2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1998
6 Type - public interface
10 -- The above warning supression flag is a temporary kludge.
11 -- While working on this module you are encouraged to remove it and fix
12 -- any warnings in the module. See
13 -- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
17 -- re-exports from TypeRep
18 TyThing(..), Type, PredType(..), ThetaType,
22 Kind, SimpleKind, KindVar,
23 kindFunResult, splitKindFunTys, splitKindFunTysN,
25 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
26 argTypeKindTyCon, ubxTupleKindTyCon,
28 liftedTypeKind, unliftedTypeKind, openTypeKind,
29 argTypeKind, ubxTupleKind,
31 tySuperKind, coSuperKind,
33 isLiftedTypeKind, isUnliftedTypeKind, isOpenTypeKind,
34 isUbxTupleKind, isArgTypeKind, isKind, isTySuperKind,
35 isCoSuperKind, isSuperKind, isCoercionKind, isEqPred,
36 mkArrowKind, mkArrowKinds,
38 isSubArgTypeKind, isSubOpenTypeKind, isSubKind, defaultKind, eqKind,
41 -- Re-exports from TyCon
44 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, isTyVarTy,
46 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
47 splitAppTy_maybe, repSplitAppTy_maybe,
49 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
50 splitFunTys, splitFunTysN,
51 funResultTy, funArgTy, zipFunTys, isFunTy,
53 mkTyConApp, mkTyConTy,
54 tyConAppTyCon, tyConAppArgs,
55 splitTyConApp_maybe, splitTyConApp,
56 splitNewTyConApp_maybe, splitNewTyConApp,
58 repType, repType', typePrimRep, coreView, tcView, kindView,
60 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
61 applyTy, applyTys, isForAllTy, dropForAlls,
64 predTypeRep, mkPredTy, mkPredTys, pprSourceTyCon, mkFamilyTyConApp,
70 isUnLiftedType, isUnboxedTupleType, isAlgType, isPrimitiveType,
71 isStrictType, isStrictPred,
74 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
75 typeKind, addFreeTyVars,
80 -- Tidying up for printing
82 tidyOpenType, tidyOpenTypes,
83 tidyTyVarBndr, tidyFreeTyVars,
84 tidyOpenTyVar, tidyOpenTyVars,
85 tidyTopType, tidyPred,
89 coreEqType, tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
90 tcEqPred, tcCmpPred, tcEqTypeX, tcPartOfType, tcPartOfPred,
96 TvSubstEnv, emptyTvSubstEnv, -- Representation widely visible
97 TvSubst(..), emptyTvSubst, -- Representation visible to a few friends
98 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
99 getTvSubstEnv, setTvSubstEnv, getTvInScope, extendTvInScope,
100 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
103 -- Performing substitution on types
104 substTy, substTys, substTyWith, substTheta,
105 substPred, substTyVar, substTyVars, substTyVarBndr, deShadowTy, lookupTyVar,
108 pprType, pprParendType, pprTypeApp, pprTyThingCategory, pprTyThing, pprForAll,
109 pprPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind
112 #include "HsVersions.h"
114 -- We import the representation and primitive functions from TypeRep.
115 -- Many things are reexported, but not the representation!
136 import Data.Maybe ( isJust )
140 %************************************************************************
144 %************************************************************************
146 In Core, we "look through" non-recursive newtypes and PredTypes.
149 {-# INLINE coreView #-}
150 coreView :: Type -> Maybe Type
151 -- Strips off the *top layer only* of a type to give
152 -- its underlying representation type.
153 -- Returns Nothing if there is nothing to look through.
155 -- In the case of newtypes, it returns
156 -- *either* a vanilla TyConApp (recursive newtype, or non-saturated)
157 -- *or* the newtype representation (otherwise), meaning the
158 -- type written in the RHS of the newtype decl,
159 -- which may itself be a newtype
161 -- Example: newtype R = MkR S
163 -- newtype T = MkT (T -> T)
164 -- expandNewTcApp on R gives Just S
166 -- on T gives Nothing (no expansion)
168 -- By being non-recursive and inlined, this case analysis gets efficiently
169 -- joined onto the case analysis that the caller is already doing
170 coreView (NoteTy _ ty) = Just ty
172 | isEqPred p = Nothing
173 | otherwise = Just (predTypeRep p)
174 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
175 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
176 -- Its important to use mkAppTys, rather than (foldl AppTy),
177 -- because the function part might well return a
178 -- partially-applied type constructor; indeed, usually will!
179 coreView ty = Nothing
183 -----------------------------------------------
184 {-# INLINE tcView #-}
185 tcView :: Type -> Maybe Type
186 -- Same, but for the type checker, which just looks through synonyms
187 tcView (NoteTy _ ty) = Just ty
188 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
189 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
192 -----------------------------------------------
193 {-# INLINE kindView #-}
194 kindView :: Kind -> Maybe Kind
195 -- C.f. coreView, tcView
196 -- For the moment, we don't even handle synonyms in kinds
197 kindView (NoteTy _ k) = Just k
198 kindView other = Nothing
202 %************************************************************************
204 \subsection{Constructor-specific functions}
206 %************************************************************************
209 ---------------------------------------------------------------------
213 mkTyVarTy :: TyVar -> Type
216 mkTyVarTys :: [TyVar] -> [Type]
217 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
219 getTyVar :: String -> Type -> TyVar
220 getTyVar msg ty = case getTyVar_maybe ty of
222 Nothing -> panic ("getTyVar: " ++ msg)
224 isTyVarTy :: Type -> Bool
225 isTyVarTy ty = isJust (getTyVar_maybe ty)
227 getTyVar_maybe :: Type -> Maybe TyVar
228 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
229 getTyVar_maybe (TyVarTy tv) = Just tv
230 getTyVar_maybe other = Nothing
235 ---------------------------------------------------------------------
238 We need to be pretty careful with AppTy to make sure we obey the
239 invariant that a TyConApp is always visibly so. mkAppTy maintains the
243 mkAppTy orig_ty1 orig_ty2
246 mk_app (NoteTy _ ty1) = mk_app ty1
247 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
248 mk_app ty1 = AppTy orig_ty1 orig_ty2
249 -- Note that the TyConApp could be an
250 -- under-saturated type synonym. GHC allows that; e.g.
