2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1998
6 Type - public interface
10 -- re-exports from TypeRep
11 TyThing(..), Type, PredType(..), ThetaType,
15 Kind, SimpleKind, KindVar,
16 kindFunResult, splitKindFunTys, splitKindFunTysN,
18 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
19 argTypeKindTyCon, ubxTupleKindTyCon,
21 liftedTypeKind, unliftedTypeKind, openTypeKind,
22 argTypeKind, ubxTupleKind,
24 tySuperKind, coSuperKind,
26 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
27 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
28 isCoSuperKind, isSuperKind, isCoercionKind, isEqPred,
29 mkArrowKind, mkArrowKinds,
31 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
34 -- Re-exports from TyCon
37 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, isTyVarTy,
39 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
40 splitAppTy_maybe, repSplitAppTy_maybe,
42 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
43 splitFunTys, splitFunTysN,
44 funResultTy, funArgTy, zipFunTys, isFunTy,
46 mkTyConApp, mkTyConTy,
47 tyConAppTyCon, tyConAppArgs,
48 splitTyConApp_maybe, splitTyConApp,
49 splitNewTyConApp_maybe, splitNewTyConApp,
51 repType, repType', typePrimRep, coreView, tcView, kindView,
53 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
54 applyTy, applyTys, isForAllTy, dropForAlls,
57 predTypeRep, mkPredTy, mkPredTys,
61 splitRecNewType_maybe, newTyConInstRhs,
64 isUnLiftedType, isUnboxedTupleType, isAlgType, isPrimitiveType,
65 isStrictType, isStrictPred,
68 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
69 typeKind, addFreeTyVars,
71 -- Tidying up for printing
73 tidyOpenType, tidyOpenTypes,
74 tidyTyVarBndr, tidyFreeTyVars,
75 tidyOpenTyVar, tidyOpenTyVars,
76 tidyTopType, tidyPred,
80 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
81 tcEqPred, tcCmpPred, tcEqTypeX,
87 TvSubstEnv, emptyTvSubstEnv, -- Representation widely visible
88 TvSubst(..), emptyTvSubst, -- Representation visible to a few friends
89 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
90 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
91 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
93 -- Performing substitution on types
94 substTy, substTys, substTyWith, substTheta,
95 substPred, substTyVar, substTyVarBndr, deShadowTy, lookupTyVar,
98 pprType, pprParendType, pprTyThingCategory, pprForAll,
99 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind
102 #include "HsVersions.h"
104 -- We import the representation and primitive functions from TypeRep.
105 -- Many things are reexported, but not the representation!
125 import Data.Maybe ( isJust )
129 %************************************************************************
133 %************************************************************************
135 In Core, we "look through" non-recursive newtypes and PredTypes.
138 {-# INLINE coreView #-}
139 coreView :: Type -> Maybe Type
140 -- Strips off the *top layer only* of a type to give
141 -- its underlying representation type.
142 -- Returns Nothing if there is nothing to look through.
144 -- In the case of newtypes, it returns
145 -- *either* a vanilla TyConApp (recursive newtype, or non-saturated)
146 -- *or* the newtype representation (otherwise), meaning the
147 -- type written in the RHS of the newtype decl,
148 -- which may itself be a newtype
150 -- Example: newtype R = MkR S
152 -- newtype T = MkT (T -> T)
153 -- expandNewTcApp on R gives Just S
155 -- on T gives Nothing (no expansion)
157 -- By being non-recursive and inlined, this case analysis gets efficiently
158 -- joined onto the case analysis that the caller is already doing
159 coreView (NoteTy _ ty) = Just ty
161 | isEqPred p = Nothing
162 | otherwise = Just (predTypeRep p)
163 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
164 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
165 -- Its important to use mkAppTys, rather than (foldl AppTy),
166 -- because the function part might well return a
167 -- partially-applied type constructor; indeed, usually will!
168 coreView ty = Nothing
172 -----------------------------------------------
173 {-# INLINE tcView #-}
174 tcView :: Type -> Maybe Type
175 -- Same, but for the type checker, which just looks through synonyms
176 tcView (NoteTy _ ty) = Just ty
177 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
178 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
181 -----------------------------------------------
182 {-# INLINE kindView #-}
183 kindView :: Kind -> Maybe Kind
184 -- C.f. coreView, tcView
185 -- For the moment, we don't even handle synonyms in kinds
186 kindView (NoteTy _ k) = Just k
187 kindView other = Nothing
191 %************************************************************************
193 \subsection{Constructor-specific functions}
195 %************************************************************************
198 ---------------------------------------------------------------------
202 mkTyVarTy :: TyVar -> Type
205 mkTyVarTys :: [TyVar] -> [Type]
206 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
208 getTyVar :: String -> Type -> TyVar
209 getTyVar msg ty = case getTyVar_maybe ty of
211 Nothing -> panic ("getTyVar: " ++ msg)
213 isTyVarTy :: Type -> Bool
214 isTyVarTy ty = isJust (getTyVar_maybe ty)
216 getTyVar_maybe :: Type -> Maybe TyVar
217 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
218 getTyVar_maybe (TyVarTy tv) = Just tv
219 getTyVar_maybe other = Nothing
224 ---------------------------------------------------------------------
227 We need to be pretty careful with AppTy to make sure we obey the
228 invariant that a TyConApp is always visibly so. mkAppTy maintains the
232 mkAppTy orig_ty1 orig_ty2
235 mk_app (NoteTy _ ty1) = mk_app ty1
236 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
237 mk_app ty1 = AppTy orig_ty1 orig_ty2
238 -- Note that the TyConApp could be an
239 -- under-saturated type synonym. GHC allows that; e.g.
