2 % (c) The University of Glasgow 2006
3 % (c) The GRASP/AQUA Project, Glasgow University, 1998
6 Type - public interface
9 -- The above warning supression flag is a temporary kludge.
10 -- While working on this module you are encouraged to remove it and fix
11 -- any warnings in the module. See
12 -- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#Warnings
15 -- | Main functions for manipulating types and type-related things
17 -- Note some of this is just re-exports from TyCon..
19 -- * Main data types representing Types
20 -- $type_classification
22 -- $representation_types
23 TyThing(..), Type, PredType(..), ThetaType,
25 -- ** Constructing and deconstructing types
26 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe,
28 mkAppTy, mkAppTys, splitAppTy, splitAppTys,
29 splitAppTy_maybe, repSplitAppTy_maybe,
31 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
32 splitFunTys, splitFunTysN,
33 funResultTy, funArgTy, zipFunTys,
35 mkTyConApp, mkTyConTy,
36 tyConAppTyCon, tyConAppArgs,
37 splitTyConApp_maybe, splitTyConApp,
39 mkForAllTy, mkForAllTys, splitForAllTy_maybe, splitForAllTys,
40 applyTy, applyTys, applyTysD, isForAllTy, dropForAlls,
43 newTyConInstRhs, carefullySplitNewType_maybe,
46 tyFamInsts, predFamInsts,
49 mkPredTy, mkPredTys, mkFamilyTyConApp, isEqPred,
51 -- ** Common type constructors
54 -- ** Predicates on types
55 isTyVarTy, isFunTy, isDictTy,
57 -- (Lifting and boxity)
58 isUnLiftedType, isUnboxedTupleType, isAlgType, isClosedAlgType,
59 isPrimitiveType, isStrictType, isStrictPred,
61 -- * Main data types representing Kinds
63 Kind, SimpleKind, KindVar,
65 -- ** Common Kinds and SuperKinds
66 liftedTypeKind, unliftedTypeKind, openTypeKind,
67 argTypeKind, ubxTupleKind,
69 tySuperKind, coSuperKind,
71 -- ** Common Kind type constructors
72 liftedTypeKindTyCon, openTypeKindTyCon, unliftedTypeKindTyCon,
73 argTypeKindTyCon, ubxTupleKindTyCon,
75 -- * Type free variables
76 tyVarsOfType, tyVarsOfTypes, tyVarsOfPred, tyVarsOfTheta,
79 -- * Tidying type related things up for printing
81 tidyOpenType, tidyOpenTypes,
82 tidyTyVarBndr, tidyFreeTyVars,
83 tidyOpenTyVar, tidyOpenTyVars,
84 tidyTopType, tidyPred,
88 coreEqType, coreEqType2,
89 tcEqType, tcEqTypes, tcCmpType, tcCmpTypes,
90 tcEqPred, tcEqPredX, tcCmpPred, tcEqTypeX, tcPartOfType, tcPartOfPred,
92 -- * Forcing evaluation of types
95 -- * Other views onto Types
96 coreView, tcView, kindView,
100 -- * Type representation for the code generator
103 typePrimRep, predTypeRep,
105 -- * Main type substitution data types
106 TvSubstEnv, -- Representation widely visible
107 TvSubst(..), -- Representation visible to a few friends
109 -- ** Manipulating type substitutions
110 emptyTvSubstEnv, emptyTvSubst,
112 mkTvSubst, mkOpenTvSubst, zipOpenTvSubst, zipTopTvSubst, mkTopTvSubst, notElemTvSubst,
113 getTvSubstEnv, setTvSubstEnv, zapTvSubstEnv, getTvInScope,
114 extendTvInScope, extendTvInScopeList,
115 extendTvSubst, extendTvSubstList, isInScope, composeTvSubst, zipTyEnv,
118 -- ** Performing substitution on types
119 substTy, substTys, substTyWith, substTysWith, substTheta,
120 substPred, substTyVar, substTyVars, substTyVarBndr, deShadowTy, lookupTyVar,
123 pprType, pprParendType, pprTypeApp, pprTyThingCategory, pprTyThing, pprForAll,
124 pprPred, pprEqPred, pprTheta, pprThetaArrow, pprClassPred, pprKind, pprParendKind,
129 #include "HsVersions.h"
131 -- We import the representation and primitive functions from TypeRep.
132 -- Many things are reexported, but not the representation!
152 import Data.Maybe ( isJust )
154 infixr 3 `mkFunTy` -- Associates to the right
158 -- $type_classification
159 -- #type_classification#
163 -- [Unboxed] Iff its representation is other than a pointer
164 -- Unboxed types are also unlifted.
166 -- [Lifted] Iff it has bottom as an element.
167 -- Closures always have lifted types: i.e. any
168 -- let-bound identifier in Core must have a lifted
169 -- type. Operationally, a lifted object is one that
171 -- Only lifted types may be unified with a type variable.
173 -- [Algebraic] Iff it is a type with one or more constructors, whether
174 -- declared with @data@ or @newtype@.
175 -- An algebraic type is one that can be deconstructed
176 -- with a case expression. This is /not/ the same as
177 -- lifted types, because we also include unboxed
178 -- tuples in this classification.
180 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
182 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
184 -- Currently, all primitive types are unlifted, but that's not necessarily
185 -- the case: for example, @Int@ could be primitive.
187 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
188 -- but unlifted (such as @ByteArray#@). The only primitive types that we
189 -- classify as algebraic are the unboxed tuples.
191 -- Some examples of type classifications that may make this a bit clearer are:
194 -- Type primitive boxed lifted algebraic
195 -- -----------------------------------------------------------------------------
197 -- ByteArray# Yes Yes No No
198 -- (\# a, b \#) Yes No No Yes
199 -- ( a, b ) No Yes Yes Yes
200 -- [a] No Yes Yes Yes
203 -- $representation_types
204 -- A /source type/ is a type that is a separate type as far as the type checker is
205 -- concerned, but which has a more low-level representation as far as Core-to-Core
206 -- passes and the rest of the back end is concerned. Notably, 'PredTy's are removed
207 -- from the representation type while they do exist in the source types.
209 -- You don't normally have to worry about this, as the utility functions in
210 -- this module will automatically convert a source into a representation type
211 -- if they are spotted, to the best of it's abilities. If you don't want this
212 -- to happen, use the equivalent functions from the "TcType" module.
215 %************************************************************************
219 %************************************************************************
222 {-# INLINE coreView #-}
223 coreView :: Type -> Maybe Type
224 -- ^ In Core, we \"look through\" non-recursive newtypes and 'PredTypes': this
225 -- function tries to obtain a different view of the supplied type given this
227 -- Strips off the /top layer only/ of a type to give
228 -- its underlying representation type.
229 -- Returns Nothing if there is nothing to look through.
231 -- In the case of @newtype@s, it returns one of:
233 -- 1) A vanilla 'TyConApp' (recursive newtype, or non-saturated)
235 -- 2) The newtype representation (otherwise), meaning the
236 -- type written in the RHS of the newtype declaration,
237 -- which may itself be a newtype
239 -- For example, with:
241 -- > newtype R = MkR S
242 -- > newtype S = MkS T
243 -- > newtype T = MkT (T -> T)
245 -- 'expandNewTcApp' on:
247 -- * @R@ gives @Just S@
248 -- * @S@ gives @Just T@
249 -- * @T@ gives @Nothing@ (no expansion)
251 -- By being non-recursive and inlined, this case analysis gets efficiently
252 -- joined onto the case analysis that the caller is already doing
254 | isEqPred p = Nothing
255 | otherwise = Just (predTypeRep p)
256 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- coreExpandTyCon_maybe tc tys
257 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
258 -- Its important to use mkAppTys, rather than (foldl AppTy),
259 -- because the function part might well return a
260 -- partially-applied type constructor; indeed, usually will!
