Caching coercion roles in NthCo and coercionKindsRole refactoring
[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, nextRole,
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 pprWithTYPE,
193
194 -- * Tidying type related things up for printing
195 tidyType, tidyTypes,
196 tidyOpenType, tidyOpenTypes,
197 tidyOpenKind,
198 tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars,
199 tidyOpenTyCoVar, tidyOpenTyCoVars,
200 tidyTyVarOcc,
201 tidyTopType,
202 tidyKind,
203 tidyTyVarBinder, tidyTyVarBinders
204 ) where
205
206 #include "HsVersions.h"
207
208 import GhcPrelude
209
210 import BasicTypes
211
212 -- We import the representation and primitive functions from TyCoRep.
213 -- Many things are reexported, but not the representation!
214
215 import Kind
216 import TyCoRep
217
218 -- friends:
219 import Var
220 import VarEnv
221 import VarSet
222 import UniqSet
223
224 import Class
225 import TyCon
226 import TysPrim
227 import {-# SOURCE #-} TysWiredIn ( listTyCon, typeNatKind
228 , typeSymbolKind, liftedTypeKind )
229 import PrelNames
230 import CoAxiom
231 import {-# SOURCE #-} Coercion
232
233 -- others
234 import Util
235 import Outputable
236 import FastString
237 import Pair
238 import DynFlags ( gopt_set, GeneralFlag(Opt_PrintExplicitRuntimeReps) )
239 import ListSetOps
240 import Digraph
241 import Unique ( nonDetCmpUnique )
242
243 import Maybes ( orElse )
244 import Data.Maybe ( isJust, mapMaybe )
245 import Control.Monad ( guard )
246 import Control.Arrow ( first, second )
247
248 -- $type_classification
249 -- #type_classification#
250 --
251 -- Types are one of:
252 --
253 -- [Unboxed] Iff its representation is other than a pointer
254 -- Unboxed types are also unlifted.
255 --
256 -- [Lifted] Iff it has bottom as an element.
257 -- Closures always have lifted types: i.e. any
258 -- let-bound identifier in Core must have a lifted
259 -- type. Operationally, a lifted object is one that
260 -- can be entered.
261 -- Only lifted types may be unified with a type variable.
262 --
263 -- [Algebraic] Iff it is a type with one or more constructors, whether
264 -- declared with @data@ or @newtype@.
265 -- An algebraic type is one that can be deconstructed
266 -- with a case expression. This is /not/ the same as
267 -- lifted types, because we also include unboxed
268 -- tuples in this classification.
269 --
270 -- [Data] Iff it is a type declared with @data@, or a boxed tuple.
271 --
272 -- [Primitive] Iff it is a built-in type that can't be expressed in Haskell.
273 --
274 -- Currently, all primitive types are unlifted, but that's not necessarily
275 -- the case: for example, @Int@ could be primitive.
276 --
277 -- Some primitive types are unboxed, such as @Int#@, whereas some are boxed
278 -- but unlifted (such as @ByteArray#@). The only primitive types that we
279 -- classify as algebraic are the unboxed tuples.
280 --
281 -- Some examples of type classifications that may make this a bit clearer are:
282 --
283 -- @
284 -- Type primitive boxed lifted algebraic
285 -- -----------------------------------------------------------------------------
286 -- Int# Yes No No No
287 -- ByteArray# Yes Yes No No
288 -- (\# a, b \#) Yes No No Yes
289 -- (\# a | b \#) Yes No No Yes
290 -- ( a, b ) No Yes Yes Yes
291 -- [a] No Yes Yes Yes
292 -- @
293
294 -- $representation_types
295 -- A /source type/ is a type that is a separate type as far as the type checker is
296 -- concerned, but which has a more low-level representation as far as Core-to-Core
297 -- passes and the rest of the back end is concerned.
298 --
299 -- You don't normally have to worry about this, as the utility functions in
300 -- this module will automatically convert a source into a representation type
301 -- if they are spotted, to the best of it's abilities. If you don't want this
302 -- to happen, use the equivalent functions from the "TcType" module.
303
304 {-
305 ************************************************************************
306 * *
307 Type representation
308 * *
309 ************************************************************************
310
311 Note [coreView vs tcView]
312 ~~~~~~~~~~~~~~~~~~~~~~~~~
313 So far as the typechecker is concerned, 'Constraint' and 'TYPE LiftedRep' are distinct kinds.
314
315 But in Core these two are treated as identical.
316
317 We implement this by making 'coreView' convert 'Constraint' to 'TYPE LiftedRep' on the fly.
318 The function tcView (used in the type checker) does not do this.
319
320 See also Trac #11715, which tracks removing this inconsistency.
321
322 -}
323
324 {-# INLINE coreView #-}
325 coreView :: Type -> Maybe Type
326 -- ^ This function Strips off the /top layer only/ of a type synonym
327 -- application (if any) its underlying representation type.
328 -- Returns Nothing if there is nothing to look through.
329 -- This function considers 'Constraint' to be a synonym of @TYPE LiftedRep@.
330 --
331 -- By being non-recursive and inlined, this case analysis gets efficiently
332 -- joined onto the case analysis that the caller is already doing
333 coreView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
334 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
335 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
336 -- ok to use 'substTy' here.
337 -- See also Note [The substitution invariant] in TyCoRep.
338 -- Its important to use mkAppTys, rather than (foldl AppTy),
339 -- because the function part might well return a
340 -- partially-applied type constructor; indeed, usually will!
341
342 coreView (TyConApp tc []) -- At the Core level, Constraint = Type
343 | isStarKindSynonymTyCon tc
344 = Just liftedTypeKind
345
346 coreView _ = Nothing
347
348 -- | Gives the typechecker view of a type. This unwraps synonyms but
349 -- leaves 'Constraint' alone. c.f. coreView, which turns Constraint into
350 -- TYPE LiftedRep. Returns Nothing if no unwrapping happens.
351 -- See also Note [coreView vs tcView] in Type.
352 {-# INLINE tcView #-}
353 tcView :: Type -> Maybe Type
354 tcView (TyConApp tc tys) | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
355 = Just (mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys')
356 -- The free vars of 'rhs' should all be bound by 'tenv', so it's
357 -- ok to use 'substTy' here.
358 -- See also Note [The substitution invariant] in TyCoRep.
359 -- Its important to use mkAppTys, rather than (foldl AppTy),
360 -- because the function part might well return a
361 -- partially-applied type constructor; indeed, usually will!
362 tcView _ = Nothing
363
364 -----------------------------------------------
365 expandTypeSynonyms :: Type -> Type
366 -- ^ Expand out all type synonyms. Actually, it'd suffice to expand out
367 -- just the ones that discard type variables (e.g. type Funny a = Int)
368 -- But we don't know which those are currently, so we just expand all.
369 --
370 -- 'expandTypeSynonyms' only expands out type synonyms mentioned in the type,
371 -- not in the kinds of any TyCon or TyVar mentioned in the type.
