Avoid quadratic complexity in typeKind
[ghc.git] / compiler / types / Type.hs
1 -- (c) The University of Glasgow 2006
2 -- (c) The GRASP/AQUA Project, Glasgow University, 1998
3 --
4 -- Type - public interface
5
6 {-# LANGUAGE CPP, FlexibleContexts #-}
7 {-# OPTIONS_GHC -fno-warn-orphans #-}
8
9 -- | Main functions for manipulating types and type-related things
10 module Type (
11 -- Note some of this is just re-exports from TyCon..
12
13 -- * Main data types representing Types
14 -- $type_classification
15
16 -- $representation_types
17 TyThing(..), Type, ArgFlag(..), KindOrType, PredType, ThetaType,
18 Var, TyVar, isTyVar, TyCoVar, TyBinder, TyVarBinder,
19
20 -- ** Constructing and deconstructing types
21 mkTyVarTy, mkTyVarTys, getTyVar, getTyVar_maybe, repGetTyVar_maybe,
22 getCastedTyVar_maybe, tyVarKind,
23
24 mkAppTy, mkAppTys, splitAppTy, splitAppTys, repSplitAppTys,
25 splitAppTy_maybe, repSplitAppTy_maybe, tcRepSplitAppTy_maybe,
26
27 mkFunTy, mkFunTys, splitFunTy, splitFunTy_maybe,
28 splitFunTys, funResultTy, funArgTy,
29
30 mkTyConApp, mkTyConTy,
31 tyConAppTyCon_maybe, tyConAppTyConPicky_maybe,
32 tyConAppArgs_maybe, tyConAppTyCon, tyConAppArgs,
33 splitTyConApp_maybe, splitTyConApp, tyConAppArgN,
34 tcRepSplitTyConApp_maybe, tcSplitTyConApp_maybe,
35 splitListTyConApp_maybe,
36 repSplitTyConApp_maybe,
37
38 mkForAllTy, mkForAllTys, mkInvForAllTys, mkSpecForAllTys,
39 mkVisForAllTys, mkInvForAllTy,
40 splitForAllTys, splitForAllTyVarBndrs,
41 splitForAllTy_maybe, splitForAllTy,
42 splitPiTy_maybe, splitPiTy, splitPiTys,
43 mkPiTy, mkPiTys, mkTyConBindersPreferAnon,
44 mkLamType, mkLamTypes,
45 piResultTy, piResultTys,
46 applyTysX, dropForAlls,
47
48 mkNumLitTy, isNumLitTy,
49 mkStrLitTy, isStrLitTy,
50
51 getRuntimeRep_maybe, getRuntimeRepFromKind_maybe,
52
53 mkCastTy, mkCoercionTy, splitCastTy_maybe,
54
55 userTypeError_maybe, pprUserTypeErrorTy,
56
57 coAxNthLHS,
58 stripCoercionTy, splitCoercionType_maybe,
59
60 splitPiTysInvisible, filterOutInvisibleTypes,
61 partitionInvisibles,
62 synTyConResKind,
63
64 modifyJoinResTy, setJoinResTy,
65
66 -- Analyzing types
67 TyCoMapper(..), mapType, mapCoercion,
68
69 -- (Newtypes)
70 newTyConInstRhs,
71
72 -- Pred types
73 mkFamilyTyConApp,
74 isDictLikeTy,
75 mkPrimEqPred, mkReprPrimEqPred, mkPrimEqPredRole,
76 equalityTyCon,
77 mkHeteroPrimEqPred, mkHeteroReprPrimEqPred,
78 mkClassPred,
79 isClassPred, isEqPred, isNomEqPred,
80 isIPPred, isIPPred_maybe, isIPTyCon, isIPClass,
81 isCTupleClass,
82
83 -- Deconstructing predicate types
84 PredTree(..), EqRel(..), eqRelRole, classifyPredType,
85 getClassPredTys, getClassPredTys_maybe,
86 getEqPredTys, getEqPredTys_maybe, getEqPredRole,
87 predTypeEqRel,
88
89 -- ** Binders
90 sameVis,
91 mkTyVarBinder, mkTyVarBinders,
92 mkAnonBinder,
93 isAnonTyBinder, isNamedTyBinder,
94 binderVar, binderVars, binderKind, binderArgFlag,
95 tyBinderType, tyBinderVar_maybe,
96 binderRelevantType_maybe, caseBinder,
97 isVisibleArgFlag, isInvisibleArgFlag, isVisibleBinder, isInvisibleBinder,
98 tyConBindersTyBinders,
99
100 -- ** Common type constructors
101 funTyCon,
102
103 -- ** Predicates on types
104 isTyVarTy, isFunTy, isDictTy, isPredTy, isCoercionTy,
105 isCoercionTy_maybe, isCoercionType, isForAllTy,
106 isPiTy, isTauTy, isFamFreeTy,
107
108 isValidJoinPointType,
109
110 -- (Lifting and boxity)
111 isLiftedType_maybe, isUnliftedType, isUnboxedTupleType, isUnboxedSumType,
112 isAlgType, isDataFamilyAppType,
113 isPrimitiveType, isStrictType,
114 isRuntimeRepTy, isRuntimeRepVar, isRuntimeRepKindedTy,
115 dropRuntimeRepArgs,
116 getRuntimeRep, getRuntimeRepFromKind,
117
118 -- * Main data types representing Kinds
119 Kind,
120
121 -- ** Finding the kind of a type
122 typeKind, isTypeLevPoly, resultIsLevPoly,
123
124 -- ** Common Kind
125 liftedTypeKind,
126
127 -- * Type free variables
128 tyCoFVsOfType, tyCoFVsBndr,
129 tyCoVarsOfType, tyCoVarsOfTypes,
130 tyCoVarsOfTypeDSet,
131 coVarsOfType,
132 coVarsOfTypes, closeOverKinds, closeOverKindsList,
133 noFreeVarsOfType,
134 splitVisVarsOfType, splitVisVarsOfTypes,
135 expandTypeSynonyms,
136 typeSize,
137
138 -- * Well-scoped lists of variables
139 dVarSetElemsWellScoped, toposortTyVars, tyCoVarsOfTypeWellScoped,
140 tyCoVarsOfTypesWellScoped,
141
142 -- * Type comparison
143 eqType, eqTypeX, eqTypes, nonDetCmpType, nonDetCmpTypes, nonDetCmpTypeX,
144 nonDetCmpTypesX, nonDetCmpTc,
145 eqVarBndrs,
146
147 -- * Forcing evaluation of types
148 seqType, seqTypes,
149
150 -- * Other views onto Types
151 coreView, tcView,
152
153 tyConsOfType,
154
155 -- * Main type substitution data types
156 TvSubstEnv, -- Representation widely visible
157 TCvSubst(..), -- Representation visible to a few friends
158
159 -- ** Manipulating type substitutions
160 emptyTvSubstEnv, emptyTCvSubst, mkEmptyTCvSubst,
161
162 mkTCvSubst, zipTvSubst, mkTvSubstPrs,
163 notElemTCvSubst,
164 getTvSubstEnv, setTvSubstEnv,
165 zapTCvSubst, getTCvInScope, getTCvSubstRangeFVs,
166 extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet,
167 extendTCvSubst, extendCvSubst,
168 extendTvSubst, extendTvSubstBinderAndInScope,
169 extendTvSubstList, extendTvSubstAndInScope,
170 extendTvSubstWithClone,
171 isInScope, composeTCvSubstEnv, composeTCvSubst, zipTyEnv, zipCoEnv,
172 isEmptyTCvSubst, unionTCvSubst,
173
174 -- ** Performing substitution on types and kinds
175 substTy, substTys, substTyWith, substTysWith, substTheta,
176 substTyAddInScope,
177 substTyUnchecked, substTysUnchecked, substThetaUnchecked,
178 substTyWithUnchecked,
179 substCoUnchecked, substCoWithUnchecked,
180 substTyVarBndr, substTyVar, substTyVars,
181 cloneTyVarBndr, cloneTyVarBndrs, lookupTyVar,
182
183 -- * Pretty-printing
184 pprType, pprParendType, pprPrecType,
185 pprTypeApp, pprTyThingCategory, pprShortTyThing,
186 pprTvBndr, pprTvBndrs, pprForAll, pprUserForAll,
187 pprSigmaType, ppSuggestExplicitKinds,
188 pprTheta, pprThetaArrowTy, pprClassPred,
189 pprKind, pprParendKind, pprSourceTyCon,
190 TyPrec(..), maybeParen,
191 pprTyVar, pprTyVars,
192
193 -- * Tidying type related things up for printing
194 tidyType, tidyTypes,
195 tidyOpenType, tidyOpenTypes,
196 tidyOpenKind,
197 tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars,
198 tidyOpenTyCoVar, tidyOpenTyCoVars,
199 tidyTyVarOcc,
200 tidyTopType,
201 tidyKind,
202 tidyTyVarBinder, tidyTyVarBinders
203 ) where
204
205 #include "HsVersions.h"
206
207 import GhcPrelude
208
209 import BasicTypes
210
211 -- We import the representation and primitive functions from TyCoRep.
212 -- Many things are reexported, but not the representation!
213
214 import Kind
215 import TyCoRep
216
217 -- friends:
218 import Var
219 import VarEnv
220 import VarSet
221 import UniqSet
222
223 import Class
224 import TyCon
225 import TysPrim
226 import {-# SOURCE #-} TysWiredIn ( listTyCon, typeNatKind
227 , typeSymbolKind, liftedTypeKind )
228 import PrelNames
229 import CoAxiom
230 import {-# SOURCE #-} Coercion
231
232 -- others
233 import Util
234 import Outputable
235 import FastString
236 import Pair
237 import ListSetOps
238 import Digraph
239 import Unique ( nonDetCmpUnique )
240
241 import Maybes ( orElse )
242 import Data.Maybe ( isJust, mapMaybe )
243 import Control.Monad ( guard )
244 import Control.Arrow ( first, second )
245
246 -- $type_classification
247 -- #type_classification#
248 --
249 -- Types are one of:
250 --
251 -- [Unboxed] Iff its representation is other than a pointer
252 -- Unboxed types are also unlifted.
253 --
254 -- [Lifted] Iff it has bottom as an element.
255 -- Closures always have lifted types: i.e. any
256 -- let-bound identifier in Core must have a lifted
257 -- type. Operationally, a lifted object is one that
258 -- can be entered.
259 -- Only lifted types may be unified with a type variable.
260 --
261 -- [Algebraic] Iff it is a type with one or more constructors, whether
262 -- declared with @data@ or @newtype@.
263 -- An algebraic type is one that can be deconstructed
264 -- with a case expression. This is /not/ the same as
265 -- lifted types, because we also include unboxed
266 -- tuples in this classification.
267 --
268 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
269 --
270 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
271 --
272 -- Currently, all primitive types are unlifted, but that's not necessarily
273 -- the case: for example, @Int@ could be primitive.
274 --
275 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
276 -- but unlifted (such as @ByteArray#@). The only primitive types that we
277 -- classify as algebraic are the unboxed tuples.
278 --
279 -- Some examples of type classifications that may make this a bit clearer are:
280 --
281 -- @
282 -- Type primitive boxed lifted algebraic
283 -- -----------------------------------------------------------------------------
284 -- Int# Yes No No No
285 -- ByteArray# Yes Yes No No
286 -- (\# a, b \#) Yes No No Yes
287 -- (\# a | b \#) Yes No No Yes
288 -- ( a, b ) No Yes Yes Yes
289 -- [a] No Yes Yes Yes
290 -- @
291
292 -- $representation_types
293 -- A /source type/ is a type that is a separate type as far as the type checker is
294 -- concerned, but which has a more low-level representation as far as Core-to-Core
295 -- passes and the rest of the back end is concerned.
296 --
297 -- You don't normally have to worry about this, as the utility functions in
298 -- this module will automatically convert a source into a representation type
299 -- if they are spotted, to the best of it's abilities. If you don't want this
300 -- to happen, use the equivalent functions from the "TcType" module.
301
302 {-
303 ************************************************************************
304 * *
305 Type representation
306 * *
307 ************************************************************************
308
309 Note [coreView vs tcView]
310 ~~~~~~~~~~~~~~~~~~~~~~~~~
311 So far as the typechecker is concerned, 'Constraint' and 'TYPE LiftedRep' are distinct kinds.
312
313 But in Core these two are treated as identical.
314
315 We implement this by making 'coreView' convert 'Constraint' to 'TYPE LiftedRep' on the fly.
316 The function tcView (used in the type checker) does not do this.
317
318 See also Trac #11715, which tracks removing this inconsistency.
319
320 -}
321
322 {-# INLINE coreView #-}
323 coreView :: Type -> Maybe Type
324 -- ^ This function Strips off the /top layer only/ of a type synonym
325 -- application (if any) its underlying representation type.
326 -- Returns Nothing if there is nothing to look through.
327 -- This function considers 'Constraint' to be a synonym of @TYPE LiftedRep@.
328 --
329 -- By being non-recursive and inlined, this case analysis gets efficiently
330 -- joined onto the case analysis that the caller is already doing
331 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
332 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
333 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
334 -- ok to use 'substTy' here.
335 -- See also Note [The substitution invariant] in TyCoRep.
336 -- Its important to use mkAppTys, rather than (foldl AppTy),
337 -- because the function part might well return a
338 -- partially-applied type constructor; indeed, usually will!
339
340 coreView (TyConApp tc []) -- At the Core level, Constraint = Type
341 | isStarKindSynonymTyCon tc
342 = Just liftedTypeKind
343
344 coreView _ = Nothing
345
346 -- | Gives the typechecker view of a type. This unwraps synonyms but
347 -- leaves 'Constraint' alone. c.f. coreView, which turns Constraint into
348 -- TYPE LiftedRep. Returns Nothing if no unwrapping happens.
349 -- See also Note [coreView vs tcView] in Type.
350 {-# INLINE tcView #-}
351 tcView :: Type -> Maybe Type
352 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
353 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
354 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
355 -- ok to use 'substTy' here.
