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)
285 | not (isOpenSynTyCon tc) || length tys > tyConArity tc
286 = case snocView tys of -- never create unsaturated type family apps
287 Just (tys', ty') -> Just (TyConApp tc tys', ty')
289 repSplitAppTy_maybe _other = Nothing
291 splitAppTy :: Type -> (Type, Type)
292 splitAppTy ty = case splitAppTy_maybe ty of
294 Nothing -> panic "splitAppTy"
297 splitAppTys :: Type -> (Type, [Type])
298 splitAppTys ty = split ty ty []
300 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
301 split orig_ty (AppTy ty arg) args = split ty ty (arg:args)
302 split orig_ty (TyConApp tc tc_args) args
303 = let -- keep type families saturated
304 n | isOpenSynTyCon tc = tyConArity tc
306 (tc_args1, tc_args2) = splitAt n tc_args
308 (TyConApp tc tc_args1, tc_args2 ++ args)
309 split orig_ty (FunTy ty1 ty2) args = ASSERT( null args )
310 (TyConApp funTyCon [], [ty1,ty2])
311 split orig_ty ty args = (orig_ty, args)
316 ---------------------------------------------------------------------
321 mkFunTy :: Type -> Type -> Type
322 mkFunTy (PredTy (EqPred ty1 ty2)) res = mkForAllTy (mkWildCoVar (PredTy (EqPred ty1 ty2))) res
323 mkFunTy arg res = FunTy arg res
325 mkFunTys :: [Type] -> Type -> Type
326 mkFunTys tys ty = foldr mkFunTy ty tys
328 isFunTy :: Type -> Bool
329 isFunTy ty = isJust (splitFunTy_maybe ty)
331 splitFunTy :: Type -> (Type, Type)
332 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
333 splitFunTy (FunTy arg res) = (arg, res)
334 splitFunTy other = pprPanic "splitFunTy" (ppr other)
336 splitFunTy_maybe :: Type -> Maybe (Type, Type)
337 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
338 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
339 splitFunTy_maybe other = Nothing
341 splitFunTys :: Type -> ([Type], Type)
342 splitFunTys ty = split [] ty ty
344 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
345 split args orig_ty (FunTy arg res) = split (arg:args) res res
346 split args orig_ty ty = (reverse args, orig_ty)
348 splitFunTysN :: Int -> Type -> ([Type], Type)
349 -- Split off exactly n arg tys
350 splitFunTysN 0 ty = ([], ty)
351 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
352 case splitFunTysN (n-1) res of { (args, res) ->
355 zipFunTys :: Outputable a => [a] -> Type -> ([(a,Type)], Type)
356 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
358 split acc [] nty ty = (reverse acc, nty)
360 | Just ty' <- coreView ty = split acc xs nty ty'
361 split acc (x:xs) nty (FunTy arg res) = split ((x,arg):acc) xs res res
362 split acc (x:xs) nty ty = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
364 funResultTy :: Type -> Type
365 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
366 funResultTy (FunTy arg res) = res
367 funResultTy ty = pprPanic "funResultTy" (ppr ty)
369 funArgTy :: Type -> Type
370 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
371 funArgTy (FunTy arg res) = arg
372 funArgTy ty = pprPanic "funArgTy" (ppr ty)
376 ---------------------------------------------------------------------
379 @mkTyConApp@ is a key function, because it builds a TyConApp, FunTy or PredTy,
383 mkTyConApp :: TyCon -> [Type] -> Type
385 | isFunTyCon tycon, [ty1,ty2] <- tys
391 mkTyConTy :: TyCon -> Type
392 mkTyConTy tycon = mkTyConApp tycon []
394 -- splitTyConApp "looks through" synonyms, because they don't
395 -- mean a distinct type, but all other type-constructor applications
396 -- including functions are returned as Just ..
398 tyConAppTyCon :: Type -> TyCon
399 tyConAppTyCon ty = fst (splitTyConApp ty)
401 tyConAppArgs :: Type -> [Type]
402 tyConAppArgs ty = snd (splitTyConApp ty)
404 splitTyConApp :: Type -> (TyCon, [Type])
405 splitTyConApp ty = case splitTyConApp_maybe ty of
407 Nothing -> pprPanic "splitTyConApp" (ppr ty)
409 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
410 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
411 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
412 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
413 splitTyConApp_maybe other = Nothing
415 -- Sometimes we do NOT want to look throught a newtype. When case matching
416 -- on a newtype we want a convenient way to access the arguments of a newty
417 -- constructor so as to properly form a coercion.