251 -- type Foo k = k a -> k a
253 -- foo :: Foo Id -> Foo Id
255 -- Here Id is partially applied in the type sig for Foo,
256 -- but once the type synonyms are expanded all is well
258 mkAppTys :: Type -> [Type] -> Type
259 mkAppTys orig_ty1 [] = orig_ty1
260 -- This check for an empty list of type arguments
261 -- avoids the needless loss of a type synonym constructor.
262 -- For example: mkAppTys Rational []
263 -- returns to (Ratio Integer), which has needlessly lost
264 -- the Rational part.
265 mkAppTys orig_ty1 orig_tys2
268 mk_app (NoteTy _ ty1) = mk_app ty1
269 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
270 -- mkTyConApp: see notes with mkAppTy
271 mk_app ty1 = foldl AppTy orig_ty1 orig_tys2
274 splitAppTy_maybe :: Type -> Maybe (Type, Type)
275 splitAppTy_maybe ty | Just ty' <- coreView ty
276 = splitAppTy_maybe ty'
277 splitAppTy_maybe ty = repSplitAppTy_maybe ty
280 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
281 -- Does the AppTy split, but assumes that any view stuff is already done
282 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
283 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
284 repSplitAppTy_maybe (TyConApp tc tys) = case snocView tys of
285 Just (tys', ty') -> Just (TyConApp tc tys', ty')
287 repSplitAppTy_maybe other = Nothing
289 splitAppTy :: Type -> (Type, Type)
290 splitAppTy ty = case splitAppTy_maybe ty of
292 Nothing -> panic "splitAppTy"
295 splitAppTys :: Type -> (Type, [Type])
296 splitAppTys ty = split ty ty []
298 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
299 split orig_ty (AppTy ty arg) args = split ty ty (arg:args)
300 split orig_ty (TyConApp tc tc_args) args = (TyConApp tc [], tc_args ++ args)
301 split orig_ty (FunTy ty1 ty2) args = ASSERT( null args )
302 (TyConApp funTyCon [], [ty1,ty2])
303 split orig_ty ty args = (orig_ty, args)
308 ---------------------------------------------------------------------
313 mkFunTy :: Type -> Type -> Type
314 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
315 mkFunTy arg res = FunTy arg res
317 mkFunTys :: [Type] -> Type -> Type
318 mkFunTys tys ty = foldr mkFunTy ty tys
320 isFunTy :: Type -> Bool
321 isFunTy ty = isJust (splitFunTy_maybe ty)
323 splitFunTy :: Type -> (Type, Type)
324 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
325 splitFunTy (FunTy arg res) = (arg, res)
326 splitFunTy other = pprPanic "splitFunTy" (ppr other)
328 splitFunTy_maybe :: Type -> Maybe (Type, Type)
329 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
330 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
331 splitFunTy_maybe other = Nothing
333 splitFunTys :: Type -> ([Type], Type)
334 splitFunTys ty = split [] ty ty
336 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
337 split args orig_ty (FunTy arg res) = split (arg:args) res res
338 split args orig_ty ty = (reverse args, orig_ty)
340 splitFunTysN :: Int -> Type -> ([Type], Type)
341 -- Split off exactly n arg tys
342 splitFunTysN 0 ty = ([], ty)
343 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
344 case splitFunTysN (n-1) res of { (args, res) ->
347 zipFunTys :: Outputable a => [a] -> Type -> ([(a,Type)], Type)
348 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
350 split acc [] nty ty = (reverse acc, nty)
352 | Just ty' <- coreView ty = split acc xs nty ty'
353 split acc (x:xs) nty (FunTy arg res) = split ((x,arg):acc) xs res res
354 split acc (x:xs) nty ty = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
356 funResultTy :: Type -> Type
357 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
358 funResultTy (FunTy arg res) = res
359 funResultTy ty = pprPanic "funResultTy" (ppr ty)
361 funArgTy :: Type -> Type
362 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
363 funArgTy (FunTy arg res) = arg
364 funArgTy ty = pprPanic "funArgTy" (ppr ty)
368 ---------------------------------------------------------------------
371 @mkTyConApp@ is a key function, because it builds a TyConApp, FunTy or PredTy,
375 mkTyConApp :: TyCon -> [Type] -> Type
377 | isFunTyCon tycon, [ty1,ty2] <- tys
383 mkTyConTy :: TyCon -> Type
384 mkTyConTy tycon = mkTyConApp tycon []
386 -- splitTyConApp "looks through" synonyms, because they don't
387 -- mean a distinct type, but all other type-constructor applications
388 -- including functions are returned as Just ..