356 -- See also Note [The substitution invariant] in TyCoRep.
357 -- Its important to use mkAppTys, rather than (foldl AppTy),
358 -- because the function part might well return a
359 -- partially-applied type constructor; indeed, usually will!
360 tcView _ = Nothing
361
362 -----------------------------------------------
363 expandTypeSynonyms :: Type -> Type
364 -- ^ Expand out all type synonyms. Actually, it'd suffice to expand out
365 -- just the ones that discard type variables (e.g. type Funny a = Int)
366 -- But we don't know which those are currently, so we just expand all.
367 --
368 -- 'expandTypeSynonyms' only expands out type synonyms mentioned in the type,
369 -- not in the kinds of any TyCon or TyVar mentioned in the type.
370 --
371 -- Keep this synchronized with 'synonymTyConsOfType'
372 expandTypeSynonyms ty
373 = go (mkEmptyTCvSubst in_scope) ty
374 where
375 in_scope = mkInScopeSet (tyCoVarsOfType ty)
376
377 go subst (TyConApp tc tys)
378 | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc expanded_tys
379 = let subst' = mkTvSubst in_scope (mkVarEnv tenv)
380 -- Make a fresh substitution; rhs has nothing to
381 -- do with anything that has happened so far
382 -- NB: if you make changes here, be sure to build an
383 -- /idempotent/ substitution, even in the nested case
384 -- type T a b = a -> b
385 -- type S x y = T y x
386 -- (Trac #11665)
387 in mkAppTys (go subst' rhs) tys'
388 | otherwise
389 = TyConApp tc expanded_tys
390 where
391 expanded_tys = (map (go subst) tys)
392
393 go _ (LitTy l) = LitTy l
394 go subst (TyVarTy tv) = substTyVar subst tv
395 go subst (AppTy t1 t2) = mkAppTy (go subst t1) (go subst t2)
396 go subst (FunTy arg res)
397 = mkFunTy (go subst arg) (go subst res)
398 go subst (ForAllTy (TvBndr tv vis) t)
399 = let (subst', tv') = substTyVarBndrCallback go subst tv in
400 ForAllTy (TvBndr tv' vis) (go subst' t)
401 go subst (CastTy ty co) = mkCastTy (go subst ty) (go_co subst co)
402 go subst (CoercionTy co) = mkCoercionTy (go_co subst co)
403
404 go_co subst (Refl r ty)
405 = mkReflCo r (go subst ty)
406 -- NB: coercions are always expanded upon creation
407 go_co subst (TyConAppCo r tc args)
408 = mkTyConAppCo r tc (map (go_co subst) args)
409 go_co subst (AppCo co arg)
410 = mkAppCo (go_co subst co) (go_co subst arg)
411 go_co subst (ForAllCo tv kind_co co)
412 = let (subst', tv', kind_co') = go_cobndr subst tv kind_co in
413 mkForAllCo tv' kind_co' (go_co subst' co)
414 go_co subst (FunCo r co1 co2)
415 = mkFunCo r (go_co subst co1) (go_co subst co2)
416 go_co subst (CoVarCo cv)
417 = substCoVar subst cv
418 go_co subst (AxiomInstCo ax ind args)
419 = mkAxiomInstCo ax ind (map (go_co subst) args)
420 go_co subst (UnivCo p r t1 t2)
421 = mkUnivCo (go_prov subst p) r (go subst t1) (go subst t2)
422 go_co subst (SymCo co)
423 = mkSymCo (go_co subst co)
424 go_co subst (TransCo co1 co2)
425 = mkTransCo (go_co subst co1) (go_co subst co2)
426 go_co subst (NthCo n co)
427 = mkNthCo n (go_co subst co)
428 go_co subst (LRCo lr co)
429 = mkLRCo lr (go_co subst co)
430 go_co subst (InstCo co arg)
431 = mkInstCo (go_co subst co) (go_co subst arg)
432 go_co subst (CoherenceCo co1 co2)
433 = mkCoherenceCo (go_co subst co1) (go_co subst co2)
434 go_co subst (KindCo co)
435 = mkKindCo (go_co subst co)
436 go_co subst (SubCo co)
437 = mkSubCo (go_co subst co)
438 go_co subst (AxiomRuleCo ax cs)
439 = AxiomRuleCo ax (map (go_co subst) cs)
440 go_co _ (HoleCo h)
441 = pprPanic "expandTypeSynonyms hit a hole" (ppr h)
442
443 go_prov _ UnsafeCoerceProv = UnsafeCoerceProv
444 go_prov subst (PhantomProv co) = PhantomProv (go_co subst co)
445 go_prov subst (ProofIrrelProv co) = ProofIrrelProv (go_co subst co)
446 go_prov _ p@(PluginProv _) = p
447
448 -- the "False" and "const" are to accommodate the type of
449 -- substForAllCoBndrCallback, which is general enough to
450 -- handle coercion optimization (which sometimes swaps the
451 -- order of a coercion)
452 go_cobndr subst = substForAllCoBndrCallback False (go_co subst) subst
453
454 {-
455 ************************************************************************
456 * *
457 Analyzing types
458 * *
459 ************************************************************************
460
461 These functions do a map-like operation over types, performing some operation
462 on all variables and binding sites. Primarily used for zonking.
463
464 Note [Efficiency for mapCoercion ForAllCo case]
465 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
466 As noted in Note [Forall coercions] in TyCoRep, a ForAllCo is a bit redundant.
467 It stores a TyVar and a Coercion, where the kind of the TyVar always matches
468 the left-hand kind of the coercion. This is convenient lots of the time, but
469 not when mapping a function over a coercion.
470
471 The problem is that tcm_tybinder will affect the TyVar's kind and
472 mapCoercion will affect the Coercion, and we hope that the results will be
473 the same. Even if they are the same (which should generally happen with
474 correct algorithms), then there is an efficiency issue. In particular,
475 this problem seems to make what should be a linear algorithm into a potentially
476 exponential one. But it's only going to be bad in the case where there's
477 lots of foralls in the kinds of other foralls. Like this:
478
479 forall a : (forall b : (forall c : ...). ...). ...
480
481 This construction seems unlikely. So we'll do the inefficient, easy way
482 for now.
483
484 Note [Specialising mappers]
485 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
486 These INLINABLE pragmas are indispensable. mapType/mapCoercion are used
487 to implement zonking, and it's vital that they get specialised to the TcM
488 monad. This specialisation happens automatically (that is, without a
489 SPECIALISE pragma) as long as the definitions are INLINABLE. For example,
490 this one change made a 20% allocation difference in perf/compiler/T5030.
491
492 -}
493
494 -- | This describes how a "map" operation over a type/coercion should behave
495 data TyCoMapper env m
496 = TyCoMapper
497 { tcm_smart :: Bool -- ^ Should the new type be created with smart
498 -- constructors?
499 , tcm_tyvar :: env -> TyVar -> m Type
500 , tcm_covar :: env -> CoVar -> m Coercion
501 , tcm_hole :: env -> CoercionHole -> m Coercion
502 -- ^ What to do with coercion holes.
503 -- See Note [Coercion holes] in TyCoRep.
504
505 , tcm_tybinder :: env -> TyVar -> ArgFlag -> m (env, TyVar)
506 -- ^ The returned env is used in the extended scope
507 }
508
509 {-# INLINABLE mapType #-} -- See Note [Specialising mappers]
510 mapType :: Monad m => TyCoMapper env m -> env -> Type -> m Type
511 mapType mapper@(TyCoMapper { tcm_smart = smart, tcm_tyvar = tyvar
512 , tcm_tybinder = tybinder })
513 env ty
514 = go ty
515 where
516 go (TyVarTy tv) = tyvar env tv
517 go (AppTy t1 t2) = mkappty <$> go t1 <*> go t2
518 go t@(TyConApp _ []) = return t -- avoid allocation in this exceedingly
519 -- common case (mostly, for *)
520 go (TyConApp tc tys) = mktyconapp tc <$> mapM go tys
521 go (FunTy arg res) = FunTy <$> go arg <*> go res
522 go (ForAllTy (TvBndr tv vis) inner)
523 = do { (env', tv') <- tybinder env tv vis
524 ; inner' <- mapType mapper env' inner
525 ; return $ ForAllTy (TvBndr tv' vis) inner' }
526 go ty@(LitTy {}) = return ty
527 go (CastTy ty co) = mkcastty <$> go ty <*> mapCoercion mapper env co
528 go (CoercionTy co) = CoercionTy <$> mapCoercion mapper env co
529
530 (mktyconapp, mkappty, mkcastty)
531 | smart = (mkTyConApp, mkAppTy, mkCastTy)
532 | otherwise = (TyConApp, AppTy, CastTy)
533
534 {-# INLINABLE mapCoercion #-} -- See Note [Specialising mappers]
535 mapCoercion :: Monad m
536 => TyCoMapper env m -> env -> Coercion -> m Coercion
537 mapCoercion mapper@(TyCoMapper { tcm_smart = smart, tcm_covar = covar
538 , tcm_hole = cohole, tcm_tybinder = tybinder })
539 env co
540 = go co
541 where
542 go (Refl r ty) = Refl r <$> mapType mapper env ty
543 go (TyConAppCo r tc args)
544 = mktyconappco r tc <$> mapM go args
545 go (AppCo c1 c2) = mkappco <$> go c1 <*> go c2
546 go (ForAllCo tv kind_co co)
547 = do { kind_co' <- go kind_co
548 ; (env', tv') <- tybinder env tv Inferred
549 ; co' <- mapCoercion mapper env' co
550 ; return $ mkforallco tv' kind_co' co' }
551 -- See Note [Efficiency for mapCoercion ForAllCo case]
552 go (FunCo r c1 c2) = mkFunCo r <$> go c1 <*> go c2
553 go (CoVarCo cv) = covar env cv
554 go (AxiomInstCo ax i args)
555 = mkaxiominstco ax i <$> mapM go args
556 go (HoleCo hole) = cohole env hole
557 go (UnivCo p r t1 t2)
558 = mkunivco <$> go_prov p <*> pure r
559 <*> mapType mapper env t1 <*> mapType mapper env t2
560 go (SymCo co) = mksymco <$> go co
561 go (TransCo c1 c2) = mktransco <$> go c1 <*> go c2
562 go (AxiomRuleCo r cos) = AxiomRuleCo r <$> mapM go cos
563 go (NthCo i co) = mknthco i <$> go co
564 go (LRCo lr co) = mklrco lr <$> go co
565 go (InstCo co arg) = mkinstco <$> go co <*> go arg
566 go (CoherenceCo c1 c2) = mkcoherenceco <$> go c1 <*> go c2
567 go (KindCo co) = mkkindco <$> go co
568 go (SubCo co) = mksubco <$> go co
569
570 go_prov UnsafeCoerceProv = return UnsafeCoerceProv
571 go_prov (PhantomProv co) = PhantomProv <$> go co
572 go_prov (ProofIrrelProv co) = ProofIrrelProv <$> go co
573 go_prov p@(PluginProv _) = return p
574
575 ( mktyconappco, mkappco, mkaxiominstco, mkunivco
576 , mksymco, mktransco, mknthco, mklrco, mkinstco, mkcoherenceco
577 , mkkindco, mksubco, mkforallco)
578 | smart
579 = ( mkTyConAppCo, mkAppCo, mkAxiomInstCo, mkUnivCo
580 , mkSymCo, mkTransCo, mkNthCo, mkLRCo, mkInstCo, mkCoherenceCo
581 , mkKindCo, mkSubCo, mkForAllCo )
582 | otherwise
583 = ( TyConAppCo, AppCo, AxiomInstCo, UnivCo
584 , SymCo, TransCo, NthCo, LRCo, InstCo, CoherenceCo
585 , KindCo, SubCo, ForAllCo )
586
587 {-
588 ************************************************************************
589 * *
590 \subsection{Constructor-specific functions}
591 * *
592 ************************************************************************
593
594
595 ---------------------------------------------------------------------
596 TyVarTy
597 ~~~~~~~
598 -}
599
600 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
601 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
602 getTyVar :: String -> Type -> TyVar
603 getTyVar msg ty = case getTyVar_maybe ty of
604 Just tv -> tv
605 Nothing -> panic ("getTyVar: " ++ msg)
606
607 isTyVarTy :: Type -> Bool
608 isTyVarTy ty = isJust (getTyVar_maybe ty)
609
610 -- | Attempts to obtain the type variable underlying a 'Type'
611 getTyVar_maybe :: Type -> Maybe TyVar
612 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
613 | otherwise = repGetTyVar_maybe ty
614
615 -- | If the type is a tyvar, possibly under a cast, returns it, along
616 -- with the coercion. Thus, the co is :: kind tv ~N kind type
617 getCastedTyVar_maybe :: Type -> Maybe (TyVar, CoercionN)
618 getCastedTyVar_maybe ty | Just ty' <- coreView ty = getCastedTyVar_maybe ty'
619 getCastedTyVar_maybe (CastTy (TyVarTy tv) co) = Just (tv, co)
620 getCastedTyVar_maybe (TyVarTy tv)
621 = Just (tv, mkReflCo Nominal (tyVarKind tv))
622 getCastedTyVar_maybe _ = Nothing
623
624 -- | Attempts to obtain the type variable underlying a 'Type', without
625 -- any expansion
626 repGetTyVar_maybe :: Type -> Maybe TyVar
627 repGetTyVar_maybe (TyVarTy tv) = Just tv
628 repGetTyVar_maybe _ = Nothing
629
630 {-
631 ---------------------------------------------------------------------
632 AppTy
633 ~~~~~
634 We need to be pretty careful with AppTy to make sure we obey the
635 invariant that a TyConApp is always visibly so. mkAppTy maintains the
636 invariant: use it.
637
638 Note [Decomposing fat arrow c=>t]
639 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
640 Can we unify (a b) with (Eq a => ty)? If we do so, we end up with
641 a partial application like ((=>) Eq a) which doesn't make sense in
642 source Haskell. In contrast, we *can* unify (a b) with (t1 -> t2).