265 -----------------------------------------------
266 {-# INLINE tcView #-}
267 tcView :: Type -> Maybe Type
268 -- ^ Similar to 'coreView', but for the type checker, which just looks through synonyms
269 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
270 = Just (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
273 -----------------------------------------------
274 expandTypeSynonyms :: Type -> Type
275 -- ^ Expand out all type synonyms. Actually, it'd suffice to expand out
276 -- just the ones that discard type variables (e.g. type Funny a = Int)
277 -- But we don't know which those are currently, so we just expand all.
278 expandTypeSynonyms ty
282 | Just (tenv, rhs, tys') <- tcExpandTyCon_maybe tc tys
283 = go (mkAppTys (substTy (mkTopTvSubst tenv) rhs) tys')
285 = TyConApp tc (map go tys)
286 go (TyVarTy tv) = TyVarTy tv
287 go (AppTy t1 t2) = AppTy (go t1) (go t2)
288 go (FunTy t1 t2) = FunTy (go t1) (go t2)
289 go (ForAllTy tv t) = ForAllTy tv (go t)
290 go (PredTy p) = PredTy (go_pred p)
292 go_pred (ClassP c ts) = ClassP c (map go ts)
293 go_pred (IParam ip t) = IParam ip (go t)
294 go_pred (EqPred t1 t2) = EqPred (go t1) (go t2)
296 -----------------------------------------------
297 {-# INLINE kindView #-}
298 kindView :: Kind -> Maybe Kind
299 -- ^ Similar to 'coreView' or 'tcView', but works on 'Kind's
301 -- For the moment, we don't even handle synonyms in kinds
306 %************************************************************************
308 \subsection{Constructor-specific functions}
310 %************************************************************************
313 ---------------------------------------------------------------------
317 mkTyVarTy :: TyVar -> Type
320 mkTyVarTys :: [TyVar] -> [Type]
321 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
323 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
324 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
325 getTyVar :: String -> Type -> TyVar
326 getTyVar msg ty = case getTyVar_maybe ty of
328 Nothing -> panic ("getTyVar: " ++ msg)
330 isTyVarTy :: Type -> Bool
331 isTyVarTy ty = isJust (getTyVar_maybe ty)
333 -- | Attempts to obtain the type variable underlying a 'Type'
334 getTyVar_maybe :: Type -> Maybe TyVar
335 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
336 getTyVar_maybe (TyVarTy tv) = Just tv
337 getTyVar_maybe _ = Nothing
342 ---------------------------------------------------------------------
345 We need to be pretty careful with AppTy to make sure we obey the
346 invariant that a TyConApp is always visibly so. mkAppTy maintains the
350 -- | Applies a type to another, as in e.g. @k a@
351 mkAppTy :: Type -> Type -> Type
352 mkAppTy orig_ty1 orig_ty2
355 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ [orig_ty2])
356 mk_app _ = AppTy orig_ty1 orig_ty2
357 -- Note that the TyConApp could be an
358 -- under-saturated type synonym. GHC allows that; e.g.
359 -- type Foo k = k a -> k a
361 -- foo :: Foo Id -> Foo Id
363 -- Here Id is partially applied in the type sig for Foo,
364 -- but once the type synonyms are expanded all is well
366 mkAppTys :: Type -> [Type] -> Type
367 mkAppTys orig_ty1 [] = orig_ty1
368 -- This check for an empty list of type arguments
369 -- avoids the needless loss of a type synonym constructor.
370 -- For example: mkAppTys Rational []
371 -- returns to (Ratio Integer), which has needlessly lost
372 -- the Rational part.
373 mkAppTys orig_ty1 orig_tys2
376 mk_app (TyConApp tc tys) = mkTyConApp tc (tys ++ orig_tys2)
377 -- mkTyConApp: see notes with mkAppTy
378 mk_app _ = foldl AppTy orig_ty1 orig_tys2
381 splitAppTy_maybe :: Type -> Maybe (Type, Type)
382 -- ^ Attempt to take a type application apart, whether it is a
383 -- function, type constructor, or plain type application. Note
384 -- that type family applications are NEVER unsaturated by this!
385 splitAppTy_maybe ty | Just ty' <- coreView ty
386 = splitAppTy_maybe ty'
387 splitAppTy_maybe ty = repSplitAppTy_maybe ty
390 repSplitAppTy_maybe :: Type -> Maybe (Type,Type)
391 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
392 -- any Core view stuff is already done
393 repSplitAppTy_maybe (FunTy ty1 ty2) = Just (TyConApp funTyCon [ty1], ty2)
394 repSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
395 repSplitAppTy_maybe (TyConApp tc tys)
396 | isDecomposableTyCon tc || length tys > tyConArity tc
397 = case snocView tys of -- never create unsaturated type family apps
398 Just (tys', ty') -> Just (TyConApp tc tys', ty')
400 repSplitAppTy_maybe _other = Nothing
402 splitAppTy :: Type -> (Type, Type)
403 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
404 -- and panics if this is not possible
405 splitAppTy ty = case splitAppTy_maybe ty of
407 Nothing -> panic "splitAppTy"
410 splitAppTys :: Type -> (Type, [Type])
411 -- ^ Recursively splits a type as far as is possible, leaving a residual
412 -- type being applied to and the type arguments applied to it. Never fails,
413 -- even if that means returning an empty list of type applications.
414 splitAppTys ty = split ty ty []
416 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
417 split _ (AppTy ty arg) args = split ty ty (arg:args)
418 split _ (TyConApp tc tc_args) args
419 = let -- keep type families saturated
420 n | isDecomposableTyCon tc = 0
421 | otherwise = tyConArity tc
422 (tc_args1, tc_args2) = splitAt n tc_args
424 (TyConApp tc tc_args1, tc_args2 ++ args)
425 split _ (FunTy ty1 ty2) args = ASSERT( null args )
426 (TyConApp funTyCon [], [ty1,ty2])
427 split orig_ty _ args = (orig_ty, args)
432 ---------------------------------------------------------------------
437 mkFunTy :: Type -> Type -> Type
438 -- ^ Creates a function type from the given argument and result type
439 mkFunTy arg@(PredTy (EqPred {})) res = ForAllTy (mkWildCoVar arg) res
440 mkFunTy arg res = FunTy arg res
442 mkFunTys :: [Type] -> Type -> Type
443 mkFunTys tys ty = foldr mkFunTy ty tys
445 isFunTy :: Type -> Bool
446 isFunTy ty = isJust (splitFunTy_maybe ty)
448 splitFunTy :: Type -> (Type, Type)
449 -- ^ Attempts to extract the argument and result types from a type, and
450 -- panics if that is not possible. See also 'splitFunTy_maybe'
451 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
452 splitFunTy (FunTy arg res) = (arg, res)
453 splitFunTy other = pprPanic "splitFunTy" (ppr other)
455 splitFunTy_maybe :: Type -> Maybe (Type, Type)
456 -- ^ Attempts to extract the argument and result types from a type
457 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
458 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
459 splitFunTy_maybe _ = Nothing
461 splitFunTys :: Type -> ([Type], Type)
462 splitFunTys ty = split [] ty ty
464 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
465 split args _ (FunTy arg res) = split (arg:args) res res
466 split args orig_ty _ = (reverse args, orig_ty)
468 splitFunTysN :: Int -> Type -> ([Type], Type)
469 -- ^ Split off exactly the given number argument types, and panics if that is not possible
470 splitFunTysN 0 ty = ([], ty)
471 splitFunTysN n ty = case splitFunTy ty of { (arg, res) ->
472 case splitFunTysN (n-1) res of { (args, res) ->
475 -- | Splits off argument types from the given type and associating
476 -- them with the things in the input list from left to right. The
477 -- final result type is returned, along with the resulting pairs of
478 -- objects and types, albeit with the list of pairs in reverse order.
479 -- Panics if there are not enough argument types for the input list.