390 tyConAppTyCon :: Type -> TyCon
391 tyConAppTyCon ty = fst (splitTyConApp ty)
393 tyConAppArgs :: Type -> [Type]
394 tyConAppArgs ty = snd (splitTyConApp ty)
396 splitTyConApp :: Type -> (TyCon, [Type])
397 splitTyConApp ty = case splitTyConApp_maybe ty of
399 Nothing -> pprPanic "splitTyConApp" (ppr ty)
401 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
402 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
403 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
404 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
405 splitTyConApp_maybe other = Nothing
407 -- Sometimes we do NOT want to look throught a newtype. When case matching
408 -- on a newtype we want a convenient way to access the arguments of a newty
409 -- constructor so as to properly form a coercion.
410 splitNewTyConApp :: Type -> (TyCon, [Type])
411 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
413 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
414 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
415 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
416 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
417 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
418 splitNewTyConApp_maybe other = Nothing
420 newTyConInstRhs :: TyCon -> [Type] -> Type
421 -- Unwrap one 'layer' of newtype
422 -- Use the eta'd version if possible
423 newTyConInstRhs tycon tys
424 = ASSERT2( equalLength tvs tys1, ppr tycon $$ ppr tys $$ ppr tvs )
425 mkAppTys (substTyWith tvs tys1 ty) tys2
427 (tvs, ty) = newTyConEtadRhs tycon
428 (tys1, tys2) = splitAtList tvs tys
432 ---------------------------------------------------------------------
436 Notes on type synonyms
437 ~~~~~~~~~~~~~~~~~~~~~~
438 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
439 to return type synonyms whereever possible. Thus
444 splitFunTys (a -> Foo a) = ([a], Foo a)
447 The reason is that we then get better (shorter) type signatures in
448 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
453 repType looks through
457 (d) usage annotations
458 (e) all newtypes, including recursive ones, but not newtype families
459 It's useful in the back end.
462 repType :: Type -> Type
463 -- Only applied to types of kind *; hence tycons are saturated
464 repType ty | Just ty' <- coreView ty = repType ty'
465 repType (ForAllTy _ ty) = repType ty
466 repType (TyConApp tc tys)
468 , (tvs, rep_ty) <- newTyConRep tc
469 = -- Recursive newtypes are opaque to coreView
470 -- but we must expand them here. Sure to
471 -- be saturated because repType is only applied
472 -- to types of kind *
473 ASSERT( tys `lengthIs` tyConArity tc )
474 repType (substTyWith tvs tys rep_ty)
478 -- repType' aims to be a more thorough version of repType
479 -- For now it simply looks through the TyConApp args too
480 repType' ty -- | pprTrace "repType'" (ppr ty $$ ppr (go1 ty)) False = undefined
484 go (TyConApp tc tys) = mkTyConApp tc (map repType' tys)
488 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
489 -- of inspecting the type directly.
490 typePrimRep :: Type -> PrimRep
491 typePrimRep ty = case repType ty of
492 TyConApp tc _ -> tyConPrimRep tc
494 AppTy _ _ -> PtrRep -- See note below
496 other -> pprPanic "typePrimRep" (ppr ty)
497 -- Types of the form 'f a' must be of kind *, not *#, so
498 -- we are guaranteed that they are represented by pointers.
499 -- The reason is that f must have kind *->*, not *->*#, because
500 -- (we claim) there is no way to constrain f's kind any other
505 ---------------------------------------------------------------------
510 mkForAllTy :: TyVar -> Type -> Type
512 = mkForAllTys [tyvar] ty
514 mkForAllTys :: [TyVar] -> Type -> Type
515 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
517 isForAllTy :: Type -> Bool
518 isForAllTy (NoteTy _ ty) = isForAllTy ty
519 isForAllTy (ForAllTy _ _) = True
520 isForAllTy other_ty = False
522 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
523 splitForAllTy_maybe ty = splitFAT_m ty
525 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
526 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
527 splitFAT_m _ = Nothing
529 splitForAllTys :: Type -> ([TyVar], Type)
530 splitForAllTys ty = split ty ty []
532 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
533 split orig_ty (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
534 split orig_ty t tvs = (reverse tvs, orig_ty)
536 dropForAlls :: Type -> Type
537 dropForAlls ty = snd (splitForAllTys ty)
540 -- (mkPiType now in CoreUtils)
544 Instantiate a for-all type with one or more type arguments.
545 Used when we have a polymorphic function applied to type args:
547 Then we use (applyTys type-of-f [t1,t2]) to compute the type of
551 applyTy :: Type -> Type -> Type
552 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
553 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
554 applyTy other arg = panic "applyTy"
556 applyTys :: Type -> [Type] -> Type
557 -- This function is interesting because
558 -- a) the function may have more for-alls than there are args
559 -- b) less obviously, it may have fewer for-alls
560 -- For case (b) think of
561 -- applyTys (forall a.a) [forall b.b, Int]
562 -- This really can happen, via dressing up polymorphic types with newtype
563 -- clothing. Here's an example:
564 -- newtype R = R (forall a. a->a)
565 -- foo = case undefined :: R of
568 applyTys orig_fun_ty [] = orig_fun_ty
569 applyTys orig_fun_ty arg_tys
570 | n_tvs == n_args -- The vastly common case
571 = substTyWith tvs arg_tys rho_ty
572 | n_tvs > n_args -- Too many for-alls
573 = substTyWith (take n_args tvs) arg_tys
574 (mkForAllTys (drop n_args tvs) rho_ty)
575 | otherwise -- Too many type args
576 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
577 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
580 (tvs, rho_ty) = splitForAllTys orig_fun_ty
582 n_args = length arg_tys
586 %************************************************************************
588 \subsection{Source types}
590 %************************************************************************
592 A "source type" is a type that is a separate type as far as the type checker is
593 concerned, but which has low-level representation as far as the back end is concerned.