372 --
373 -- Keep this synchronized with 'synonymTyConsOfType'
374 expandTypeSynonyms ty
375 = go (mkEmptyTCvSubst in_scope) ty
376 where
377 in_scope = mkInScopeSet (tyCoVarsOfType ty)
378
379 go subst (TyConApp tc tys)
380 | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc expanded_tys
381 = let subst' = mkTvSubst in_scope (mkVarEnv tenv)
382 -- Make a fresh substitution; rhs has nothing to
383 -- do with anything that has happened so far
384 -- NB: if you make changes here, be sure to build an
385 -- /idempotent/ substitution, even in the nested case
386 -- type T a b = a -> b
387 -- type S x y = T y x
388 -- (Trac #11665)
389 in mkAppTys (go subst' rhs) tys'
390 | otherwise
391 = TyConApp tc expanded_tys
392 where
393 expanded_tys = (map (go subst) tys)
394
395 go _ (LitTy l) = LitTy l
396 go subst (TyVarTy tv) = substTyVar subst tv
397 go subst (AppTy t1 t2) = mkAppTy (go subst t1) (go subst t2)
398 go subst (FunTy arg res)
399 = mkFunTy (go subst arg) (go subst res)
400 go subst (ForAllTy (TvBndr tv vis) t)
401 = let (subst', tv') = substTyVarBndrCallback go subst tv in
402 ForAllTy (TvBndr tv' vis) (go subst' t)
403 go subst (CastTy ty co) = mkCastTy (go subst ty) (go_co subst co)
404 go subst (CoercionTy co) = mkCoercionTy (go_co subst co)
405
406 go_co subst (Refl r ty)
407 = mkReflCo r (go subst ty)
408 -- NB: coercions are always expanded upon creation
409 go_co subst (TyConAppCo r tc args)
410 = mkTyConAppCo r tc (map (go_co subst) args)
411 go_co subst (AppCo co arg)
412 = mkAppCo (go_co subst co) (go_co subst arg)
413 go_co subst (ForAllCo tv kind_co co)
414 = let (subst', tv', kind_co') = go_cobndr subst tv kind_co in
415 mkForAllCo tv' kind_co' (go_co subst' co)
416 go_co subst (FunCo r co1 co2)
417 = mkFunCo r (go_co subst co1) (go_co subst co2)
418 go_co subst (CoVarCo cv)
419 = substCoVar subst cv
420 go_co subst (AxiomInstCo ax ind args)
421 = mkAxiomInstCo ax ind (map (go_co subst) args)
422 go_co subst (UnivCo p r t1 t2)
423 = mkUnivCo (go_prov subst p) r (go subst t1) (go subst t2)
424 go_co subst (SymCo co)
425 = mkSymCo (go_co subst co)
426 go_co subst (TransCo co1 co2)
427 = mkTransCo (go_co subst co1) (go_co subst co2)
428 go_co subst (NthCo r n co)
429 = mkNthCo r n (go_co subst co)
430 go_co subst (LRCo lr co)
431 = mkLRCo lr (go_co subst co)
432 go_co subst (InstCo co arg)
433 = mkInstCo (go_co subst co) (go_co subst arg)
434 go_co subst (CoherenceCo co1 co2)
435 = mkCoherenceCo (go_co subst co1) (go_co subst co2)
436 go_co subst (KindCo co)
437 = mkKindCo (go_co subst co)
438 go_co subst (SubCo co)
439 = mkSubCo (go_co subst co)
440 go_co subst (AxiomRuleCo ax cs)
441 = AxiomRuleCo ax (map (go_co subst) cs)
442 go_co _ (HoleCo h)
443 = pprPanic "expandTypeSynonyms hit a hole" (ppr h)
444
445 go_prov _ UnsafeCoerceProv = UnsafeCoerceProv
446 go_prov subst (PhantomProv co) = PhantomProv (go_co subst co)
447 go_prov subst (ProofIrrelProv co) = ProofIrrelProv (go_co subst co)
448 go_prov _ p@(PluginProv _) = p
449
450 -- the "False" and "const" are to accommodate the type of
451 -- substForAllCoBndrCallback, which is general enough to
452 -- handle coercion optimization (which sometimes swaps the
453 -- order of a coercion)
454 go_cobndr subst = substForAllCoBndrCallback False (go_co subst) subst
455
456 {-
457 ************************************************************************
458 * *
459 Analyzing types
460 * *
461 ************************************************************************
462
463 These functions do a map-like operation over types, performing some operation
464 on all variables and binding sites. Primarily used for zonking.
465
466 Note [Efficiency for mapCoercion ForAllCo case]
467 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
468 As noted in Note [Forall coercions] in TyCoRep, a ForAllCo is a bit redundant.
469 It stores a TyVar and a Coercion, where the kind of the TyVar always matches
470 the left-hand kind of the coercion. This is convenient lots of the time, but
471 not when mapping a function over a coercion.
472
473 The problem is that tcm_tybinder will affect the TyVar's kind and
474 mapCoercion will affect the Coercion, and we hope that the results will be
475 the same. Even if they are the same (which should generally happen with
476 correct algorithms), then there is an efficiency issue. In particular,
477 this problem seems to make what should be a linear algorithm into a potentially
478 exponential one. But it's only going to be bad in the case where there's
479 lots of foralls in the kinds of other foralls. Like this:
480
481 forall a : (forall b : (forall c : ...). ...). ...
482
483 This construction seems unlikely. So we'll do the inefficient, easy way
484 for now.
485
486 Note [Specialising mappers]
487 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
488 These INLINABLE pragmas are indispensable. mapType/mapCoercion are used
489 to implement zonking, and it's vital that they get specialised to the TcM
490 monad. This specialisation happens automatically (that is, without a
491 SPECIALISE pragma) as long as the definitions are INLINABLE. For example,
492 this one change made a 20% allocation difference in perf/compiler/T5030.
493
494 -}
495
496 -- | This describes how a "map" operation over a type/coercion should behave
497 data TyCoMapper env m
498 = TyCoMapper
499 { tcm_smart :: Bool -- ^ Should the new type be created with smart
500 -- constructors?
501 , tcm_tyvar :: env -> TyVar -> m Type
502 , tcm_covar :: env -> CoVar -> m Coercion
503 , tcm_hole :: env -> CoercionHole -> m Coercion
504 -- ^ What to do with coercion holes.
505 -- See Note [Coercion holes] in TyCoRep.