480 zipFunTys :: Outputable a => [a] -> Type -> ([(a, Type)], Type)
481 zipFunTys orig_xs orig_ty = split [] orig_xs orig_ty orig_ty
483 split acc [] nty _ = (reverse acc, nty)
485 | Just ty' <- coreView ty = split acc xs nty ty'
486 split acc (x:xs) _ (FunTy arg res) = split ((x,arg):acc) xs res res
487 split _ _ _ _ = pprPanic "zipFunTys" (ppr orig_xs <+> ppr orig_ty)
489 funResultTy :: Type -> Type
490 -- ^ Extract the function result type and panic if that is not possible
491 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
492 funResultTy (FunTy _arg res) = res
493 funResultTy ty = pprPanic "funResultTy" (ppr ty)
495 funArgTy :: Type -> Type
496 -- ^ Extract the function argument type and panic if that is not possible
497 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
498 funArgTy (FunTy arg _res) = arg
499 funArgTy ty = pprPanic "funArgTy" (ppr ty)
502 ---------------------------------------------------------------------
507 -- | A key function: builds a 'TyConApp' or 'FunTy' as apppropriate to its arguments.
508 -- Applies its arguments to the constructor from left to right
509 mkTyConApp :: TyCon -> [Type] -> Type
511 | isFunTyCon tycon, [ty1,ty2] <- tys
517 -- | Create the plain type constructor type which has been applied to no type arguments at all.
518 mkTyConTy :: TyCon -> Type
519 mkTyConTy tycon = mkTyConApp tycon []
521 -- splitTyConApp "looks through" synonyms, because they don't
522 -- mean a distinct type, but all other type-constructor applications
523 -- including functions are returned as Just ..
525 -- | The same as @fst . splitTyConApp@
526 tyConAppTyCon :: Type -> TyCon
527 tyConAppTyCon ty = fst (splitTyConApp ty)
529 -- | The same as @snd . splitTyConApp@
530 tyConAppArgs :: Type -> [Type]
531 tyConAppArgs ty = snd (splitTyConApp ty)
533 -- | Attempts to tease a type apart into a type constructor and the application
534 -- of a number of arguments to that constructor. Panics if that is not possible.
535 -- See also 'splitTyConApp_maybe'
536 splitTyConApp :: Type -> (TyCon, [Type])
537 splitTyConApp ty = case splitTyConApp_maybe ty of
539 Nothing -> pprPanic "splitTyConApp" (ppr ty)
541 -- | Attempts to tease a type apart into a type constructor and the application
542 -- of a number of arguments to that constructor
543 splitTyConApp_maybe :: Type -> Maybe (TyCon, [Type])
544 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
545 splitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
546 splitTyConApp_maybe (FunTy arg res) = Just (funTyCon, [arg,res])
547 splitTyConApp_maybe _ = Nothing
549 newTyConInstRhs :: TyCon -> [Type] -> Type
550 -- ^ Unwrap one 'layer' of newtype on a type constructor and its arguments, using an
551 -- eta-reduced version of the @newtype@ if possible
552 newTyConInstRhs tycon tys
553 = ASSERT2( equalLength tvs tys1, ppr tycon $$ ppr tys $$ ppr tvs )
554 mkAppTys (substTyWith tvs tys1 ty) tys2
556 (tvs, ty) = newTyConEtadRhs tycon
557 (tys1, tys2) = splitAtList tvs tys
561 ---------------------------------------------------------------------
565 Notes on type synonyms
566 ~~~~~~~~~~~~~~~~~~~~~~
567 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
568 to return type synonyms whereever possible. Thus
573 splitFunTys (a -> Foo a) = ([a], Foo a)
576 The reason is that we then get better (shorter) type signatures in
577 interfaces. Notably this plays a role in tcTySigs in TcBinds.lhs.
580 Note [Expanding newtypes]
581 ~~~~~~~~~~~~~~~~~~~~~~~~~
582 When expanding a type to expose a data-type constructor, we need to be
583 careful about newtypes, lest we fall into an infinite loop. Here are
586 newtype Id x = MkId x
587 newtype Fix f = MkFix (f (Fix f))
588 newtype T = MkT (T -> T)
591 --------------------------
593 Fix Maybe Maybe (Fix Maybe)
597 Notice that we can expand T, even though it's recursive.
598 And we can expand Id (Id Int), even though the Id shows up
599 twice at the outer level.
601 So, when expanding, we keep track of when we've seen a recursive
602 newtype at outermost level; and bale out if we see it again.
614 -- 4. All newtypes, including recursive ones, but not newtype families
616 -- It's useful in the back end of the compiler.
617 repType :: Type -> Type
618 -- Only applied to types of kind *; hence tycons are saturated
622 go :: [TyCon] -> Type -> Type
623 go rec_nts ty | Just ty' <- coreView ty -- Expand synonyms
626 go rec_nts (ForAllTy _ ty) -- Look through foralls
629 go rec_nts (TyConApp tc tys) -- Expand newtypes
630 | Just (rec_nts', ty') <- carefullySplitNewType_maybe rec_nts tc tys
636 carefullySplitNewType_maybe :: [TyCon] -> TyCon -> [Type] -> Maybe ([TyCon],Type)
637 -- Return the representation of a newtype, unless
638 -- we've seen it already: see Note [Expanding newtypes]
639 carefullySplitNewType_maybe rec_nts tc tys
641 , not (tc `elem` rec_nts) = Just (rec_nts', newTyConInstRhs tc tys)
642 | otherwise = Nothing
644 rec_nts' | isRecursiveTyCon tc = tc:rec_nts
645 | otherwise = rec_nts
648 -- ToDo: this could be moved to the code generator, using splitTyConApp instead
649 -- of inspecting the type directly.
651 -- | Discovers the primitive representation of a more abstract 'Type'
652 typePrimRep :: Type -> PrimRep
653 typePrimRep ty = case repType ty of
654 TyConApp tc _ -> tyConPrimRep tc
656 AppTy _ _ -> PtrRep -- See note below
658 _ -> pprPanic "typePrimRep" (ppr ty)
659 -- Types of the form 'f a' must be of kind *, not *#, so
660 -- we are guaranteed that they are represented by pointers.
661 -- The reason is that f must have kind *->*, not *->*#, because
662 -- (we claim) there is no way to constrain f's kind any other
667 ---------------------------------------------------------------------
672 mkForAllTy :: TyVar -> Type -> Type
676 -- | Wraps foralls over the type using the provided 'TyVar's from left to right
677 mkForAllTys :: [TyVar] -> Type -> Type
678 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
680 isForAllTy :: Type -> Bool
681 isForAllTy (ForAllTy _ _) = True
684 -- | Attempts to take a forall type apart, returning the bound type variable
685 -- and the remainder of the type
686 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
687 splitForAllTy_maybe ty = splitFAT_m ty
689 splitFAT_m ty | Just ty' <- coreView ty = splitFAT_m ty'
690 splitFAT_m (ForAllTy tyvar ty) = Just(tyvar, ty)
691 splitFAT_m _ = Nothing
693 -- | Attempts to take a forall type apart, returning all the immediate such bound
694 -- type variables and the remainder of the type. Always suceeds, even if that means
695 -- returning an empty list of 'TyVar's
696 splitForAllTys :: Type -> ([TyVar], Type)
697 splitForAllTys ty = split ty ty []
699 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
700 split _ (ForAllTy tv ty) tvs = split ty ty (tv:tvs)
701 split orig_ty _ tvs = (reverse tvs, orig_ty)
703 -- | Equivalent to @snd . splitForAllTys@
704 dropForAlls :: Type -> Type
705 dropForAlls ty = snd (splitForAllTys ty)
708 -- (mkPiType now in CoreUtils)
714 -- | Instantiate a forall type with one or more type arguments.
715 -- Used when we have a polymorphic function applied to type args:
719 -- We use @applyTys type-of-f [t1,t2]@ to compute the type of the expression.
720 -- Panics if no application is possible.