643 Here's an example (Trac #9858) of how you might do it:
644 i :: (Typeable a, Typeable b) => Proxy (a b) -> TypeRep
645 i p = typeRep p
646
647 j = i (Proxy :: Proxy (Eq Int => Int))
648 The type (Proxy (Eq Int => Int)) is only accepted with -XImpredicativeTypes,
649 but suppose we want that. But then in the call to 'i', we end
650 up decomposing (Eq Int => Int), and we definitely don't want that.
651
652 This really only applies to the type checker; in Core, '=>' and '->'
653 are the same, as are 'Constraint' and '*'. But for now I've put
654 the test in repSplitAppTy_maybe, which applies throughout, because
655 the other calls to splitAppTy are in Unify, which is also used by
656 the type checker (e.g. when matching type-function equations).
657
658 -}
659
660 -- | Applies a type to another, as in e.g. @k a@
661 mkAppTy :: Type -> Type -> Type
662 -- See Note [Respecting definitional equality], invariant (EQ1).
663 mkAppTy (CastTy fun_ty co) arg_ty
664 | ([arg_co], res_co) <- decomposePiCos (typeKind fun_ty) [arg_ty] co
665 = (fun_ty `mkAppTy` (arg_ty `mkCastTy` arg_co)) `mkCastTy` res_co
666
667 mkAppTy (TyConApp tc tys) ty2 = mkTyConApp tc (tys ++ [ty2])
668 mkAppTy ty1 ty2 = AppTy ty1 ty2
669 -- Note that the TyConApp could be an
670 -- under-saturated type synonym. GHC allows that; e.g.
671 -- type Foo k = k a -> k a
672 -- type Id x = x
673 -- foo :: Foo Id -> Foo Id
674 --
675 -- Here Id is partially applied in the type sig for Foo,
676 -- but once the type synonyms are expanded all is well
677
678 mkAppTys :: Type -> [Type] -> Type
679 mkAppTys ty1 [] = ty1
680 mkAppTys (CastTy fun_ty co) arg_tys -- much more efficient then nested mkAppTy
681 -- Why do this? See (EQ1) of
682 -- Note [Respecting definitional equality]
683 -- in TyCoRep
684 = foldl AppTy ((mkAppTys fun_ty casted_arg_tys) `mkCastTy` res_co) leftovers
685 where
686 (arg_cos, res_co) = decomposePiCos (typeKind fun_ty) arg_tys co
687 (args_to_cast, leftovers) = splitAtList arg_cos arg_tys
688 casted_arg_tys = zipWith mkCastTy args_to_cast arg_cos
689 mkAppTys (TyConApp tc tys1) tys2 = mkTyConApp tc (tys1 ++ tys2)
690 mkAppTys ty1 tys2 = foldl AppTy ty1 tys2
691
692 -------------
693 splitAppTy_maybe :: Type -> Maybe (Type, Type)
694 -- ^ Attempt to take a type application apart, whether it is a
695 -- function, type constructor, or plain type application. Note
696 -- that type family applications are NEVER unsaturated by this!
697 splitAppTy_maybe ty | Just ty' <- coreView ty
698 = splitAppTy_maybe ty'
699 splitAppTy_maybe ty = repSplitAppTy_maybe ty
700
701 -------------
702 repSplitAppTy_maybe :: HasDebugCallStack => Type -> Maybe (Type,Type)
703 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
704 -- any Core view stuff is already done
705 repSplitAppTy_maybe (FunTy ty1 ty2)
706 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
707 where
708 rep1 = getRuntimeRep ty1
709 rep2 = getRuntimeRep ty2
710
711 repSplitAppTy_maybe (AppTy ty1 ty2)
712 = Just (ty1, ty2)
713
714 repSplitAppTy_maybe (TyConApp tc tys)
715 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
716 , Just (tys', ty') <- snocView tys
717 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
718
719 repSplitAppTy_maybe _other = Nothing
720
721 -- this one doesn't braek apart (c => t).
722 -- See Note [Decomposing fat arrow c=>t]
723 -- Defined here to avoid module loops between Unify and TcType.
724 tcRepSplitAppTy_maybe :: Type -> Maybe (Type,Type)
725 -- ^ Does the AppTy split as in 'tcSplitAppTy_maybe', but assumes that
726 -- any coreView stuff is already done. Refuses to look through (c => t)
727 tcRepSplitAppTy_maybe (FunTy ty1 ty2)
728 | isConstraintKind (typeKind ty1)
729 = Nothing -- See Note [Decomposing fat arrow c=>t]
730
731 | otherwise
732 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
733 where
734 rep1 = getRuntimeRep ty1
735 rep2 = getRuntimeRep ty2
736
737 tcRepSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
738 tcRepSplitAppTy_maybe (TyConApp tc tys)
739 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
740 , Just (tys', ty') <- snocView tys
741 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
742 tcRepSplitAppTy_maybe _other = Nothing
743
744 -- | Split a type constructor application into its type constructor and
745 -- applied types. Note that this may fail in the case of a 'FunTy' with an
746 -- argument of unknown kind 'FunTy' (e.g. @FunTy (a :: k) Int@. since the kind
747 -- of @a@ isn't of the form @TYPE rep@). Consequently, you may need to zonk your
748 -- type before using this function.
749 --
750 -- If you only need the 'TyCon', consider using 'tcTyConAppTyCon_maybe'.
751 tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
752 -- Defined here to avoid module loops between Unify and TcType.
753 tcSplitTyConApp_maybe ty | Just ty' <- tcView ty = tcSplitTyConApp_maybe ty'
754 tcSplitTyConApp_maybe ty = tcRepSplitTyConApp_maybe ty
755
756 -- | Like 'tcSplitTyConApp_maybe' but doesn't look through type synonyms.
757 tcRepSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
758 -- Defined here to avoid module loops between Unify and TcType.
759 tcRepSplitTyConApp_maybe (TyConApp tc tys)
760 = Just (tc, tys)
761
762 tcRepSplitTyConApp_maybe (FunTy arg res)
763 = Just (funTyCon, [arg_rep, res_rep, arg, res])
764 where
765 arg_rep = getRuntimeRep arg
766 res_rep = getRuntimeRep res
767
768 tcRepSplitTyConApp_maybe _
769 = Nothing
770
771 -------------
772 splitAppTy :: Type -> (Type, Type)
773 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
774 -- and panics if this is not possible
775 splitAppTy ty = case splitAppTy_maybe ty of
776 Just pr -> pr
777 Nothing -> panic "splitAppTy"
778
779 -------------
780 splitAppTys :: Type -> (Type, [Type])
781 -- ^ Recursively splits a type as far as is possible, leaving a residual
782 -- type being applied to and the type arguments applied to it. Never fails,
783 -- even if that means returning an empty list of type applications.
784 splitAppTys ty = split ty ty []
785 where
786 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
787 split _ (AppTy ty arg) args = split ty ty (arg:args)
788 split _ (TyConApp tc tc_args) args
789 = let -- keep type families saturated
790 n | mightBeUnsaturatedTyCon tc = 0
791 | otherwise = tyConArity tc
792 (tc_args1, tc_args2) = splitAt n tc_args
793 in
794 (TyConApp tc tc_args1, tc_args2 ++ args)
795 split _ (FunTy ty1 ty2) args
796 = ASSERT( null args )
797 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
798 where
799 rep1 = getRuntimeRep ty1
800 rep2 = getRuntimeRep ty2
801
802 split orig_ty _ args = (orig_ty, args)
803
804 -- | Like 'splitAppTys', but doesn't look through type synonyms
805 repSplitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
806 repSplitAppTys ty = split ty []
807 where
808 split (AppTy ty arg) args = split ty (arg:args)
809 split (TyConApp tc tc_args) args
810 = let n | mightBeUnsaturatedTyCon tc = 0
811 | otherwise = tyConArity tc
812 (tc_args1, tc_args2) = splitAt n tc_args
813 in
814 (TyConApp tc tc_args1, tc_args2 ++ args)
815 split (FunTy ty1 ty2) args
816 = ASSERT( null args )
817 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
818 where
819 rep1 = getRuntimeRep ty1
820 rep2 = getRuntimeRep ty2
821
822 split ty args = (ty, args)
823
824 {-
825 LitTy
826 ~~~~~
827 -}
828
829 mkNumLitTy :: Integer -> Type
830 mkNumLitTy n = LitTy (NumTyLit n)
831
832 -- | Is this a numeric literal. We also look through type synonyms.
833 isNumLitTy :: Type -> Maybe Integer
834 isNumLitTy ty | Just ty1 <- coreView ty = isNumLitTy ty1
835 isNumLitTy (LitTy (NumTyLit n)) = Just n
836 isNumLitTy _ = Nothing
837
838 mkStrLitTy :: FastString -> Type
839 mkStrLitTy s = LitTy (StrTyLit s)
840
841 -- | Is this a symbol literal. We also look through type synonyms.
842 isStrLitTy :: Type -> Maybe FastString
843 isStrLitTy ty | Just ty1 <- coreView ty = isStrLitTy ty1
844 isStrLitTy (LitTy (StrTyLit s)) = Just s
845 isStrLitTy _ = Nothing
846
847
848 -- | Is this type a custom user error?
849 -- If so, give us the kind and the error message.
850 userTypeError_maybe :: Type -> Maybe Type
851 userTypeError_maybe t
852 = do { (tc, _kind : msg : _) <- splitTyConApp_maybe t
853 -- There may be more than 2 arguments, if the type error is
854 -- used as a type constructor (e.g. at kind `Type -> Type`).
855
856 ; guard (tyConName tc == errorMessageTypeErrorFamName)
857 ; return msg }
858
859 -- | Render a type corresponding to a user type error into a SDoc.
860 pprUserTypeErrorTy :: Type -> SDoc
861 pprUserTypeErrorTy ty =
862 case splitTyConApp_maybe ty of
863
864 -- Text "Something"
865 Just (tc,[txt])
866 | tyConName tc == typeErrorTextDataConName
867 , Just str <- isStrLitTy txt -> ftext str
868
869 -- ShowType t
870 Just (tc,[_k,t])
871 | tyConName tc == typeErrorShowTypeDataConName -> ppr t
872
873 -- t1 :<>: t2
874 Just (tc,[t1,t2])
875 | tyConName tc == typeErrorAppendDataConName ->
876 pprUserTypeErrorTy t1 <> pprUserTypeErrorTy t2
877
878 -- t1 :$$: t2
879 Just (tc,[t1,t2])
880 | tyConName tc == typeErrorVAppendDataConName ->
881 pprUserTypeErrorTy t1 $$ pprUserTypeErrorTy t2
882
883 -- An unevaluated type function
884 _ -> ppr ty
885
886
887
888
889 {-
890 ---------------------------------------------------------------------
891 FunTy
892 ~~~~~
893
894 Note [Representation of function types]
895 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
896
897 Functions (e.g. Int -> Char) are can be thought of as being applications
898 of funTyCon (known in Haskell surface syntax as (->)),
899
900 (->) :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep)
901 (a :: TYPE r1) (b :: TYPE r2).
902 a -> b -> Type
903
904 However, for efficiency's sake we represent saturated applications of (->)
905 with FunTy. For instance, the type,
906
907 (->) r1 r2 a b
908
909 is equivalent to,
910
911 FunTy (Anon a) b
912
913 Note how the RuntimeReps are implied in the FunTy representation. For this
914 reason we must be careful when recontructing the TyConApp representation (see,
915 for instance, splitTyConApp_maybe).
916
917 In the compiler we maintain the invariant that all saturated applications of
918 (->) are represented with FunTy.
919
920 See #11714.
921 -}
922
923 isFunTy :: Type -> Bool
924 isFunTy ty = isJust (splitFunTy_maybe ty)
925
926 splitFunTy :: Type -> (Type, Type)
927 -- ^ Attempts to extract the argument and result types from a type, and
928 -- panics if that is not possible. See also 'splitFunTy_maybe'
929 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
930 splitFunTy (FunTy arg res) = (arg, res)
931 splitFunTy other = pprPanic "splitFunTy" (ppr other)
932
933 splitFunTy_maybe :: Type -> Maybe (Type, Type)
934 -- ^ Attempts to extract the argument and result types from a type
935 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
936 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
937 splitFunTy_maybe _ = Nothing
938
939 splitFunTys :: Type -> ([Type], Type)
940 splitFunTys ty = split [] ty ty
941 where
942 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
943 split args _ (FunTy arg res) = split (arg:args) res res
944 split args orig_ty _ = (reverse args, orig_ty)
945
946 funResultTy :: Type -> Type
947 -- ^ Extract the function result type and panic if that is not possible
948 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
949 funResultTy (FunTy _ res) = res
950 funResultTy ty = pprPanic "funResultTy" (ppr ty)
951
952 funArgTy :: Type -> Type
953 -- ^ Extract the function argument type and panic if that is not possible
954 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
955 funArgTy (FunTy arg _res) = arg
956 funArgTy ty = pprPanic "funArgTy" (ppr ty)
957
958 piResultTy :: HasDebugCallStack => Type -> Type -> Type
959 piResultTy ty arg = case piResultTy_maybe ty arg of
960 Just res -> res
961 Nothing -> pprPanic "piResultTy" (ppr ty $$ ppr arg)
962
963 piResultTy_maybe :: Type -> Type -> Maybe Type
964
965 -- ^ Just like 'piResultTys' but for a single argument
966 -- Try not to iterate 'piResultTy', because it's inefficient to substitute
967 -- one variable at a time; instead use 'piResultTys"
968 piResultTy_maybe ty arg
969 | Just ty' <- coreView ty = piResultTy_maybe ty' arg
970
971 | FunTy _ res <- ty
972 = Just res
973
974 | ForAllTy (TvBndr tv _) res <- ty
975 = let empty_subst = mkEmptyTCvSubst $ mkInScopeSet $
976 tyCoVarsOfTypes [arg,res]
977 in Just (substTy (extendTvSubst empty_subst tv arg) res)
978
979 | otherwise
980 = Nothing
981
982 -- | (piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn)
983 -- where f :: f_ty
984 -- 'piResultTys' is interesting because:
985 -- 1. 'f_ty' may have more for-alls than there are args
986 -- 2. Less obviously, it may have fewer for-alls
987 -- For case 2. think of:
988 -- piResultTys (forall a.a) [forall b.b, Int]
989 -- This really can happen, but only (I think) in situations involving
990 -- undefined. For example:
991 -- undefined :: forall a. a
992 -- Term: undefined @(forall b. b->b) @Int
993 -- This term should have type (Int -> Int), but notice that
994 -- there are more type args than foralls in 'undefined's type.