506
507 , tcm_tybinder :: env -> TyVar -> ArgFlag -> m (env, TyVar)
508 -- ^ The returned env is used in the extended scope
509 }
510
511 {-# INLINABLE mapType #-} -- See Note [Specialising mappers]
512 mapType :: Monad m => TyCoMapper env m -> env -> Type -> m Type
513 mapType mapper@(TyCoMapper { tcm_smart = smart, tcm_tyvar = tyvar
514 , tcm_tybinder = tybinder })
515 env ty
516 = go ty
517 where
518 go (TyVarTy tv) = tyvar env tv
519 go (AppTy t1 t2) = mkappty <$> go t1 <*> go t2
520 go t@(TyConApp _ []) = return t -- avoid allocation in this exceedingly
521 -- common case (mostly, for *)
522 go (TyConApp tc tys) = mktyconapp tc <$> mapM go tys
523 go (FunTy arg res) = FunTy <$> go arg <*> go res
524 go (ForAllTy (TvBndr tv vis) inner)
525 = do { (env', tv') <- tybinder env tv vis
526 ; inner' <- mapType mapper env' inner
527 ; return $ ForAllTy (TvBndr tv' vis) inner' }
528 go ty@(LitTy {}) = return ty
529 go (CastTy ty co) = mkcastty <$> go ty <*> mapCoercion mapper env co
530 go (CoercionTy co) = CoercionTy <$> mapCoercion mapper env co
531
532 (mktyconapp, mkappty, mkcastty)
533 | smart = (mkTyConApp, mkAppTy, mkCastTy)
534 | otherwise = (TyConApp, AppTy, CastTy)
535
536 {-# INLINABLE mapCoercion #-} -- See Note [Specialising mappers]
537 mapCoercion :: Monad m
538 => TyCoMapper env m -> env -> Coercion -> m Coercion
539 mapCoercion mapper@(TyCoMapper { tcm_smart = smart, tcm_covar = covar
540 , tcm_hole = cohole, tcm_tybinder = tybinder })
541 env co
542 = go co
543 where
544 go (Refl r ty) = Refl r <$> mapType mapper env ty
545 go (TyConAppCo r tc args)
546 = mktyconappco r tc <$> mapM go args
547 go (AppCo c1 c2) = mkappco <$> go c1 <*> go c2
548 go (ForAllCo tv kind_co co)
549 = do { kind_co' <- go kind_co
550 ; (env', tv') <- tybinder env tv Inferred
551 ; co' <- mapCoercion mapper env' co
552 ; return $ mkforallco tv' kind_co' co' }
553 -- See Note [Efficiency for mapCoercion ForAllCo case]
554 go (FunCo r c1 c2) = mkFunCo r <$> go c1 <*> go c2
555 go (CoVarCo cv) = covar env cv
556 go (AxiomInstCo ax i args)
557 = mkaxiominstco ax i <$> mapM go args
558 go (HoleCo hole) = cohole env hole
559 go (UnivCo p r t1 t2)
560 = mkunivco <$> go_prov p <*> pure r
561 <*> mapType mapper env t1 <*> mapType mapper env t2
562 go (SymCo co) = mksymco <$> go co
563 go (TransCo c1 c2) = mktransco <$> go c1 <*> go c2
564 go (AxiomRuleCo r cos) = AxiomRuleCo r <$> mapM go cos
565 go (NthCo r i co) = mknthco r i <$> go co
566 go (LRCo lr co) = mklrco lr <$> go co
567 go (InstCo co arg) = mkinstco <$> go co <*> go arg
568 go (CoherenceCo c1 c2) = mkcoherenceco <$> go c1 <*> go c2
569 go (KindCo co) = mkkindco <$> go co
570 go (SubCo co) = mksubco <$> go co
571
572 go_prov UnsafeCoerceProv = return UnsafeCoerceProv
573 go_prov (PhantomProv co) = PhantomProv <$> go co
574 go_prov (ProofIrrelProv co) = ProofIrrelProv <$> go co
575 go_prov p@(PluginProv _) = return p
576
577 ( mktyconappco, mkappco, mkaxiominstco, mkunivco
578 , mksymco, mktransco, mknthco, mklrco, mkinstco, mkcoherenceco
579 , mkkindco, mksubco, mkforallco)
580 | smart
581 = ( mkTyConAppCo, mkAppCo, mkAxiomInstCo, mkUnivCo
582 , mkSymCo, mkTransCo, mkNthCo, mkLRCo, mkInstCo, mkCoherenceCo
583 , mkKindCo, mkSubCo, mkForAllCo )
584 | otherwise
585 = ( TyConAppCo, AppCo, AxiomInstCo, UnivCo
586 , SymCo, TransCo, NthCo, LRCo, InstCo, CoherenceCo
587 , KindCo, SubCo, ForAllCo )
588
589 {-
590 ************************************************************************
591 * *
592 \subsection{Constructor-specific functions}
593 * *
594 ************************************************************************
595
596
597 ---------------------------------------------------------------------
598 TyVarTy
599 ~~~~~~~
600 -}
601
602 -- | Attempts to obtain the type variable underlying a 'Type', and panics with the
603 -- given message if this is not a type variable type. See also 'getTyVar_maybe'
604 getTyVar :: String -> Type -> TyVar
605 getTyVar msg ty = case getTyVar_maybe ty of
606 Just tv -> tv
607 Nothing -> panic ("getTyVar: " ++ msg)
608
609 isTyVarTy :: Type -> Bool
610 isTyVarTy ty = isJust (getTyVar_maybe ty)
611
612 -- | Attempts to obtain the type variable underlying a 'Type'
613 getTyVar_maybe :: Type -> Maybe TyVar
614 getTyVar_maybe ty | Just ty' <- coreView ty = getTyVar_maybe ty'
615 | otherwise = repGetTyVar_maybe ty
616
617 -- | If the type is a tyvar, possibly under a cast, returns it, along
618 -- with the coercion. Thus, the co is :: kind tv ~N kind type
619 getCastedTyVar_maybe :: Type -> Maybe (TyVar, CoercionN)
620 getCastedTyVar_maybe ty | Just ty' <- coreView ty = getCastedTyVar_maybe ty'
621 getCastedTyVar_maybe (CastTy (TyVarTy tv) co) = Just (tv, co)
622 getCastedTyVar_maybe (TyVarTy tv)
623 = Just (tv, mkReflCo Nominal (tyVarKind tv))
624 getCastedTyVar_maybe _ = Nothing
625
626 -- | Attempts to obtain the type variable underlying a 'Type', without
627 -- any expansion
628 repGetTyVar_maybe :: Type -> Maybe TyVar
629 repGetTyVar_maybe (TyVarTy tv) = Just tv
630 repGetTyVar_maybe _ = Nothing
631
632 {-
633 ---------------------------------------------------------------------
634 AppTy
635 ~~~~~
636 We need to be pretty careful with AppTy to make sure we obey the
637 invariant that a TyConApp is always visibly so. mkAppTy maintains the
638 invariant: use it.
639
640 Note [Decomposing fat arrow c=>t]
641 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
642 Can we unify (a b) with (Eq a => ty)? If we do so, we end up with
643 a partial application like ((=>) Eq a) which doesn't make sense in
644 source Haskell. In contrast, we *can* unify (a b) with (t1 -> t2).
645 Here's an example (Trac #9858) of how you might do it:
646 i :: (Typeable a, Typeable b) => Proxy (a b) -> TypeRep
647 i p = typeRep p
648
649 j = i (Proxy :: Proxy (Eq Int => Int))
650 The type (Proxy (Eq Int => Int)) is only accepted with -XImpredicativeTypes,
651 but suppose we want that. But then in the call to 'i', we end
652 up decomposing (Eq Int => Int), and we definitely don't want that.
653
654 This really only applies to the type checker; in Core, '=>' and '->'
655 are the same, as are 'Constraint' and '*'. But for now I've put
656 the test in repSplitAppTy_maybe, which applies throughout, because
657 the other calls to splitAppTy are in Unify, which is also used by
658 the type checker (e.g. when matching type-function equations).
659
660 -}
661
662 -- | Applies a type to another, as in e.g. @k a@
663 mkAppTy :: Type -> Type -> Type
664 -- See Note [Respecting definitional equality], invariant (EQ1).
665 mkAppTy (CastTy fun_ty co) arg_ty
666 | ([arg_co], res_co) <- decomposePiCos (typeKind fun_ty) [arg_ty] co
667 = (fun_ty `mkAppTy` (arg_ty `mkCastTy` arg_co)) `mkCastTy` res_co
668
669 mkAppTy (TyConApp tc tys) ty2 = mkTyConApp tc (tys ++ [ty2])
670 mkAppTy ty1 ty2 = AppTy ty1 ty2
671 -- Note that the TyConApp could be an
672 -- under-saturated type synonym. GHC allows that; e.g.