721 applyTy :: Type -> Type -> Type
722 applyTy ty arg | Just ty' <- coreView ty = applyTy ty' arg
723 applyTy (ForAllTy tv ty) arg = substTyWith [tv] [arg] ty
724 applyTy _ _ = panic "applyTy"
726 applyTys :: Type -> [Type] -> Type
727 -- ^ This function is interesting because:
729 -- 1. The function may have more for-alls than there are args
731 -- 2. Less obviously, it may have fewer for-alls
733 -- For case 2. think of:
735 -- > applyTys (forall a.a) [forall b.b, Int]
737 -- This really can happen, via dressing up polymorphic types with newtype
738 -- clothing. Here's an example:
740 -- > newtype R = R (forall a. a->a)
741 -- > foo = case undefined :: R of
744 applyTys ty args = applyTysD empty ty args
746 applyTysD :: SDoc -> Type -> [Type] -> Type -- Debug version
747 applyTysD _ orig_fun_ty [] = orig_fun_ty
748 applyTysD doc orig_fun_ty arg_tys
749 | n_tvs == n_args -- The vastly common case
750 = substTyWith tvs arg_tys rho_ty
751 | n_tvs > n_args -- Too many for-alls
752 = substTyWith (take n_args tvs) arg_tys
753 (mkForAllTys (drop n_args tvs) rho_ty)
754 | otherwise -- Too many type args
755 = ASSERT2( n_tvs > 0, doc $$ ppr orig_fun_ty ) -- Zero case gives infnite loop!
756 applyTysD doc (substTyWith tvs (take n_tvs arg_tys) rho_ty)
759 (tvs, rho_ty) = splitForAllTys orig_fun_ty
761 n_args = length arg_tys
765 %************************************************************************
767 \subsection{Source types}
769 %************************************************************************
771 Source types are always lifted.
773 The key function is predTypeRep which gives the representation of a source type:
776 mkPredTy :: PredType -> Type
777 mkPredTy pred = PredTy pred
779 mkPredTys :: ThetaType -> [Type]
780 mkPredTys preds = map PredTy preds
782 isEqPred :: PredType -> Bool
783 isEqPred (EqPred _ _) = True
786 predTypeRep :: PredType -> Type
787 -- ^ Convert a 'PredType' to its representation type. However, it unwraps
788 -- only the outermost level; for example, the result might be a newtype application
789 predTypeRep (IParam _ ty) = ty
790 predTypeRep (ClassP clas tys) = mkTyConApp (classTyCon clas) tys
791 -- Result might be a newtype application, but the consumer will
792 -- look through that too if necessary
793 predTypeRep (EqPred ty1 ty2) = pprPanic "predTypeRep" (ppr (EqPred ty1 ty2))
795 mkFamilyTyConApp :: TyCon -> [Type] -> Type
796 -- ^ Given a family instance TyCon and its arg types, return the
797 -- corresponding family type. E.g:
800 -- > data instance T (Maybe b) = MkT b
802 -- Where the instance tycon is :RTL, so:
804 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
805 mkFamilyTyConApp tc tys
806 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
807 , let fam_subst = zipTopTvSubst (tyConTyVars tc) tys
808 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
812 -- | Pretty prints a 'TyCon', using the family instance in case of a
813 -- representation tycon. For example:
815 -- > data T [a] = ...
817 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
818 pprSourceTyCon :: TyCon -> SDoc
820 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
821 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
825 isDictTy :: Type -> Bool
826 isDictTy ty = case splitTyConApp_maybe ty of
827 Just (tc, _) -> isClassTyCon tc
832 %************************************************************************
834 The free variables of a type
836 %************************************************************************
839 tyVarsOfType :: Type -> TyVarSet
840 -- ^ NB: for type synonyms tyVarsOfType does /not/ expand the synonym
841 tyVarsOfType (TyVarTy tv) = unitVarSet tv
842 tyVarsOfType (TyConApp _ tys) = tyVarsOfTypes tys
843 tyVarsOfType (PredTy sty) = tyVarsOfPred sty
844 tyVarsOfType (FunTy arg res) = tyVarsOfType arg `unionVarSet` tyVarsOfType res
845 tyVarsOfType (AppTy fun arg) = tyVarsOfType fun `unionVarSet` tyVarsOfType arg
846 tyVarsOfType (ForAllTy tyvar ty) = delVarSet (tyVarsOfType ty) tyvar
848 tyVarsOfTypes :: [Type] -> TyVarSet
849 tyVarsOfTypes tys = foldr (unionVarSet.tyVarsOfType) emptyVarSet tys
851 tyVarsOfPred :: PredType -> TyVarSet
852 tyVarsOfPred (IParam _ ty) = tyVarsOfType ty
853 tyVarsOfPred (ClassP _ tys) = tyVarsOfTypes tys
854 tyVarsOfPred (EqPred ty1 ty2) = tyVarsOfType ty1 `unionVarSet` tyVarsOfType ty2
856 tyVarsOfTheta :: ThetaType -> TyVarSet
857 tyVarsOfTheta = foldr (unionVarSet . tyVarsOfPred) emptyVarSet
861 %************************************************************************
863 \subsection{Type families}
865 %************************************************************************
868 -- | Finds type family instances occuring in a type after expanding synonyms.
869 tyFamInsts :: Type -> [(TyCon, [Type])]
871 | Just exp_ty <- tcView ty = tyFamInsts exp_ty
872 tyFamInsts (TyVarTy _) = []
873 tyFamInsts (TyConApp tc tys)
874 | isOpenSynTyCon tc = [(tc, tys)]
875 | otherwise = concat (map tyFamInsts tys)
876 tyFamInsts (FunTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
877 tyFamInsts (AppTy ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
878 tyFamInsts (ForAllTy _ ty) = tyFamInsts ty
879 tyFamInsts (PredTy pty) = predFamInsts pty
881 -- | Finds type family instances occuring in a predicate type after expanding
883 predFamInsts :: PredType -> [(TyCon, [Type])]
884 predFamInsts (ClassP _cla tys) = concat (map tyFamInsts tys)
885 predFamInsts (IParam _ ty) = tyFamInsts ty
886 predFamInsts (EqPred ty1 ty2) = tyFamInsts ty1 ++ tyFamInsts ty2
890 %************************************************************************
892 \subsection{TidyType}
894 %************************************************************************
897 -- | This tidies up a type for printing in an error message, or in
898 -- an interface file.
900 -- It doesn't change the uniques at all, just the print names.
901 tidyTyVarBndr :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
902 tidyTyVarBndr env@(tidy_env, subst) tyvar
903 = case tidyOccName tidy_env (getOccName name) of
904 (tidy', occ') -> ((tidy', subst'), tyvar'')
906 subst' = extendVarEnv subst tyvar tyvar''
907 tyvar' = setTyVarName tyvar name'
908 name' = tidyNameOcc name occ'
909 -- Don't forget to tidy the kind for coercions!