240 -- type Foo k = k a -> k a
242 -- foo :: Foo Id -> Foo Id
244 -- Here Id is partially applied in the type sig for Foo,
245 -- but once the type synonyms are expanded all is well
247 mkAppTys :: Type -> [Type] -> Type
248 mkAppTys orig_ty1 [] = orig_ty1
249 -- This check for an empty list of type arguments
250 -- avoids the needless loss of a type synonym constructor.
251 -- For example: mkAppTys Rational []
252 -- returns to (Ratio Integer), which has needlessly lost
253 -- the Rational part.
254 mkAppTys orig_ty1 orig_tys2
257 mk_app (NoteTy _ ty1) = mk_app ty1
258 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
259 -- mkTyConApp: see notes with mkAppTy
260 mk_app ty1 = foldl AppTy orig_ty1 orig_tys2
263 splitAppTy_maybe :: Type -> Maybe (Type, Type)
264 splitAppTy_maybe ty | Just ty' <- coreView ty
265 = splitAppTy_maybe ty'
266 splitAppTy_maybe ty = repSplitAppTy_maybe ty
269 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
270 -- Does the AppTy split, but assumes that any view stuff is already done
271 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
272 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
273 repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of
274 Just (tys', ty') -> Just (TyConApp tc tys', ty')
276 repSplitAppTy_maybe other = Nothing
278 splitAppTy :: Type -> (Type, Type)
279 splitAppTy ty = case splitAppTy_maybe ty of
281 Nothing -> panic "splitAppTy"
284 splitAppTys :: Type -> (Type, [Type])
285 splitAppTys ty = split ty ty []
287 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
288 split orig_ty (AppTy ty arg) args = split ty ty (arg:args)
289 split orig_ty (TyConApp tc tc_args) args = (TyConApp tc [], tc_args ++ args)
290 split orig_ty (FunTy ty1 ty2) args = ASSERT( null args )
291 (TyConApp funTyCon [], [ty1,ty2])
292 split orig_ty ty args = (orig_ty, args)
297 ---------------------------------------------------------------------
302 mkFunTy :: Type -> Type -> Type
303 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
304 mkFunTy arg res = FunTy arg res
306 mkFunTys :: [Type] -> Type -> Type
307 mkFunTys tys ty = foldr mkFunTy ty tys
309 isFunTy :: Type -> Bool
310 isFunTy ty = isJust (splitFunTy_maybe ty)
312 splitFunTy :: Type -> (Type, Type)
313 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
314 splitFunTy (FunTy arg res) = (arg, res)
315 splitFunTy other = pprPanic "splitFunTy" (ppr other)
317 splitFunTy_maybe :: Type -> Maybe (Type, Type)
318 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
319 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
320 splitFunTy_maybe other = Nothing
322 splitFunTys :: Type -> ([Type], Type)
323 splitFunTys ty = split [] ty ty
325 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
326 split args orig_ty (FunTy arg res) = split (arg:args) res res
327 split args orig_ty ty = (reverse args, orig_ty)
329 splitFunTysN :: Int -> Type -> ([Type], Type)
330 -- Split off exactly n arg tys
331 splitFunTysN 0 ty = ([], ty)
332 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
333 case splitFunTysN (n-1) res of { (args, res) ->
336 zipFunTys :: Outputable a => [a] -> Type -> ([(a,Type)], Type)
337 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
339 split acc [] nty ty = (reverse acc, nty)
341 | Just ty' <- coreView ty = split acc xs nty ty'
342 split acc (x:xs) nty (FunTy arg res) = split ((x,arg):acc) xs res res
343 split acc (x:xs) nty ty = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
345 funResultTy :: Type -> Type
346 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
347 funResultTy (FunTy arg res) = res
348 funResultTy ty = pprPanic "funResultTy" (ppr ty)
350 funArgTy :: Type -> Type
351 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
352 funArgTy (FunTy arg res) = arg
353 funArgTy ty = pprPanic "funArgTy" (ppr ty)
357 ---------------------------------------------------------------------
360 @mkTyConApp@ is a key function, because it builds a TyConApp, FunTy or PredTy,
364 mkTyConApp :: TyCon -> [Type] -> Type
366 | isFunTyCon tycon, [ty1,ty2] <- tys
372 mkTyConTy :: TyCon -> Type
373 mkTyConTy tycon = mkTyConApp tycon []
375 -- splitTyConApp "looks through" synonyms, because they don't
376 -- mean a distinct type, but all other type-constructor applications
377 -- including functions are returned as Just ..
379 tyConAppTyCon :: Type -> TyCon
380 tyConAppTyCon ty = fst (splitTyConApp ty)
382 tyConAppArgs :: Type -> [Type]
383 tyConAppArgs ty = snd (splitTyConApp ty)
385 splitTyConApp :: Type -> (TyCon, [Type])
386 splitTyConApp ty = case splitTyConApp_maybe ty of
388 Nothing -> pprPanic "splitTyConApp" (ppr ty)
390 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
391 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
392 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
393 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
394 splitTyConApp_maybe other = Nothing
396 -- Sometimes we do NOT want to look throught a newtype. When case matching
397 -- on a newtype we want a convenient way to access the arguments of a newty
398 -- constructor so as to properly form a coercion.