595 Source types are always lifted.
597 The key function is predTypeRep which gives the representation of a source type:
600 mkPredTy :: PredType -> Type
601 mkPredTy pred = PredTy pred
603 mkPredTys :: ThetaType -> [Type]
604 mkPredTys preds = map PredTy preds
606 predTypeRep :: PredType -> Type
607 -- Convert a PredType to its "representation type";
608 -- the post-type-checking type used by all the Core passes of GHC.
609 -- Unwraps only the outermost level; for example, the result might
610 -- be a newtype application
611 predTypeRep (IParam _ ty) = ty
612 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
613 -- Result might be a newtype application, but the consumer will
614 -- look through that too if necessary
615 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
617 mkFamilyTyConApp :: TyCon -> [Type] -> Type
618 -- Given a family instance TyCon and its arg types, return the
619 -- corresponding family type. E.g.
621 -- data instance T (Maybe b) = MkT b -- Instance tycon :RTL
623 -- mkFamilyTyConApp :RTL Int = T (Maybe Int)
624 mkFamilyTyConApp tc tys
625 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
626 , let fam_subst = zipTopTvSubst (tyConTyVars tc) tys
627 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
631 -- Pretty prints a tycon, using the family instance in case of a
632 -- representation tycon. For example
633 -- e.g. data T [a] = ...
634 -- In that case we want to print `T [a]', where T is the family TyCon
636 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
637 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
643 %************************************************************************
645 \subsection{Kinds and free variables}
647 %************************************************************************
649 ---------------------------------------------------------------------
650 Finding the kind of a type
651 ~~~~~~~~~~~~~~~~~~~~~~~~~~
653 typeKind :: Type -> Kind
654 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
655 -- We should be looking for the coercion kind,
657 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
658 typeKind (NoteTy _ ty) = typeKind ty
659 typeKind (PredTy pred) = predKind pred
660 typeKind (AppTy fun arg) = kindFunResult (typeKind fun)
661 typeKind (ForAllTy tv ty) = typeKind ty
662 typeKind (TyVarTy tyvar) = tyVarKind tyvar
663 typeKind (FunTy arg res)
664 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
665 -- not unliftedTypKind (#)
666 -- The only things that can be after a function arrow are
667 -- (a) types (of kind openTypeKind or its sub-kinds)
668 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
669 | isTySuperKind k = k
670 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
674 predKind :: PredType -> Kind
675 predKind (EqPred {}) = coSuperKind -- A coercion kind!
676 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
677 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
681 ---------------------------------------------------------------------
682 Free variables of a type
683 ~~~~~~~~~~~~~~~~~~~~~~~~
685 tyVarsOfType :: Type -> TyVarSet
686 -- NB: for type synonyms tyVarsOfType does *not* expand the synonym
687 tyVarsOfType (TyVarTy tv) = unitVarSet tv
688 tyVarsOfType (TyConApp tycon tys) = tyVarsOfTypes tys
689 tyVarsOfType (NoteTy (FTVNote tvs) ty2) = tvs
690 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
691 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
692 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
693 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
695 tyVarsOfTypes :: [Type] -> TyVarSet
696 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
698 tyVarsOfPred :: PredType -> TyVarSet
699 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
700 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
701 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
703 tyVarsOfTheta :: ThetaType -> TyVarSet
704 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
706 -- Add a Note with the free tyvars to the top of the type
707 addFreeTyVars :: Type -> Type
708 addFreeTyVars ty@(NoteTy (FTVNote _) _) = ty
709 addFreeTyVars ty = NoteTy (FTVNote (tyVarsOfType ty)) ty
713 %************************************************************************
715 \subsection{Type families}
717 %************************************************************************
719 Type family instances occuring in a type after expanding synonyms.
722 tyFamInsts :: Type -> [(TyCon, [Type])]
724 | Just exp_ty <- tcView ty = tyFamInsts exp_ty
725 tyFamInsts (TyVarTy _) = []
726 tyFamInsts (TyConApp tc tys)
727 | isOpenSynTyCon tc = [(tc, tys)]
728 | otherwise = concat (map tyFamInsts tys)
729 tyFamInsts (FunTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
730 tyFamInsts (AppTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
731 tyFamInsts (ForAllTy _ ty) = tyFamInsts ty
735 %************************************************************************
737 \subsection{TidyType}
739 %************************************************************************
741 tidyTy tidies up a type for printing in an error message, or in
744 It doesn't change the uniques at all, just the print names.
747 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
748 tidyTyVarBndr env@(tidy_env, subst) tyvar
749 = case tidyOccName tidy_env (getOccName name) of
750 (tidy', occ') -> ((tidy', subst'), tyvar'')
752 subst' = extendVarEnv subst tyvar tyvar''
753 tyvar' = setTyVarName tyvar name'
754 name' = tidyNameOcc name occ'
755 -- Don't forget to tidy the kind for coercions!