910 tyvar'' | isCoVar tyvar = setTyVarKind tyvar' kind'
912 kind' = tidyType env (tyVarKind tyvar)
914 name = tyVarName tyvar
916 tidyFreeTyVars :: TidyEnv -> TyVarSet -> TidyEnv
917 -- ^ Add the free 'TyVar's to the env in tidy form,
918 -- so that we can tidy the type they are free in
919 tidyFreeTyVars env tyvars = fst (tidyOpenTyVars env (varSetElems tyvars))
921 tidyOpenTyVars :: TidyEnv -> [TyVar] -> (TidyEnv, [TyVar])
922 tidyOpenTyVars env tyvars = mapAccumL tidyOpenTyVar env tyvars
924 tidyOpenTyVar :: TidyEnv -> TyVar -> (TidyEnv, TyVar)
925 -- ^ Treat a new 'TyVar' as a binder, and give it a fresh tidy name
926 -- using the environment if one has not already been allocated. See
927 -- also 'tidyTyVarBndr'
928 tidyOpenTyVar env@(_, subst) tyvar
929 = case lookupVarEnv subst tyvar of
930 Just tyvar' -> (env, tyvar') -- Already substituted
931 Nothing -> tidyTyVarBndr env tyvar -- Treat it as a binder
933 tidyType :: TidyEnv -> Type -> Type
934 tidyType env@(_, subst) ty
937 go (TyVarTy tv) = case lookupVarEnv subst tv of
938 Nothing -> TyVarTy tv
939 Just tv' -> TyVarTy tv'
940 go (TyConApp tycon tys) = let args = map go tys
941 in args `seqList` TyConApp tycon args
942 go (PredTy sty) = PredTy (tidyPred env sty)
943 go (AppTy fun arg) = (AppTy $! (go fun)) $! (go arg)
944 go (FunTy fun arg) = (FunTy $! (go fun)) $! (go arg)
945 go (ForAllTy tv ty) = ForAllTy tvp $! (tidyType envp ty)
947 (envp, tvp) = tidyTyVarBndr env tv
949 tidyTypes :: TidyEnv -> [Type] -> [Type]
950 tidyTypes env tys = map (tidyType env) tys
952 tidyPred :: TidyEnv -> PredType -> PredType
953 tidyPred env (IParam n ty) = IParam n (tidyType env ty)
954 tidyPred env (ClassP clas tys) = ClassP clas (tidyTypes env tys)
955 tidyPred env (EqPred ty1 ty2) = EqPred (tidyType env ty1) (tidyType env ty2)
960 -- | Grabs the free type variables, tidies them
961 -- and then uses 'tidyType' to work over the type itself
962 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
964 = (env', tidyType env' ty)
966 env' = tidyFreeTyVars env (tyVarsOfType ty)
968 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
969 tidyOpenTypes env tys = mapAccumL tidyOpenType env tys
971 -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment)
972 tidyTopType :: Type -> Type
973 tidyTopType ty = tidyType emptyTidyEnv ty
978 tidyKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
979 tidyKind env k = tidyOpenType env k
984 %************************************************************************
986 \subsection{Liftedness}
988 %************************************************************************
991 -- | See "Type#type_classification" for what an unlifted type is
992 isUnLiftedType :: Type -> Bool
993 -- isUnLiftedType returns True for forall'd unlifted types:
994 -- x :: forall a. Int#
995 -- I found bindings like these were getting floated to the top level.
996 -- They are pretty bogus types, mind you. It would be better never to
999 isUnLiftedType ty | Just ty' <- coreView ty = isUnLiftedType ty'
1000 isUnLiftedType (ForAllTy _ ty) = isUnLiftedType ty
1001 isUnLiftedType (TyConApp tc _) = isUnLiftedTyCon tc
1002 isUnLiftedType _ = False
1004 isUnboxedTupleType :: Type -> Bool
1005 isUnboxedTupleType ty = case splitTyConApp_maybe ty of
1006 Just (tc, _ty_args) -> isUnboxedTupleTyCon tc
1009 -- | See "Type#type_classification" for what an algebraic type is.
1010 -- Should only be applied to /types/, as opposed to e.g. partially
1011 -- saturated type constructors
1012 isAlgType :: Type -> Bool
1014 = case splitTyConApp_maybe ty of
1015 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1019 -- | See "Type#type_classification" for what an algebraic type is.
1020 -- Should only be applied to /types/, as opposed to e.g. partially
1021 -- saturated type constructors. Closed type constructors are those
1022 -- with a fixed right hand side, as opposed to e.g. associated types
1023 isClosedAlgType :: Type -> Bool
1025 = case splitTyConApp_maybe ty of
1026 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1027 isAlgTyCon tc && not (isOpenTyCon tc)
1032 -- | Computes whether an argument (or let right hand side) should
1033 -- be computed strictly or lazily, based only on its type.
1034 -- Works just like 'isUnLiftedType', except that it has a special case
1035 -- for dictionaries (i.e. does not work purely on representation types)
1037 -- Since it takes account of class 'PredType's, you might think
1038 -- this function should be in 'TcType', but 'isStrictType' is used by 'DataCon',
1039 -- which is below 'TcType' in the hierarchy, so it's convenient to put it here.
1040 isStrictType :: Type -> Bool
1041 isStrictType (PredTy pred) = isStrictPred pred
1042 isStrictType ty | Just ty' <- coreView ty = isStrictType ty'
1043 isStrictType (ForAllTy _ ty) = isStrictType ty
1044 isStrictType (TyConApp tc _) = isUnLiftedTyCon tc
1045 isStrictType _ = False
1047 -- | We may be strict in dictionary types, but only if it
1048 -- has more than one component.
1050 -- (Being strict in a single-component dictionary risks
1051 -- poking the dictionary component, which is wrong.)
1052 isStrictPred :: PredType -> Bool
1053 isStrictPred (ClassP clas _) = opt_DictsStrict && not (isNewTyCon (classTyCon clas))
1054 isStrictPred _ = False
1058 isPrimitiveType :: Type -> Bool
1059 -- ^ Returns true of types that are opaque to Haskell.
1060 -- Most of these are unlifted, but now that we interact with .NET, we
1061 -- may have primtive (foreign-imported) types that are lifted
1062 isPrimitiveType ty = case splitTyConApp_maybe ty of
1063 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1069 %************************************************************************
1071 \subsection{Sequencing on types}
1073 %************************************************************************
1076 seqType :: Type -> ()
1077 seqType (TyVarTy tv) = tv `seq` ()
1078 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
1079 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
1080 seqType (PredTy p) = seqPred p
1081 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
1082 seqType (ForAllTy tv ty) = tv `seq` seqType ty
1084 seqTypes :: [Type] -> ()
1086 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
1088 seqPred :: PredType -> ()
1089 seqPred (ClassP c tys) = c `seq` seqTypes tys
1090 seqPred (IParam n ty) = n `seq` seqType ty
1091 seqPred (EqPred ty1 ty2) = seqType ty1 `seq` seqType ty2
1095 %************************************************************************
1097 Equality for Core types
1098 (We don't use instances so that we know where it happens)
1100 %************************************************************************
1102 Note that eqType works right even for partial applications of newtypes.
1103 See Note [Newtype eta] in TyCon.lhs
1106 -- | Type equality test for Core types (i.e. ignores predicate-types, synonyms etc.)
1107 coreEqType :: Type -> Type -> Bool
1108 coreEqType t1 t2 = coreEqType2 rn_env t1 t2
1110 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1112 coreEqType2 :: RnEnv2 -> Type -> Type -> Bool
1113 coreEqType2 rn_env t1 t2
1116 eq env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 == rnOccR env tv2
1117 eq env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = eq (rnBndr2 env tv1 tv2) t1 t2
1118 eq env (AppTy s1 t1) (AppTy s2 t2) = eq env s1 s2 && eq env t1 t2
1119 eq env (FunTy s1 t1) (FunTy s2 t2) = eq env s1 s2 && eq env t1 t2
1120 eq env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
1121 | tc1 == tc2, all2 (eq env) tys1 tys2 = True
1122 -- The lengths should be equal because
1123 -- the two types have the same kind
1124 -- NB: if the type constructors differ that does not
1125 -- necessarily mean that the types aren't equal
1126 -- (synonyms, newtypes)
1127 -- Even if the type constructors are the same, but the arguments
1128 -- differ, the two types could be the same (e.g. if the arg is just
1129 -- ignored in the RHS). In both these cases we fall through to an
1130 -- attempt to expand one side or the other.
1132 -- Now deal with newtypes, synonyms, pred-tys
1133 eq env t1 t2 | Just t1' <- coreView t1 = eq env t1' t2
1134 | Just t2' <- coreView t2 = eq env t1 t2'
1136 -- Fall through case; not equal!
1141 %************************************************************************
1143 Comparision for source types
1144 (We don't use instances so that we know where it happens)
1146 %************************************************************************
1149 tcEqType :: Type -> Type -> Bool
1150 -- ^ Type equality on source types. Does not look through @newtypes@ or
1151 -- 'PredType's, but it does look through type synonyms.