995
996 -- If you edit this function, you may need to update the GHC formalism
997 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
998
999 -- This is a heavily used function (e.g. from typeKind),
1000 -- so we pay attention to efficiency, especially in the special case
1001 -- where there are no for-alls so we are just dropping arrows from
1002 -- a function type/kind.
1003 piResultTys :: HasDebugCallStack => Type -> [Type] -> Type
1004 piResultTys ty [] = ty
1005 piResultTys ty orig_args@(arg:args)
1006 | Just ty' <- coreView ty
1007 = piResultTys ty' orig_args
1008
1009 | FunTy _ res <- ty
1010 = piResultTys res args
1011
1012 | ForAllTy (TvBndr tv _) res <- ty
1013 = go (extendVarEnv emptyTvSubstEnv tv arg) res args
1014
1015 | otherwise
1016 = pprPanic "piResultTys1" (ppr ty $$ ppr orig_args)
1017 where
1018 in_scope = mkInScopeSet (tyCoVarsOfTypes (ty:orig_args))
1019
1020 go :: TvSubstEnv -> Type -> [Type] -> Type
1021 go tv_env ty [] = substTy (mkTvSubst in_scope tv_env) ty
1022
1023 go tv_env ty all_args@(arg:args)
1024 | Just ty' <- coreView ty
1025 = go tv_env ty' all_args
1026
1027 | FunTy _ res <- ty
1028 = go tv_env res args
1029
1030 | ForAllTy (TvBndr tv _) res <- ty
1031 = go (extendVarEnv tv_env tv arg) res args
1032
1033 | TyVarTy tv <- ty
1034 , Just ty' <- lookupVarEnv tv_env tv
1035 -- Deals with piResultTys (forall a. a) [forall b.b, Int]
1036 = piResultTys ty' all_args
1037
1038 | otherwise
1039 = pprPanic "piResultTys2" (ppr ty $$ ppr orig_args $$ ppr all_args)
1040
1041 applyTysX :: [TyVar] -> Type -> [Type] -> Type
1042 -- applyTyxX beta-reduces (/\tvs. body_ty) arg_tys
1043 -- Assumes that (/\tvs. body_ty) is closed
1044 applyTysX tvs body_ty arg_tys
1045 = ASSERT2( arg_tys `lengthAtLeast` n_tvs, pp_stuff )
1046 ASSERT2( tyCoVarsOfType body_ty `subVarSet` mkVarSet tvs, pp_stuff )
1047 mkAppTys (substTyWith tvs (take n_tvs arg_tys) body_ty)
1048 (drop n_tvs arg_tys)
1049 where
1050 pp_stuff = vcat [ppr tvs, ppr body_ty, ppr arg_tys]
1051 n_tvs = length tvs
1052
1053 {-
1054 ---------------------------------------------------------------------
1055 TyConApp
1056 ~~~~~~~~
1057 -}
1058
1059 -- | A key function: builds a 'TyConApp' or 'FunTy' as appropriate to
1060 -- its arguments. Applies its arguments to the constructor from left to right.
1061 mkTyConApp :: TyCon -> [Type] -> Type
1062 mkTyConApp tycon tys
1063 | isFunTyCon tycon
1064 , [_rep1,_rep2,ty1,ty2] <- tys
1065 = FunTy ty1 ty2
1066
1067 | otherwise
1068 = TyConApp tycon tys
1069
1070 -- splitTyConApp "looks through" synonyms, because they don't
1071 -- mean a distinct type, but all other type-constructor applications
1072 -- including functions are returned as Just ..
1073
1074 -- | Retrieve the tycon heading this type, if there is one. Does /not/
1075 -- look through synonyms.
1076 tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
1077 tyConAppTyConPicky_maybe (TyConApp tc _) = Just tc
1078 tyConAppTyConPicky_maybe (FunTy {}) = Just funTyCon
1079 tyConAppTyConPicky_maybe _ = Nothing
1080
1081
1082 -- | The same as @fst . splitTyConApp@
1083 tyConAppTyCon_maybe :: Type -> Maybe TyCon
1084 tyConAppTyCon_maybe ty | Just ty' <- coreView ty = tyConAppTyCon_maybe ty'
1085 tyConAppTyCon_maybe (TyConApp tc _) = Just tc
1086 tyConAppTyCon_maybe (FunTy {}) = Just funTyCon
1087 tyConAppTyCon_maybe _ = Nothing
1088
1089 tyConAppTyCon :: Type -> TyCon
1090 tyConAppTyCon ty = tyConAppTyCon_maybe ty `orElse` pprPanic "tyConAppTyCon" (ppr ty)
1091
1092 -- | The same as @snd . splitTyConApp@
1093 tyConAppArgs_maybe :: Type -> Maybe [Type]
1094 tyConAppArgs_maybe ty | Just ty' <- coreView ty = tyConAppArgs_maybe ty'
1095 tyConAppArgs_maybe (TyConApp _ tys) = Just tys
1096 tyConAppArgs_maybe (FunTy arg res)
1097 | Just rep1 <- getRuntimeRep_maybe arg
1098 , Just rep2 <- getRuntimeRep_maybe res
1099 = Just [rep1, rep2, arg, res]
1100 tyConAppArgs_maybe _ = Nothing
1101
1102 tyConAppArgs :: Type -> [Type]
1103 tyConAppArgs ty = tyConAppArgs_maybe ty `orElse` pprPanic "tyConAppArgs" (ppr ty)
1104
1105 tyConAppArgN :: Int -> Type -> Type
1106 -- Executing Nth
1107 tyConAppArgN n ty
1108 = case tyConAppArgs_maybe ty of
1109 Just tys -> ASSERT2( tys `lengthExceeds` n, ppr n <+> ppr tys ) tys `getNth` n
1110 Nothing -> pprPanic "tyConAppArgN" (ppr n <+> ppr ty)
1111
1112 -- | Attempts to tease a type apart into a type constructor and the application
1113 -- of a number of arguments to that constructor. Panics if that is not possible.
1114 -- See also 'splitTyConApp_maybe'
1115 splitTyConApp :: Type -> (TyCon, [Type])
1116 splitTyConApp ty = case splitTyConApp_maybe ty of
1117 Just stuff -> stuff
1118 Nothing -> pprPanic "splitTyConApp" (ppr ty)
1119
1120 -- | Attempts to tease a type apart into a type constructor and the application
1121 -- of a number of arguments to that constructor
1122 splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1123 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
1124 splitTyConApp_maybe ty = repSplitTyConApp_maybe ty
1125
1126 -- | Like 'splitTyConApp_maybe', but doesn't look through synonyms. This
1127 -- assumes the synonyms have already been dealt with.
1128 repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1129 repSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
1130 repSplitTyConApp_maybe (FunTy arg res)
1131 | Just arg_rep <- getRuntimeRep_maybe arg
1132 , Just res_rep <- getRuntimeRep_maybe res
1133 = Just (funTyCon, [arg_rep, res_rep, arg, res])
1134 repSplitTyConApp_maybe _ = Nothing
1135
1136 -- | Attempts to tease a list type apart and gives the type of the elements if
1137 -- successful (looks through type synonyms)
1138 splitListTyConApp_maybe :: Type -> Maybe Type
1139 splitListTyConApp_maybe ty = case splitTyConApp_maybe ty of
1140 Just (tc,[e]) | tc == listTyCon -> Just e
1141 _other -> Nothing
1142
1143 newTyConInstRhs :: TyCon -> [Type] -> Type
1144 -- ^ Unwrap one 'layer' of newtype on a type constructor and its
1145 -- arguments, using an eta-reduced version of the @newtype@ if possible.
1146 -- This requires tys to have at least @newTyConInstArity tycon@ elements.
1147 newTyConInstRhs tycon tys
1148 = ASSERT2( tvs `leLength` tys, ppr tycon $$ ppr tys $$ ppr tvs )
1149 applyTysX tvs rhs tys
1150 where
1151 (tvs, rhs) = newTyConEtadRhs tycon
1152
1153 {-
1154 ---------------------------------------------------------------------
1155 CastTy
1156 ~~~~~~
1157 A casted type has its *kind* casted into something new.
1158
1159 -}
1160
1161 splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
1162 splitCastTy_maybe ty | Just ty' <- coreView ty = splitCastTy_maybe ty'
1163 splitCastTy_maybe (CastTy ty co) = Just (ty, co)
1164 splitCastTy_maybe _ = Nothing
1165
1166 -- | Make a 'CastTy'. The Coercion must be nominal. Checks the
1167 -- Coercion for reflexivity, dropping it if it's reflexive.
1168 -- See Note [Respecting definitional equality] in TyCoRep
1169 mkCastTy :: Type -> Coercion -> Type
1170 mkCastTy ty co | isReflexiveCo co = ty -- (EQ2) from the Note
1171 -- NB: Do the slow check here. This is important to keep the splitXXX
1172 -- functions working properly. Otherwise, we may end up with something
1173 -- like (((->) |> something_reflexive_but_not_obviously_so) biz baz)
1174 -- fails under splitFunTy_maybe. This happened with the cheaper check
1175 -- in test dependent/should_compile/dynamic-paper.
1176
1177 mkCastTy (CastTy ty co1) co2 = mkCastTy ty (co1 `mkTransCo` co2) -- (EQ3) from the Note
1178 -- call mkCastTy again for the reflexivity check
1179 mkCastTy ty co = CastTy ty co
1180
1181 tyConBindersTyBinders :: [TyConBinder] -> [TyBinder]
1182 -- Return the tyConBinders in TyBinder form
1183 tyConBindersTyBinders = map to_tyb
1184 where
1185 to_tyb (TvBndr tv (NamedTCB vis)) = Named (TvBndr tv vis)
1186 to_tyb (TvBndr tv AnonTCB) = Anon (tyVarKind tv)
1187
1188 {-
1189 --------------------------------------------------------------------
1190 CoercionTy
1191 ~~~~~~~~~~
1192 CoercionTy allows us to inject coercions into types. A CoercionTy
1193 should appear only in the right-hand side of an application.
1194 -}
1195
1196 mkCoercionTy :: Coercion -> Type
1197 mkCoercionTy = CoercionTy
1198
1199 isCoercionTy :: Type -> Bool
1200 isCoercionTy (CoercionTy _) = True
1201 isCoercionTy _ = False
1202
1203 isCoercionTy_maybe :: Type -> Maybe Coercion
1204 isCoercionTy_maybe (CoercionTy co) = Just co
1205 isCoercionTy_maybe _ = Nothing
1206
1207 stripCoercionTy :: Type -> Coercion
1208 stripCoercionTy (CoercionTy co) = co
1209 stripCoercionTy ty = pprPanic "stripCoercionTy" (ppr ty)
1210
1211 {-
1212 ---------------------------------------------------------------------
1213 SynTy
1214 ~~~~~
1215
1216 Notes on type synonyms
1217 ~~~~~~~~~~~~~~~~~~~~~~
1218 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
1219 to return type synonyms wherever possible. Thus
1220
1221 type Foo a = a -> a
1222
1223 we want
1224 splitFunTys (a -> Foo a) = ([a], Foo a)
1225 not ([a], a -> a)
1226
1227 The reason is that we then get better (shorter) type signatures in
1228 interfaces. Notably this plays a role in tcTySigs in TcBinds.hs.
1229
1230
1231 ---------------------------------------------------------------------
1232 ForAllTy
1233 ~~~~~~~~
1234 -}
1235
1236 -- | Make a dependent forall over an Inferred (as opposed to Specified)
1237 -- variable
1238 mkInvForAllTy :: TyVar -> Type -> Type
1239 mkInvForAllTy tv ty = ASSERT( isTyVar tv )
1240 ForAllTy (TvBndr tv Inferred) ty
1241
1242 -- | Like mkForAllTys, but assumes all variables are dependent and Inferred,
1243 -- a common case
1244 mkInvForAllTys :: [TyVar] -> Type -> Type
1245 mkInvForAllTys tvs ty = ASSERT( all isTyVar tvs )
1246 foldr mkInvForAllTy ty tvs
1247
1248 -- | Like mkForAllTys, but assumes all variables are dependent and specified,
1249 -- a common case
1250 mkSpecForAllTys :: [TyVar] -> Type -> Type
1251 mkSpecForAllTys tvs = ASSERT( all isTyVar tvs )
1252 mkForAllTys [ TvBndr tv Specified | tv <- tvs ]
1253
1254 -- | Like mkForAllTys, but assumes all variables are dependent and visible
1255 mkVisForAllTys :: [TyVar] -> Type -> Type
1256 mkVisForAllTys tvs = ASSERT( all isTyVar tvs )
1257 mkForAllTys [ TvBndr tv Required | tv <- tvs ]
1258
1259 mkLamType :: Var -> Type -> Type
1260 -- ^ Makes a @(->)@ type or an implicit forall type, depending
1261 -- on whether it is given a type variable or a term variable.
1262 -- This is used, for example, when producing the type of a lambda.
1263 -- Always uses Inferred binders.