399 splitNewTyConApp :: Type -> (TyCon, [Type])
400 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
402 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
403 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
404 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
405 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
406 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
407 splitNewTyConApp_maybe other = Nothing
409 -- get instantiated newtype rhs, the arguments had better saturate
411 newTyConInstRhs :: TyCon -> [Type] -> Type
412 newTyConInstRhs tycon tys =
413 let (tvs, ty) = newTyConRhs tycon in substTyWith tvs tys ty
418 ---------------------------------------------------------------------
422 Notes on type synonyms
423 ~~~~~~~~~~~~~~~~~~~~~~
424 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
425 to return type synonyms whereever possible. Thus
430 splitFunTys (a -> Foo a) = ([a], Foo a)
433 The reason is that we then get better (shorter) type signatures in
434 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
439 repType looks through
443 (d) usage annotations
444 (e) all newtypes, including recursive ones, but not newtype families
445 It's useful in the back end.
448 repType :: Type -> Type
449 -- Only applied to types of kind *; hence tycons are saturated
450 repType ty | Just ty' <- coreView ty = repType ty'
451 repType (ForAllTy _ ty) = repType ty
452 repType (TyConApp tc tys)
453 | isClosedNewTyCon tc = -- Recursive newtypes are opaque to coreView
454 -- but we must expand them here. Sure to
455 -- be saturated because repType is only applied
456 -- to types of kind *
457 ASSERT( {- isRecursiveTyCon tc && -} tys `lengthIs` tyConArity tc )
458 repType (new_type_rep tc tys)
461 -- repType' aims to be a more thorough version of repType
462 -- For now it simply looks through the TyConApp args too
463 repType' ty -- | pprTrace "repType'" (ppr ty $$ ppr (go1 ty)) False = undefined
467 go (TyConApp tc tys) = mkTyConApp tc (map repType' tys)
471 -- new_type_rep doesn't ask any questions:
472 -- it just expands newtype, whether recursive or not
473 new_type_rep new_tycon tys = ASSERT( tys `lengthIs` tyConArity new_tycon )
474 case newTyConRep new_tycon of
475 (tvs, rep_ty) -> substTyWith tvs tys rep_ty
477 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
478 -- of inspecting the type directly.
479 typePrimRep :: Type -> PrimRep
480 typePrimRep ty = case repType ty of
481 TyConApp tc _ -> tyConPrimRep tc
483 AppTy _ _ -> PtrRep -- See note below
485 other -> pprPanic "typePrimRep" (ppr ty)
486 -- Types of the form 'f a' must be of kind *, not *#, so
487 -- we are guaranteed that they are represented by pointers.
488 -- The reason is that f must have kind *->*, not *->*#, because
489 -- (we claim) there is no way to constrain f's kind any other
495 ---------------------------------------------------------------------
500 mkForAllTy :: TyVar -> Type -> Type
502 = mkForAllTys [tyvar] ty
504 mkForAllTys :: [TyVar] -> Type -> Type
505 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
507 isForAllTy :: Type -> Bool
508 isForAllTy (NoteTy _ ty) = isForAllTy ty
509 isForAllTy (ForAllTy _ _) = True
510 isForAllTy other_ty = False
512 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
513 splitForAllTy_maybe ty = splitFAT_m ty
515 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
516 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
517 splitFAT_m _ = Nothing
519 splitForAllTys :: Type -> ([TyVar], Type)
520 splitForAllTys ty = split ty ty []
522 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
523 split orig_ty (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
524 split orig_ty t tvs = (reverse tvs, orig_ty)
526 dropForAlls :: Type -> Type
527 dropForAlls ty = snd (splitForAllTys ty)
530 -- (mkPiType now in CoreUtils)
534 Instantiate a for-all type with one or more type arguments.
535 Used when we have a polymorphic function applied to type args:
537 Then we use (applyTys type-of-f [t1,t2]) to compute the type of
541 applyTy :: Type -> Type -> Type
542 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
543 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
544 applyTy other arg = panic "applyTy"
546 applyTys :: Type -> [Type] -> Type
547 -- This function is interesting because
548 -- a) the function may have more for-alls than there are args
549 -- b) less obviously, it may have fewer for-alls
550 -- For case (b) think of
551 -- applyTys (forall a.a) [forall b.b, Int]
552 -- This really can happen, via dressing up polymorphic types with newtype
553 -- clothing. Here's an example:
554 -- newtype R = R (forall a. a->a)
555 -- foo = case undefined :: R of
558 applyTys orig_fun_ty [] = orig_fun_ty
559 applyTys orig_fun_ty arg_tys
560 | n_tvs == n_args -- The vastly common case
561 = substTyWith tvs arg_tys rho_ty
562 | n_tvs > n_args -- Too many for-alls
563 = substTyWith (take n_args tvs) arg_tys
564 (mkForAllTys (drop n_args tvs) rho_ty)
565 | otherwise -- Too many type args
566 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
567 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
570 (tvs, rho_ty) = splitForAllTys orig_fun_ty
572 n_args = length arg_tys
576 %************************************************************************
578 \subsection{Source types}
580 %************************************************************************
582 A "source type" is a type that is a separate type as far as the type checker is
583 concerned, but which has low-level representation as far as the back end is concerned.