418 splitNewTyConApp :: Type -> (TyCon, [Type])
419 splitNewTyConApp ty = case splitNewTyConApp_maybe ty of
421 Nothing -> pprPanic "splitNewTyConApp" (ppr ty)
422 splitNewTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
423 splitNewTyConApp_maybe ty | Just ty' <- tcView ty = splitNewTyConApp_maybe ty'
424 splitNewTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
425 splitNewTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
426 splitNewTyConApp_maybe other = Nothing
428 newTyConInstRhs :: TyCon -> [Type] -> Type
429 -- Unwrap one 'layer' of newtype
430 -- Use the eta'd version if possible
431 newTyConInstRhs tycon tys
432 = ASSERT2( equalLength tvs tys1, ppr tycon $$ ppr tys $$ ppr tvs )
433 mkAppTys (substTyWith tvs tys1 ty) tys2
435 (tvs, ty) = newTyConEtadRhs tycon
436 (tys1, tys2) = splitAtList tvs tys
440 ---------------------------------------------------------------------
444 Notes on type synonyms
445 ~~~~~~~~~~~~~~~~~~~~~~
446 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
447 to return type synonyms whereever possible. Thus
452 splitFunTys (a -> Foo a) = ([a], Foo a)
455 The reason is that we then get better (shorter) type signatures in
456 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
461 repType looks through
465 (d) usage annotations
466 (e) all newtypes, including recursive ones, but not newtype families
467 It's useful in the back end.
470 repType :: Type -> Type
471 -- Only applied to types of kind *; hence tycons are saturated
472 repType ty | Just ty' <- coreView ty = repType ty'
473 repType (ForAllTy _ ty) = repType ty
474 repType (TyConApp tc tys)
476 , (tvs, rep_ty) <- newTyConRep tc
477 = -- Recursive newtypes are opaque to coreView
478 -- but we must expand them here. Sure to
479 -- be saturated because repType is only applied
480 -- to types of kind *
481 ASSERT( tys `lengthIs` tyConArity tc )
482 repType (substTyWith tvs tys rep_ty)
486 -- repType' aims to be a more thorough version of repType
487 -- For now it simply looks through the TyConApp args too
488 repType' ty -- | pprTrace "repType'" (ppr ty $$ ppr (go1 ty)) False = undefined
492 go (TyConApp tc tys) = mkTyConApp tc (map repType' tys)
496 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
497 -- of inspecting the type directly.
498 typePrimRep :: Type -> PrimRep
499 typePrimRep ty = case repType ty of
500 TyConApp tc _ -> tyConPrimRep tc
502 AppTy _ _ -> PtrRep -- See note below
504 other -> pprPanic "typePrimRep" (ppr ty)
505 -- Types of the form 'f a' must be of kind *, not *#, so
506 -- we are guaranteed that they are represented by pointers.
507 -- The reason is that f must have kind *->*, not *->*#, because
508 -- (we claim) there is no way to constrain f's kind any other
513 ---------------------------------------------------------------------
518 mkForAllTy :: TyVar -> Type -> Type
520 = mkForAllTys [tyvar] ty
522 mkForAllTys :: [TyVar] -> Type -> Type
523 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
525 isForAllTy :: Type -> Bool
526 isForAllTy (NoteTy _ ty) = isForAllTy ty
527 isForAllTy (ForAllTy _ _) = True
528 isForAllTy other_ty = False
530 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
531 splitForAllTy_maybe ty = splitFAT_m ty
533 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
534 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
535 splitFAT_m _ = Nothing
537 splitForAllTys :: Type -> ([TyVar], Type)
538 splitForAllTys ty = split ty ty []
540 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
541 split orig_ty (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
542 split orig_ty t tvs = (reverse tvs, orig_ty)
544 dropForAlls :: Type -> Type
545 dropForAlls ty = snd (splitForAllTys ty)
548 -- (mkPiType now in CoreUtils)
552 Instantiate a for-all type with one or more type arguments.
553 Used when we have a polymorphic function applied to type args:
555 Then we use (applyTys type-of-f [t1,t2]) to compute the type of
559 applyTy :: Type -> Type -> Type
560 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
561 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
562 applyTy other arg = panic "applyTy"
564 applyTys :: Type -> [Type] -> Type
565 -- This function is interesting because
566 -- a) the function may have more for-alls than there are args
567 -- b) less obviously, it may have fewer for-alls
568 -- For case (b) think of
569 -- applyTys (forall a.a) [forall b.b, Int]
570 -- This really can happen, via dressing up polymorphic types with newtype
571 -- clothing. Here's an example:
572 -- newtype R = R (forall a. a->a)
573 -- foo = case undefined :: R of
576 applyTys orig_fun_ty [] = orig_fun_ty
577 applyTys orig_fun_ty arg_tys
578 | n_tvs == n_args -- The vastly common case
579 = substTyWith tvs arg_tys rho_ty
580 | n_tvs > n_args -- Too many for-alls
581 = substTyWith (take n_args tvs) arg_tys
582 (mkForAllTys (drop n_args tvs) rho_ty)
583 | otherwise -- Too many type args
584 = ASSERT2( n_tvs > 0, ppr orig_fun_ty ) -- Zero case gives infnite loop!
585 applyTys (substTyWith tvs (take n_tvs arg_tys) rho_ty)
588 (tvs, rho_ty) = splitForAllTys orig_fun_ty
590 n_args = length arg_tys
594 %************************************************************************
596 \subsection{Source types}
598 %************************************************************************
600 A "source type" is a type that is a separate type as far as the type checker is
601 concerned, but which has low-level representation as far as the back end is concerned.