1264 mkLamTypes :: [Var] -> Type -> Type
1265 -- ^ 'mkLamType' for multiple type or value arguments
1266
1267 mkLamType v ty
1268 | isTyVar v = ForAllTy (TvBndr v Inferred) ty
1269 | otherwise = FunTy (varType v) ty
1270
1271 mkLamTypes vs ty = foldr mkLamType ty vs
1272
1273 -- | Given a list of type-level vars and a result kind,
1274 -- makes TyBinders, preferring anonymous binders
1275 -- if the variable is, in fact, not dependent.
1276 -- e.g. mkTyConBindersPreferAnon [(k:*),(b:k),(c:k)] (k->k)
1277 -- We want (k:*) Named, (a;k) Anon, (c:k) Anon
1278 --
1279 -- All binders are /visible/.
1280 mkTyConBindersPreferAnon :: [TyVar] -> Type -> [TyConBinder]
1281 mkTyConBindersPreferAnon vars inner_ty = fst (go vars)
1282 where
1283 go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars
1284 go [] = ([], tyCoVarsOfType inner_ty)
1285 go (v:vs) | v `elemVarSet` fvs
1286 = ( TvBndr v (NamedTCB Required) : binders
1287 , fvs `delVarSet` v `unionVarSet` kind_vars )
1288 | otherwise
1289 = ( TvBndr v AnonTCB : binders
1290 , fvs `unionVarSet` kind_vars )
1291 where
1292 (binders, fvs) = go vs
1293 kind_vars = tyCoVarsOfType $ tyVarKind v
1294
1295 -- | Take a ForAllTy apart, returning the list of tyvars and the result type.
1296 -- This always succeeds, even if it returns only an empty list. Note that the
1297 -- result type returned may have free variables that were bound by a forall.
1298 splitForAllTys :: Type -> ([TyVar], Type)
1299 splitForAllTys ty = split ty ty []
1300 where
1301 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
1302 split _ (ForAllTy (TvBndr tv _) ty) tvs = split ty ty (tv:tvs)
1303 split orig_ty _ tvs = (reverse tvs, orig_ty)
1304
1305 -- | Like 'splitPiTys' but split off only /named/ binders.
1306 splitForAllTyVarBndrs :: Type -> ([TyVarBinder], Type)
1307 splitForAllTyVarBndrs ty = split ty ty []
1308 where
1309 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1310 split _ (ForAllTy b res) bs = split res res (b:bs)
1311 split orig_ty _ bs = (reverse bs, orig_ty)
1312 {-# INLINE splitForAllTyVarBndrs #-}
1313
1314 -- | Checks whether this is a proper forall (with a named binder)
1315 isForAllTy :: Type -> Bool
1316 isForAllTy ty | Just ty' <- coreView ty = isForAllTy ty'
1317 isForAllTy (ForAllTy {}) = True
1318 isForAllTy _ = False
1319
1320 -- | Is this a function or forall?
1321 isPiTy :: Type -> Bool
1322 isPiTy ty | Just ty' <- coreView ty = isForAllTy ty'
1323 isPiTy (ForAllTy {}) = True
1324 isPiTy (FunTy {}) = True
1325 isPiTy _ = False
1326
1327 -- | Take a forall type apart, or panics if that is not possible.
1328 splitForAllTy :: Type -> (TyVar, Type)
1329 splitForAllTy ty
1330 | Just answer <- splitForAllTy_maybe ty = answer
1331 | otherwise = pprPanic "splitForAllTy" (ppr ty)
1332
1333 -- | Drops all ForAllTys
1334 dropForAlls :: Type -> Type
1335 dropForAlls ty = go ty
1336 where
1337 go ty | Just ty' <- coreView ty = go ty'
1338 go (ForAllTy _ res) = go res
1339 go res = res
1340
1341 -- | Attempts to take a forall type apart, but only if it's a proper forall,
1342 -- with a named binder
1343 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
1344 splitForAllTy_maybe ty = go ty
1345 where
1346 go ty | Just ty' <- coreView ty = go ty'
1347 go (ForAllTy (TvBndr tv _) ty) = Just (tv, ty)
1348 go _ = Nothing
1349
1350 -- | Attempts to take a forall type apart; works with proper foralls and
1351 -- functions
1352 splitPiTy_maybe :: Type -> Maybe (TyBinder, Type)
1353 splitPiTy_maybe ty = go ty
1354 where
1355 go ty | Just ty' <- coreView ty = go ty'
1356 go (ForAllTy bndr ty) = Just (Named bndr, ty)
1357 go (FunTy arg res) = Just (Anon arg, res)
1358 go _ = Nothing
1359
1360 -- | Takes a forall type apart, or panics
1361 splitPiTy :: Type -> (TyBinder, Type)
1362 splitPiTy ty
1363 | Just answer <- splitPiTy_maybe ty = answer
1364 | otherwise = pprPanic "splitPiTy" (ppr ty)
1365
1366 -- | Split off all TyBinders to a type, splitting both proper foralls
1367 -- and functions
1368 splitPiTys :: Type -> ([TyBinder], Type)
1369 splitPiTys ty = split ty ty
1370 where
1371 split orig_ty ty | Just ty' <- coreView ty = split orig_ty ty'
1372 split _ (ForAllTy b res) = let (bs, ty) = split res res
1373 in (Named b : bs, ty)
1374 split _ (FunTy arg res) = let (bs, ty) = split res res
1375 in (Anon arg : bs, ty)
1376 split orig_ty _ = ([], orig_ty)
1377
1378 -- Like splitPiTys, but returns only *invisible* binders, including constraints
1379 -- Stops at the first visible binder
1380 splitPiTysInvisible :: Type -> ([TyBinder], Type)
1381 splitPiTysInvisible ty = split ty ty []
1382 where
1383 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1384 split _ (ForAllTy b@(TvBndr _ vis) res) bs
1385 | isInvisibleArgFlag vis = split res res (Named b : bs)
1386 split _ (FunTy arg res) bs
1387 | isPredTy arg = split res res (Anon arg : bs)
1388 split orig_ty _ bs = (reverse bs, orig_ty)
1389
1390 -- | Given a tycon and its arguments, filters out any invisible arguments
1391 filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
1392 filterOutInvisibleTypes tc tys = snd $ partitionInvisibles tc id tys
1393
1394 -- | Given a tycon and a list of things (which correspond to arguments),
1395 -- partitions the things into
1396 -- Inferred or Specified ones and
1397 -- Required ones
1398 -- The callback function is necessary for this scenario:
1399 --
1400 -- > T :: forall k. k -> k
1401 -- > partitionInvisibles T [forall m. m -> m -> m, S, R, Q]
1402 --
1403 -- After substituting, we get
1404 --
1405 -- > T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n
1406 --
1407 -- Thus, the first argument is invisible, @S@ is visible, @R@ is invisible again,
1408 -- and @Q@ is visible.
1409 --
1410 -- If you're absolutely sure that your tycon's kind doesn't end in a variable,
1411 -- it's OK if the callback function panics, as that's the only time it's
1412 -- consulted.
1413 partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])
1414 partitionInvisibles tc get_ty = go emptyTCvSubst (tyConKind tc)
1415 where
1416 go _ _ [] = ([], [])
1417 go subst (ForAllTy (TvBndr tv vis) res_ki) (x:xs)
1418 | isVisibleArgFlag vis = second (x :) (go subst' res_ki xs)
1419 | otherwise = first (x :) (go subst' res_ki xs)
1420 where
1421 subst' = extendTvSubst subst tv (get_ty x)
1422 go subst (TyVarTy tv) xs
1423 | Just ki <- lookupTyVar subst tv = go subst ki xs
1424 go _ _ xs = ([], xs) -- something is ill-kinded. But this can happen
1425 -- when printing errors. Assume everything is visible.
1426
1427 -- @isTauTy@ tests if a type has no foralls
1428 isTauTy :: Type -> Bool
1429 isTauTy ty | Just ty' <- coreView ty = isTauTy ty'
1430 isTauTy (TyVarTy _) = True
1431 isTauTy (LitTy {}) = True
1432 isTauTy (TyConApp tc tys) = all isTauTy tys && isTauTyCon tc
1433 isTauTy (AppTy a b) = isTauTy a && isTauTy b
1434 isTauTy (FunTy a b) = isTauTy a && isTauTy b
1435 isTauTy (ForAllTy {}) = False
1436 isTauTy (CastTy ty _) = isTauTy ty
1437 isTauTy (CoercionTy _) = False -- Not sure about this
1438
1439 {-
1440 %************************************************************************
1441 %* *
1442 TyBinders
1443 %* *
1444 %************************************************************************
1445 -}
1446
1447 -- | Make an anonymous binder
1448 mkAnonBinder :: Type -> TyBinder
1449 mkAnonBinder = Anon
1450
1451 -- | Does this binder bind a variable that is /not/ erased? Returns
1452 -- 'True' for anonymous binders.
1453 isAnonTyBinder :: TyBinder -> Bool
1454 isAnonTyBinder (Named {}) = False
1455 isAnonTyBinder (Anon {}) = True
1456
1457 isNamedTyBinder :: TyBinder -> Bool
1458 isNamedTyBinder (Named {}) = True
1459 isNamedTyBinder (Anon {}) = False
1460
1461 tyBinderVar_maybe :: TyBinder -> Maybe TyVar
1462 tyBinderVar_maybe (Named tv) = Just $ binderVar tv
1463 tyBinderVar_maybe _ = Nothing
1464
1465 tyBinderType :: TyBinder -> Type
1466 -- Barely used
1467 tyBinderType (Named tvb) = binderKind tvb
1468 tyBinderType (Anon ty) = ty
1469
1470 -- | Extract a relevant type, if there is one.
1471 binderRelevantType_maybe :: TyBinder -> Maybe Type
1472 binderRelevantType_maybe (Named {}) = Nothing
1473 binderRelevantType_maybe (Anon ty) = Just ty
1474
1475 -- | Like 'maybe', but for binders.
1476 caseBinder :: TyBinder -- ^ binder to scrutinize
1477 -> (TyVarBinder -> a) -- ^ named case
1478 -> (Type -> a) -- ^ anonymous case
1479 -> a
1480 caseBinder (Named v) f _ = f v
1481 caseBinder (Anon t) _ d = d t
1482
1483
1484 {-
1485 %************************************************************************
1486 %* *
1487 Pred
1488 * *
1489 ************************************************************************
1490
1491 Predicates on PredType
1492
1493 Note [isPredTy complications]
1494 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1495 You would think that we could define
1496 isPredTy ty = isConstraintKind (typeKind ty)
1497 But there are a number of complications:
1498
1499 * isPredTy is used when printing types, which can happen in debug
1500 printing during type checking of not-fully-zonked types. So it's
1501 not cool to say isConstraintKind (typeKind ty) because, absent
1502 zonking, the type might be ill-kinded, and typeKind crashes. Hence the
1503 rather tiresome story here
1504
1505 * isPredTy must return "True" to *unlifted* coercions, such as (t1 ~# t2)
1506 and (t1 ~R# t2), which are not of kind Constraint! Currently they are
1507 of kind #.
1508
1509 * If we do form the type '(C a => C [a]) => blah', then we'd like to
1510 print it as such. But that means that isPredTy must return True for
1511 (C a => C [a]). Admittedly that type is illegal in Haskell, but we
1512 want to print it nicely in error messages.
1513 -}
1514
1515 -- | Is the type suitable to classify a given/wanted in the typechecker?
1516 isPredTy :: Type -> Bool
1517 -- See Note [isPredTy complications]
1518 isPredTy ty = go ty []
1519 where
1520 go :: Type -> [KindOrType] -> Bool
1521 go (AppTy ty1 ty2) args = go ty1 (ty2 : args)
1522 go (TyVarTy tv) args = go_k (tyVarKind tv) args
1523 go (TyConApp tc tys) args = ASSERT( null args ) -- TyConApp invariant
1524 go_tc tc tys
1525 go (FunTy arg res) []
1526 | isPredTy arg = isPredTy res -- (Eq a => C a)
1527 | otherwise = False -- (Int -> Bool)
1528 go (ForAllTy _ ty) [] = go ty []
1529 go (CastTy _ co) args = go_k (pSnd (coercionKind co)) args
1530 go _ _ = False
1531
1532 go_tc :: TyCon -> [KindOrType] -> Bool
1533 go_tc tc args
1534 | tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1535 = args `lengthIs` 4 -- ~# and ~R# sadly have result kind #
1536 -- not Constraint; but we still want
1537 -- isPredTy to reply True.
1538 | otherwise = go_k (tyConKind tc) args
1539
1540 go_k :: Kind -> [KindOrType] -> Bool
1541 -- True <=> ('k' applied to 'kts') = Constraint
1542 go_k k [] = isConstraintKind k
1543 go_k k (arg:args) = case piResultTy_maybe k arg of
1544 Just k' -> go_k k' args
1545 Nothing -> WARN( True, text "isPredTy" <+> ppr ty )
1546 False
1547 -- This last case shouldn't happen under most circumstances. It can
1548 -- occur if we call isPredTy during kind checking, especially if one
1549 -- of the following happens:
1550 --
1551 -- 1. There is actually a kind error. Example in which this showed up:
1552 -- polykinds/T11399
1553 --
1554 -- 2. A type constructor application appears to be oversaturated. An
1555 -- example of this occurred in GHC Trac #13187:
1556 --
1557 -- {-# LANGUAGE PolyKinds #-}
1558 -- type Const a b = b
1559 -- f :: Const Int (,) Bool Char -> Char
1560 --
1561 -- We call isPredTy (Const k1 k2 Int (,) Bool Char
1562 -- where k1,k2 are unification variables that have been
1563 -- unified to *, and (*->*->*) resp, /but not zonked/.
1564 -- This shows that isPredTy can report a false negative
1565 -- if a constraint is similarly oversaturated, but
1566 -- it's hard to do better than isPredTy currently does without
1567 -- zonking, so we punt on such cases for now. This only happens
1568 -- during debug-printing, so it doesn't matter.