585 Source types are always lifted.
587 The key function is predTypeRep which gives the representation of a source type:
590 mkPredTy :: PredType -> Type
591 mkPredTy pred = PredTy pred
593 mkPredTys :: ThetaType -> [Type]
594 mkPredTys preds = map PredTy preds
596 predTypeRep :: PredType -> Type
597 -- Convert a PredType to its "representation type";
598 -- the post-type-checking type used by all the Core passes of GHC.
599 -- Unwraps only the outermost level; for example, the result might
600 -- be a newtype application
601 predTypeRep (IParam _ ty) = ty
602 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
603 -- Result might be a newtype application, but the consumer will
604 -- look through that too if necessary
605 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
607 -- The original head is the tycon and its variables for a vanilla tycon and it
608 -- is the family tycon and its type indexes for a family instance.
609 tyConOrigHead :: TyCon -> (TyCon, [Type])
610 tyConOrigHead tycon = case tyConFamInst_maybe tycon of
611 Nothing -> (tycon, mkTyVarTys (tyConTyVars tycon))
612 Just famInst -> famInst
616 %************************************************************************
620 %************************************************************************
623 splitRecNewType_maybe :: Type -> Maybe Type
624 -- Sometimes we want to look through a recursive newtype, and that's what happens here
625 -- It only strips *one layer* off, so the caller will usually call itself recursively
626 -- Only applied to types of kind *, hence the newtype is always saturated
627 splitRecNewType_maybe ty | Just ty' <- coreView ty = splitRecNewType_maybe ty'
628 splitRecNewType_maybe (TyConApp tc tys)
629 | isClosedNewTyCon tc
630 = ASSERT( tys `lengthIs` tyConArity tc ) -- splitRecNewType_maybe only be applied
631 -- to *types* (of kind *)
632 ASSERT( isRecursiveTyCon tc ) -- Guaranteed by coreView
633 case newTyConRhs tc of
634 (tvs, rep_ty) -> ASSERT( length tvs == length tys )
635 Just (substTyWith tvs tys rep_ty)
637 splitRecNewType_maybe other = Nothing
644 %************************************************************************
646 \subsection{Kinds and free variables}
648 %************************************************************************
650 ---------------------------------------------------------------------
651 Finding the kind of a type
652 ~~~~~~~~~~~~~~~~~~~~~~~~~~
654 typeKind :: Type -> Kind
655 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
656 -- We should be looking for the coercion kind,
658 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
659 typeKind (NoteTy _ ty) = typeKind ty
660 typeKind (PredTy pred) = predKind pred
661 typeKind (AppTy fun arg) = kindFunResult (typeKind fun)
662 typeKind (ForAllTy tv ty) = typeKind ty
663 typeKind (TyVarTy tyvar) = tyVarKind tyvar
664 typeKind (FunTy arg res)
665 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
666 -- not unliftedTypKind (#)
667 -- The only things that can be after a function arrow are
668 -- (a) types (of kind openTypeKind or its sub-kinds)
669 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
670 | isTySuperKind k = k
671 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
675 predKind :: PredType -> Kind
676 predKind (EqPred {}) = coSuperKind -- A coercion kind!