673 -- type Foo k = k a -> k a
674 -- type Id x = x
675 -- foo :: Foo Id -> Foo Id
676 --
677 -- Here Id is partially applied in the type sig for Foo,
678 -- but once the type synonyms are expanded all is well
679
680 mkAppTys :: Type -> [Type] -> Type
681 mkAppTys ty1 [] = ty1
682 mkAppTys (CastTy fun_ty co) arg_tys -- much more efficient then nested mkAppTy
683 -- Why do this? See (EQ1) of
684 -- Note [Respecting definitional equality]
685 -- in TyCoRep
686 = foldl AppTy ((mkAppTys fun_ty casted_arg_tys) `mkCastTy` res_co) leftovers
687 where
688 (arg_cos, res_co) = decomposePiCos (typeKind fun_ty) arg_tys co
689 (args_to_cast, leftovers) = splitAtList arg_cos arg_tys
690 casted_arg_tys = zipWith mkCastTy args_to_cast arg_cos
691 mkAppTys (TyConApp tc tys1) tys2 = mkTyConApp tc (tys1 ++ tys2)
692 mkAppTys ty1 tys2 = foldl AppTy ty1 tys2
693
694 -------------
695 splitAppTy_maybe :: Type -> Maybe (Type, Type)
696 -- ^ Attempt to take a type application apart, whether it is a
697 -- function, type constructor, or plain type application. Note
698 -- that type family applications are NEVER unsaturated by this!
699 splitAppTy_maybe ty | Just ty' <- coreView ty
700 = splitAppTy_maybe ty'
701 splitAppTy_maybe ty = repSplitAppTy_maybe ty
702
703 -------------
704 repSplitAppTy_maybe :: HasDebugCallStack => Type -> Maybe (Type,Type)
705 -- ^ Does the AppTy split as in 'splitAppTy_maybe', but assumes that
706 -- any Core view stuff is already done
707 repSplitAppTy_maybe (FunTy ty1 ty2)
708 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
709 where
710 rep1 = getRuntimeRep ty1
711 rep2 = getRuntimeRep ty2
712
713 repSplitAppTy_maybe (AppTy ty1 ty2)
714 = Just (ty1, ty2)
715
716 repSplitAppTy_maybe (TyConApp tc tys)
717 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
718 , Just (tys', ty') <- snocView tys
719 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
720
721 repSplitAppTy_maybe _other = Nothing
722
723 -- this one doesn't braek apart (c => t).
724 -- See Note [Decomposing fat arrow c=>t]
725 -- Defined here to avoid module loops between Unify and TcType.
726 tcRepSplitAppTy_maybe :: Type -> Maybe (Type,Type)
727 -- ^ Does the AppTy split as in 'tcSplitAppTy_maybe', but assumes that
728 -- any coreView stuff is already done. Refuses to look through (c => t)
729 tcRepSplitAppTy_maybe (FunTy ty1 ty2)
730 | isConstraintKind (typeKind ty1)
731 = Nothing -- See Note [Decomposing fat arrow c=>t]
732
733 | otherwise
734 = Just (TyConApp funTyCon [rep1, rep2, ty1], ty2)
735 where
736 rep1 = getRuntimeRep ty1
737 rep2 = getRuntimeRep ty2
738
739 tcRepSplitAppTy_maybe (AppTy ty1 ty2) = Just (ty1, ty2)
740 tcRepSplitAppTy_maybe (TyConApp tc tys)
741 | mightBeUnsaturatedTyCon tc || tys `lengthExceeds` tyConArity tc
742 , Just (tys', ty') <- snocView tys
743 = Just (TyConApp tc tys', ty') -- Never create unsaturated type family apps!
744 tcRepSplitAppTy_maybe _other = Nothing
745
746 -- | Split a type constructor application into its type constructor and
747 -- applied types. Note that this may fail in the case of a 'FunTy' with an
748 -- argument of unknown kind 'FunTy' (e.g. @FunTy (a :: k) Int@. since the kind
749 -- of @a@ isn't of the form @TYPE rep@). Consequently, you may need to zonk your
750 -- type before using this function.
751 --
752 -- If you only need the 'TyCon', consider using 'tcTyConAppTyCon_maybe'.
753 tcSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
754 -- Defined here to avoid module loops between Unify and TcType.
755 tcSplitTyConApp_maybe ty | Just ty' <- tcView ty = tcSplitTyConApp_maybe ty'
756 tcSplitTyConApp_maybe ty = tcRepSplitTyConApp_maybe ty
757
758 -- | Like 'tcSplitTyConApp_maybe' but doesn't look through type synonyms.
759 tcRepSplitTyConApp_maybe :: HasCallStack => Type -> Maybe (TyCon, [Type])
760 -- Defined here to avoid module loops between Unify and TcType.
761 tcRepSplitTyConApp_maybe (TyConApp tc tys)
762 = Just (tc, tys)
763
764 tcRepSplitTyConApp_maybe (FunTy arg res)
765 = Just (funTyCon, [arg_rep, res_rep, arg, res])
766 where
767 arg_rep = getRuntimeRep arg
768 res_rep = getRuntimeRep res
769
770 tcRepSplitTyConApp_maybe _
771 = Nothing
772
773 -------------
774 splitAppTy :: Type -> (Type, Type)
775 -- ^ Attempts to take a type application apart, as in 'splitAppTy_maybe',
776 -- and panics if this is not possible
777 splitAppTy ty = case splitAppTy_maybe ty of
778 Just pr -> pr
779 Nothing -> panic "splitAppTy"
780
781 -------------
782 splitAppTys :: Type -> (Type, [Type])
783 -- ^ Recursively splits a type as far as is possible, leaving a residual
784 -- type being applied to and the type arguments applied to it. Never fails,
785 -- even if that means returning an empty list of type applications.
786 splitAppTys ty = split ty ty []
787 where
788 split orig_ty ty args | Just ty' <- coreView ty = split orig_ty ty' args
789 split _ (AppTy ty arg) args = split ty ty (arg:args)
790 split _ (TyConApp tc tc_args) args
791 = let -- keep type families saturated
792 n | mightBeUnsaturatedTyCon tc = 0
793 | otherwise = tyConArity tc
794 (tc_args1, tc_args2) = splitAt n tc_args
795 in
796 (TyConApp tc tc_args1, tc_args2 ++ args)
797 split _ (FunTy ty1 ty2) args
798 = ASSERT( null args )
799 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
800 where
801 rep1 = getRuntimeRep ty1
802 rep2 = getRuntimeRep ty2
803
804 split orig_ty _ args = (orig_ty, args)
805
806 -- | Like 'splitAppTys', but doesn't look through type synonyms
807 repSplitAppTys :: HasDebugCallStack => Type -> (Type, [Type])
808 repSplitAppTys ty = split ty []
809 where
810 split (AppTy ty arg) args = split ty (arg:args)
811 split (TyConApp tc tc_args) args
812 = let n | mightBeUnsaturatedTyCon tc = 0
813 | otherwise = tyConArity tc
814 (tc_args1, tc_args2) = splitAt n tc_args
815 in
816 (TyConApp tc tc_args1, tc_args2 ++ args)
817 split (FunTy ty1 ty2) args
818 = ASSERT( null args )
819 (TyConApp funTyCon [], [rep1, rep2, ty1, ty2])
820 where
821 rep1 = getRuntimeRep ty1
822 rep2 = getRuntimeRep ty2
823
824 split ty args = (ty, args)
825
826 {-
827 LitTy
828 ~~~~~
829 -}
830
831 mkNumLitTy :: Integer -> Type
832 mkNumLitTy n = LitTy (NumTyLit n)
833
834 -- | Is this a numeric literal. We also look through type synonyms.
835 isNumLitTy :: Type -> Maybe Integer
836 isNumLitTy ty | Just ty1 <- coreView ty = isNumLitTy ty1
837 isNumLitTy (LitTy (NumTyLit n)) = Just n
838 isNumLitTy _ = Nothing
839
840 mkStrLitTy :: FastString -> Type
841 mkStrLitTy s = LitTy (StrTyLit s)
842
843 -- | Is this a symbol literal. We also look through type synonyms.
