :: GlobalAnnos -> Term -> Range -> State Env ()
checkForUninstantiatedVars ga t p = let
tys = getAllVarTypes t
in unless (null tys) $ addDiags
[(mkDiag Error ("in term '" ++ showGlobalDoc ga t
"'\n are uninstantiated type variables")
$ Set.toList $ Set.unions
$ map (Set.fromList . freeTVarIds) tys)
{diagPos = p}]
simplifyTypedTerms :: Env -> Term -> Term
simplifyTypedTerms e = foldTerm mapRec
{ foldTypedTerm = \ _ nt q ty ps ->
let ntyped = TypedTerm nt q ty ps
ityped = TypedTerm nt Inferred ty ps
in case getTypeOf nt of
Nothing -> ntyped
Just ty2 -> let isSubT = lesserType e ty2 ty in
case q of
InType | isSubT -> unitTerm trueId ps
_ -> case nt of
TypedTerm nt2 q2 _ _
| q2 == AsType && q /= InType && lesserType e ty ty2
-> TypedTerm nt2 q2 ty ps
| q == AsType && elem q2 [OfType, Inferred] && isSubT
-> ityped
| otherwise -> ntyped
_ -> if q == AsType && isSubT then ityped else ntyped }
-- | type checking a term
typeCheck :: Type -> Term -> State Env (Maybe Term)
typeCheck exTy trm =
do alts0 <- inferWithMaybeType False (Just exTy) trm
alts <- reduce True alts0
te <- get
let p = getRange trm
ga = globAnnos te
case typeNub te q2p alts of
[] -> do
addDiags [mkNiceDiag ga Error "no typing for" trm]
return Nothing
[(_, rcs, ty, t)] -> do
unless (Set.null rcs)
$ addDiags [(mkDiag Error ("in term '"
++ showGlobalDoc ga t "' of type '"
++ showDoc ty "'\n unresolved constraints")
rcs) {diagPos = p}]
checkForUninstantiatedVars ga t p
return $ Just $ simplifyTypedTerms te t
falts -> do
addDiags [Diag Error
("ambiguous typings\n " ++
showSepList ("\n " ++)
( \ (n, t) -> shows n . (". " ++) . showDoc t)
(zip [1 .. (5 :: Int)] $ map ( \ (_, _, _, t) ->
t) falts) "")
p]
return Nothing
freshTypeVar :: Term -> State Env Type
freshTypeVar t =
do (var, c) <- toEnvState $ freshVar $ Id [] [] $ getRange t
return $ TypeName var rStar c
substVarTypes s = Map.map ( \ (VarDefn t) -> VarDefn $ subst s t)
warnEmpty :: Maybe Type -> Term -> [a] -> State Env ()
warnEmpty mt trm res = do
ga <- gets globAnnos
when (null res) $ addDiags [mkNiceDiag ga Hint ("untypeable term" ++
case mt of
Nothing -> ""
Just ty -> " (with type: " ++ showGlobalDoc ga ty ")") trm]
-- | infer type of application, consider lifting for lazy types
inferAppl :: Bool -> Range -> Term -> Term
-> State Env [(Subst, Constraints, Type, Term)]
inferAppl isP ps t1 t2 = do
ops <- infer isP t1
warnEmpty Nothing t1 ops
vs <- gets localVars
e <- get
combs <- mapM ( \ (sf, cf, funty, tf) -> do
(ok, sfty, frty, sub) <- case getTypeAppl funty of
(topTy, [paty, prty]) |
lesserType e topTy $ toFunType PFunArr ->
return (True, Just paty, prty, False)
(topTy, [prty]) |
lesserType e topTy lazyTypeConstr ->
return (True, Just unitType, prty, False)
(TypeName _ _ c, []) | c > 0 -> do
rty <- freshTypeVar t1
return (True, Nothing, rty, True)
_ -> return (False, Nothing, funty, False)
if ok then do
putLocalVars $ substVarTypes sf vs
args <- inferWithMaybeType isP sfty t2
warnEmpty sfty t2 args
putLocalVars vs
return $ map ( \ (sa, ca, arty, ta) ->
let nTy = subst sa frty in
(compSubst sf sa, (if sub then
insertC (Subtyping (subst sa funty)
$ mkFunArrType arty PFunArr nTy) else id)
$ joinC ca $ substC sa cf, nTy,
TypedTerm (ApplTerm tf ta ps)
Inferred nTy ps)) args
else return []) ops
reduce False $ concat combs
getAllVarTypes :: Term -> [Type]
getAllVarTypes = filter (not . null . freeTVars) . getAllTypes
mkTypedTerm :: Term -> Type -> Term
mkTypedTerm trm ty = case trm of
TupleTerm ts ps | not (null ts) -> let
n = length ts
(topTy, tArgs) = getTypeAppl ty