677 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
678 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
682 ---------------------------------------------------------------------
683 Free variables of a type
684 ~~~~~~~~~~~~~~~~~~~~~~~~
686 tyVarsOfType :: Type -> TyVarSet
687 -- NB: for type synonyms tyVarsOfType does *not* expand the synonym
688 tyVarsOfType (TyVarTy tv) = unitVarSet tv
689 tyVarsOfType (TyConApp tycon tys) = tyVarsOfTypes tys
690 tyVarsOfType (NoteTy (FTVNote tvs) ty2) = tvs
691 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
692 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
693 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
694 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
696 tyVarsOfTypes :: [Type] -> TyVarSet
697 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
699 tyVarsOfPred :: PredType -> TyVarSet
700 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
701 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
702 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
704 tyVarsOfTheta :: ThetaType -> TyVarSet
705 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
707 -- Add a Note with the free tyvars to the top of the type
708 addFreeTyVars :: Type -> Type
709 addFreeTyVars ty@(NoteTy (FTVNote _) _) = ty
710 addFreeTyVars ty = NoteTy (FTVNote (tyVarsOfType ty)) ty
714 %************************************************************************
716 \subsection{TidyType}
718 %************************************************************************
720 tidyTy tidies up a type for printing in an error message, or in
723 It doesn't change the uniques at all, just the print names.
726 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
727 tidyTyVarBndr (tidy_env, subst) tyvar
728 = case tidyOccName tidy_env (getOccName name) of
729 (tidy', occ') -> ((tidy', subst'), tyvar')
731 subst' = extendVarEnv subst tyvar tyvar'
732 tyvar' = setTyVarName tyvar name'
733 name' = tidyNameOcc name occ'
735 name = tyVarName tyvar
737 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
738 -- Add the free tyvars to the env in tidy form,
739 -- so that we can tidy the type they are free in
740 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
742 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
743 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
745 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
746 -- Treat a new tyvar as a binder, and give it a fresh tidy name
747 tidyOpenTyVar env@(tidy_env, subst) tyvar
748 = case lookupVarEnv subst tyvar of
749 Just tyvar' -> (env, tyvar') -- Already substituted
750 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
752 tidyType :: TidyEnv -> Type -> Type
753 tidyType env@(tidy_env, subst) ty
756 go (TyVarTy tv) = case lookupVarEnv subst tv of
757 Nothing -> TyVarTy tv
758 Just tv' -> TyVarTy tv'
759 go (TyConApp tycon tys) = let args = map go tys
760 in args `seqList` TyConApp tycon args
761 go (NoteTy note ty) = (NoteTy $! (go_note note)) $! (go ty)
762 go (PredTy sty) = PredTy (tidyPred env sty)
763 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
764 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
765 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
767 (envp, tvp) = tidyTyVarBndr env tv
769 go_note note@(FTVNote ftvs) = note -- No need to tidy the free tyvars
771 tidyTypes env tys = map (tidyType env) tys
773 tidyPred :: TidyEnv -> PredType -> PredType
774 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
775 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
776 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
780 @tidyOpenType@ grabs the free type variables, tidies them
781 and then uses @tidyType@ to work over the type itself
784 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
786 = (env', tidyType env' ty)
788 env' = tidyFreeTyVars env (tyVarsOfType ty)
790 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
791 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
793 tidyTopType :: Type -> Type
794 tidyTopType ty = tidyType emptyTidyEnv ty
799 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
800 tidyKind env k = tidyOpenType env k
805 %************************************************************************
807 \subsection{Liftedness}
809 %************************************************************************
812 isUnLiftedType :: Type -> Bool
813 -- isUnLiftedType returns True for forall'd unlifted types:
814 -- x :: forall a. Int#
815 -- I found bindings like these were getting floated to the top level.
816 -- They are pretty bogus types, mind you. It would be better never to
819 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
820 isUnLiftedType (ForAllTy tv ty) = isUnLiftedType ty
821 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
822 isUnLiftedType other = False
824 isUnboxedTupleType :: Type -> Bool
825 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
826 Just (tc, ty_args) -> isUnboxedTupleTyCon tc
829 -- Should only be applied to *types*; hence the assert
830 isAlgType :: Type -> Bool
831 isAlgType ty = case splitTyConApp_maybe ty of
832 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
837 @isStrictType@ computes whether an argument (or let RHS) should
838 be computed strictly or lazily, based only on its type.
839 Works just like isUnLiftedType, except that it has a special case
840 for dictionaries. Since it takes account of ClassP, you might think
841 this function should be in TcType, but isStrictType is used by DataCon,
842 which is below TcType in the hierarchy, so it's convenient to put it here.
845 isStrictType (PredTy pred) = isStrictPred pred
846 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
847 isStrictType (ForAllTy tv ty) = isStrictType ty
848 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
849 isStrictType other = False
851 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
852 isStrictPred other = False
853 -- We may be strict in dictionary types, but only if it
854 -- has more than one component.
855 -- [Being strict in a single-component dictionary risks
856 -- poking the dictionary component, which is wrong.]
860 isPrimitiveType :: Type -> Bool
861 -- Returns types that are opaque to Haskell.
862 -- Most of these are unlifted, but now that we interact with .NET, we
863 -- may have primtive (foreign-imported) types that are lifted
864 isPrimitiveType ty = case splitTyConApp_maybe ty of
865 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
871 %************************************************************************
873 \subsection{Sequencing on types
875 %************************************************************************
878 seqType :: Type -> ()
879 seqType (TyVarTy tv) = tv `seq` ()
880 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
881 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
882 seqType (NoteTy note t2) = seqNote note `seq` seqType t2
883 seqType (PredTy p) = seqPred p
884 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
885 seqType (ForAllTy tv ty) = tv `seq` seqType ty
887 seqTypes :: [Type] -> ()
889 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
891 seqNote :: TyNote -> ()
892 seqNote (FTVNote set) = sizeUniqSet set `seq` ()
894 seqPred :: PredType -> ()
895 seqPred (ClassP c tys) = c `seq` seqTypes tys
896 seqPred (IParam n ty) = n `seq` seqType ty
897 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
901 %************************************************************************
903 Equality for Core types
904 (We don't use instances so that we know where it happens)
906 %************************************************************************
908 Note that eqType works right even for partial applications of newtypes.
909 See Note [Newtype eta] in TyCon.lhs
912 coreEqType :: Type -> Type -> Bool
916 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
918 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
919 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
920 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
921 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
922 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
923 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
924 -- The lengths should be equal because
925 -- the two types have the same kind
926 -- NB: if the type constructors differ that does not
927 -- necessarily mean that the types aren't equal
928 -- (synonyms, newtypes)
929 -- Even if the type constructors are the same, but the arguments
930 -- differ, the two types could be the same (e.g. if the arg is just
931 -- ignored in the RHS). In both these cases we fall through to an
932 -- attempt to expand one side or the other.
934 -- Now deal with newtypes, synonyms, pred-tys
935 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
936 | Just t2' <- coreView t2 = eq env t1 t2'
938 -- Fall through case; not equal!