603 Source types are always lifted.
605 The key function is predTypeRep which gives the representation of a source type:
608 mkPredTy :: PredType -> Type
609 mkPredTy pred = PredTy pred
611 mkPredTys :: ThetaType -> [Type]
612 mkPredTys preds = map PredTy preds
614 predTypeRep :: PredType -> Type
615 -- Convert a PredType to its "representation type";
616 -- the post-type-checking type used by all the Core passes of GHC.
617 -- Unwraps only the outermost level; for example, the result might
618 -- be a newtype application
619 predTypeRep (IParam _ ty) = ty
620 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
621 -- Result might be a newtype application, but the consumer will
622 -- look through that too if necessary
623 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
625 mkFamilyTyConApp :: TyCon -> [Type] -> Type
626 -- Given a family instance TyCon and its arg types, return the
627 -- corresponding family type. E.g.
629 -- data instance T (Maybe b) = MkT b -- Instance tycon :RTL
631 -- mkFamilyTyConApp :RTL Int = T (Maybe Int)
632 mkFamilyTyConApp tc tys
633 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
634 , let fam_subst = zipTopTvSubst (tyConTyVars tc) tys
635 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
639 -- Pretty prints a tycon, using the family instance in case of a
640 -- representation tycon. For example
641 -- e.g. data T [a] = ...
642 -- In that case we want to print `T [a]', where T is the family TyCon
644 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
645 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
651 %************************************************************************
653 \subsection{Kinds and free variables}
655 %************************************************************************
657 ---------------------------------------------------------------------
658 Finding the kind of a type
659 ~~~~~~~~~~~~~~~~~~~~~~~~~~
661 typeKind :: Type -> Kind
662 typeKind (TyConApp tycon tys) = ASSERT( not (isCoercionTyCon tycon) )
663 -- We should be looking for the coercion kind,
665 foldr (\_ k -> kindFunResult k) (tyConKind tycon) tys
666 typeKind (NoteTy _ ty) = typeKind ty
667 typeKind (PredTy pred) = predKind pred
668 typeKind (AppTy fun arg) = kindFunResult (typeKind fun)
669 typeKind (ForAllTy tv ty) = typeKind ty
670 typeKind (TyVarTy tyvar) = tyVarKind tyvar
671 typeKind (FunTy arg res)
672 -- Hack alert. The kind of (Int -> Int#) is liftedTypeKind (*),
673 -- not unliftedTypKind (#)
674 -- The only things that can be after a function arrow are
675 -- (a) types (of kind openTypeKind or its sub-kinds)
676 -- (b) kinds (of super-kind TY) (e.g. * -> (* -> *))
677 | isTySuperKind k = k
678 | otherwise = ASSERT( isSubOpenTypeKind k) liftedTypeKind
682 predKind :: PredType -> Kind
683 predKind (EqPred {}) = coSuperKind -- A coercion kind!
684 predKind (ClassP {}) = liftedTypeKind -- Class and implicitPredicates are
685 predKind (IParam {}) = liftedTypeKind -- always represented by lifted types
689 ---------------------------------------------------------------------
690 Free variables of a type
691 ~~~~~~~~~~~~~~~~~~~~~~~~
693 tyVarsOfType :: Type -> TyVarSet
694 -- NB: for type synonyms tyVarsOfType does *not* expand the synonym
695 tyVarsOfType (TyVarTy tv) = unitVarSet tv
696 tyVarsOfType (TyConApp tycon tys) = tyVarsOfTypes tys
697 tyVarsOfType (NoteTy (FTVNote tvs) ty2) = tvs
698 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
699 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
700 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
701 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
703 tyVarsOfTypes :: [Type] -> TyVarSet
704 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
706 tyVarsOfPred :: PredType -> TyVarSet
707 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
708 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
709 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
711 tyVarsOfTheta :: ThetaType -> TyVarSet
712 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
714 -- Add a Note with the free tyvars to the top of the type
715 addFreeTyVars :: Type -> Type
716 addFreeTyVars ty@(NoteTy (FTVNote _) _) = ty
717 addFreeTyVars ty = NoteTy (FTVNote (tyVarsOfType ty)) ty
721 %************************************************************************
723 \subsection{Type families}
725 %************************************************************************
727 Type family instances occuring in a type after expanding synonyms.
730 tyFamInsts :: Type -> [(TyCon, [Type])]
732 | Just exp_ty <- tcView ty = tyFamInsts exp_ty
733 tyFamInsts (TyVarTy _) = []
734 tyFamInsts (TyConApp tc tys)
735 | isOpenSynTyCon tc = [(tc, tys)]
736 | otherwise = concat (map tyFamInsts tys)
737 tyFamInsts (FunTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
738 tyFamInsts (AppTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
739 tyFamInsts (ForAllTy _ ty) = tyFamInsts ty
743 %************************************************************************
745 \subsection{TidyType}
747 %************************************************************************
749 tidyTy tidies up a type for printing in an error message, or in
752 It doesn't change the uniques at all, just the print names.
755 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
756 tidyTyVarBndr env@(tidy_env, subst) tyvar
757 = case tidyOccName tidy_env (getOccName name) of
758 (tidy', occ') -> ((tidy', subst'), tyvar'')
760 subst' = extendVarEnv subst tyvar tyvar''
761 tyvar' = setTyVarName tyvar name'
762 name' = tidyNameOcc name occ'
763 -- Don't forget to tidy the kind for coercions!