1569
1570 isClassPred, isEqPred, isNomEqPred, isIPPred :: PredType -> Bool
1571 isClassPred ty = case tyConAppTyCon_maybe ty of
1572 Just tyCon | isClassTyCon tyCon -> True
1573 _ -> False
1574 isEqPred ty = case tyConAppTyCon_maybe ty of
1575 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1576 || tyCon `hasKey` eqReprPrimTyConKey
1577 _ -> False
1578
1579 isNomEqPred ty = case tyConAppTyCon_maybe ty of
1580 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1581 _ -> False
1582
1583 isIPPred ty = case tyConAppTyCon_maybe ty of
1584 Just tc -> isIPTyCon tc
1585 _ -> False
1586
1587 isIPTyCon :: TyCon -> Bool
1588 isIPTyCon tc = tc `hasKey` ipClassKey
1589 -- Class and its corresponding TyCon have the same Unique
1590
1591 isIPClass :: Class -> Bool
1592 isIPClass cls = cls `hasKey` ipClassKey
1593
1594 isCTupleClass :: Class -> Bool
1595 isCTupleClass cls = isTupleTyCon (classTyCon cls)
1596
1597 isIPPred_maybe :: Type -> Maybe (FastString, Type)
1598 isIPPred_maybe ty =
1599 do (tc,[t1,t2]) <- splitTyConApp_maybe ty
1600 guard (isIPTyCon tc)
1601 x <- isStrLitTy t1
1602 return (x,t2)
1603
1604 {-
1605 Make PredTypes
1606
1607 --------------------- Equality types ---------------------------------
1608 -}
1609
1610 -- | Makes a lifted equality predicate at the given role
1611 mkPrimEqPredRole :: Role -> Type -> Type -> PredType
1612 mkPrimEqPredRole Nominal = mkPrimEqPred
1613 mkPrimEqPredRole Representational = mkReprPrimEqPred
1614 mkPrimEqPredRole Phantom = panic "mkPrimEqPredRole phantom"
1615
1616 -- | Creates a primitive type equality predicate.
1617 -- Invariant: the types are not Coercions
1618 mkPrimEqPred :: Type -> Type -> Type
1619 mkPrimEqPred ty1 ty2
1620 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1621 where
1622 k1 = typeKind ty1
1623 k2 = typeKind ty2
1624
1625 -- | Creates a primite type equality predicate with explicit kinds
1626 mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1627 mkHeteroPrimEqPred k1 k2 ty1 ty2 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1628
1629 -- | Creates a primitive representational type equality predicate
1630 -- with explicit kinds
1631 mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1632 mkHeteroReprPrimEqPred k1 k2 ty1 ty2
1633 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1634
1635 -- | Try to split up a coercion type into the types that it coerces
1636 splitCoercionType_maybe :: Type -> Maybe (Type, Type)
1637 splitCoercionType_maybe ty
1638 = do { (tc, [_, _, ty1, ty2]) <- splitTyConApp_maybe ty
1639 ; guard $ tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1640 ; return (ty1, ty2) }
1641
1642 mkReprPrimEqPred :: Type -> Type -> Type
1643 mkReprPrimEqPred ty1 ty2
1644 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1645 where
1646 k1 = typeKind ty1
1647 k2 = typeKind ty2
1648
1649 equalityTyCon :: Role -> TyCon
1650 equalityTyCon Nominal = eqPrimTyCon
1651 equalityTyCon Representational = eqReprPrimTyCon
1652 equalityTyCon Phantom = eqPhantPrimTyCon
1653
1654 -- --------------------- Dictionary types ---------------------------------
1655
1656 mkClassPred :: Class -> [Type] -> PredType
1657 mkClassPred clas tys = TyConApp (classTyCon clas) tys
1658
1659 isDictTy :: Type -> Bool
1660 isDictTy = isClassPred
1661
1662 isDictLikeTy :: Type -> Bool
1663 -- Note [Dictionary-like types]
1664 isDictLikeTy ty | Just ty' <- coreView ty = isDictLikeTy ty'
1665 isDictLikeTy ty = case splitTyConApp_maybe ty of
1666 Just (tc, tys) | isClassTyCon tc -> True
1667 | isTupleTyCon tc -> all isDictLikeTy tys
1668 _other -> False
1669
1670 {-
1671 Note [Dictionary-like types]
1672 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1673 Being "dictionary-like" means either a dictionary type or a tuple thereof.
1674 In GHC 6.10 we build implication constraints which construct such tuples,
1675 and if we land up with a binding
1676 t :: (C [a], Eq [a])
1677 t = blah
1678 then we want to treat t as cheap under "-fdicts-cheap" for example.
1679 (Implication constraints are normally inlined, but sadly not if the
1680 occurrence is itself inside an INLINE function! Until we revise the
1681 handling of implication constraints, that is.) This turned out to
1682 be important in getting good arities in DPH code. Example:
1683
1684 class C a
1685 class D a where { foo :: a -> a }
1686 instance C a => D (Maybe a) where { foo x = x }
1687
1688 bar :: (C a, C b) => a -> b -> (Maybe a, Maybe b)
1689 {-# INLINE bar #-}
1690 bar x y = (foo (Just x), foo (Just y))
1691
1692 Then 'bar' should jolly well have arity 4 (two dicts, two args), but
1693 we ended up with something like
1694 bar = __inline_me__ (\d1,d2. let t :: (D (Maybe a), D (Maybe b)) = ...
1695 in \x,y. <blah>)
1696
1697 This is all a bit ad-hoc; eg it relies on knowing that implication
1698 constraints build tuples.
1699
1700
1701 Decomposing PredType
1702 -}
1703
1704 -- | A choice of equality relation. This is separate from the type 'Role'
1705 -- because 'Phantom' does not define a (non-trivial) equality relation.
1706 data EqRel = NomEq | ReprEq
1707 deriving (Eq, Ord)
1708
1709 instance Outputable EqRel where
1710 ppr NomEq = text "nominal equality"
1711 ppr ReprEq = text "representational equality"
1712
1713 eqRelRole :: EqRel -> Role
1714 eqRelRole NomEq = Nominal
1715 eqRelRole ReprEq = Representational
1716
1717 data PredTree = ClassPred Class [Type]
1718 | EqPred EqRel Type Type
1719 | IrredPred PredType
1720 -- NB: There is no TuplePred case
1721 -- Tuple predicates like (Eq a, Ord b) are just treated
1722 -- as ClassPred, as if we had a tuple class with two superclasses
1723 -- class (c1, c2) => (%,%) c1 c2
1724
1725 classifyPredType :: PredType -> PredTree
1726 classifyPredType ev_ty = case splitTyConApp_maybe ev_ty of
1727 Just (tc, [_, _, ty1, ty2])
1728 | tc `hasKey` eqReprPrimTyConKey -> EqPred ReprEq ty1 ty2
1729 | tc `hasKey` eqPrimTyConKey -> EqPred NomEq ty1 ty2
1730 Just (tc, tys)
1731 | Just clas <- tyConClass_maybe tc -> ClassPred clas tys
1732 _ -> IrredPred ev_ty
1733
1734 getClassPredTys :: HasDebugCallStack => PredType -> (Class, [Type])
1735 getClassPredTys ty = case getClassPredTys_maybe ty of
1736 Just (clas, tys) -> (clas, tys)
1737 Nothing -> pprPanic "getClassPredTys" (ppr ty)
1738
1739 getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
1740 getClassPredTys_maybe ty = case splitTyConApp_maybe ty of
1741 Just (tc, tys) | Just clas <- tyConClass_maybe tc -> Just (clas, tys)
1742 _ -> Nothing
1743
1744 getEqPredTys :: PredType -> (Type, Type)
1745 getEqPredTys ty
1746 = case splitTyConApp_maybe ty of
1747 Just (tc, [_, _, ty1, ty2])
1748 | tc `hasKey` eqPrimTyConKey
1749 || tc `hasKey` eqReprPrimTyConKey
1750 -> (ty1, ty2)
1751 _ -> pprPanic "getEqPredTys" (ppr ty)
1752
1753 getEqPredTys_maybe :: PredType -> Maybe (Role, Type, Type)
1754 getEqPredTys_maybe ty
1755 = case splitTyConApp_maybe ty of
1756 Just (tc, [_, _, ty1, ty2])
1757 | tc `hasKey` eqPrimTyConKey -> Just (Nominal, ty1, ty2)
1758 | tc `hasKey` eqReprPrimTyConKey -> Just (Representational, ty1, ty2)
1759 _ -> Nothing
1760
1761 getEqPredRole :: PredType -> Role
1762 getEqPredRole ty = eqRelRole (predTypeEqRel ty)
1763
1764 -- | Get the equality relation relevant for a pred type.
1765 predTypeEqRel :: PredType -> EqRel
1766 predTypeEqRel ty
1767 | Just (tc, _) <- splitTyConApp_maybe ty
1768 , tc `hasKey` eqReprPrimTyConKey
1769 = ReprEq
1770 | otherwise
1771 = NomEq
1772
1773 {-
1774 %************************************************************************
1775 %* *
1776 Well-scoped tyvars
1777 * *
1778 ************************************************************************
1779 -}
1780
1781 -- | Do a topological sort on a list of tyvars,
1782 -- so that binders occur before occurrences
1783 -- E.g. given [ a::k, k::*, b::k ]
1784 -- it'll return a well-scoped list [ k::*, a::k, b::k ]
1785 --
1786 -- This is a deterministic sorting operation
1787 -- (that is, doesn't depend on Uniques).
1788 toposortTyVars :: [TyCoVar] -> [TyCoVar]
1789 toposortTyVars tvs = reverse $
1790 [ node_payload node | node <- topologicalSortG $
1791 graphFromEdgedVerticesOrd nodes ]
1792 where
1793 var_ids :: VarEnv Int
1794 var_ids = mkVarEnv (zip tvs [1..])
1795
1796 nodes :: [ Node Int TyVar ]
1797 nodes = [ DigraphNode
1798 tv
1799 (lookupVarEnv_NF var_ids tv)
1800 (mapMaybe (lookupVarEnv var_ids)
1801 (tyCoVarsOfTypeList (tyVarKind tv)))
1802 | tv <- tvs ]
1803
1804 -- | Extract a well-scoped list of variables from a deterministic set of
1805 -- variables. The result is deterministic.
1806 -- NB: There used to exist varSetElemsWellScoped :: VarSet -> [Var] which
1807 -- took a non-deterministic set and produced a non-deterministic
1808 -- well-scoped list. If you care about the list being well-scoped you also
1809 -- most likely care about it being in deterministic order.
1810 dVarSetElemsWellScoped :: DVarSet -> [Var]
1811 dVarSetElemsWellScoped = toposortTyVars . dVarSetElems
1812
1813 -- | Get the free vars of a type in scoped order
1814 tyCoVarsOfTypeWellScoped :: Type -> [TyVar]
1815 tyCoVarsOfTypeWellScoped = toposortTyVars . tyCoVarsOfTypeList
1816
1817 -- | Get the free vars of types in scoped order
1818 tyCoVarsOfTypesWellScoped :: [Type] -> [TyVar]
1819 tyCoVarsOfTypesWellScoped = toposortTyVars . tyCoVarsOfTypesList
1820
1821 {-
1822 ************************************************************************
1823 * *
1824 \subsection{Type families}
1825 * *
1826 ************************************************************************
1827 -}
1828
1829 mkFamilyTyConApp :: TyCon -> [Type] -> Type
1830 -- ^ Given a family instance TyCon and its arg types, return the
1831 -- corresponding family type. E.g:
1832 --
1833 -- > data family T a
1834 -- > data instance T (Maybe b) = MkT b
1835 --
1836 -- Where the instance tycon is :RTL, so:
1837 --
1838 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
1839 mkFamilyTyConApp tc tys
1840 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
1841 , let tvs = tyConTyVars tc
1842 fam_subst = ASSERT2( tvs `equalLength` tys, ppr tc <+> ppr tys )
1843 zipTvSubst tvs tys
1844 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
1845 | otherwise
1846 = mkTyConApp tc tys
1847
1848 -- | Get the type on the LHS of a coercion induced by a type/data
1849 -- family instance.
1850 coAxNthLHS :: CoAxiom br -> Int -> Type
1851 coAxNthLHS ax ind =
1852 mkTyConApp (coAxiomTyCon ax) (coAxBranchLHS (coAxiomNthBranch ax ind))
1853
1854 -- | Pretty prints a 'TyCon', using the family instance in case of a
1855 -- representation tycon. For example:
1856 --
1857 -- > data T [a] = ...
1858 --
1859 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
1860 pprSourceTyCon :: TyCon -> SDoc
1861 pprSourceTyCon tycon
1862 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
1863 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
1864 | otherwise
1865 = ppr tycon
1866
1867 -- @isTauTy@ tests if a type has no foralls
1868 isFamFreeTy :: Type -> Bool
1869 isFamFreeTy ty | Just ty' <- coreView ty = isFamFreeTy ty'
1870 isFamFreeTy (TyVarTy _) = True
1871 isFamFreeTy (LitTy {}) = True
1872 isFamFreeTy (TyConApp tc tys) = all isFamFreeTy tys && isFamFreeTyCon tc
1873 isFamFreeTy (AppTy a b) = isFamFreeTy a && isFamFreeTy b
1874 isFamFreeTy (FunTy a b) = isFamFreeTy a && isFamFreeTy b
1875 isFamFreeTy (ForAllTy _ ty) = isFamFreeTy ty
1876 isFamFreeTy (CastTy ty _) = isFamFreeTy ty
1877 isFamFreeTy (CoercionTy _) = False -- Not sure about this
1878
1879 {-
1880 ************************************************************************
1881 * *
1882 \subsection{Liftedness}
1883 * *
1884 ************************************************************************
1885 -}
1886
1887 -- | Returns Just True if this type is surely lifted, Just False
1888 -- if it is surely unlifted, Nothing if we can't be sure (i.e., it is
1889 -- levity polymorphic), and panics if the kind does not have the shape
1890 -- TYPE r.