in if n > 1 && topTy == toProdType n ps
&& length tArgs == n then
TupleTerm (zipWith mkTypedTerm ts tArgs) ps
else TypedTerm trm Inferred ty ps
LetTerm br eqs inTrm ps -> LetTerm br eqs (mkTypedTerm inTrm ty) ps
QuantifiedTerm quant decls t ps ->
QuantifiedTerm quant decls (mkTypedTerm t ty) ps
_ -> TypedTerm trm Inferred ty $ getRange trm
-- | efficiently infer type of a monomorphic tuple term
inferWithMaybeType :: Bool -> Maybe Type -> Term
-> State Env [(Subst, Constraints, Type, Term)]
inferWithMaybeType isP mt trm = case (trm, mt) of
(TupleTerm ts@(_ : _ : _) ps, Just ty) -> case getTypeAppl ty of
(TypeName i _ _, argTys@(_ : _ : _)) | isProductId i ->
if length ts == length argTys then
if all (null . freeTVars) argTys then do
-- remaining type variables would not become instantiated
ls <- checkList isP (map Just argTys) ts
return $ map ( \ (su, cs, tys, trms) ->
( su, cs, mkProductTypeWithRange tys ps
, mkTupleTerm trms ps)) ls
else inferWithMaybeTypeAux isP mt trm
else return [] -- fail for tuples of different lengths
_ -> inferWithMaybeTypeAux isP mt trm
_ -> inferWithMaybeTypeAux isP mt trm
-- | infer type of term (or a pattern if the Bool is True)
inferWithMaybeTypeAux :: Bool -> Maybe Type -> Term
-> State Env [(Subst, Constraints, Type, Term)]
inferWithMaybeTypeAux isP mt trm = do
rs <- infer isP trm
te <- get
case mt of
Nothing -> return rs
Just inTy -> do
combs <- mapM (\ q@(s, c, ty, t) -> let nTy = subst s inTy in
if ty == nTy then return [q] else do
Result ds mc <- toEnvState $ reduceR False te
(s, insertC (Subtyping ty nTy) c, nTy, mkTypedTerm t nTy)
case mc of
Nothing -> do
addDiags ds
return []
Just alt -> return [alt]) rs
return $ concat combs
-- | infer type of term (or a pattern if the Bool is True)
infer :: Bool -> Term -> State Env [(Subst, Constraints, Type, Term)]
infer isP trm = do
e <- get
let tm = typeMap e
bs = binders e
vs = localVars e
ga = globAnnos e
case trm of
qv@(QualVar (VarDecl _ ty _ _)) -> return [(eps, noC, ty, qv)]
QualOp br i sc tys k ps -> do
ms <- instOpInfo tys OpInfo { opType = sc
, opAttrs = Set.empty
, opDefn = NoOpDefn br }
return $ case ms of
Nothing -> []
Just (ty, inst, cs, _) ->
let qv = TypedTerm (QualOp br i sc inst k ps)
Inferred ty ps
in [(eps, cs, ty, qv)]
ResolvedMixTerm i tys ts ps -> case (Map.lookup i bs, ts) of
(Just j, pat : rt@(_ : _)) -> case reverse rt of
lt : ft -> infer isP $ ResolvedMixTerm j tys
(reverse $ LambdaTerm [pat] Partial lt ps : ft) ps
[] -> error "ResolvedMixTerm: binder"
_ ->
if null ts then case Map.lookup i vs of
Just (VarDefn t) ->
infer isP $ QualVar $ VarDecl i t Other ps
Nothing -> do
insts <- mapM (instOpInfo tys) $ getMinAssumps e i
let ls = map ( \ (ty, is, cs, oi) ->
(eps, ty, is, cs, oi)) $ catMaybes insts
-- possibly fresh variable
vl <- if isP && null tys && null ls
&& (isSimpleId i || i == simpleIdToId uTok) then do
vty <- freshTypeVar trm
return
[(eps, noC, vty, QualVar $ VarDecl i vty Other ps)]
else do
when (null ls) $
addDiags [mkDiag Hint "no type found for" i]
return []
return $ vl ++ map
( \ (s, ty, is, cs, oi) ->
let od = opDefn oi
br = case od of
NoOpDefn v -> v
Definition v _ -> v
_ -> Op
ik = if null tys then Infer else UserGiven
in (s, cs, ty, case opType oi of
sc@(TypeScheme [] _ _) ->
QualOp br (PolyId i [] ps) sc [] ik ps
sc -> TypedTerm (QualOp br (PolyId i [] ps)
sc is ik ps)
Inferred ty ps)) ls
else inferAppl isP ps (ResolvedMixTerm i tys [] ps)
$ mkTupleTerm ts ps
ApplTerm t1 t2 ps -> inferAppl isP ps t1 t2
TupleTerm ts ps -> if null ts then return [(eps, noC, unitType, trm)]
