{- |

Module : $Header$

Description : type checking terms and program equations

Copyright : (c) Christian Maeder and Uni Bremen 2003

License : similar to LGPL, see HetCATS/LICENSE.txt or LIZENZ.txt

Maintainer : Christian.Maeder@dfki.de

Stability : experimental

Portability : portable

type inference based on

<http://www.cs.fiu.edu/~smithg/papers/>

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.AsUtils

import HasCASL.Merge

import HasCASL.VarDecl

import HasCASL.As

import HasCASL.Le

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 qualified Common.Lib.Rel as Rel

import Common.Id

import Common.Result

import Common.DocUtils

import Common.GlobalAnnotations

import Common.Lib.State

import Data.List as List

import Data.Maybe (catMaybes)

import Control.Exception(assert)

substTerm :: Subst -> Term -> Term

substTerm s = mapTerm (id, subst s)

-- | mixfix and type resolution

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

-- | 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 (subst 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

checkList :: [Maybe Type] -> [Term]

-> State Env [(Subst, Constraints, [Type], [Term])]

checkList mtys trms = case (mtys, trms) of

(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

_ -> return [(eps, noC, [], [])]

-- | 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

-- | type checking a term

typeCheck :: Maybe Type -> Term -> State Env (Maybe Term)

typeCheck mt trm =

do alts <- infer mt trm >>= reduce True

te <- get

let p = getRange trm

ga = globAnnos te

if null alts then

do addDiags [mkNiceDiag ga 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

tys = getAllVarTypes t

addDiags es

if Set.null rcs then return ()

else addDiags [(mkDiag Error ("in term '"

++ showGlobalDoc ga t "' of type '"

++ showDoc ty "'\n unresolved constraints")

rcs){diagPos = p}]

if null tys then return ()

else addDiags [(mkDiag Error ("in term '"

++ showGlobalDoc ga t

"'\n are uninstantiated type variables")

$ Set.toList $ Set.unions $ map

(Set.fromList . map (fst . snd) .

leaves (> 0)) tys)

{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 [mkNiceDiag ga 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 . (". " ++) . showDoc 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 :: Subst -> Map.Map Id VarDefn -> Map.Map Id VarDefn

substVarTypes s = Map.map ( \ (VarDefn t) -> VarDefn $ subst s t)

-- | infer type of application, 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 <- case t2 of

TupleTerm [] _ -> return unitType

_ -> 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

lops <- case t2 of

TupleTerm [] _ ->

infer (Just $ TypeAppl lazyTypeConstr rty) t1

>>= reduce False

_ -> return []

te <- get

let ga = globAnnos te

combs <- mapM ( \ (sf, cf, funty, tf) -> do

let (sfty, frty) = case getTypeAppl funty of

(topTy, [paty, prty]) |

lesserType te topTy $ toFunType PFunArr ->

(paty, prty)

(topTy, [prty]) |

lesserType te topTy lazyTypeConstr ->

(unitType, 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) (lops ++ ops)

let res = concat combs

if null res then

addDiags [case mt of

Nothing -> mkNiceDiag ga Hint

"untypable application" origAppl

Just ty -> mkNiceDiag ga Hint

("untypable application (with result type: "

++ showDoc 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"

getAllVarTypes :: Term -> [Type]

getAllVarTypes = filter (not . null . leaves (> 0)) . foldTerm FoldRec

{ foldQualVar = \ _ (VarDecl _ t _ _) -> [t]

, foldQualOp = \ _ _ _ _ ts _ -> ts

, foldApplTerm = \ _ t1 t2 _ -> t1 ++ t2

, foldTupleTerm = \ _ tts _ -> concat tts

, foldTypedTerm = \ _ ts _ t _ -> t : ts

, foldAsPattern = \ _ (VarDecl _ t _ _) ts _ -> t : ts

, foldQuantifiedTerm = \ _ _ gvs ts _ -> ts ++ concatMap

( \ gv -> case gv of

GenVarDecl (VarDecl _ t _ _) -> [t]

_ -> []) gvs

, foldLambdaTerm = \ _ _ _ ts _ -> ts

, foldCaseTerm = \ _ ts tts _ -> concat $ ts : tts

, foldLetTerm = \ _ _ tts ts _ -> concat $ ts : tts

, foldResolvedMixTerm = \ _ _ ts tts _ -> ts ++ concat tts

, foldTermToken = \ _ _ -> []

, foldMixTypeTerm = \ _ _ _ _ -> []

, foldMixfixTerm = \ _ tts -> concat tts

, foldBracketTerm = \ _ _ tts _ -> concat tts

, foldProgEq = \ _ ps ts _ -> ps ++ ts

}

-- | infer type of term

infer :: Maybe Type -> Term -> State Env [(Subst, Constraints, Type, Term)]

infer mt trm = do

e <- get

let tm = typeMap e

as = assumps e

vs = localVars e

ga = globAnnos e

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 i sc tys ps -> do

ms <- instOpInfo tys OpInfo { opType = sc

, opAttrs = []

, opDefn = NoOpDefn br }

return $ case ms of

Nothing -> []

Just (ty, inst, cs, _) ->

let qv = TypedTerm (QualOp br i sc inst ps)

Inferred ty ps

in case mt of

Nothing -> [(eps, cs, ty, qv)]

Just inTy ->

[(eps, insertC (Subtyping ty inTy) cs, ty, qv)]

ResolvedMixTerm i tys 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 tys) ois

let ls = map ( \ (ty, is, cs, oi) ->

(eps, ty, is, case mt of

Just inTy -> insertC (Subtyping ty inTy) cs

Nothing -> cs, oi)) $ catMaybes insts

if null ls then

addDiags [mkDiag Hint "no type found for" 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 i sc [] ps

sc -> TypedTerm (QualOp br i sc is ps)

Inferred ty ps)) ls

else inferAppl ps mt (ResolvedMixTerm i tys [] 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 [mkNiceDiag ga 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 [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 (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

ga = globAnnos e

if null pats then addDiags [mkNiceDiag ga 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 (\ (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