764 tyvar'' | isCoVar tyvar = setTyVarKind tyvar' kind'
766 kind' = tidyType env (tyVarKind tyvar)
768 name = tyVarName tyvar
770 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
771 -- Add the free tyvars to the env in tidy form,
772 -- so that we can tidy the type they are free in
773 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
775 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
776 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
778 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
779 -- Treat a new tyvar as a binder, and give it a fresh tidy name
780 tidyOpenTyVar env@(tidy_env, subst) tyvar
781 = case lookupVarEnv subst tyvar of
782 Just tyvar' -> (env, tyvar') -- Already substituted
783 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
785 tidyType :: TidyEnv -> Type -> Type
786 tidyType env@(tidy_env, subst) ty
789 go (TyVarTy tv) = case lookupVarEnv subst tv of
790 Nothing -> TyVarTy tv
791 Just tv' -> TyVarTy tv'
792 go (TyConApp tycon tys) = let args = map go tys
793 in args `seqList` TyConApp tycon args
794 go (NoteTy note ty) = (NoteTy $! (go_note note)) $! (go ty)
795 go (PredTy sty) = PredTy (tidyPred env sty)
796 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
797 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
798 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
800 (envp, tvp) = tidyTyVarBndr env tv
802 go_note note@(FTVNote ftvs) = note -- No need to tidy the free tyvars
804 tidyTypes env tys = map (tidyType env) tys
806 tidyPred :: TidyEnv -> PredType -> PredType
807 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
808 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
809 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
813 @tidyOpenType@ grabs the free type variables, tidies them
814 and then uses @tidyType@ to work over the type itself
817 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
819 = (env', tidyType env' ty)
821 env' = tidyFreeTyVars env (tyVarsOfType ty)
823 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
824 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
826 tidyTopType :: Type -> Type
827 tidyTopType ty = tidyType emptyTidyEnv ty
832 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
833 tidyKind env k = tidyOpenType env k
838 %************************************************************************
840 \subsection{Liftedness}
842 %************************************************************************
845 isUnLiftedType :: Type -> Bool
846 -- isUnLiftedType returns True for forall'd unlifted types:
847 -- x :: forall a. Int#
848 -- I found bindings like these were getting floated to the top level.
849 -- They are pretty bogus types, mind you. It would be better never to
852 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
853 isUnLiftedType (ForAllTy tv ty) = isUnLiftedType ty
854 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
855 isUnLiftedType other = False
857 isUnboxedTupleType :: Type -> Bool
858 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
859 Just (tc, ty_args) -> isUnboxedTupleTyCon tc
862 -- Should only be applied to *types*; hence the assert
863 isAlgType :: Type -> Bool
864 isAlgType ty = case splitTyConApp_maybe ty of
865 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
870 @isStrictType@ computes whether an argument (or let RHS) should
871 be computed strictly or lazily, based only on its type.
872 Works just like isUnLiftedType, except that it has a special case
873 for dictionaries. Since it takes account of ClassP, you might think
874 this function should be in TcType, but isStrictType is used by DataCon,
875 which is below TcType in the hierarchy, so it's convenient to put it here.
878 isStrictType (PredTy pred) = isStrictPred pred
879 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
880 isStrictType (ForAllTy tv ty) = isStrictType ty
881 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
882 isStrictType other = False
884 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
885 isStrictPred other = False
886 -- We may be strict in dictionary types, but only if it
887 -- has more than one component.
888 -- [Being strict in a single-component dictionary risks
889 -- poking the dictionary component, which is wrong.]
893 isPrimitiveType :: Type -> Bool
894 -- Returns types that are opaque to Haskell.
895 -- Most of these are unlifted, but now that we interact with .NET, we
896 -- may have primtive (foreign-imported) types that are lifted
897 isPrimitiveType ty = case splitTyConApp_maybe ty of
898 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
904 %************************************************************************
906 \subsection{Sequencing on types
908 %************************************************************************
911 seqType :: Type -> ()
912 seqType (TyVarTy tv) = tv `seq` ()
913 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
914 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
915 seqType (NoteTy note t2) = seqNote note `seq` seqType t2
916 seqType (PredTy p) = seqPred p
917 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
918 seqType (ForAllTy tv ty) = tv `seq` seqType ty
920 seqTypes :: [Type] -> ()
922 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
924 seqNote :: TyNote -> ()
925 seqNote (FTVNote set) = sizeUniqSet set `seq` ()
927 seqPred :: PredType -> ()
928 seqPred (ClassP c tys) = c `seq` seqTypes tys
929 seqPred (IParam n ty) = n `seq` seqType ty
930 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
934 %************************************************************************
936 Equality for Core types
937 (We don't use instances so that we know where it happens)
939 %************************************************************************
941 Note that eqType works right even for partial applications of newtypes.
942 See Note [Newtype eta] in TyCon.lhs
945 coreEqType :: Type -> Type -> Bool
949 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
951 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
952 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
953 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
954 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
955 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
956 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
957 -- The lengths should be equal because
958 -- the two types have the same kind
959 -- NB: if the type constructors differ that does not
960 -- necessarily mean that the types aren't equal
961 -- (synonyms, newtypes)
962 -- Even if the type constructors are the same, but the arguments
963 -- differ, the two types could be the same (e.g. if the arg is just
964 -- ignored in the RHS). In both these cases we fall through to an
965 -- attempt to expand one side or the other.