else do
ls <- checkList isP (map (const Nothing) ts) ts
return $ map ( \ (su, cs, tys, trms) ->
(su, cs, mkProductTypeWithRange tys ps, mkTupleTerm trms ps)) ls
TypedTerm t qual ty ps ->
case qual of
InType -> do
vTy <- freshTypeVar t
rs <- infer False t
return $ map ( \ (s, cs, typ, tr) ->
let sTy = subst s ty in
( s, insertC (Subtyping sTy vTy)
$ insertC (Subtyping typ vTy) cs
, unitType, TypedTerm tr qual sTy ps)) rs
AsType -> do
vTy <- freshTypeVar t
rs <- infer False t
return $ map ( \ (s, cs, typ, tr) ->
let sTy = subst s ty in
( s, insertC (Subtyping sTy vTy)
$ insertC (Subtyping typ vTy) cs
, sTy, TypedTerm tr qual sTy ps)) rs
_ -> do
let decl = case t of
ResolvedMixTerm _ tys ts _
| isP && null tys && null ts && qual == OfType
-> True
_ -> False
rs <- inferWithMaybeType isP
(if decl then Nothing else Just ty) t
return $ map ( \ (s, cs, _, tr) ->
let sTy = subst s ty in
(s, cs, sTy, case tr of
QualVar (VarDecl vp _ po _)
| decl -- shadow
-> QualVar (VarDecl vp sTy po ps)
_ -> if (qual == Inferred || case tr of
QualVar _ -> True
QualOp {} -> True
TypedTerm _ OfType _ _ -> True
_ -> False)
&& maybe False (eqStrippedType sTy)
(getTypeOf tr)
then tr
else TypedTerm tr qual sTy ps)) rs
QuantifiedTerm quant decls t ps -> do
mapM_ addGenVarDecl decls
rs <- inferWithMaybeType False (Just $ mkLazyType unitType) t
putLocalVars vs
putTypeMap tm
return $ map ( \ (s, cs, typ, tr) ->
(s, cs, typ, QuantifiedTerm quant decls tr ps)) rs
LambdaTerm pats part resTrm ps -> do
ls <- checkList True (map (const Nothing) pats) pats
rs <- mapM ( \ ( s, cs, patys, nps) -> do
mapM_ (addLocalVar True) $ concatMap extractVars nps
es <- infer False resTrm
putLocalVars vs
return $ map ( \ (s2, cr, rty, rtm) ->
let s3 = compSubst s s2
typ = getFunType (subst s rty)
part $ map (subst s2) patys
in
(s3, joinC (substC s2 cs) $ substC s cr
, typ,
TypedTerm
(LambdaTerm nps part rtm ps)
Inferred typ ps)) es) ls
return $ concat rs
CaseTerm ofTrm eqs ps -> do
ts <- infer False ofTrm
rty <- freshTypeVar trm
when (null ts) $ addDiags [mkNiceDiag ga Hint
"unresolved of-term in case" ofTrm]
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 False inTrm
return $ map ( \ (s2, cr, ty, nt) ->
(compSubst s1 s2,
substC s2 cs `joinC` cr,
ty, LetTerm br nes nt ps)) ts) es
putLocalVars vs
return $ concat rs
AsPattern (VarDecl v _ ok qs) pat ps -> do
pats <- infer True pat
return $ map ( \ (s1, cs, t1, p1) -> (s1, cs, t1,
AsPattern (VarDecl v t1 ok qs) p1 ps)) pats
_ -> do ty <- freshTypeVar trm
addDiags [mkNiceDiag ga 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 True (map (const Nothing) pats) pats
combs <- mapM ( \ (sf, pcs, tys, pps) -> do
mapM_ (addLocalVar True) $ concatMap extractVars pps
newTrms <- checkList False (map Just tys) trms
return $ map ( \ (sr, tcs, tys2, tts ) ->
(compSubst sf sr,
joinC tcs $ substC sr pcs, tys2,
zipWith3 (ProgEq . substTerm sr)
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 <- inferWithMaybeType True (Just pty) pat
e <- get
let pats = filter ( \ (_, _, _, p) -> isPat e p) pats1
ga = globAnnos e
when (null pats)
$ addDiags [mkNiceDiag ga Hint "unresolved case pattern" pat]
vs <- gets localVars
es <- mapM ( \ (s, cs, ty, p) -> do
mapM_ (addLocalVar True) $ extractVars p
ts <- inferWithMaybeType False (Just $ subst s tty) trm
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 (\ (s, cs, pty1, tty1, ne) -> do
rts <- inferCaseEqs pty1 tty1 eqs
return $ map ( \ (s2, cr, pty2, tty2, nes) ->
(compSubst s s2,
substC s2 cs `joinC` cr,
pty2, tty2, ne : nes)) rts) fts
return $ concat rs