943 %************************************************************************
945 Comparision for source types
946 (We don't use instances so that we know where it happens)
948 %************************************************************************
952 do *not* look through newtypes, PredTypes
955 tcEqType :: Type -> Type -> Bool
956 tcEqType t1 t2 = isEqual $ cmpType t1 t2
958 tcEqTypes :: [Type] -> [Type] -> Bool
959 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
961 tcCmpType :: Type -> Type -> Ordering
962 tcCmpType t1 t2 = cmpType t1 t2
964 tcCmpTypes :: [Type] -> [Type] -> Ordering
965 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
967 tcEqPred :: PredType -> PredType -> Bool
968 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
970 tcCmpPred :: PredType -> PredType -> Ordering
971 tcCmpPred p1 p2 = cmpPred p1 p2
973 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
974 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
977 Now here comes the real worker
980 cmpType :: Type -> Type -> Ordering
981 cmpType t1 t2 = cmpTypeX rn_env t1 t2
983 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
985 cmpTypes :: [Type] -> [Type] -> Ordering
986 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
988 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
990 cmpPred :: PredType -> PredType -> Ordering
991 cmpPred p1 p2 = cmpPredX rn_env p1 p2
993 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
995 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
996 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
997 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
999 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1000 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1001 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1002 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1003 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1004 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1005 cmpTypeX env t1 (NoteTy _ t2) = cmpTypeX env t1 t2
1007 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1008 cmpTypeX env (AppTy _ _) (TyVarTy _) = GT
1010 cmpTypeX env (FunTy _ _) (TyVarTy _) = GT
1011 cmpTypeX env (FunTy _ _) (AppTy _ _) = GT
1013 cmpTypeX env (TyConApp _ _) (TyVarTy _) = GT
1014 cmpTypeX env (TyConApp _ _) (AppTy _ _) = GT
1015 cmpTypeX env (TyConApp _ _) (FunTy _ _) = GT
1017 cmpTypeX env (ForAllTy _ _) (TyVarTy _) = GT
1018 cmpTypeX env (ForAllTy _ _) (AppTy _ _) = GT
1019 cmpTypeX env (ForAllTy _ _) (FunTy _ _) = GT
1020 cmpTypeX env (ForAllTy _ _) (TyConApp _ _) = GT
1022 cmpTypeX env (PredTy _) t2 = GT
1024 cmpTypeX env _ _ = LT
1027 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1028 cmpTypesX env [] [] = EQ
1029 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1030 cmpTypesX env [] tys = LT
1031 cmpTypesX env ty [] = GT
1034 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1035 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1036 -- Compare names only for implicit parameters
1037 -- This comparison is used exclusively (I believe)
1038 -- for the Avails finite map built in TcSimplify
1039 -- If the types differ we keep them distinct so that we see
1040 -- a distinct pair to run improvement on
1041 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1042 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1044 -- Constructor order: IParam < ClassP < EqPred
1045 cmpPredX env (IParam {}) _ = LT
1046 cmpPredX env (ClassP {}) (IParam {}) = GT
1047 cmpPredX env (ClassP {}) (EqPred {}) = LT
1048 cmpPredX env (EqPred {}) _ = GT
1051 PredTypes are used as a FM key in TcSimplify,
1052 so we take the easy path and make them an instance of Ord
1055 instance Eq PredType where { (==) = tcEqPred }
1056 instance Ord PredType where { compare = tcCmpPred }
1060 %************************************************************************
1064 %************************************************************************
1068 = TvSubst InScopeSet -- The in-scope type variables
1069 TvSubstEnv -- The substitution itself
1070 -- See Note [Apply Once]
1071 -- and Note [Extending the TvSubstEnv]
1073 {- ----------------------------------------------------------
1077 We use TvSubsts to instantiate things, and we might instantiate
1081 So the substition might go [a->b, b->a]. A similar situation arises in Core
1082 when we find a beta redex like
1083 (/\ a /\ b -> e) b a
1084 Then we also end up with a substition that permutes type variables. Other
1085 variations happen to; for example [a -> (a, b)].
1087 ***************************************************
1088 *** So a TvSubst must be applied precisely once ***
1089 ***************************************************
1091 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1092 we use during unifications, it must not be repeatedly applied.
1094 Note [Extending the TvSubst]
1095 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1096 The following invariant should hold of a TvSubst
1098 The in-scope set is needed *only* to
1099 guide the generation of fresh uniques
1101 In particular, the *kind* of the type variables in
1102 the in-scope set is not relevant
1104 This invariant allows a short-cut when the TvSubstEnv is empty:
1105 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1106 then (substTy subst ty) does nothing.