756 tyvar'' | isCoVar tyvar = setTyVarKind tyvar' kind'
758 kind' = tidyType env (tyVarKind tyvar)
760 name = tyVarName tyvar
762 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
763 -- Add the free tyvars to the env in tidy form,
764 -- so that we can tidy the type they are free in
765 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
767 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
768 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
770 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
771 -- Treat a new tyvar as a binder, and give it a fresh tidy name
772 tidyOpenTyVar env@(tidy_env, subst) tyvar
773 = case lookupVarEnv subst tyvar of
774 Just tyvar' -> (env, tyvar') -- Already substituted
775 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
777 tidyType :: TidyEnv -> Type -> Type
778 tidyType env@(tidy_env, subst) ty
781 go (TyVarTy tv) = case lookupVarEnv subst tv of
782 Nothing -> TyVarTy tv
783 Just tv' -> TyVarTy tv'
784 go (TyConApp tycon tys) = let args = map go tys
785 in args `seqList` TyConApp tycon args
786 go (NoteTy note ty) = (NoteTy $! (go_note note)) $! (go ty)
787 go (PredTy sty) = PredTy (tidyPred env sty)
788 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
789 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
790 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
792 (envp, tvp) = tidyTyVarBndr env tv
794 go_note note@(FTVNote ftvs) = note -- No need to tidy the free tyvars
796 tidyTypes env tys = map (tidyType env) tys
798 tidyPred :: TidyEnv -> PredType -> PredType
799 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
800 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
801 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
805 @tidyOpenType@ grabs the free type variables, tidies them
806 and then uses @tidyType@ to work over the type itself
809 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
811 = (env', tidyType env' ty)
813 env' = tidyFreeTyVars env (tyVarsOfType ty)
815 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
816 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
818 tidyTopType :: Type -> Type
819 tidyTopType ty = tidyType emptyTidyEnv ty
824 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
825 tidyKind env k = tidyOpenType env k
830 %************************************************************************
832 \subsection{Liftedness}
834 %************************************************************************
837 isUnLiftedType :: Type -> Bool
838 -- isUnLiftedType returns True for forall'd unlifted types:
839 -- x :: forall a. Int#
840 -- I found bindings like these were getting floated to the top level.
841 -- They are pretty bogus types, mind you. It would be better never to
844 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
845 isUnLiftedType (ForAllTy tv ty) = isUnLiftedType ty
846 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
847 isUnLiftedType other = False
849 isUnboxedTupleType :: Type -> Bool
850 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
851 Just (tc, ty_args) -> isUnboxedTupleTyCon tc
854 -- Should only be applied to *types*; hence the assert
855 isAlgType :: Type -> Bool
856 isAlgType ty = case splitTyConApp_maybe ty of
857 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
862 @isStrictType@ computes whether an argument (or let RHS) should
863 be computed strictly or lazily, based only on its type.
864 Works just like isUnLiftedType, except that it has a special case
865 for dictionaries. Since it takes account of ClassP, you might think
866 this function should be in TcType, but isStrictType is used by DataCon,
867 which is below TcType in the hierarchy, so it's convenient to put it here.
870 isStrictType (PredTy pred) = isStrictPred pred
871 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
872 isStrictType (ForAllTy tv ty) = isStrictType ty
873 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
874 isStrictType other = False
876 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
877 isStrictPred other = False
878 -- We may be strict in dictionary types, but only if it
879 -- has more than one component.
880 -- [Being strict in a single-component dictionary risks
881 -- poking the dictionary component, which is wrong.]
885 isPrimitiveType :: Type -> Bool
886 -- Returns types that are opaque to Haskell.
887 -- Most of these are unlifted, but now that we interact with .NET, we
888 -- may have primtive (foreign-imported) types that are lifted
889 isPrimitiveType ty = case splitTyConApp_maybe ty of
890 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
896 %************************************************************************
898 \subsection{Sequencing on types
900 %************************************************************************
903 seqType :: Type -> ()
904 seqType (TyVarTy tv) = tv `seq` ()
905 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
906 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
907 seqType (NoteTy note t2) = seqNote note `seq` seqType t2
908 seqType (PredTy p) = seqPred p
909 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
910 seqType (ForAllTy tv ty) = tv `seq` seqType ty
912 seqTypes :: [Type] -> ()
914 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
916 seqNote :: TyNote -> ()
917 seqNote (FTVNote set) = sizeUniqSet set `seq` ()
919 seqPred :: PredType -> ()
920 seqPred (ClassP c tys) = c `seq` seqTypes tys
921 seqPred (IParam n ty) = n `seq` seqType ty
922 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
926 %************************************************************************
928 Equality for Core types
929 (We don't use instances so that we know where it happens)
931 %************************************************************************
933 Note that eqType works right even for partial applications of newtypes.
934 See Note [Newtype eta] in TyCon.lhs
937 coreEqType :: Type -> Type -> Bool
941 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
943 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
944 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
945 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
946 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
947 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
948 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
949 -- The lengths should be equal because
950 -- the two types have the same kind
951 -- NB: if the type constructors differ that does not
952 -- necessarily mean that the types aren't equal
953 -- (synonyms, newtypes)
954 -- Even if the type constructors are the same, but the arguments
955 -- differ, the two types could be the same (e.g. if the arg is just
956 -- ignored in the RHS). In both these cases we fall through to an
957 -- attempt to expand one side or the other.
959 -- Now deal with newtypes, synonyms, pred-tys
960 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
961 | Just t2' <- coreView t2 = eq env t1 t2'
963 -- Fall through case; not equal!
968 %************************************************************************
970 Comparision for source types
971 (We don't use instances so that we know where it happens)
973 %************************************************************************
977 do *not* look through newtypes, PredTypes
980 tcEqType :: Type -> Type -> Bool
981 tcEqType t1 t2 = isEqual $ cmpType t1 t2
983 tcEqTypes :: [Type] -> [Type] -> Bool
984 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
986 tcCmpType :: Type -> Type -> Ordering
987 tcCmpType t1 t2 = cmpType t1 t2
989 tcCmpTypes :: [Type] -> [Type] -> Ordering
990 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
992 tcEqPred :: PredType -> PredType -> Bool
993 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
995 tcCmpPred :: PredType -> PredType -> Ordering
996 tcCmpPred p1 p2 = cmpPred p1 p2
998 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
999 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
1002 Checks whether the second argument is a subterm of the first. (We don't care
1003 about binders, as we are only interested in syntactic subterms.)