844 isStrLitTy :: Type -> Maybe FastString
845 isStrLitTy ty | Just ty1 <- coreView ty = isStrLitTy ty1
846 isStrLitTy (LitTy (StrTyLit s)) = Just s
847 isStrLitTy _ = Nothing
848
849
850 -- | Is this type a custom user error?
851 -- If so, give us the kind and the error message.
852 userTypeError_maybe :: Type -> Maybe Type
853 userTypeError_maybe t
854 = do { (tc, _kind : msg : _) <- splitTyConApp_maybe t
855 -- There may be more than 2 arguments, if the type error is
856 -- used as a type constructor (e.g. at kind `Type -> Type`).
857
858 ; guard (tyConName tc == errorMessageTypeErrorFamName)
859 ; return msg }
860
861 -- | Render a type corresponding to a user type error into a SDoc.
862 pprUserTypeErrorTy :: Type -> SDoc
863 pprUserTypeErrorTy ty =
864 case splitTyConApp_maybe ty of
865
866 -- Text "Something"
867 Just (tc,[txt])
868 | tyConName tc == typeErrorTextDataConName
869 , Just str <- isStrLitTy txt -> ftext str
870
871 -- ShowType t
872 Just (tc,[_k,t])
873 | tyConName tc == typeErrorShowTypeDataConName -> ppr t
874
875 -- t1 :<>: t2
876 Just (tc,[t1,t2])
877 | tyConName tc == typeErrorAppendDataConName ->
878 pprUserTypeErrorTy t1 <> pprUserTypeErrorTy t2
879
880 -- t1 :$$: t2
881 Just (tc,[t1,t2])
882 | tyConName tc == typeErrorVAppendDataConName ->
883 pprUserTypeErrorTy t1 $$ pprUserTypeErrorTy t2
884
885 -- An unevaluated type function
886 _ -> ppr ty
887
888
889
890
891 {-
892 ---------------------------------------------------------------------
893 FunTy
894 ~~~~~
895
896 Note [Representation of function types]
897 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
898
899 Functions (e.g. Int -> Char) are can be thought of as being applications
900 of funTyCon (known in Haskell surface syntax as (->)),
901
902 (->) :: forall (r1 :: RuntimeRep) (r2 :: RuntimeRep)
903 (a :: TYPE r1) (b :: TYPE r2).
904 a -> b -> Type
905
906 However, for efficiency's sake we represent saturated applications of (->)
907 with FunTy. For instance, the type,
908
909 (->) r1 r2 a b
910
911 is equivalent to,
912
913 FunTy (Anon a) b
914
915 Note how the RuntimeReps are implied in the FunTy representation. For this
916 reason we must be careful when recontructing the TyConApp representation (see,
917 for instance, splitTyConApp_maybe).
918
919 In the compiler we maintain the invariant that all saturated applications of
920 (->) are represented with FunTy.
921
922 See #11714.
923 -}
924
925 isFunTy :: Type -> Bool
926 isFunTy ty = isJust (splitFunTy_maybe ty)
927
928 splitFunTy :: Type -> (Type, Type)
929 -- ^ Attempts to extract the argument and result types from a type, and
930 -- panics if that is not possible. See also 'splitFunTy_maybe'
931 splitFunTy ty | Just ty' <- coreView ty = splitFunTy ty'
932 splitFunTy (FunTy arg res) = (arg, res)
933 splitFunTy other = pprPanic "splitFunTy" (ppr other)
934
935 splitFunTy_maybe :: Type -> Maybe (Type, Type)
936 -- ^ Attempts to extract the argument and result types from a type
937 splitFunTy_maybe ty | Just ty' <- coreView ty = splitFunTy_maybe ty'
938 splitFunTy_maybe (FunTy arg res) = Just (arg, res)
939 splitFunTy_maybe _ = Nothing
940
941 splitFunTys :: Type -> ([Type], Type)
942 splitFunTys ty = split [] ty ty
943 where
944 split args orig_ty ty | Just ty' <- coreView ty = split args orig_ty ty'
945 split args _ (FunTy arg res) = split (arg:args) res res
946 split args orig_ty _ = (reverse args, orig_ty)
947
948 funResultTy :: Type -> Type
949 -- ^ Extract the function result type and panic if that is not possible
950 funResultTy ty | Just ty' <- coreView ty = funResultTy ty'
951 funResultTy (FunTy _ res) = res
952 funResultTy ty = pprPanic "funResultTy" (ppr ty)
953
954 funArgTy :: Type -> Type
955 -- ^ Extract the function argument type and panic if that is not possible
956 funArgTy ty | Just ty' <- coreView ty = funArgTy ty'
957 funArgTy (FunTy arg _res) = arg
958 funArgTy ty = pprPanic "funArgTy" (ppr ty)
959
960 piResultTy :: HasDebugCallStack => Type -> Type -> Type
961 piResultTy ty arg = case piResultTy_maybe ty arg of
962 Just res -> res
963 Nothing -> pprPanic "piResultTy" (ppr ty $$ ppr arg)
964
965 piResultTy_maybe :: Type -> Type -> Maybe Type
966
967 -- ^ Just like 'piResultTys' but for a single argument
968 -- Try not to iterate 'piResultTy', because it's inefficient to substitute
969 -- one variable at a time; instead use 'piResultTys"
970 piResultTy_maybe ty arg
971 | Just ty' <- coreView ty = piResultTy_maybe ty' arg
972
973 | FunTy _ res <- ty
974 = Just res
975
976 | ForAllTy (TvBndr tv _) res <- ty
977 = let empty_subst = mkEmptyTCvSubst $ mkInScopeSet $
978 tyCoVarsOfTypes [arg,res]
979 in Just (substTy (extendTvSubst empty_subst tv arg) res)
980
981 | otherwise
982 = Nothing
983
984 -- | (piResultTys f_ty [ty1, .., tyn]) gives the type of (f ty1 .. tyn)
985 -- where f :: f_ty
986 -- 'piResultTys' is interesting because:
987 -- 1. 'f_ty' may have more for-alls than there are args
988 -- 2. Less obviously, it may have fewer for-alls
989 -- For case 2. think of:
990 -- piResultTys (forall a.a) [forall b.b, Int]
991 -- This really can happen, but only (I think) in situations involving
992 -- undefined. For example:
993 -- undefined :: forall a. a
994 -- Term: undefined @(forall b. b->b) @Int
995 -- This term should have type (Int -> Int), but notice that
996 -- there are more type args than foralls in 'undefined's type.
997
998 -- If you edit this function, you may need to update the GHC formalism
999 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
1000
1001 -- This is a heavily used function (e.g. from typeKind),
1002 -- so we pay attention to efficiency, especially in the special case
1003 -- where there are no for-alls so we are just dropping arrows from
1004 -- a function type/kind.