1108 For example, consider:
1109 (/\a. /\b:(a~Int). ...b..) Int
1110 We substitute Int for 'a'. The Unique of 'b' does not change, but
1111 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1113 This invariant has several crucial consequences:
1115 * In substTyVarBndr, we need extend the TvSubstEnv
1116 - if the unique has changed
1117 - or if the kind has changed
1119 * In substTyVar, we do not need to consult the in-scope set;
1120 the TvSubstEnv is enough
1122 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1125 -------------------------------------------------------------- -}
1128 type TvSubstEnv = TyVarEnv Type
1129 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1130 -- invariant discussed in Note [Apply Once]), and also independently
1131 -- in the middle of matching, and unification (see Types.Unify)
1132 -- So you have to look at the context to know if it's idempotent or
1133 -- apply-once or whatever
1134 emptyTvSubstEnv :: TvSubstEnv
1135 emptyTvSubstEnv = emptyVarEnv
1137 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1138 -- (compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1
1139 -- It assumes that both are idempotent
1140 -- Typically, env1 is the refinement to a base substitution env2
1141 composeTvSubst in_scope env1 env2
1142 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1143 -- First apply env1 to the range of env2
1144 -- Then combine the two, making sure that env1 loses if
1145 -- both bind the same variable; that's why env1 is the
1146 -- *left* argument to plusVarEnv, because the right arg wins
1148 subst1 = TvSubst in_scope env1
1150 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1152 isEmptyTvSubst :: TvSubst -> Bool
1153 -- See Note [Extending the TvSubstEnv]
1154 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1156 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1159 getTvSubstEnv :: TvSubst -> TvSubstEnv
1160 getTvSubstEnv (TvSubst _ env) = env
1162 getTvInScope :: TvSubst -> InScopeSet
1163 getTvInScope (TvSubst in_scope _) = in_scope
1165 isInScope :: Var -> TvSubst -> Bool
1166 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1168 notElemTvSubst :: TyVar -> TvSubst -> Bool
1169 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1171 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1172 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1174 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1175 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1177 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1178 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1180 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1181 extendTvSubstList (TvSubst in_scope env) tvs tys
1182 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1184 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1185 -- the types given; but it's just a thunk so with a bit of luck
1186 -- it'll never be evaluated
1188 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1189 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1191 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1192 zipOpenTvSubst tyvars tys
1194 | length tyvars /= length tys
1195 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1198 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1200 -- mkTopTvSubst is called when doing top-level substitutions.
1201 -- Here we expect that the free vars of the range of the
1202 -- substitution will be empty.
1203 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1204 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1206 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1207 zipTopTvSubst tyvars tys
1209 | length tyvars /= length tys
1210 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1213 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1215 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1218 | length tyvars /= length tys
1219 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1222 = zip_ty_env tyvars tys emptyVarEnv
1224 -- Later substitutions in the list over-ride earlier ones,
1225 -- but there should be no loops
1226 zip_ty_env [] [] env = env
1227 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1228 -- There used to be a special case for when
1230 -- (a not-uncommon case) in which case the substitution was dropped.
1231 -- But the type-tidier changes the print-name of a type variable without
1232 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1233 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1234 -- And it happened that t was the type variable of the class. Post-tiding,
1235 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1236 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1237 -- and so generated a rep type mentioning t not t2.
1239 -- Simplest fix is to nuke the "optimisation"
1240 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1241 -- zip_ty_env _ _ env = env
1243 instance Outputable TvSubst where
1244 ppr (TvSubst ins env)
1245 = brackets $ sep[ ptext SLIT("TvSubst"),
1246 nest 2 (ptext SLIT("In scope:") <+> ppr ins),
1247 nest 2 (ptext SLIT("Env:") <+> ppr env) ]
1250 %************************************************************************
1252 Performing type substitutions
1254 %************************************************************************
1257 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1258 substTyWith tvs tys = ASSERT( length tvs == length tys )
1259 substTy (zipOpenTvSubst tvs tys)
1261 substTy :: TvSubst -> Type -> Type
1262 substTy subst ty | isEmptyTvSubst subst = ty
1263 | otherwise = subst_ty subst ty
1265 substTys :: TvSubst -> [Type] -> [Type]
1266 substTys subst tys | isEmptyTvSubst subst = tys
1267 | otherwise = map (subst_ty subst) tys
1269 substTheta :: TvSubst -> ThetaType -> ThetaType
1270 substTheta subst theta
1271 | isEmptyTvSubst subst = theta
1272 | otherwise = map (substPred subst) theta
1274 substPred :: TvSubst -> PredType -> PredType
1275 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1276 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1277 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1279 deShadowTy :: TyVarSet -> Type -> Type -- Remove any nested binders mentioning tvs
1281 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1283 in_scope = mkInScopeSet tvs
1285 subst_ty :: TvSubst -> Type -> Type
1286 -- subst_ty is the main workhorse for type substitution
1288 -- Note that the in_scope set is poked only if we hit a forall
1289 -- so it may often never be fully computed
1293 go (TyVarTy tv) = substTyVar subst tv
1294 go (TyConApp tc tys) = let args = map go tys
1295 in args `seqList` TyConApp tc args
1297 go (PredTy p) = PredTy $! (substPred subst p)
1299 go (NoteTy (FTVNote _) ty2) = go ty2 -- Discard the free tyvar note
1301 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1302 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1303 -- The mkAppTy smart constructor is important