967 -- Now deal with newtypes, synonyms, pred-tys
968 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
969 | Just t2' <- coreView t2 = eq env t1 t2'
971 -- Fall through case; not equal!
976 %************************************************************************
978 Comparision for source types
979 (We don't use instances so that we know where it happens)
981 %************************************************************************
985 do *not* look through newtypes, PredTypes
988 tcEqType :: Type -> Type -> Bool
989 tcEqType t1 t2 = isEqual $ cmpType t1 t2
991 tcEqTypes :: [Type] -> [Type] -> Bool
992 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
994 tcCmpType :: Type -> Type -> Ordering
995 tcCmpType t1 t2 = cmpType t1 t2
997 tcCmpTypes :: [Type] -> [Type] -> Ordering
998 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
1000 tcEqPred :: PredType -> PredType -> Bool
1001 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
1003 tcCmpPred :: PredType -> PredType -> Ordering
1004 tcCmpPred p1 p2 = cmpPred p1 p2
1006 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
1007 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
1010 Checks whether the second argument is a subterm of the first. (We don't care
1011 about binders, as we are only interested in syntactic subterms.)
1014 tcPartOfType :: Type -> Type -> Bool
1016 | tcEqType t1 t2 = True
1018 | Just t2' <- tcView t2 = tcPartOfType t1 t2'
1019 tcPartOfType _ (TyVarTy _) = False
1020 tcPartOfType t1 (ForAllTy _ t2) = tcPartOfType t1 t2
1021 tcPartOfType t1 (AppTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1022 tcPartOfType t1 (FunTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1023 tcPartOfType t1 (PredTy p2) = tcPartOfPred t1 p2
1024 tcPartOfType t1 (TyConApp _ ts) = any (tcPartOfType t1) ts
1025 tcPartOfType t1 (NoteTy _ t2) = tcPartOfType t1 t2
1027 tcPartOfPred :: Type -> PredType -> Bool
1028 tcPartOfPred t1 (IParam _ t2) = tcPartOfType t1 t2
1029 tcPartOfPred t1 (ClassP _ ts) = any (tcPartOfType t1) ts
1030 tcPartOfPred t1 (EqPred s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1033 Now here comes the real worker
1036 cmpType :: Type -> Type -> Ordering
1037 cmpType t1 t2 = cmpTypeX rn_env t1 t2
1039 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1041 cmpTypes :: [Type] -> [Type] -> Ordering
1042 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
1044 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
1046 cmpPred :: PredType -> PredType -> Ordering
1047 cmpPred p1 p2 = cmpPredX rn_env p1 p2
1049 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
1051 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
1052 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
1053 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
1055 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1056 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1057 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1058 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1059 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1060 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1061 cmpTypeX env t1 (NoteTy _ t2) = cmpTypeX env t1 t2
1063 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1064 cmpTypeX env (AppTy _ _) (TyVarTy _) = GT
1066 cmpTypeX env (FunTy _ _) (TyVarTy _) = GT
1067 cmpTypeX env (FunTy _ _) (AppTy _ _) = GT
1069 cmpTypeX env (TyConApp _ _) (TyVarTy _) = GT
1070 cmpTypeX env (TyConApp _ _) (AppTy _ _) = GT
1071 cmpTypeX env (TyConApp _ _) (FunTy _ _) = GT
1073 cmpTypeX env (ForAllTy _ _) (TyVarTy _) = GT
1074 cmpTypeX env (ForAllTy _ _) (AppTy _ _) = GT
1075 cmpTypeX env (ForAllTy _ _) (FunTy _ _) = GT
1076 cmpTypeX env (ForAllTy _ _) (TyConApp _ _) = GT
1078 cmpTypeX env (PredTy _) t2 = GT
1080 cmpTypeX env _ _ = LT
1083 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1084 cmpTypesX env [] [] = EQ
1085 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1086 cmpTypesX env [] tys = LT
1087 cmpTypesX env ty [] = GT
1090 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1091 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1092 -- Compare names only for implicit parameters
1093 -- This comparison is used exclusively (I believe)
1094 -- for the Avails finite map built in TcSimplify
1095 -- If the types differ we keep them distinct so that we see
1096 -- a distinct pair to run improvement on
1097 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1098 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1100 -- Constructor order: IParam < ClassP < EqPred
1101 cmpPredX env (IParam {}) _ = LT
1102 cmpPredX env (ClassP {}) (IParam {}) = GT
1103 cmpPredX env (ClassP {}) (EqPred {}) = LT
1104 cmpPredX env (EqPred {}) _ = GT
1107 PredTypes are used as a FM key in TcSimplify,
1108 so we take the easy path and make them an instance of Ord
1111 instance Eq PredType where { (==) = tcEqPred }
1112 instance Ord PredType where { compare = tcCmpPred }
1116 %************************************************************************
1120 %************************************************************************
1124 = TvSubst InScopeSet -- The in-scope type variables
1125 TvSubstEnv -- The substitution itself
1126 -- See Note [Apply Once]
1127 -- and Note [Extending the TvSubstEnv]
1129 {- ----------------------------------------------------------
1133 We use TvSubsts to instantiate things, and we might instantiate
1137 So the substition might go [a->b, b->a]. A similar situation arises in Core
1138 when we find a beta redex like
1139 (/\ a /\ b -> e) b a
1140 Then we also end up with a substition that permutes type variables. Other
1141 variations happen to; for example [a -> (a, b)].