1006 tcPartOfType :: Type -> Type -> Bool
1008 | tcEqType t1 t2 = True
1010 | Just t2' <- tcView t2 = tcPartOfType t1 t2'
1011 tcPartOfType _ (TyVarTy _) = False
1012 tcPartOfType t1 (ForAllTy _ t2) = tcPartOfType t1 t2
1013 tcPartOfType t1 (AppTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1014 tcPartOfType t1 (FunTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1015 tcPartOfType t1 (PredTy p2) = tcPartOfPred t1 p2
1016 tcPartOfType t1 (TyConApp _ ts) = any (tcPartOfType t1) ts
1017 tcPartOfType t1 (NoteTy _ t2) = tcPartOfType t1 t2
1019 tcPartOfPred :: Type -> PredType -> Bool
1020 tcPartOfPred t1 (IParam _ t2) = tcPartOfType t1 t2
1021 tcPartOfPred t1 (ClassP _ ts) = any (tcPartOfType t1) ts
1022 tcPartOfPred t1 (EqPred s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1025 Now here comes the real worker
1028 cmpType :: Type -> Type -> Ordering
1029 cmpType t1 t2 = cmpTypeX rn_env t1 t2
1031 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1033 cmpTypes :: [Type] -> [Type] -> Ordering
1034 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
1036 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
1038 cmpPred :: PredType -> PredType -> Ordering
1039 cmpPred p1 p2 = cmpPredX rn_env p1 p2
1041 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
1043 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
1044 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
1045 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
1047 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1048 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1049 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1050 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1051 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1052 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1053 cmpTypeX env t1 (NoteTy _ t2) = cmpTypeX env t1 t2
1055 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1056 cmpTypeX env (AppTy _ _) (TyVarTy _) = GT
1058 cmpTypeX env (FunTy _ _) (TyVarTy _) = GT
1059 cmpTypeX env (FunTy _ _) (AppTy _ _) = GT
1061 cmpTypeX env (TyConApp _ _) (TyVarTy _) = GT
1062 cmpTypeX env (TyConApp _ _) (AppTy _ _) = GT
1063 cmpTypeX env (TyConApp _ _) (FunTy _ _) = GT
1065 cmpTypeX env (ForAllTy _ _) (TyVarTy _) = GT
1066 cmpTypeX env (ForAllTy _ _) (AppTy _ _) = GT
1067 cmpTypeX env (ForAllTy _ _) (FunTy _ _) = GT
1068 cmpTypeX env (ForAllTy _ _) (TyConApp _ _) = GT
1070 cmpTypeX env (PredTy _) t2 = GT
1072 cmpTypeX env _ _ = LT
1075 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1076 cmpTypesX env [] [] = EQ
1077 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1078 cmpTypesX env [] tys = LT
1079 cmpTypesX env ty [] = GT
1082 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1083 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1084 -- Compare names only for implicit parameters
1085 -- This comparison is used exclusively (I believe)
1086 -- for the Avails finite map built in TcSimplify
1087 -- If the types differ we keep them distinct so that we see
1088 -- a distinct pair to run improvement on
1089 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1090 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1092 -- Constructor order: IParam < ClassP < EqPred
1093 cmpPredX env (IParam {}) _ = LT
1094 cmpPredX env (ClassP {}) (IParam {}) = GT
1095 cmpPredX env (ClassP {}) (EqPred {}) = LT
1096 cmpPredX env (EqPred {}) _ = GT
1099 PredTypes are used as a FM key in TcSimplify,
1100 so we take the easy path and make them an instance of Ord
1103 instance Eq PredType where { (==) = tcEqPred }
1104 instance Ord PredType where { compare = tcCmpPred }
1108 %************************************************************************
1112 %************************************************************************
1116 = TvSubst InScopeSet -- The in-scope type variables
1117 TvSubstEnv -- The substitution itself
1118 -- See Note [Apply Once]
1119 -- and Note [Extending the TvSubstEnv]
1121 {- ----------------------------------------------------------
1125 We use TvSubsts to instantiate things, and we might instantiate
1129 So the substition might go [a->b, b->a]. A similar situation arises in Core
1130 when we find a beta redex like
1131 (/\ a /\ b -> e) b a
1132 Then we also end up with a substition that permutes type variables. Other
1133 variations happen to; for example [a -> (a, b)].
1135 ***************************************************
1136 *** So a TvSubst must be applied precisely once ***
1137 ***************************************************
1139 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1140 we use during unifications, it must not be repeatedly applied.
1142 Note [Extending the TvSubst]
1143 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1144 The following invariant should hold of a TvSubst
1146 The in-scope set is needed *only* to
1147 guide the generation of fresh uniques
1149 In particular, the *kind* of the type variables in
1150 the in-scope set is not relevant
1152 This invariant allows a short-cut when the TvSubstEnv is empty:
1153 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1154 then (substTy subst ty) does nothing.