1304 -- we might be replacing (a Int), represented with App
1305 -- by [Int], represented with TyConApp
1306 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1307 (subst', tv') -> ForAllTy tv' $! (subst_ty subst' ty)
1309 substTyVar :: TvSubst -> TyVar -> Type
1310 substTyVar subst@(TvSubst in_scope env) tv
1311 = case lookupTyVar subst tv of {
1312 Nothing -> TyVarTy tv;
1313 Just ty -> ty -- See Note [Apply Once]
1316 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1317 -- See Note [Extending the TvSubst]
1318 lookupTyVar (TvSubst in_scope env) tv = lookupVarEnv env tv
1320 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1321 substTyVarBndr subst@(TvSubst in_scope env) old_var
1322 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1324 is_co_var = isCoVar old_var
1326 new_env | no_change = delVarEnv env old_var
1327 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1329 no_change = new_var == old_var && not is_co_var
1330 -- no_change means that the new_var is identical in
1331 -- all respects to the old_var (same unique, same kind)
1332 -- See Note [Extending the TvSubst]
1334 -- In that case we don't need to extend the substitution
1335 -- to map old to new. But instead we must zap any
1336 -- current substitution for the variable. For example:
1337 -- (\x.e) with id_subst = [x |-> e']
1338 -- Here we must simply zap the substitution for x
1340 new_var = uniqAway in_scope subst_old_var
1341 -- The uniqAway part makes sure the new variable is not already in scope
1343 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1344 -- It's only worth doing the substitution for coercions,
1345 -- becuase only they can have free type variables
1346 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1347 | otherwise = old_var
1350 ----------------------------------------------------
1355 There's a little subtyping at the kind level:
1364 where * [LiftedTypeKind] means boxed type
1365 # [UnliftedTypeKind] means unboxed type
1366 (#) [UbxTupleKind] means unboxed tuple
1367 ?? [ArgTypeKind] is the lub of *,#
1368 ? [OpenTypeKind] means any type at all
1372 error :: forall a:?. String -> a
1373 (->) :: ?? -> ? -> *
1374 (\(x::t) -> ...) Here t::?? (i.e. not unboxed tuple)
1377 type KindVar = TyVar -- invariant: KindVar will always be a
1378 -- TcTyVar with details MetaTv TauTv ...
1379 -- kind var constructors and functions are in TcType
1381 type SimpleKind = Kind
1386 During kind inference, a kind variable unifies only with
1388 sk ::= * | sk1 -> sk2
1390 data T a = MkT a (T Int#)
1391 fails. We give T the kind (k -> *), and the kind variable k won't unify
1392 with # (the kind of Int#).
1396 When creating a fresh internal type variable, we give it a kind to express
1397 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1400 During unification we only bind an internal type variable to a type
1401 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1403 When unifying two internal type variables, we collect their kind constraints by
1404 finding the GLB of the two. Since the partial order is a tree, they only
1405 have a glb if one is a sub-kind of the other. In that case, we bind the
1406 less-informative one to the more informative one. Neat, eh?
1413 %************************************************************************
1415 Functions over Kinds
1417 %************************************************************************
1420 kindFunResult :: Kind -> Kind
1421 kindFunResult k = funResultTy k
1423 splitKindFunTys :: Kind -> ([Kind],Kind)
1424 splitKindFunTys k = splitFunTys k
1426 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1427 splitKindFunTysN k = splitFunTysN k
1429 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1431 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1433 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1434 isOpenTypeKind other = False
1436 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1438 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1439 isUbxTupleKind other = False
1441 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1443 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1444 isArgTypeKind other = False
1446 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1448 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1449 isUnliftedTypeKind other = False
1451 isSubOpenTypeKind :: Kind -> Bool
1452 -- True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1453 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1454 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1456 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1457 isSubOpenTypeKind other = ASSERT( isKind other ) False
1458 -- This is a conservative answer
1459 -- It matters in the call to isSubKind in
1460 -- checkExpectedKind.
1462 isSubArgTypeKindCon kc
1463 | isUnliftedTypeKindCon kc = True
1464 | isLiftedTypeKindCon kc = True
1465 | isArgTypeKindCon kc = True
1468 isSubArgTypeKind :: Kind -> Bool
1469 -- True of any sub-kind of ArgTypeKind
1470 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1471 isSubArgTypeKind other = False
1473 isSuperKind :: Type -> Bool
1474 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1475 isSuperKind other = False
1477 isKind :: Kind -> Bool
1478 isKind k = isSuperKind (typeKind k)
1482 isSubKind :: Kind -> Kind -> Bool
1483 -- (k1 `isSubKind` k2) checks that k1 <: k2
1484 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1485 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1486 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1487 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1488 isSubKind k1 k2 = False
1490 eqKind :: Kind -> Kind -> Bool
1493 isSubKindCon :: TyCon -> TyCon -> Bool
1494 -- (kc1 `isSubKindCon` kc2) checks that kc1 <: kc2
1495 isSubKindCon kc1 kc2
1496 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1497 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1498 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1499 | isOpenTypeKindCon kc2 = True
1500 -- we already know kc1 is not a fun, its a TyCon
1501 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1504 defaultKind :: Kind -> Kind
1505 -- Used when generalising: default kind '?' and '??' to '*'
1507 -- When we generalise, we make generic type variables whose kind is
1508 -- simple (* or *->* etc). So generic type variables (other than
1509 -- built-in constants like 'error') always have simple kinds. This is important;
1512 -- We want f to get type
1513 -- f :: forall (a::*). a -> Bool
1515 -- f :: forall (a::??). a -> Bool
1516 -- because that would allow a call like (f 3#) as well as (f True),
1517 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1519 | isSubOpenTypeKind k = liftedTypeKind
1520 | isSubArgTypeKind k = liftedTypeKind
1523 isEqPred :: PredType -> Bool
1524 isEqPred (EqPred _ _) = True
1525 isEqPred other = False