1143 ***************************************************
1144 *** So a TvSubst must be applied precisely once ***
1145 ***************************************************
1147 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1148 we use during unifications, it must not be repeatedly applied.
1150 Note [Extending the TvSubst]
1151 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1152 The following invariant should hold of a TvSubst
1154 The in-scope set is needed *only* to
1155 guide the generation of fresh uniques
1157 In particular, the *kind* of the type variables in
1158 the in-scope set is not relevant
1160 This invariant allows a short-cut when the TvSubstEnv is empty:
1161 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1162 then (substTy subst ty) does nothing.
1164 For example, consider:
1165 (/\a. /\b:(a~Int). ...b..) Int
1166 We substitute Int for 'a'. The Unique of 'b' does not change, but
1167 nevertheless we add 'b' to the TvSubstEnv, because b's type does change
1169 This invariant has several crucial consequences:
1171 * In substTyVarBndr, we need extend the TvSubstEnv
1172 - if the unique has changed
1173 - or if the kind has changed
1175 * In substTyVar, we do not need to consult the in-scope set;
1176 the TvSubstEnv is enough
1178 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1181 -------------------------------------------------------------- -}
1184 type TvSubstEnv = TyVarEnv Type
1185 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1186 -- invariant discussed in Note [Apply Once]), and also independently
1187 -- in the middle of matching, and unification (see Types.Unify)
1188 -- So you have to look at the context to know if it's idempotent or
1189 -- apply-once or whatever
1190 emptyTvSubstEnv :: TvSubstEnv
1191 emptyTvSubstEnv = emptyVarEnv
1193 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1194 -- (compose env1 env2)(x) is env1(env2(x)); i.e. apply env2 then env1
1195 -- It assumes that both are idempotent
1196 -- Typically, env1 is the refinement to a base substitution env2
1197 composeTvSubst in_scope env1 env2
1198 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1199 -- First apply env1 to the range of env2
1200 -- Then combine the two, making sure that env1 loses if
1201 -- both bind the same variable; that's why env1 is the
1202 -- *left* argument to plusVarEnv, because the right arg wins
1204 subst1 = TvSubst in_scope env1
1206 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1208 isEmptyTvSubst :: TvSubst -> Bool
1209 -- See Note [Extending the TvSubstEnv]
1210 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1212 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1215 getTvSubstEnv :: TvSubst -> TvSubstEnv
1216 getTvSubstEnv (TvSubst _ env) = env
1218 getTvInScope :: TvSubst -> InScopeSet
1219 getTvInScope (TvSubst in_scope _) = in_scope
1221 isInScope :: Var -> TvSubst -> Bool
1222 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1224 notElemTvSubst :: TyVar -> TvSubst -> Bool
1225 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1227 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1228 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1230 extendTvInScope :: TvSubst -> [Var] -> TvSubst
1231 extendTvInScope (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1233 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1234 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1236 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1237 extendTvSubstList (TvSubst in_scope env) tvs tys
1238 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1240 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1241 -- the types given; but it's just a thunk so with a bit of luck
1242 -- it'll never be evaluated
1244 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1245 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1247 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1248 zipOpenTvSubst tyvars tys
1250 | length tyvars /= length tys
1251 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1254 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1256 -- mkTopTvSubst is called when doing top-level substitutions.
1257 -- Here we expect that the free vars of the range of the
1258 -- substitution will be empty.
1259 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1260 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1262 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1263 zipTopTvSubst tyvars tys
1265 | length tyvars /= length tys
1266 = pprTrace "zipTopTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1269 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1271 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1274 | length tyvars /= length tys
1275 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1278 = zip_ty_env tyvars tys emptyVarEnv
1280 -- Later substitutions in the list over-ride earlier ones,
1281 -- but there should be no loops
1282 zip_ty_env [] [] env = env
1283 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1284 -- There used to be a special case for when
1286 -- (a not-uncommon case) in which case the substitution was dropped.
1287 -- But the type-tidier changes the print-name of a type variable without
1288 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1289 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1290 -- And it happened that t was the type variable of the class. Post-tiding,
1291 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1292 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1293 -- and so generated a rep type mentioning t not t2.