1005 piResultTys :: HasDebugCallStack => Type -> [Type] -> Type
1006 piResultTys ty [] = ty
1007 piResultTys ty orig_args@(arg:args)
1008 | Just ty' <- coreView ty
1009 = piResultTys ty' orig_args
1010
1011 | FunTy _ res <- ty
1012 = piResultTys res args
1013
1014 | ForAllTy (TvBndr tv _) res <- ty
1015 = go (extendVarEnv emptyTvSubstEnv tv arg) res args
1016
1017 | otherwise
1018 = pprPanic "piResultTys1" (ppr ty $$ ppr orig_args)
1019 where
1020 in_scope = mkInScopeSet (tyCoVarsOfTypes (ty:orig_args))
1021
1022 go :: TvSubstEnv -> Type -> [Type] -> Type
1023 go tv_env ty [] = substTy (mkTvSubst in_scope tv_env) ty
1024
1025 go tv_env ty all_args@(arg:args)
1026 | Just ty' <- coreView ty
1027 = go tv_env ty' all_args
1028
1029 | FunTy _ res <- ty
1030 = go tv_env res args
1031
1032 | ForAllTy (TvBndr tv _) res <- ty
1033 = go (extendVarEnv tv_env tv arg) res args
1034
1035 | TyVarTy tv <- ty
1036 , Just ty' <- lookupVarEnv tv_env tv
1037 -- Deals with piResultTys (forall a. a) [forall b.b, Int]
1038 = piResultTys ty' all_args
1039
1040 | otherwise
1041 = pprPanic "piResultTys2" (ppr ty $$ ppr orig_args $$ ppr all_args)
1042
1043 applyTysX :: [TyVar] -> Type -> [Type] -> Type
1044 -- applyTyxX beta-reduces (/\tvs. body_ty) arg_tys
1045 -- Assumes that (/\tvs. body_ty) is closed
1046 applyTysX tvs body_ty arg_tys
1047 = ASSERT2( arg_tys `lengthAtLeast` n_tvs, pp_stuff )
1048 ASSERT2( tyCoVarsOfType body_ty `subVarSet` mkVarSet tvs, pp_stuff )
1049 mkAppTys (substTyWith tvs (take n_tvs arg_tys) body_ty)
1050 (drop n_tvs arg_tys)
1051 where
1052 pp_stuff = vcat [ppr tvs, ppr body_ty, ppr arg_tys]
1053 n_tvs = length tvs
1054
1055 {-
1056 ---------------------------------------------------------------------
1057 TyConApp
1058 ~~~~~~~~
1059 -}
1060
1061 -- | A key function: builds a 'TyConApp' or 'FunTy' as appropriate to
1062 -- its arguments. Applies its arguments to the constructor from left to right.
1063 mkTyConApp :: TyCon -> [Type] -> Type
1064 mkTyConApp tycon tys
1065 | isFunTyCon tycon
1066 , [_rep1,_rep2,ty1,ty2] <- tys
1067 = FunTy ty1 ty2
1068
1069 | otherwise
1070 = TyConApp tycon tys
1071
1072 -- splitTyConApp "looks through" synonyms, because they don't
1073 -- mean a distinct type, but all other type-constructor applications
1074 -- including functions are returned as Just ..
1075
1076 -- | Retrieve the tycon heading this type, if there is one. Does /not/
1077 -- look through synonyms.
1078 tyConAppTyConPicky_maybe :: Type -> Maybe TyCon
1079 tyConAppTyConPicky_maybe (TyConApp tc _) = Just tc
1080 tyConAppTyConPicky_maybe (FunTy {}) = Just funTyCon
1081 tyConAppTyConPicky_maybe _ = Nothing
1082
1083
1084 -- | The same as @fst . splitTyConApp@
1085 tyConAppTyCon_maybe :: Type -> Maybe TyCon
1086 tyConAppTyCon_maybe ty | Just ty' <- coreView ty = tyConAppTyCon_maybe ty'
1087 tyConAppTyCon_maybe (TyConApp tc _) = Just tc
1088 tyConAppTyCon_maybe (FunTy {}) = Just funTyCon
1089 tyConAppTyCon_maybe _ = Nothing
1090
1091 tyConAppTyCon :: Type -> TyCon
1092 tyConAppTyCon ty = tyConAppTyCon_maybe ty `orElse` pprPanic "tyConAppTyCon" (ppr ty)
1093
1094 -- | The same as @snd . splitTyConApp@
1095 tyConAppArgs_maybe :: Type -> Maybe [Type]
1096 tyConAppArgs_maybe ty | Just ty' <- coreView ty = tyConAppArgs_maybe ty'
1097 tyConAppArgs_maybe (TyConApp _ tys) = Just tys
1098 tyConAppArgs_maybe (FunTy arg res)
1099 | Just rep1 <- getRuntimeRep_maybe arg
1100 , Just rep2 <- getRuntimeRep_maybe res
1101 = Just [rep1, rep2, arg, res]
1102 tyConAppArgs_maybe _ = Nothing
1103
1104 tyConAppArgs :: Type -> [Type]
1105 tyConAppArgs ty = tyConAppArgs_maybe ty `orElse` pprPanic "tyConAppArgs" (ppr ty)
1106
1107 tyConAppArgN :: Int -> Type -> Type
1108 -- Executing Nth
1109 tyConAppArgN n ty
1110 = case tyConAppArgs_maybe ty of
1111 Just tys -> ASSERT2( tys `lengthExceeds` n, ppr n <+> ppr tys ) tys `getNth` n
1112 Nothing -> pprPanic "tyConAppArgN" (ppr n <+> ppr ty)
1113
1114 -- | Attempts to tease a type apart into a type constructor and the application
1115 -- of a number of arguments to that constructor. Panics if that is not possible.
1116 -- See also 'splitTyConApp_maybe'
1117 splitTyConApp :: Type -> (TyCon, [Type])
1118 splitTyConApp ty = case splitTyConApp_maybe ty of
1119 Just stuff -> stuff
1120 Nothing -> pprPanic "splitTyConApp" (ppr ty)
1121
1122 -- | Attempts to tease a type apart into a type constructor and the application
1123 -- of a number of arguments to that constructor
1124 splitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1125 splitTyConApp_maybe ty | Just ty' <- coreView ty = splitTyConApp_maybe ty'
1126 splitTyConApp_maybe ty = repSplitTyConApp_maybe ty
1127
1128 -- | Like 'splitTyConApp_maybe', but doesn't look through synonyms. This
1129 -- assumes the synonyms have already been dealt with.
1130 repSplitTyConApp_maybe :: HasDebugCallStack => Type -> Maybe (TyCon, [Type])
1131 repSplitTyConApp_maybe (TyConApp tc tys) = Just (tc, tys)
1132 repSplitTyConApp_maybe (FunTy arg res)
1133 | Just arg_rep <- getRuntimeRep_maybe arg
1134 , Just res_rep <- getRuntimeRep_maybe res
1135 = Just (funTyCon, [arg_rep, res_rep, arg, res])
1136 repSplitTyConApp_maybe _ = Nothing
1137
1138 -- | Attempts to tease a list type apart and gives the type of the elements if
1139 -- successful (looks through type synonyms)
1140 splitListTyConApp_maybe :: Type -> Maybe Type
1141 splitListTyConApp_maybe ty = case splitTyConApp_maybe ty of
1142 Just (tc,[e]) | tc == listTyCon -> Just e
1143 _other -> Nothing
1144
1145 nextRole :: Type -> Role
1146 nextRole ty
1147 | Just (tc, tys) <- splitTyConApp_maybe ty
1148 , let num_tys = length tys
1149 , num_tys < tyConArity tc
1150 = tyConRoles tc `getNth` num_tys
1151
1152 | otherwise
1153 = Nominal
1154
1155 newTyConInstRhs :: TyCon -> [Type] -> Type
1156 -- ^ Unwrap one 'layer' of newtype on a type constructor and its
1157 -- arguments, using an eta-reduced version of the @newtype@ if possible.
1158 -- This requires tys to have at least @newTyConInstArity tycon@ elements.