1156 For example, consider:
1157 (/\a. /\b:(a~Int). ...b..) Int
1158 We substitute Int for 'a'. The Unique of 'b' does not change, but
1159 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1161 This invariant has several crucial consequences:
1163 * In substTyVarBndr, we need extend the TvSubstEnv
1164 - if the unique has changed
1165 - or if the kind has changed
1167 * In substTyVar, we do not need to consult the in-scope set;
1168 the TvSubstEnv is enough
1170 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1173 -------------------------------------------------------------- -}
1176 type TvSubstEnv = TyVarEnv Type
1177 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1178 -- invariant discussed in Note [Apply Once]), and also independently
1179 -- in the middle of matching, and unification (see Types.Unify)
1180 -- So you have to look at the context to know if it's idempotent or
1181 -- apply-once or whatever
1182 emptyTvSubstEnv :: TvSubstEnv
1183 emptyTvSubstEnv = emptyVarEnv
1185 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1186 -- (compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1
1187 -- It assumes that both are idempotent
1188 -- Typically, env1 is the refinement to a base substitution env2
1189 composeTvSubst in_scope env1 env2
1190 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1191 -- First apply env1 to the range of env2
1192 -- Then combine the two, making sure that env1 loses if
1193 -- both bind the same variable; that's why env1 is the
1194 -- *left* argument to plusVarEnv, because the right arg wins
1196 subst1 = TvSubst in_scope env1
1198 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1200 isEmptyTvSubst :: TvSubst -> Bool
1201 -- See Note [Extending the TvSubstEnv]
1202 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1204 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1207 getTvSubstEnv :: TvSubst -> TvSubstEnv
1208 getTvSubstEnv (TvSubst _ env) = env
1210 getTvInScope :: TvSubst -> InScopeSet
1211 getTvInScope (TvSubst in_scope _) = in_scope
1213 isInScope :: Var -> TvSubst -> Bool
1214 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1216 notElemTvSubst :: TyVar -> TvSubst -> Bool
1217 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1219 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1220 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1222 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1223 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1225 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1226 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1228 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1229 extendTvSubstList (TvSubst in_scope env) tvs tys
1230 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1232 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1233 -- the types given; but it's just a thunk so with a bit of luck
1234 -- it'll never be evaluated
1236 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1237 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1239 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1240 zipOpenTvSubst tyvars tys
1242 | length tyvars /= length tys
1243 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1246 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1248 -- mkTopTvSubst is called when doing top-level substitutions.
1249 -- Here we expect that the free vars of the range of the
1250 -- substitution will be empty.
1251 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1252 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1254 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1255 zipTopTvSubst tyvars tys
1257 | length tyvars /= length tys
1258 = pprTrace "zipTopTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1261 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1263 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1266 | length tyvars /= length tys
1267 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1270 = zip_ty_env tyvars tys emptyVarEnv
1272 -- Later substitutions in the list over-ride earlier ones,
1273 -- but there should be no loops
1274 zip_ty_env [] [] env = env
1275 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1276 -- There used to be a special case for when
1278 -- (a not-uncommon case) in which case the substitution was dropped.
1279 -- But the type-tidier changes the print-name of a type variable without
1280 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1281 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1282 -- And it happened that t was the type variable of the class. Post-tiding,
1283 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1284 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1285 -- and so generated a rep type mentioning t not t2.
1287 -- Simplest fix is to nuke the "optimisation"
1288 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1289 -- zip_ty_env _ _ env = env
1291 instance Outputable TvSubst where
1292 ppr (TvSubst ins env)
1293 = brackets $ sep[ ptext SLIT("TvSubst"),
1294 nest 2 (ptext SLIT("In scope:") <+> ppr ins),
1295 nest 2 (ptext SLIT("Env:") <+> ppr env) ]
1298 %************************************************************************
1300 Performing type substitutions
1302 %************************************************************************
1305 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1306 substTyWith tvs tys = ASSERT( length tvs == length tys )
1307 substTy (zipOpenTvSubst tvs tys)
1309 substTy :: TvSubst -> Type -> Type
1310 substTy subst ty | isEmptyTvSubst subst = ty
1311 | otherwise = subst_ty subst ty
1313 substTys :: TvSubst -> [Type] -> [Type]
1314 substTys subst tys | isEmptyTvSubst subst = tys
1315 | otherwise = map (subst_ty subst) tys
1317 substTheta :: TvSubst -> ThetaType -> ThetaType
1318 substTheta subst theta
1319 | isEmptyTvSubst subst = theta
1320 | otherwise = map (substPred subst) theta
1322 substPred :: TvSubst -> PredType -> PredType
1323 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1324 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1325 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1327 deShadowTy :: TyVarSet -> Type -> Type -- Remove any nested binders mentioning tvs
1329 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1331 in_scope = mkInScopeSet tvs
1333 subst_ty :: TvSubst -> Type -> Type
1334 -- subst_ty is the main workhorse for type substitution
1336 -- Note that the in_scope set is poked only if we hit a forall
1337 -- so it may often never be fully computed
1341 go (TyVarTy tv) = substTyVar subst tv
1342 go (TyConApp tc tys) = let args = map go tys
1343 in args `seqList` TyConApp tc args
1345 go (PredTy p) = PredTy $! (substPred subst p)
1347 go (NoteTy (FTVNote _) ty2) = go ty2 -- Discard the free tyvar note
1349 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1350 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1351 -- The mkAppTy smart constructor is important