1295 -- Simplest fix is to nuke the "optimisation"
1296 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1297 -- zip_ty_env _ _ env = env
1299 instance Outputable TvSubst where
1300 ppr (TvSubst ins env)
1301 = brackets $ sep[ ptext SLIT("TvSubst"),
1302 nest 2 (ptext SLIT("In scope:") <+> ppr ins),
1303 nest 2 (ptext SLIT("Env:") <+> ppr env) ]
1306 %************************************************************************
1308 Performing type substitutions
1310 %************************************************************************
1313 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1314 substTyWith tvs tys = ASSERT( length tvs == length tys )
1315 substTy (zipOpenTvSubst tvs tys)
1317 substTy :: TvSubst -> Type -> Type
1318 substTy subst ty | isEmptyTvSubst subst = ty
1319 | otherwise = subst_ty subst ty
1321 substTys :: TvSubst -> [Type] -> [Type]
1322 substTys subst tys | isEmptyTvSubst subst = tys
1323 | otherwise = map (subst_ty subst) tys
1325 substTheta :: TvSubst -> ThetaType -> ThetaType
1326 substTheta subst theta
1327 | isEmptyTvSubst subst = theta
1328 | otherwise = map (substPred subst) theta
1330 substPred :: TvSubst -> PredType -> PredType
1331 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1332 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1333 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1335 deShadowTy :: TyVarSet -> Type -> Type -- Remove any nested binders mentioning tvs
1337 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1339 in_scope = mkInScopeSet tvs
1341 subst_ty :: TvSubst -> Type -> Type
1342 -- subst_ty is the main workhorse for type substitution
1344 -- Note that the in_scope set is poked only if we hit a forall
1345 -- so it may often never be fully computed
1349 go (TyVarTy tv) = substTyVar subst tv
1350 go (TyConApp tc tys) = let args = map go tys
1351 in args `seqList` TyConApp tc args
1353 go (PredTy p) = PredTy $! (substPred subst p)
1355 go (NoteTy (FTVNote _) ty2) = go ty2 -- Discard the free tyvar note
1357 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1358 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1359 -- The mkAppTy smart constructor is important
1360 -- we might be replacing (a Int), represented with App
1361 -- by [Int], represented with TyConApp
1362 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1363 (subst', tv') -> ForAllTy tv' $! (subst_ty subst' ty)
1365 substTyVar :: TvSubst -> TyVar -> Type
1366 substTyVar subst@(TvSubst in_scope env) tv
1367 = case lookupTyVar subst tv of {
1368 Nothing -> TyVarTy tv;
1369 Just ty -> ty -- See Note [Apply Once]
1372 substTyVars :: TvSubst -> [TyVar] -> [Type]
1373 substTyVars subst tvs = map (substTyVar subst) tvs
1375 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1376 -- See Note [Extending the TvSubst]
1377 lookupTyVar (TvSubst in_scope env) tv = lookupVarEnv env tv
1379 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1380 substTyVarBndr subst@(TvSubst in_scope env) old_var
1381 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1383 is_co_var = isCoVar old_var
1385 new_env | no_change = delVarEnv env old_var
1386 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1388 no_change = new_var == old_var && not is_co_var
1389 -- no_change means that the new_var is identical in
1390 -- all respects to the old_var (same unique, same kind)
1391 -- See Note [Extending the TvSubst]
1393 -- In that case we don't need to extend the substitution
1394 -- to map old to new. But instead we must zap any
1395 -- current substitution for the variable. For example:
1396 -- (\x.e) with id_subst = [x |-> e']
1397 -- Here we must simply zap the substitution for x
1399 new_var = uniqAway in_scope subst_old_var
1400 -- The uniqAway part makes sure the new variable is not already in scope
1402 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1403 -- It's only worth doing the substitution for coercions,
1404 -- becuase only they can have free type variables
1405 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1406 | otherwise = old_var
1409 ----------------------------------------------------
1414 There's a little subtyping at the kind level:
1423 where * [LiftedTypeKind] means boxed type
1424 # [UnliftedTypeKind] means unboxed type
1425 (#) [UbxTupleKind] means unboxed tuple
1426 ?? [ArgTypeKind] is the lub of *,#
1427 ? [OpenTypeKind] means any type at all
1431 error :: forall a:?. String -> a
1432 (->) :: ?? -> ? -> *
1433 (\(x::t) -> ...) Here t::?? (i.e. not unboxed tuple)
1436 type KindVar = TyVar -- invariant: KindVar will always be a
1437 -- TcTyVar with details MetaTv TauTv ...
1438 -- kind var constructors and functions are in TcType
1440 type SimpleKind = Kind
1445 During kind inference, a kind variable unifies only with
1447 sk ::= * | sk1 -> sk2
1449 data T a = MkT a (T Int#)
1450 fails. We give T the kind (k -> *), and the kind variable k won't unify
1451 with # (the kind of Int#).
1455 When creating a fresh internal type variable, we give it a kind to express
1456 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1459 During unification we only bind an internal type variable to a type
1460 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1462 When unifying two internal type variables, we collect their kind constraints by
1463 finding the GLB of the two. Since the partial order is a tree, they only
1464 have a glb if one is a sub-kind of the other. In that case, we bind the
1465 less-informative one to the more informative one. Neat, eh?