1152 tcEqType t1 t2 = isEqual $ cmpType t1 t2
1154 tcEqTypes :: [Type] -> [Type] -> Bool
1155 tcEqTypes tys1 tys2 = isEqual $ cmpTypes tys1 tys2
1157 tcCmpType :: Type -> Type -> Ordering
1158 -- ^ Type ordering on source types. Does not look through @newtypes@ or
1159 -- 'PredType's, but it does look through type synonyms.
1160 tcCmpType t1 t2 = cmpType t1 t2
1162 tcCmpTypes :: [Type] -> [Type] -> Ordering
1163 tcCmpTypes tys1 tys2 = cmpTypes tys1 tys2
1165 tcEqPred :: PredType -> PredType -> Bool
1166 tcEqPred p1 p2 = isEqual $ cmpPred p1 p2
1168 tcEqPredX :: RnEnv2 -> PredType -> PredType -> Bool
1169 tcEqPredX env p1 p2 = isEqual $ cmpPredX env p1 p2
1171 tcCmpPred :: PredType -> PredType -> Ordering
1172 tcCmpPred p1 p2 = cmpPred p1 p2
1174 tcEqTypeX :: RnEnv2 -> Type -> Type -> Bool
1175 tcEqTypeX env t1 t2 = isEqual $ cmpTypeX env t1 t2
1179 -- | Checks whether the second argument is a subterm of the first. (We don't care
1180 -- about binders, as we are only interested in syntactic subterms.)
1181 tcPartOfType :: Type -> Type -> Bool
1183 | tcEqType t1 t2 = True
1185 | Just t2' <- tcView t2 = tcPartOfType t1 t2'
1186 tcPartOfType _ (TyVarTy _) = False
1187 tcPartOfType t1 (ForAllTy _ t2) = tcPartOfType t1 t2
1188 tcPartOfType t1 (AppTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1189 tcPartOfType t1 (FunTy s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1190 tcPartOfType t1 (PredTy p2) = tcPartOfPred t1 p2
1191 tcPartOfType t1 (TyConApp _ ts) = any (tcPartOfType t1) ts
1193 tcPartOfPred :: Type -> PredType -> Bool
1194 tcPartOfPred t1 (IParam _ t2) = tcPartOfType t1 t2
1195 tcPartOfPred t1 (ClassP _ ts) = any (tcPartOfType t1) ts
1196 tcPartOfPred t1 (EqPred s2 t2) = tcPartOfType t1 s2 || tcPartOfType t1 t2
1199 Now here comes the real worker
1202 cmpType :: Type -> Type -> Ordering
1203 cmpType t1 t2 = cmpTypeX rn_env t1 t2
1205 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfType t1 `unionVarSet` tyVarsOfType t2))
1207 cmpTypes :: [Type] -> [Type] -> Ordering
1208 cmpTypes ts1 ts2 = cmpTypesX rn_env ts1 ts2
1210 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfTypes ts1 `unionVarSet` tyVarsOfTypes ts2))
1212 cmpPred :: PredType -> PredType -> Ordering
1213 cmpPred p1 p2 = cmpPredX rn_env p1 p2
1215 rn_env = mkRnEnv2 (mkInScopeSet (tyVarsOfPred p1 `unionVarSet` tyVarsOfPred p2))
1217 cmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
1218 cmpTypeX env t1 t2 | Just t1' <- tcView t1 = cmpTypeX env t1' t2
1219 | Just t2' <- tcView t2 = cmpTypeX env t1 t2'
1221 cmpTypeX env (TyVarTy tv1) (TyVarTy tv2) = rnOccL env tv1 `compare` rnOccR env tv2
1222 cmpTypeX env (ForAllTy tv1 t1) (ForAllTy tv2 t2) = cmpTypeX (rnBndr2 env tv1 tv2) t1 t2
1223 cmpTypeX env (AppTy s1 t1) (AppTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1224 cmpTypeX env (FunTy s1 t1) (FunTy s2 t2) = cmpTypeX env s1 s2 `thenCmp` cmpTypeX env t1 t2
1225 cmpTypeX env (PredTy p1) (PredTy p2) = cmpPredX env p1 p2
1226 cmpTypeX env (TyConApp tc1 tys1) (TyConApp tc2 tys2) = (tc1 `compare` tc2) `thenCmp` cmpTypesX env tys1 tys2
1228 -- Deal with the rest: TyVarTy < AppTy < FunTy < TyConApp < ForAllTy < PredTy
1229 cmpTypeX _ (AppTy _ _) (TyVarTy _) = GT
1231 cmpTypeX _ (FunTy _ _) (TyVarTy _) = GT
1232 cmpTypeX _ (FunTy _ _) (AppTy _ _) = GT
1234 cmpTypeX _ (TyConApp _ _) (TyVarTy _) = GT
1235 cmpTypeX _ (TyConApp _ _) (AppTy _ _) = GT
1236 cmpTypeX _ (TyConApp _ _) (FunTy _ _) = GT
1238 cmpTypeX _ (ForAllTy _ _) (TyVarTy _) = GT
1239 cmpTypeX _ (ForAllTy _ _) (AppTy _ _) = GT
1240 cmpTypeX _ (ForAllTy _ _) (FunTy _ _) = GT
1241 cmpTypeX _ (ForAllTy _ _) (TyConApp _ _) = GT
1243 cmpTypeX _ (PredTy _) _ = GT
1248 cmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
1249 cmpTypesX _ [] [] = EQ
1250 cmpTypesX env (t1:tys1) (t2:tys2) = cmpTypeX env t1 t2 `thenCmp` cmpTypesX env tys1 tys2
1251 cmpTypesX _ [] _ = LT
1252 cmpTypesX _ _ [] = GT
1255 cmpPredX :: RnEnv2 -> PredType -> PredType -> Ordering
1256 cmpPredX env (IParam n1 ty1) (IParam n2 ty2) = (n1 `compare` n2) `thenCmp` cmpTypeX env ty1 ty2
1257 -- Compare names only for implicit parameters
1258 -- This comparison is used exclusively (I believe)
1259 -- for the Avails finite map built in TcSimplify
1260 -- If the types differ we keep them distinct so that we see
1261 -- a distinct pair to run improvement on
1262 cmpPredX env (ClassP c1 tys1) (ClassP c2 tys2) = (c1 `compare` c2) `thenCmp` (cmpTypesX env tys1 tys2)
1263 cmpPredX env (EqPred ty1 ty2) (EqPred ty1' ty2') = (cmpTypeX env ty1 ty1') `thenCmp` (cmpTypeX env ty2 ty2')
1265 -- Constructor order: IParam < ClassP < EqPred
1266 cmpPredX _ (IParam {}) _ = LT
1267 cmpPredX _ (ClassP {}) (IParam {}) = GT
1268 cmpPredX _ (ClassP {}) (EqPred {}) = LT
1269 cmpPredX _ (EqPred {}) _ = GT
1272 PredTypes are used as a FM key in TcSimplify,
1273 so we take the easy path and make them an instance of Ord
1276 instance Eq PredType where { (==) = tcEqPred }
1277 instance Ord PredType where { compare = tcCmpPred }
1281 %************************************************************************
1285 %************************************************************************
1288 -- | Type substitution
1290 -- #tvsubst_invariant#
1291 -- The following invariants must hold of a 'TvSubst':
1293 -- 1. The in-scope set is needed /only/ to
1294 -- guide the generation of fresh uniques
1296 -- 2. In particular, the /kind/ of the type variables in
1297 -- the in-scope set is not relevant
1299 -- 3. The substition is only applied ONCE! This is because
1300 -- in general such application will not reached a fixed point.