1352 -- we might be replacing (a Int), represented with App
1353 -- by [Int], represented with TyConApp
1354 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1355 (subst', tv') -> ForAllTy tv' $! (subst_ty subst' ty)
1357 substTyVar :: TvSubst -> TyVar -> Type
1358 substTyVar subst@(TvSubst in_scope env) tv
1359 = case lookupTyVar subst tv of {
1360 Nothing -> TyVarTy tv;
1361 Just ty -> ty -- See Note [Apply Once]
1364 substTyVars :: TvSubst -> [TyVar] -> [Type]
1365 substTyVars subst tvs = map (substTyVar subst) tvs
1367 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1368 -- See Note [Extending the TvSubst]
1369 lookupTyVar (TvSubst in_scope env) tv = lookupVarEnv env tv
1371 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1372 substTyVarBndr subst@(TvSubst in_scope env) old_var
1373 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1375 is_co_var = isCoVar old_var
1377 new_env | no_change = delVarEnv env old_var
1378 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1380 no_change = new_var == old_var && not is_co_var
1381 -- no_change means that the new_var is identical in
1382 -- all respects to the old_var (same unique, same kind)
1383 -- See Note [Extending the TvSubst]
1385 -- In that case we don't need to extend the substitution
1386 -- to map old to new. But instead we must zap any
1387 -- current substitution for the variable. For example:
1388 -- (\x.e) with id_subst = [x |-> e']
1389 -- Here we must simply zap the substitution for x
1391 new_var = uniqAway in_scope subst_old_var
1392 -- The uniqAway part makes sure the new variable is not already in scope
1394 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1395 -- It's only worth doing the substitution for coercions,
1396 -- becuase only they can have free type variables
1397 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1398 | otherwise = old_var
1401 ----------------------------------------------------
1406 There's a little subtyping at the kind level:
1415 where * [LiftedTypeKind] means boxed type
1416 # [UnliftedTypeKind] means unboxed type
1417 (#) [UbxTupleKind] means unboxed tuple
1418 ?? [ArgTypeKind] is the lub of *,#
1419 ? [OpenTypeKind] means any type at all
1423 error :: forall a:?. String -> a
1424 (->) :: ?? -> ? -> *
1425 (\(x::t) -> ...) Here t::?? (i.e. not unboxed tuple)
1428 type KindVar = TyVar -- invariant: KindVar will always be a
1429 -- TcTyVar with details MetaTv TauTv ...
1430 -- kind var constructors and functions are in TcType
1432 type SimpleKind = Kind
1437 During kind inference, a kind variable unifies only with
1439 sk ::= * | sk1 -> sk2
1441 data T a = MkT a (T Int#)
1442 fails. We give T the kind (k -> *), and the kind variable k won't unify
1443 with # (the kind of Int#).
1447 When creating a fresh internal type variable, we give it a kind to express
1448 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1451 During unification we only bind an internal type variable to a type
1452 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1454 When unifying two internal type variables, we collect their kind constraints by
1455 finding the GLB of the two. Since the partial order is a tree, they only
1456 have a glb if one is a sub-kind of the other. In that case, we bind the
1457 less-informative one to the more informative one. Neat, eh?
1464 %************************************************************************
1466 Functions over Kinds
1468 %************************************************************************
1471 kindFunResult :: Kind -> Kind
1472 kindFunResult k = funResultTy k
1474 splitKindFunTys :: Kind -> ([Kind],Kind)
1475 splitKindFunTys k = splitFunTys k
1477 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1478 splitKindFunTysN k = splitFunTysN k
1480 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1482 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1484 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1485 isOpenTypeKind other = False
1487 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1489 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1490 isUbxTupleKind other = False
1492 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1494 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1495 isArgTypeKind other = False
1497 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1499 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1500 isUnliftedTypeKind other = False
1502 isSubOpenTypeKind :: Kind -> Bool
1503 -- True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1504 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1505 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1507 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1508 isSubOpenTypeKind other = ASSERT( isKind other ) False
1509 -- This is a conservative answer
1510 -- It matters in the call to isSubKind in
1511 -- checkExpectedKind.
1513 isSubArgTypeKindCon kc
1514 | isUnliftedTypeKindCon kc = True
1515 | isLiftedTypeKindCon kc = True
1516 | isArgTypeKindCon kc = True
1519 isSubArgTypeKind :: Kind -> Bool
1520 -- True of any sub-kind of ArgTypeKind
1521 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1522 isSubArgTypeKind other = False
1524 isSuperKind :: Type -> Bool
1525 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1526 isSuperKind other = False
1528 isKind :: Kind -> Bool
1529 isKind k = isSuperKind (typeKind k)
1531 isSubKind :: Kind -> Kind -> Bool
1532 -- (k1 `isSubKind` k2) checks that k1 <: k2
1533 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1534 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1535 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1536 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1537 isSubKind k1 k2 = False
1539 eqKind :: Kind -> Kind -> Bool
1542 isSubKindCon :: TyCon -> TyCon -> Bool
1543 -- (kc1 `isSubKindCon` kc2) checks that kc1 <: kc2
1544 isSubKindCon kc1 kc2
1545 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1546 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1547 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1548 | isOpenTypeKindCon kc2 = True
1549 -- we already know kc1 is not a fun, its a TyCon
1550 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1553 defaultKind :: Kind -> Kind
1554 -- Used when generalising: default kind '?' and '??' to '*'
1556 -- When we generalise, we make generic type variables whose kind is
1557 -- simple (* or *->* etc). So generic type variables (other than
1558 -- built-in constants like 'error') always have simple kinds. This is important;
1561 -- We want f to get type
1562 -- f :: forall (a::*). a -> Bool
1564 -- f :: forall (a::??). a -> Bool
1565 -- because that would allow a call like (f 3#) as well as (f True),
1566 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1568 | isSubOpenTypeKind k = liftedTypeKind
1569 | isSubArgTypeKind k = liftedTypeKind
1572 isEqPred :: PredType -> Bool
1573 isEqPred (EqPred _ _) = True
1574 isEqPred other = False