1472 %************************************************************************
1474 Functions over Kinds
1476 %************************************************************************
1479 kindFunResult :: Kind -> Kind
1480 kindFunResult k = funResultTy k
1482 splitKindFunTys :: Kind -> ([Kind],Kind)
1483 splitKindFunTys k = splitFunTys k
1485 splitKindFunTysN :: Int -> Kind -> ([Kind],Kind)
1486 splitKindFunTysN k = splitFunTysN k
1488 isUbxTupleKind, isOpenTypeKind, isArgTypeKind, isUnliftedTypeKind :: Kind -> Bool
1490 isOpenTypeKindCon tc = tyConUnique tc == openTypeKindTyConKey
1492 isOpenTypeKind (TyConApp tc _) = isOpenTypeKindCon tc
1493 isOpenTypeKind other = False
1495 isUbxTupleKindCon tc = tyConUnique tc == ubxTupleKindTyConKey
1497 isUbxTupleKind (TyConApp tc _) = isUbxTupleKindCon tc
1498 isUbxTupleKind other = False
1500 isArgTypeKindCon tc = tyConUnique tc == argTypeKindTyConKey
1502 isArgTypeKind (TyConApp tc _) = isArgTypeKindCon tc
1503 isArgTypeKind other = False
1505 isUnliftedTypeKindCon tc = tyConUnique tc == unliftedTypeKindTyConKey
1507 isUnliftedTypeKind (TyConApp tc _) = isUnliftedTypeKindCon tc
1508 isUnliftedTypeKind other = False
1510 isSubOpenTypeKind :: Kind -> Bool
1511 -- True of any sub-kind of OpenTypeKind (i.e. anything except arrow)
1512 isSubOpenTypeKind (FunTy k1 k2) = ASSERT2 ( isKind k1, text "isSubOpenTypeKind" <+> ppr k1 <+> text "::" <+> ppr (typeKind k1) )
1513 ASSERT2 ( isKind k2, text "isSubOpenTypeKind" <+> ppr k2 <+> text "::" <+> ppr (typeKind k2) )
1515 isSubOpenTypeKind (TyConApp kc []) = ASSERT( isKind (TyConApp kc []) ) True
1516 isSubOpenTypeKind other = ASSERT( isKind other ) False
1517 -- This is a conservative answer
1518 -- It matters in the call to isSubKind in
1519 -- checkExpectedKind.
1521 isSubArgTypeKindCon kc
1522 | isUnliftedTypeKindCon kc = True
1523 | isLiftedTypeKindCon kc = True
1524 | isArgTypeKindCon kc = True
1527 isSubArgTypeKind :: Kind -> Bool
1528 -- True of any sub-kind of ArgTypeKind
1529 isSubArgTypeKind (TyConApp kc []) = isSubArgTypeKindCon kc
1530 isSubArgTypeKind other = False
1532 isSuperKind :: Type -> Bool
1533 isSuperKind (TyConApp (skc) []) = isSuperKindTyCon skc
1534 isSuperKind other = False
1536 isKind :: Kind -> Bool
1537 isKind k = isSuperKind (typeKind k)
1539 isSubKind :: Kind -> Kind -> Bool
1540 -- (k1 `isSubKind` k2) checks that k1 <: k2
1541 isSubKind (TyConApp kc1 []) (TyConApp kc2 []) = kc1 `isSubKindCon` kc2
1542 isSubKind (FunTy a1 r1) (FunTy a2 r2) = (a2 `isSubKind` a1) && (r1 `isSubKind` r2)
1543 isSubKind (PredTy (EqPred ty1 ty2)) (PredTy (EqPred ty1' ty2'))
1544 = ty1 `tcEqType` ty1' && ty2 `tcEqType` ty2'
1545 isSubKind k1 k2 = False
1547 eqKind :: Kind -> Kind -> Bool
1550 isSubKindCon :: TyCon -> TyCon -> Bool
1551 -- (kc1 `isSubKindCon` kc2) checks that kc1 <: kc2
1552 isSubKindCon kc1 kc2
1553 | isLiftedTypeKindCon kc1 && isLiftedTypeKindCon kc2 = True
1554 | isUnliftedTypeKindCon kc1 && isUnliftedTypeKindCon kc2 = True
1555 | isUbxTupleKindCon kc1 && isUbxTupleKindCon kc2 = True
1556 | isOpenTypeKindCon kc2 = True
1557 -- we already know kc1 is not a fun, its a TyCon
1558 | isArgTypeKindCon kc2 && isSubArgTypeKindCon kc1 = True
1561 defaultKind :: Kind -> Kind
1562 -- Used when generalising: default kind '?' and '??' to '*'
1564 -- When we generalise, we make generic type variables whose kind is
1565 -- simple (* or *->* etc). So generic type variables (other than
1566 -- built-in constants like 'error') always have simple kinds. This is important;
1569 -- We want f to get type
1570 -- f :: forall (a::*). a -> Bool
1572 -- f :: forall (a::??). a -> Bool
1573 -- because that would allow a call like (f 3#) as well as (f True),
1574 --and the calling conventions differ. This defaulting is done in TcMType.zonkTcTyVarBndr.
1576 | isSubOpenTypeKind k = liftedTypeKind
1577 | isSubArgTypeKind k = liftedTypeKind
1580 isEqPred :: PredType -> Bool
1581 isEqPred (EqPred _ _) = True
1582 isEqPred other = False