1302 = TvSubst InScopeSet -- The in-scope type variables
1303 TvSubstEnv -- The substitution itself
1304 -- See Note [Apply Once]
1305 -- and Note [Extending the TvSubstEnv]
1307 {- ----------------------------------------------------------
1311 We use TvSubsts to instantiate things, and we might instantiate
1315 So the substition might go [a->b, b->a]. A similar situation arises in Core
1316 when we find a beta redex like
1317 (/\ a /\ b -> e) b a
1318 Then we also end up with a substition that permutes type variables. Other
1319 variations happen to; for example [a -> (a, b)].
1321 ***************************************************
1322 *** So a TvSubst must be applied precisely once ***
1323 ***************************************************
1325 A TvSubst is not idempotent, but, unlike the non-idempotent substitution
1326 we use during unifications, it must not be repeatedly applied.
1328 Note [Extending the TvSubst]
1329 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1330 See #tvsubst_invariant# for the invariants that must hold.
1332 This invariant allows a short-cut when the TvSubstEnv is empty:
1333 if the TvSubstEnv is empty --- i.e. (isEmptyTvSubt subst) holds ---
1334 then (substTy subst ty) does nothing.
1336 For example, consider:
1337 (/\a. /\b:(a~Int). ...b..) Int
1338 We substitute Int for 'a'. The Unique of 'b' does not change, but
1339 nevertheless we add 'b' to the TvSubstEnv, because b's kind does change
1341 This invariant has several crucial consequences:
1343 * In substTyVarBndr, we need extend the TvSubstEnv
1344 - if the unique has changed
1345 - or if the kind has changed
1347 * In substTyVar, we do not need to consult the in-scope set;
1348 the TvSubstEnv is enough
1350 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1353 -------------------------------------------------------------- -}
1355 -- | A substitition of 'Type's for 'TyVar's
1356 type TvSubstEnv = TyVarEnv Type
1357 -- A TvSubstEnv is used both inside a TvSubst (with the apply-once
1358 -- invariant discussed in Note [Apply Once]), and also independently
1359 -- in the middle of matching, and unification (see Types.Unify)
1360 -- So you have to look at the context to know if it's idempotent or
1361 -- apply-once or whatever
1363 emptyTvSubstEnv :: TvSubstEnv
1364 emptyTvSubstEnv = emptyVarEnv
1366 composeTvSubst :: InScopeSet -> TvSubstEnv -> TvSubstEnv -> TvSubstEnv
1367 -- ^ @(compose env1 env2)(x)@ is @env1(env2(x))@; i.e. apply @env2@ then @env1@.
1368 -- It assumes that both are idempotent.
1369 -- Typically, @env1@ is the refinement to a base substitution @env2@
1370 composeTvSubst in_scope env1 env2
1371 = env1 `plusVarEnv` mapVarEnv (substTy subst1) env2
1372 -- First apply env1 to the range of env2
1373 -- Then combine the two, making sure that env1 loses if
1374 -- both bind the same variable; that's why env1 is the
1375 -- *left* argument to plusVarEnv, because the right arg wins
1377 subst1 = TvSubst in_scope env1
1379 emptyTvSubst :: TvSubst
1380 emptyTvSubst = TvSubst emptyInScopeSet emptyVarEnv
1382 isEmptyTvSubst :: TvSubst -> Bool
1383 -- See Note [Extending the TvSubstEnv]
1384 isEmptyTvSubst (TvSubst _ env) = isEmptyVarEnv env
1386 mkTvSubst :: InScopeSet -> TvSubstEnv -> TvSubst
1389 getTvSubstEnv :: TvSubst -> TvSubstEnv
1390 getTvSubstEnv (TvSubst _ env) = env
1392 getTvInScope :: TvSubst -> InScopeSet
1393 getTvInScope (TvSubst in_scope _) = in_scope
1395 isInScope :: Var -> TvSubst -> Bool
1396 isInScope v (TvSubst in_scope _) = v `elemInScopeSet` in_scope
1398 notElemTvSubst :: TyVar -> TvSubst -> Bool
1399 notElemTvSubst tv (TvSubst _ env) = not (tv `elemVarEnv` env)
1401 setTvSubstEnv :: TvSubst -> TvSubstEnv -> TvSubst
1402 setTvSubstEnv (TvSubst in_scope _) env = TvSubst in_scope env
1404 zapTvSubstEnv :: TvSubst -> TvSubst
1405 zapTvSubstEnv (TvSubst in_scope _) = TvSubst in_scope emptyVarEnv
1407 extendTvInScope :: TvSubst -> Var -> TvSubst
1408 extendTvInScope (TvSubst in_scope env) var = TvSubst (extendInScopeSet in_scope var) env
1410 extendTvInScopeList :: TvSubst -> [Var] -> TvSubst
1411 extendTvInScopeList (TvSubst in_scope env) vars = TvSubst (extendInScopeSetList in_scope vars) env
1413 extendTvSubst :: TvSubst -> TyVar -> Type -> TvSubst
1414 extendTvSubst (TvSubst in_scope env) tv ty = TvSubst in_scope (extendVarEnv env tv ty)
1416 extendTvSubstList :: TvSubst -> [TyVar] -> [Type] -> TvSubst
1417 extendTvSubstList (TvSubst in_scope env) tvs tys
1418 = TvSubst in_scope (extendVarEnvList env (tvs `zip` tys))
1420 -- mkOpenTvSubst and zipOpenTvSubst generate the in-scope set from
1421 -- the types given; but it's just a thunk so with a bit of luck
1422 -- it'll never be evaluated
1424 -- Note [Generating the in-scope set for a substitution]
1425 -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1426 -- If we want to substitute [a -> ty1, b -> ty2] I used to
1427 -- think it was enough to generate an in-scope set that includes
1428 -- fv(ty1,ty2). But that's not enough; we really should also take the
1429 -- free vars of the type we are substituting into! Example:
1430 -- (forall b. (a,b,x)) [a -> List b]
1431 -- Then if we use the in-scope set {b}, there is a danger we will rename
1432 -- the forall'd variable to 'x' by mistake, getting this:
1433 -- (forall x. (List b, x, x)
1434 -- Urk! This means looking at all the calls to mkOpenTvSubst....
1437 -- | Generates the in-scope set for the 'TvSubst' from the types in the incoming
1438 -- environment, hence "open"
1439 mkOpenTvSubst :: TvSubstEnv -> TvSubst
1440 mkOpenTvSubst env = TvSubst (mkInScopeSet (tyVarsOfTypes (varEnvElts env))) env
1442 -- | Generates the in-scope set for the 'TvSubst' from the types in the incoming
1443 -- environment, hence "open"
1444 zipOpenTvSubst :: [TyVar] -> [Type] -> TvSubst
1445 zipOpenTvSubst tyvars tys
1446 | debugIsOn && (length tyvars /= length tys)
1447 = pprTrace "zipOpenTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1449 = TvSubst (mkInScopeSet (tyVarsOfTypes tys)) (zipTyEnv tyvars tys)
1451 -- | Called when doing top-level substitutions. Here we expect that the
1452 -- free vars of the range of the substitution will be empty.
1453 mkTopTvSubst :: [(TyVar, Type)] -> TvSubst
1454 mkTopTvSubst prs = TvSubst emptyInScopeSet (mkVarEnv prs)
1456 zipTopTvSubst :: [TyVar] -> [Type] -> TvSubst
1457 zipTopTvSubst tyvars tys
1458 | debugIsOn && (length tyvars /= length tys)
1459 = pprTrace "zipTopTvSubst" (ppr tyvars $$ ppr tys) emptyTvSubst
1461 = TvSubst emptyInScopeSet (zipTyEnv tyvars tys)
1463 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
1465 | debugIsOn && (length tyvars /= length tys)
1466 = pprTrace "mkTopTvSubst" (ppr tyvars $$ ppr tys) emptyVarEnv
1468 = zip_ty_env tyvars tys emptyVarEnv
1470 -- Later substitutions in the list over-ride earlier ones,
1471 -- but there should be no loops
1472 zip_ty_env :: [TyVar] -> [Type] -> TvSubstEnv -> TvSubstEnv
1473 zip_ty_env [] [] env = env
1474 zip_ty_env (tv:tvs) (ty:tys) env = zip_ty_env tvs tys (extendVarEnv env tv ty)
1475 -- There used to be a special case for when
1477 -- (a not-uncommon case) in which case the substitution was dropped.