1159 newTyConInstRhs tycon tys
1160 = ASSERT2( tvs `leLength` tys, ppr tycon $$ ppr tys $$ ppr tvs )
1161 applyTysX tvs rhs tys
1162 where
1163 (tvs, rhs) = newTyConEtadRhs tycon
1164
1165 {-
1166 ---------------------------------------------------------------------
1167 CastTy
1168 ~~~~~~
1169 A casted type has its *kind* casted into something new.
1170
1171 -}
1172
1173 splitCastTy_maybe :: Type -> Maybe (Type, Coercion)
1174 splitCastTy_maybe ty | Just ty' <- coreView ty = splitCastTy_maybe ty'
1175 splitCastTy_maybe (CastTy ty co) = Just (ty, co)
1176 splitCastTy_maybe _ = Nothing
1177
1178 -- | Make a 'CastTy'. The Coercion must be nominal. Checks the
1179 -- Coercion for reflexivity, dropping it if it's reflexive.
1180 -- See Note [Respecting definitional equality] in TyCoRep
1181 mkCastTy :: Type -> Coercion -> Type
1182 mkCastTy ty co | isReflexiveCo co = ty -- (EQ2) from the Note
1183 -- NB: Do the slow check here. This is important to keep the splitXXX
1184 -- functions working properly. Otherwise, we may end up with something
1185 -- like (((->) |> something_reflexive_but_not_obviously_so) biz baz)
1186 -- fails under splitFunTy_maybe. This happened with the cheaper check
1187 -- in test dependent/should_compile/dynamic-paper.
1188
1189 mkCastTy (CastTy ty co1) co2 = mkCastTy ty (co1 `mkTransCo` co2) -- (EQ3) from the Note
1190 -- call mkCastTy again for the reflexivity check
1191 mkCastTy ty co = CastTy ty co
1192
1193 tyConBindersTyBinders :: [TyConBinder] -> [TyBinder]
1194 -- Return the tyConBinders in TyBinder form
1195 tyConBindersTyBinders = map to_tyb
1196 where
1197 to_tyb (TvBndr tv (NamedTCB vis)) = Named (TvBndr tv vis)
1198 to_tyb (TvBndr tv AnonTCB) = Anon (tyVarKind tv)
1199
1200 {-
1201 --------------------------------------------------------------------
1202 CoercionTy
1203 ~~~~~~~~~~
1204 CoercionTy allows us to inject coercions into types. A CoercionTy
1205 should appear only in the right-hand side of an application.
1206 -}
1207
1208 mkCoercionTy :: Coercion -> Type
1209 mkCoercionTy = CoercionTy
1210
1211 isCoercionTy :: Type -> Bool
1212 isCoercionTy (CoercionTy _) = True
1213 isCoercionTy _ = False
1214
1215 isCoercionTy_maybe :: Type -> Maybe Coercion
1216 isCoercionTy_maybe (CoercionTy co) = Just co
1217 isCoercionTy_maybe _ = Nothing
1218
1219 stripCoercionTy :: Type -> Coercion
1220 stripCoercionTy (CoercionTy co) = co
1221 stripCoercionTy ty = pprPanic "stripCoercionTy" (ppr ty)
1222
1223 {-
1224 ---------------------------------------------------------------------
1225 SynTy
1226 ~~~~~
1227
1228 Notes on type synonyms
1229 ~~~~~~~~~~~~~~~~~~~~~~
1230 The various "split" functions (splitFunTy, splitRhoTy, splitForAllTy) try
1231 to return type synonyms wherever possible. Thus
1232
1233 type Foo a = a -> a
1234
1235 we want
1236 splitFunTys (a -> Foo a) = ([a], Foo a)
1237 not ([a], a -> a)
1238
1239 The reason is that we then get better (shorter) type signatures in
1240 interfaces. Notably this plays a role in tcTySigs in TcBinds.hs.
1241
1242
1243 ---------------------------------------------------------------------
1244 ForAllTy
1245 ~~~~~~~~
1246 -}
1247
1248 -- | Make a dependent forall over an Inferred (as opposed to Specified)
1249 -- variable
1250 mkInvForAllTy :: TyVar -> Type -> Type
1251 mkInvForAllTy tv ty = ASSERT( isTyVar tv )
1252 ForAllTy (TvBndr tv Inferred) ty
1253
1254 -- | Like mkForAllTys, but assumes all variables are dependent and Inferred,
1255 -- a common case
1256 mkInvForAllTys :: [TyVar] -> Type -> Type
1257 mkInvForAllTys tvs ty = ASSERT( all isTyVar tvs )
1258 foldr mkInvForAllTy ty tvs
1259
1260 -- | Like mkForAllTys, but assumes all variables are dependent and specified,
1261 -- a common case
1262 mkSpecForAllTys :: [TyVar] -> Type -> Type
1263 mkSpecForAllTys tvs = ASSERT( all isTyVar tvs )
1264 mkForAllTys [ TvBndr tv Specified | tv <- tvs ]
1265
1266 -- | Like mkForAllTys, but assumes all variables are dependent and visible
1267 mkVisForAllTys :: [TyVar] -> Type -> Type
1268 mkVisForAllTys tvs = ASSERT( all isTyVar tvs )
1269 mkForAllTys [ TvBndr tv Required | tv <- tvs ]
1270
1271 mkLamType :: Var -> Type -> Type
1272 -- ^ Makes a @(->)@ type or an implicit forall type, depending
1273 -- on whether it is given a type variable or a term variable.
1274 -- This is used, for example, when producing the type of a lambda.
1275 -- Always uses Inferred binders.
1276 mkLamTypes :: [Var] -> Type -> Type
1277 -- ^ 'mkLamType' for multiple type or value arguments
1278
1279 mkLamType v ty
1280 | isTyVar v = ForAllTy (TvBndr v Inferred) ty
1281 | otherwise = FunTy (varType v) ty
1282
1283 mkLamTypes vs ty = foldr mkLamType ty vs
1284
1285 -- | Given a list of type-level vars and a result kind,
1286 -- makes TyBinders, preferring anonymous binders
1287 -- if the variable is, in fact, not dependent.
1288 -- e.g. mkTyConBindersPreferAnon [(k:*),(b:k),(c:k)] (k->k)
1289 -- We want (k:*) Named, (a;k) Anon, (c:k) Anon
1290 --
1291 -- All binders are /visible/.
1292 mkTyConBindersPreferAnon :: [TyVar] -> Type -> [TyConBinder]
1293 mkTyConBindersPreferAnon vars inner_ty = fst (go vars)
1294 where
1295 go :: [TyVar] -> ([TyConBinder], VarSet) -- also returns the free vars
1296 go [] = ([], tyCoVarsOfType inner_ty)
1297 go (v:vs) | v `elemVarSet` fvs
1298 = ( TvBndr v (NamedTCB Required) : binders
1299 , fvs `delVarSet` v `unionVarSet` kind_vars )
1300 | otherwise
1301 = ( TvBndr v AnonTCB : binders
1302 , fvs `unionVarSet` kind_vars )
1303 where
1304 (binders, fvs) = go vs
1305 kind_vars = tyCoVarsOfType $ tyVarKind v
1306
1307 -- | Take a ForAllTy apart, returning the list of tyvars and the result type.
1308 -- This always succeeds, even if it returns only an empty list. Note that the
1309 -- result type returned may have free variables that were bound by a forall.
1310 splitForAllTys :: Type -> ([TyVar], Type)
1311 splitForAllTys ty = split ty ty []
1312 where
1313 split orig_ty ty tvs | Just ty' <- coreView ty = split orig_ty ty' tvs
1314 split _ (ForAllTy (TvBndr tv _) ty) tvs = split ty ty (tv:tvs)
1315 split orig_ty _ tvs = (reverse tvs, orig_ty)
1316
1317 -- | Like 'splitPiTys' but split off only /named/ binders.