1891 isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool
1892 isLiftedType_maybe ty = go (getRuntimeRep ty)
1893 where
1894 go rr | Just rr' <- coreView rr = go rr'
1895 go (TyConApp lifted_rep [])
1896 | lifted_rep `hasKey` liftedRepDataConKey = Just True
1897 go (TyConApp {}) = Just False -- everything else is unlifted
1898 go _ = Nothing -- levity polymorphic
1899
1900 -- | See "Type#type_classification" for what an unlifted type is.
1901 -- Panics on levity polymorphic types.
1902 isUnliftedType :: HasDebugCallStack => Type -> Bool
1903 -- isUnliftedType returns True for forall'd unlifted types:
1904 -- x :: forall a. Int#
1905 -- I found bindings like these were getting floated to the top level.
1906 -- They are pretty bogus types, mind you. It would be better never to
1907 -- construct them
1908 isUnliftedType ty
1909 = not (isLiftedType_maybe ty `orElse`
1910 pprPanic "isUnliftedType" (ppr ty <+> dcolon <+> ppr (typeKind ty)))
1911
1912 -- | Is this a type of kind RuntimeRep? (e.g. LiftedRep)
1913 isRuntimeRepKindedTy :: Type -> Bool
1914 isRuntimeRepKindedTy = isRuntimeRepTy . typeKind
1915
1916 -- | Drops prefix of RuntimeRep constructors in 'TyConApp's. Useful for e.g.
1917 -- dropping 'LiftedRep arguments of unboxed tuple TyCon applications:
1918 --
1919 -- dropRuntimeRepArgs [ 'LiftedRep, 'IntRep
1920 -- , String, Int# ] == [String, Int#]
1921 --
1922 dropRuntimeRepArgs :: [Type] -> [Type]
1923 dropRuntimeRepArgs = dropWhile isRuntimeRepKindedTy
1924
1925 -- | Extract the RuntimeRep classifier of a type. For instance,
1926 -- @getRuntimeRep_maybe Int = LiftedRep@. Returns 'Nothing' if this is not
1927 -- possible.
1928 getRuntimeRep_maybe :: HasDebugCallStack
1929 => Type -> Maybe Type
1930 getRuntimeRep_maybe = getRuntimeRepFromKind_maybe . typeKind
1931
1932 -- | Extract the RuntimeRep classifier of a type. For instance,
1933 -- @getRuntimeRep_maybe Int = LiftedRep@. Panics if this is not possible.
1934 getRuntimeRep :: HasDebugCallStack => Type -> Type
1935 getRuntimeRep ty
1936 = case getRuntimeRep_maybe ty of
1937 Just r -> r
1938 Nothing -> pprPanic "getRuntimeRep" (ppr ty <+> dcolon <+> ppr (typeKind ty))
1939
1940 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1941 -- @getRuntimeRepFromKind * = LiftedRep@; Panics if this is not possible.
1942 getRuntimeRepFromKind :: HasDebugCallStack
1943 => Type -> Type
1944 getRuntimeRepFromKind k =
1945 case getRuntimeRepFromKind_maybe k of
1946 Just r -> r
1947 Nothing -> pprPanic "getRuntimeRepFromKind"
1948 (ppr k <+> dcolon <+> ppr (typeKind k))
1949
1950 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1951 -- @getRuntimeRepFromKind * = LiftedRep@; Returns 'Nothing' if this is not
1952 -- possible.
1953 getRuntimeRepFromKind_maybe :: HasDebugCallStack
1954 => Type -> Maybe Type
1955 getRuntimeRepFromKind_maybe = go
1956 where
1957 go k | Just k' <- coreView k = go k'
1958 go k
1959 | Just (_tc, [arg]) <- splitTyConApp_maybe k
1960 = ASSERT2( _tc `hasKey` tYPETyConKey, ppr k )
1961 Just arg
1962 go _ = Nothing
1963
1964 isUnboxedTupleType :: Type -> Bool
1965 isUnboxedTupleType ty
1966 = tyConAppTyCon (getRuntimeRep ty) `hasKey` tupleRepDataConKey
1967 -- NB: Do not use typePrimRep, as that can't tell the difference between
1968 -- unboxed tuples and unboxed sums
1969
1970
1971 isUnboxedSumType :: Type -> Bool
1972 isUnboxedSumType ty
1973 = tyConAppTyCon (getRuntimeRep ty) `hasKey` sumRepDataConKey
1974
1975 -- | See "Type#type_classification" for what an algebraic type is.
1976 -- Should only be applied to /types/, as opposed to e.g. partially
1977 -- saturated type constructors
1978 isAlgType :: Type -> Bool
1979 isAlgType ty
1980 = case splitTyConApp_maybe ty of
1981 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1982 isAlgTyCon tc
1983 _other -> False
1984
1985 -- | Check whether a type is a data family type
1986 isDataFamilyAppType :: Type -> Bool
1987 isDataFamilyAppType ty = case tyConAppTyCon_maybe ty of
1988 Just tc -> isDataFamilyTyCon tc
1989 _ -> False
1990
1991 -- | Computes whether an argument (or let right hand side) should
1992 -- be computed strictly or lazily, based only on its type.
1993 -- Currently, it's just 'isUnliftedType'. Panics on levity-polymorphic types.
1994 isStrictType :: HasDebugCallStack => Type -> Bool
1995 isStrictType = isUnliftedType
1996
1997 isPrimitiveType :: Type -> Bool
1998 -- ^ Returns true of types that are opaque to Haskell.
1999 isPrimitiveType ty = case splitTyConApp_maybe ty of
2000 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
2001 isPrimTyCon tc
2002 _ -> False
2003
2004 {-
2005 ************************************************************************
2006 * *
2007 \subsection{Join points}
2008 * *
2009 ************************************************************************
2010 -}
2011
2012 -- | Determine whether a type could be the type of a join point of given total
2013 -- arity, according to the polymorphism rule. A join point cannot be polymorphic
2014 -- in its return type, since given
2015 -- join j @a @b x y z = e1 in e2,
2016 -- the types of e1 and e2 must be the same, and a and b are not in scope for e2.
2017 -- (See Note [The polymorphism rule of join points] in CoreSyn.) Returns False
2018 -- also if the type simply doesn't have enough arguments.
2019 --
2020 -- Note that we need to know how many arguments (type *and* value) the putative
2021 -- join point takes; for instance, if
2022 -- j :: forall a. a -> Int
2023 -- then j could be a binary join point returning an Int, but it could *not* be a
2024 -- unary join point returning a -> Int.
2025 --
2026 -- TODO: See Note [Excess polymorphism and join points]
2027 isValidJoinPointType :: JoinArity -> Type -> Bool
2028 isValidJoinPointType arity ty
2029 = valid_under emptyVarSet arity ty
2030 where
2031 valid_under tvs arity ty
2032 | arity == 0
2033 = isEmptyVarSet (tvs `intersectVarSet` tyCoVarsOfType ty)
2034 | Just (t, ty') <- splitForAllTy_maybe ty
2035 = valid_under (tvs `extendVarSet` t) (arity-1) ty'
2036 | Just (_, res_ty) <- splitFunTy_maybe ty
2037 = valid_under tvs (arity-1) res_ty
2038 | otherwise
2039 = False
2040
2041 {- Note [Excess polymorphism and join points]
2042 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2043 In principle, if a function would be a join point except that it fails
2044 the polymorphism rule (see Note [The polymorphism rule of join points] in
2045 CoreSyn), it can still be made a join point with some effort. This is because
2046 all tail calls must return the same type (they return to the same context!), and
2047 thus if the return type depends on an argument, that argument must always be the
2048 same.
2049
2050 For instance, consider:
2051
2052 let f :: forall a. a -> Char -> [a]
2053 f @a x c = ... f @a y 'a' ...
2054 in ... f @Int 1 'b' ... f @Int 2 'c' ...
2055
2056 (where the calls are tail calls). `f` fails the polymorphism rule because its
2057 return type is [a], where [a] is bound. But since the type argument is always
2058 'Int', we can rewrite it as:
2059
2060 let f' :: Int -> Char -> [Int]
2061 f' x c = ... f' y 'a' ...
2062 in ... f' 1 'b' ... f 2 'c' ...
2063
2064 and now we can make f' a join point:
2065
2066 join f' :: Int -> Char -> [Int]
2067 f' x c = ... jump f' y 'a' ...
2068 in ... jump f' 1 'b' ... jump f' 2 'c' ...
2069
2070 It's not clear that this comes up often, however. TODO: Measure how often and
2071 add this analysis if necessary. See Trac #14620.
2072
2073
2074 ************************************************************************
2075 * *
2076 \subsection{Sequencing on types}
2077 * *
2078 ************************************************************************
2079 -}
2080
2081 seqType :: Type -> ()
2082 seqType (LitTy n) = n `seq` ()
2083 seqType (TyVarTy tv) = tv `seq` ()
2084 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
2085 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
2086 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
2087 seqType (ForAllTy (TvBndr tv _) ty) = seqType (tyVarKind tv) `seq` seqType ty
2088 seqType (CastTy ty co) = seqType ty `seq` seqCo co
2089 seqType (CoercionTy co) = seqCo co
2090
2091 seqTypes :: [Type] -> ()
2092 seqTypes [] = ()
2093 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
2094
2095 {-
2096 ************************************************************************
2097 * *
2098 Comparison for types
2099 (We don't use instances so that we know where it happens)
2100 * *
2101 ************************************************************************
2102
2103 Note [Equality on AppTys]
2104 ~~~~~~~~~~~~~~~~~~~~~~~~~
2105 In our cast-ignoring equality, we want to say that the following two
2106 are equal:
2107
2108 (Maybe |> co) (Int |> co') ~? Maybe Int
2109
2110 But the left is an AppTy while the right is a TyConApp. The solution is
2111 to use repSplitAppTy_maybe to break up the TyConApp into its pieces and
2112 then continue. Easy to do, but also easy to forget to do.
2113
2114 -}
2115
2116 eqType :: Type -> Type -> Bool
2117 -- ^ Type equality on source types. Does not look through @newtypes@ or
2118 -- 'PredType's, but it does look through type synonyms.
2119 -- This first checks that the kinds of the types are equal and then
2120 -- checks whether the types are equal, ignoring casts and coercions.
2121 -- (The kind check is a recursive call, but since all kinds have type
2122 -- @Type@, there is no need to check the types of kinds.)
2123 -- See also Note [Non-trivial definitional equality] in TyCoRep.
2124 eqType t1 t2 = isEqual $ nonDetCmpType t1 t2
2125 -- It's OK to use nonDetCmpType here and eqType is deterministic,
2126 -- nonDetCmpType does equality deterministically
2127
2128 -- | Compare types with respect to a (presumably) non-empty 'RnEnv2'.
2129 eqTypeX :: RnEnv2 -> Type -> Type -> Bool
2130 eqTypeX env t1 t2 = isEqual $ nonDetCmpTypeX env t1 t2
2131 -- It's OK to use nonDetCmpType here and eqTypeX is deterministic,
2132 -- nonDetCmpTypeX does equality deterministically
2133
2134 -- | Type equality on lists of types, looking through type synonyms
2135 -- but not newtypes.
2136 eqTypes :: [Type] -> [Type] -> Bool
2137 eqTypes tys1 tys2 = isEqual $ nonDetCmpTypes tys1 tys2
2138 -- It's OK to use nonDetCmpType here and eqTypes is deterministic,
2139 -- nonDetCmpTypes does equality deterministically
2140
2141 eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2
2142 -- Check that the var lists are the same length
2143 -- and have matching kinds; if so, extend the RnEnv2
2144 -- Returns Nothing if they don't match
2145 eqVarBndrs env [] []
2146 = Just env
2147 eqVarBndrs env (tv1:tvs1) (tv2:tvs2)
2148 | eqTypeX env (tyVarKind tv1) (tyVarKind tv2)
2149 = eqVarBndrs (rnBndr2 env tv1 tv2) tvs1 tvs2
2150 eqVarBndrs _ _ _= Nothing
2151
2152 -- Now here comes the real worker
2153
2154 {-
2155 Note [nonDetCmpType nondeterminism]
2156 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2157 nonDetCmpType is implemented in terms of nonDetCmpTypeX. nonDetCmpTypeX
2158 uses nonDetCmpTc which compares TyCons by their Unique value. Using Uniques for
2159 ordering leads to nondeterminism. We hit the same problem in the TyVarTy case,
2160 comparing type variables is nondeterministic, note the call to nonDetCmpVar in
2161 nonDetCmpTypeX.
2162 See Note [Unique Determinism] for more details.
2163 -}
2164
2165 nonDetCmpType :: Type -> Type -> Ordering
2166 nonDetCmpType t1 t2
2167 -- we know k1 and k2 have the same kind, because they both have kind *.
2168 = nonDetCmpTypeX rn_env t1 t2
2169 where
2170 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes [t1, t2]))
2171
2172 nonDetCmpTypes :: [Type] -> [Type] -> Ordering
2173 nonDetCmpTypes ts1 ts2 = nonDetCmpTypesX rn_env ts1 ts2
2174 where
2175 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes (ts1 ++ ts2)))
2176
2177 -- | An ordering relation between two 'Type's (known below as @t1 :: k1@
2178 -- and @t2 :: k2@)
2179 data TypeOrdering = TLT -- ^ @t1 < t2@
2180 | TEQ -- ^ @t1 ~ t2@ and there are no casts in either,
2181 -- therefore we can conclude @k1 ~ k2@
2182 | TEQX -- ^ @t1 ~ t2@ yet one of the types contains a cast so
2183 -- they may differ in kind.