1478 -- But the type-tidier changes the print-name of a type variable without
1479 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
1480 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
1481 -- And it happened that t was the type variable of the class. Post-tiding,
1482 -- it got turned into {Foo t2}. The ext-core printer expanded this using
1483 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
1484 -- and so generated a rep type mentioning t not t2.
1486 -- Simplest fix is to nuke the "optimisation"
1487 zip_ty_env tvs tys env = pprTrace "Var/Type length mismatch: " (ppr tvs $$ ppr tys) env
1488 -- zip_ty_env _ _ env = env
1490 instance Outputable TvSubst where
1491 ppr (TvSubst ins env)
1492 = brackets $ sep[ ptext (sLit "TvSubst"),
1493 nest 2 (ptext (sLit "In scope:") <+> ppr ins),
1494 nest 2 (ptext (sLit "Env:") <+> ppr env) ]
1497 %************************************************************************
1499 Performing type substitutions
1501 %************************************************************************
1504 -- | Type substitution making use of an 'TvSubst' that
1505 -- is assumed to be open, see 'zipOpenTvSubst'
1506 substTyWith :: [TyVar] -> [Type] -> Type -> Type
1507 substTyWith tvs tys = ASSERT( length tvs == length tys )
1508 substTy (zipOpenTvSubst tvs tys)
1510 -- | Type substitution making use of an 'TvSubst' that
1511 -- is assumed to be open, see 'zipOpenTvSubst'
1512 substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
1513 substTysWith tvs tys = ASSERT( length tvs == length tys )
1514 substTys (zipOpenTvSubst tvs tys)
1516 -- | Substitute within a 'Type'
1517 substTy :: TvSubst -> Type -> Type
1518 substTy subst ty | isEmptyTvSubst subst = ty
1519 | otherwise = subst_ty subst ty
1521 -- | Substitute within several 'Type's
1522 substTys :: TvSubst -> [Type] -> [Type]
1523 substTys subst tys | isEmptyTvSubst subst = tys
1524 | otherwise = map (subst_ty subst) tys
1526 -- | Substitute within a 'ThetaType'
1527 substTheta :: TvSubst -> ThetaType -> ThetaType
1528 substTheta subst theta
1529 | isEmptyTvSubst subst = theta
1530 | otherwise = map (substPred subst) theta
1532 -- | Substitute within a 'PredType'
1533 substPred :: TvSubst -> PredType -> PredType
1534 substPred subst (IParam n ty) = IParam n (subst_ty subst ty)
1535 substPred subst (ClassP clas tys) = ClassP clas (map (subst_ty subst) tys)
1536 substPred subst (EqPred ty1 ty2) = EqPred (subst_ty subst ty1) (subst_ty subst ty2)
1538 -- | Remove any nested binders mentioning the 'TyVar's in the 'TyVarSet'
1539 deShadowTy :: TyVarSet -> Type -> Type
1541 = subst_ty (mkTvSubst in_scope emptyTvSubstEnv) ty
1543 in_scope = mkInScopeSet tvs
1545 subst_ty :: TvSubst -> Type -> Type
1546 -- subst_ty is the main workhorse for type substitution
1548 -- Note that the in_scope set is poked only if we hit a forall
1549 -- so it may often never be fully computed
1553 go (TyVarTy tv) = substTyVar subst tv
1554 go (TyConApp tc tys) = let args = map go tys
1555 in args `seqList` TyConApp tc args
1557 go (PredTy p) = PredTy $! (substPred subst p)
1559 go (FunTy arg res) = (FunTy $! (go arg)) $! (go res)
1560 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
1561 -- The mkAppTy smart constructor is important
1562 -- we might be replacing (a Int), represented with App
1563 -- by [Int], represented with TyConApp
1564 go (ForAllTy tv ty) = case substTyVarBndr subst tv of
1566 ForAllTy tv' $! (subst_ty subst' ty)
1568 substTyVar :: TvSubst -> TyVar -> Type
1569 substTyVar subst@(TvSubst _ _) tv
1570 = case lookupTyVar subst tv of {
1571 Nothing -> TyVarTy tv;
1572 Just ty -> ty -- See Note [Apply Once]
1575 substTyVars :: TvSubst -> [TyVar] -> [Type]
1576 substTyVars subst tvs = map (substTyVar subst) tvs
1578 lookupTyVar :: TvSubst -> TyVar -> Maybe Type
1579 -- See Note [Extending the TvSubst]
1580 lookupTyVar (TvSubst _ env) tv = lookupVarEnv env tv
1582 substTyVarBndr :: TvSubst -> TyVar -> (TvSubst, TyVar)
1583 substTyVarBndr subst@(TvSubst in_scope env) old_var
1584 = (TvSubst (in_scope `extendInScopeSet` new_var) new_env, new_var)
1586 is_co_var = isCoVar old_var
1588 new_env | no_change = delVarEnv env old_var
1589 | otherwise = extendVarEnv env old_var (TyVarTy new_var)
1591 no_change = new_var == old_var && not is_co_var
1592 -- no_change means that the new_var is identical in
1593 -- all respects to the old_var (same unique, same kind)
1594 -- See Note [Extending the TvSubst]
1596 -- In that case we don't need to extend the substitution
1597 -- to map old to new. But instead we must zap any
1598 -- current substitution for the variable. For example:
1599 -- (\x.e) with id_subst = [x |-> e']
1600 -- Here we must simply zap the substitution for x
1602 new_var = uniqAway in_scope subst_old_var
1603 -- The uniqAway part makes sure the new variable is not already in scope
1605 subst_old_var -- subst_old_var is old_var with the substitution applied to its kind
1606 -- It's only worth doing the substitution for coercions,
1607 -- becuase only they can have free type variables
1608 | is_co_var = setTyVarKind old_var (substTy subst (tyVarKind old_var))
1609 | otherwise = old_var
1612 ----------------------------------------------------
1621 -- There's a little subtyping at the kind level:
1631 -- Where: \* [LiftedTypeKind] means boxed type
1632 -- \# [UnliftedTypeKind] means unboxed type
1633 -- (\#) [UbxTupleKind] means unboxed tuple
1634 -- ?? [ArgTypeKind] is the lub of {\*, \#}
1635 -- ? [OpenTypeKind] means any type at all
1640 -- > error :: forall a:?. String -> a
1641 -- > (->) :: ?? -> ? -> \*
1642 -- > (\\(x::t) -> ...)
1644 -- Where in the last example @t :: ??@ (i.e. is not an unboxed tuple)
1646 type KindVar = TyVar -- invariant: KindVar will always be a
1647 -- TcTyVar with details MetaTv TauTv ...
1648 -- kind var constructors and functions are in TcType
1650 type SimpleKind = Kind
1655 During kind inference, a kind variable unifies only with
1657 sk ::= * | sk1 -> sk2
1659 data T a = MkT a (T Int#)
1660 fails. We give T the kind (k -> *), and the kind variable k won't unify
1661 with # (the kind of Int#).
1665 When creating a fresh internal type variable, we give it a kind to express
1666 constraints on it. E.g. in (\x->e) we make up a fresh type variable for x,
1669 During unification we only bind an internal type variable to a type
1670 whose kind is lower in the sub-kind hierarchy than the kind of the tyvar.
1672 When unifying two internal type variables, we collect their kind constraints by
1673 finding the GLB of the two. Since the partial order is a tree, they only
1674 have a glb if one is a sub-kind of the other. In that case, we bind the
1675 less-informative one to the more informative one. Neat, eh?