2184 | TGT -- ^ @t1 > t2@
2185 deriving (Eq, Ord, Enum, Bounded)
2186
2187 nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
2188 -- See Note [Non-trivial definitional equality] in TyCoRep
2189 nonDetCmpTypeX env orig_t1 orig_t2 =
2190 case go env orig_t1 orig_t2 of
2191 -- If there are casts then we also need to do a comparison of the kinds of
2192 -- the types being compared
2193 TEQX -> toOrdering $ go env k1 k2
2194 ty_ordering -> toOrdering ty_ordering
2195 where
2196 k1 = typeKind orig_t1
2197 k2 = typeKind orig_t2
2198
2199 toOrdering :: TypeOrdering -> Ordering
2200 toOrdering TLT = LT
2201 toOrdering TEQ = EQ
2202 toOrdering TEQX = EQ
2203 toOrdering TGT = GT
2204
2205 liftOrdering :: Ordering -> TypeOrdering
2206 liftOrdering LT = TLT
2207 liftOrdering EQ = TEQ
2208 liftOrdering GT = TGT
2209
2210 thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering
2211 thenCmpTy TEQ rel = rel
2212 thenCmpTy TEQX rel = hasCast rel
2213 thenCmpTy rel _ = rel
2214
2215 hasCast :: TypeOrdering -> TypeOrdering
2216 hasCast TEQ = TEQX
2217 hasCast rel = rel
2218
2219 -- Returns both the resulting ordering relation between the two types
2220 -- and whether either contains a cast.
2221 go :: RnEnv2 -> Type -> Type -> TypeOrdering
2222 go env t1 t2
2223 | Just t1' <- coreView t1 = go env t1' t2
2224 | Just t2' <- coreView t2 = go env t1 t2'
2225
2226 go env (TyVarTy tv1) (TyVarTy tv2)
2227 = liftOrdering $ rnOccL env tv1 `nonDetCmpVar` rnOccR env tv2
2228 go env (ForAllTy (TvBndr tv1 _) t1) (ForAllTy (TvBndr tv2 _) t2)
2229 = go env (tyVarKind tv1) (tyVarKind tv2)
2230 `thenCmpTy` go (rnBndr2 env tv1 tv2) t1 t2
2231 -- See Note [Equality on AppTys]
2232 go env (AppTy s1 t1) ty2
2233 | Just (s2, t2) <- repSplitAppTy_maybe ty2
2234 = go env s1 s2 `thenCmpTy` go env t1 t2
2235 go env ty1 (AppTy s2 t2)
2236 | Just (s1, t1) <- repSplitAppTy_maybe ty1
2237 = go env s1 s2 `thenCmpTy` go env t1 t2
2238 go env (FunTy s1 t1) (FunTy s2 t2)
2239 = go env s1 s2 `thenCmpTy` go env t1 t2
2240 go env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
2241 = liftOrdering (tc1 `nonDetCmpTc` tc2) `thenCmpTy` gos env tys1 tys2
2242 go _ (LitTy l1) (LitTy l2) = liftOrdering (compare l1 l2)
2243 go env (CastTy t1 _) t2 = hasCast $ go env t1 t2
2244 go env t1 (CastTy t2 _) = hasCast $ go env t1 t2
2245
2246 go _ (CoercionTy {}) (CoercionTy {}) = TEQ
2247
2248 -- Deal with the rest: TyVarTy < CoercionTy < AppTy < LitTy < TyConApp < ForAllTy
2249 go _ ty1 ty2
2250 = liftOrdering $ (get_rank ty1) `compare` (get_rank ty2)
2251 where get_rank :: Type -> Int
2252 get_rank (CastTy {})
2253 = pprPanic "nonDetCmpTypeX.get_rank" (ppr [ty1,ty2])
2254 get_rank (TyVarTy {}) = 0
2255 get_rank (CoercionTy {}) = 1
2256 get_rank (AppTy {}) = 3
2257 get_rank (LitTy {}) = 4
2258 get_rank (TyConApp {}) = 5
2259 get_rank (FunTy {}) = 6
2260 get_rank (ForAllTy {}) = 7
2261
2262 gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering
2263 gos _ [] [] = TEQ
2264 gos _ [] _ = TLT
2265 gos _ _ [] = TGT
2266 gos env (ty1:tys1) (ty2:tys2) = go env ty1 ty2 `thenCmpTy` gos env tys1 tys2
2267
2268 -------------
2269 nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
2270 nonDetCmpTypesX _ [] [] = EQ
2271 nonDetCmpTypesX env (t1:tys1) (t2:tys2) = nonDetCmpTypeX env t1 t2
2272 `thenCmp` nonDetCmpTypesX env tys1 tys2
2273 nonDetCmpTypesX _ [] _ = LT
2274 nonDetCmpTypesX _ _ [] = GT
2275
2276 -------------
2277 -- | Compare two 'TyCon's. NB: This should /never/ see the "star synonyms",
2278 -- as recognized by Kind.isStarKindSynonymTyCon. See Note
2279 -- [Kind Constraint and kind *] in Kind.
2280 -- See Note [nonDetCmpType nondeterminism]
2281 nonDetCmpTc :: TyCon -> TyCon -> Ordering
2282 nonDetCmpTc tc1 tc2
2283 = ASSERT( not (isStarKindSynonymTyCon tc1) && not (isStarKindSynonymTyCon tc2) )
2284 u1 `nonDetCmpUnique` u2
2285 where
2286 u1 = tyConUnique tc1
2287 u2 = tyConUnique tc2
2288
2289 {-
2290 ************************************************************************
2291 * *
2292 The kind of a type
2293 * *
2294 ************************************************************************
2295 -}
2296
2297 typeKind :: HasDebugCallStack => Type -> Kind
2298 typeKind (TyConApp tc tys) = piResultTys (tyConKind tc) tys
2299 typeKind (AppTy fun arg) = typeKind_apps fun [arg]
2300 typeKind (LitTy l) = typeLiteralKind l
2301 typeKind (FunTy {}) = liftedTypeKind
2302 typeKind (ForAllTy _ ty) = typeKind ty
2303 typeKind (TyVarTy tyvar) = tyVarKind tyvar
2304 typeKind (CastTy _ty co) = pSnd $ coercionKind co
2305 typeKind (CoercionTy co) = coercionType co
2306
2307 typeKind_apps :: HasDebugCallStack => Type -> [Type] -> Kind
2308 -- The sole purpose of the function is to accumulate
2309 -- the type arugments, so we can call piResultTys, rather than
2310 -- a succession of calls to piResultTy (which is asymptotically
2311 -- less efficient as the number of arguments increases)
2312 typeKind_apps (AppTy fun arg) args = typeKind_apps fun (arg:args)
2313 typeKind_apps fun args = piResultTys (typeKind fun) args
2314
2315 --------------------------
2316 typeLiteralKind :: TyLit -> Kind
2317 typeLiteralKind l =
2318 case l of
2319 NumTyLit _ -> typeNatKind
2320 StrTyLit _ -> typeSymbolKind
2321
2322 -- | Returns True if a type is levity polymorphic. Should be the same
2323 -- as (isKindLevPoly . typeKind) but much faster.
2324 -- Precondition: The type has kind (TYPE blah)
2325 isTypeLevPoly :: Type -> Bool
2326 isTypeLevPoly = go
2327 where
2328 go ty@(TyVarTy {}) = check_kind ty
2329 go ty@(AppTy {}) = check_kind ty
2330 go ty@(TyConApp tc _) | not (isTcLevPoly tc) = False
2331 | otherwise = check_kind ty
2332 go (ForAllTy _ ty) = go ty
2333 go (FunTy {}) = False
2334 go (LitTy {}) = False
2335 go ty@(CastTy {}) = check_kind ty
2336 go ty@(CoercionTy {}) = pprPanic "isTypeLevPoly co" (ppr ty)
2337
2338 check_kind = isKindLevPoly . typeKind
2339
2340 -- | Looking past all pi-types, is the end result potentially levity polymorphic?
2341 -- Example: True for (forall r (a :: TYPE r). String -> a)
2342 -- Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type)
2343 resultIsLevPoly :: Type -> Bool
2344 resultIsLevPoly = isTypeLevPoly . snd . splitPiTys
2345
2346 {-
2347 %************************************************************************
2348 %* *
2349 Miscellaneous functions
2350 %* *
2351 %************************************************************************
2352
2353 -}
2354 -- | All type constructors occurring in the type; looking through type
2355 -- synonyms, but not newtypes.
2356 -- When it finds a Class, it returns the class TyCon.
2357 tyConsOfType :: Type -> UniqSet TyCon
2358 tyConsOfType ty
2359 = go ty
2360 where
2361 go :: Type -> UniqSet TyCon -- The UniqSet does duplicate elim
2362 go ty | Just ty' <- coreView ty = go ty'
2363 go (TyVarTy {}) = emptyUniqSet
2364 go (LitTy {}) = emptyUniqSet
2365 go (TyConApp tc tys) = go_tc tc `unionUniqSets` go_s tys
2366 go (AppTy a b) = go a `unionUniqSets` go b
2367 go (FunTy a b) = go a `unionUniqSets` go b `unionUniqSets` go_tc funTyCon
2368 go (ForAllTy (TvBndr tv _) ty) = go ty `unionUniqSets` go (tyVarKind tv)
2369 go (CastTy ty co) = go ty `unionUniqSets` go_co co
2370 go (CoercionTy co) = go_co co
2371
2372 go_co (Refl _ ty) = go ty
2373 go_co (TyConAppCo _ tc args) = go_tc tc `unionUniqSets` go_cos args
2374 go_co (AppCo co arg) = go_co co `unionUniqSets` go_co arg
2375 go_co (ForAllCo _ kind_co co) = go_co kind_co `unionUniqSets` go_co co
2376 go_co (FunCo _ co1 co2) = go_co co1 `unionUniqSets` go_co co2
2377 go_co (AxiomInstCo ax _ args) = go_ax ax `unionUniqSets` go_cos args
2378 go_co (UnivCo p _ t1 t2) = go_prov p `unionUniqSets` go t1 `unionUniqSets` go t2
2379 go_co (CoVarCo {}) = emptyUniqSet
2380 go_co (HoleCo {}) = emptyUniqSet
2381 go_co (SymCo co) = go_co co
2382 go_co (TransCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2383 go_co (NthCo _ co) = go_co co
2384 go_co (LRCo _ co) = go_co co
2385 go_co (InstCo co arg) = go_co co `unionUniqSets` go_co arg
2386 go_co (CoherenceCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2387 go_co (KindCo co) = go_co co
2388 go_co (SubCo co) = go_co co
2389 go_co (AxiomRuleCo _ cs) = go_cos cs
2390
2391 go_prov UnsafeCoerceProv = emptyUniqSet
2392 go_prov (PhantomProv co) = go_co co
2393 go_prov (ProofIrrelProv co) = go_co co
2394 go_prov (PluginProv _) = emptyUniqSet
2395 -- this last case can happen from the tyConsOfType used from
2396 -- checkTauTvUpdate
2397
2398 go_s tys = foldr (unionUniqSets . go) emptyUniqSet tys
2399 go_cos cos = foldr (unionUniqSets . go_co) emptyUniqSet cos
2400
2401 go_tc tc = unitUniqSet tc
2402 go_ax ax = go_tc $ coAxiomTyCon ax
2403
2404 -- | Find the result 'Kind' of a type synonym,
2405 -- after applying it to its 'arity' number of type variables
2406 -- Actually this function works fine on data types too,
2407 -- but they'd always return '*', so we never need to ask
2408 synTyConResKind :: TyCon -> Kind
2409 synTyConResKind tycon = piResultTys (tyConKind tycon) (mkTyVarTys (tyConTyVars tycon))
2410
2411 -- | Retrieve the free variables in this type, splitting them based
2412 -- on whether they are used visibly or invisibly. Invisible ones come
2413 -- first.
2414 splitVisVarsOfType :: Type -> Pair TyCoVarSet
2415 splitVisVarsOfType orig_ty = Pair invis_vars vis_vars
2416 where
2417 Pair invis_vars1 vis_vars = go orig_ty
2418 invis_vars = invis_vars1 `minusVarSet` vis_vars
2419
2420 go (TyVarTy tv) = Pair (tyCoVarsOfType $ tyVarKind tv) (unitVarSet tv)
2421 go (AppTy t1 t2) = go t1 `mappend` go t2
2422 go (TyConApp tc tys) = go_tc tc tys
2423 go (FunTy t1 t2) = go t1 `mappend` go t2
2424 go (ForAllTy (TvBndr tv _) ty)
2425 = ((`delVarSet` tv) <$> go ty) `mappend`
2426 (invisible (tyCoVarsOfType $ tyVarKind tv))
2427 go (LitTy {}) = mempty
2428 go (CastTy ty co) = go ty `mappend` invisible (tyCoVarsOfCo co)
2429 go (CoercionTy co) = invisible $ tyCoVarsOfCo co
2430
2431 invisible vs = Pair vs emptyVarSet
2432
2433 go_tc tc tys = let (invis, vis) = partitionInvisibles tc id tys in
2434 invisible (tyCoVarsOfTypes invis) `mappend` foldMap go vis
2435
2436 splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
2437 splitVisVarsOfTypes = foldMap splitVisVarsOfType
2438
2439 modifyJoinResTy :: Int -- Number of binders to skip
2440 -> (Type -> Type) -- Function to apply to result type
2441 -> Type -- Type of join point
2442 -> Type -- New type
2443 -- INVARIANT: If any of the first n binders are foralls, those tyvars cannot
2444 -- appear in the original result type. See isValidJoinPointType.
2445 modifyJoinResTy orig_ar f orig_ty
2446 = go orig_ar orig_ty
2447 where
2448 go 0 ty = f ty
2449 go n ty | Just (arg_bndr, res_ty) <- splitPiTy_maybe ty
2450 = mkPiTy arg_bndr (go (n-1) res_ty)
2451 | otherwise
2452 = pprPanic "modifyJoinResTy" (ppr orig_ar <+> ppr orig_ty)
2453
2454 setJoinResTy :: Int -- Number of binders to skip
2455 -> Type -- New result type
2456 -> Type -- Type of join point
2457 -> Type -- New type
2458 -- INVARIANT: Same as for modifyJoinResTy
2459 setJoinResTy ar new_res_ty ty
2460 = modifyJoinResTy ar (const new_res_ty) ty