1318 splitForAllTyVarBndrs :: Type -> ([TyVarBinder], Type)
1319 splitForAllTyVarBndrs ty = split ty ty []
1320 where
1321 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1322 split _ (ForAllTy b res) bs = split res res (b:bs)
1323 split orig_ty _ bs = (reverse bs, orig_ty)
1324 {-# INLINE splitForAllTyVarBndrs #-}
1325
1326 -- | Checks whether this is a proper forall (with a named binder)
1327 isForAllTy :: Type -> Bool
1328 isForAllTy ty | Just ty' <- coreView ty = isForAllTy ty'
1329 isForAllTy (ForAllTy {}) = True
1330 isForAllTy _ = False
1331
1332 -- | Is this a function or forall?
1333 isPiTy :: Type -> Bool
1334 isPiTy ty | Just ty' <- coreView ty = isForAllTy ty'
1335 isPiTy (ForAllTy {}) = True
1336 isPiTy (FunTy {}) = True
1337 isPiTy _ = False
1338
1339 -- | Take a forall type apart, or panics if that is not possible.
1340 splitForAllTy :: Type -> (TyVar, Type)
1341 splitForAllTy ty
1342 | Just answer <- splitForAllTy_maybe ty = answer
1343 | otherwise = pprPanic "splitForAllTy" (ppr ty)
1344
1345 -- | Drops all ForAllTys
1346 dropForAlls :: Type -> Type
1347 dropForAlls ty = go ty
1348 where
1349 go ty | Just ty' <- coreView ty = go ty'
1350 go (ForAllTy _ res) = go res
1351 go res = res
1352
1353 -- | Attempts to take a forall type apart, but only if it's a proper forall,
1354 -- with a named binder
1355 splitForAllTy_maybe :: Type -> Maybe (TyVar, Type)
1356 splitForAllTy_maybe ty = go ty
1357 where
1358 go ty | Just ty' <- coreView ty = go ty'
1359 go (ForAllTy (TvBndr tv _) ty) = Just (tv, ty)
1360 go _ = Nothing
1361
1362 -- | Attempts to take a forall type apart; works with proper foralls and
1363 -- functions
1364 splitPiTy_maybe :: Type -> Maybe (TyBinder, Type)
1365 splitPiTy_maybe ty = go ty
1366 where
1367 go ty | Just ty' <- coreView ty = go ty'
1368 go (ForAllTy bndr ty) = Just (Named bndr, ty)
1369 go (FunTy arg res) = Just (Anon arg, res)
1370 go _ = Nothing
1371
1372 -- | Takes a forall type apart, or panics
1373 splitPiTy :: Type -> (TyBinder, Type)
1374 splitPiTy ty
1375 | Just answer <- splitPiTy_maybe ty = answer
1376 | otherwise = pprPanic "splitPiTy" (ppr ty)
1377
1378 -- | Split off all TyBinders to a type, splitting both proper foralls
1379 -- and functions
1380 splitPiTys :: Type -> ([TyBinder], Type)
1381 splitPiTys ty = split ty ty
1382 where
1383 split orig_ty ty | Just ty' <- coreView ty = split orig_ty ty'
1384 split _ (ForAllTy b res) = let (bs, ty) = split res res
1385 in (Named b : bs, ty)
1386 split _ (FunTy arg res) = let (bs, ty) = split res res
1387 in (Anon arg : bs, ty)
1388 split orig_ty _ = ([], orig_ty)
1389
1390 -- Like splitPiTys, but returns only *invisible* binders, including constraints
1391 -- Stops at the first visible binder
1392 splitPiTysInvisible :: Type -> ([TyBinder], Type)
1393 splitPiTysInvisible ty = split ty ty []
1394 where
1395 split orig_ty ty bs | Just ty' <- coreView ty = split orig_ty ty' bs
1396 split _ (ForAllTy b@(TvBndr _ vis) res) bs
1397 | isInvisibleArgFlag vis = split res res (Named b : bs)
1398 split _ (FunTy arg res) bs
1399 | isPredTy arg = split res res (Anon arg : bs)
1400 split orig_ty _ bs = (reverse bs, orig_ty)
1401
1402 -- | Given a tycon and its arguments, filters out any invisible arguments
1403 filterOutInvisibleTypes :: TyCon -> [Type] -> [Type]
1404 filterOutInvisibleTypes tc tys = snd $ partitionInvisibles tc id tys
1405
1406 -- | Given a tycon and a list of things (which correspond to arguments),
1407 -- partitions the things into
1408 -- Inferred or Specified ones and
1409 -- Required ones
1410 -- The callback function is necessary for this scenario:
1411 --
1412 -- > T :: forall k. k -> k
1413 -- > partitionInvisibles T [forall m. m -> m -> m, S, R, Q]
1414 --
1415 -- After substituting, we get
1416 --
1417 -- > T (forall m. m -> m -> m) :: (forall m. m -> m -> m) -> forall n. n -> n -> n
1418 --
1419 -- Thus, the first argument is invisible, @S@ is visible, @R@ is invisible again,
1420 -- and @Q@ is visible.
1421 --
1422 -- If you're absolutely sure that your tycon's kind doesn't end in a variable,
1423 -- it's OK if the callback function panics, as that's the only time it's
1424 -- consulted.
1425 partitionInvisibles :: TyCon -> (a -> Type) -> [a] -> ([a], [a])
1426 partitionInvisibles tc get_ty = go emptyTCvSubst (tyConKind tc)
1427 where
1428 go _ _ [] = ([], [])
1429 go subst (ForAllTy (TvBndr tv vis) res_ki) (x:xs)
1430 | isVisibleArgFlag vis = second (x :) (go subst' res_ki xs)
1431 | otherwise = first (x :) (go subst' res_ki xs)
1432 where
1433 subst' = extendTvSubst subst tv (get_ty x)
1434 go subst (TyVarTy tv) xs
1435 | Just ki <- lookupTyVar subst tv = go subst ki xs
1436 go _ _ xs = ([], xs) -- something is ill-kinded. But this can happen
1437 -- when printing errors. Assume everything is visible.
1438
1439 -- @isTauTy@ tests if a type has no foralls
1440 isTauTy :: Type -> Bool
1441 isTauTy ty | Just ty' <- coreView ty = isTauTy ty'
1442 isTauTy (TyVarTy _) = True
1443 isTauTy (LitTy {}) = True
1444 isTauTy (TyConApp tc tys) = all isTauTy tys && isTauTyCon tc
1445 isTauTy (AppTy a b) = isTauTy a && isTauTy b
1446 isTauTy (FunTy a b) = isTauTy a && isTauTy b
1447 isTauTy (ForAllTy {}) = False
1448 isTauTy (CastTy ty _) = isTauTy ty
1449 isTauTy (CoercionTy _) = False -- Not sure about this
1450
1451 {-
1452 %************************************************************************
1453 %* *
1454 TyBinders
1455 %* *
1456 %************************************************************************
1457 -}
1458
1459 -- | Make an anonymous binder
1460 mkAnonBinder :: Type -> TyBinder
1461 mkAnonBinder = Anon
1462
1463 -- | Does this binder bind a variable that is /not/ erased? Returns
1464 -- 'True' for anonymous binders.
1465 isAnonTyBinder :: TyBinder -> Bool
1466 isAnonTyBinder (Named {}) = False
1467 isAnonTyBinder (Anon {}) = True
1468
1469 isNamedTyBinder :: TyBinder -> Bool
1470 isNamedTyBinder (Named {}) = True
1471 isNamedTyBinder (Anon {}) = False
1472
1473 tyBinderVar_maybe :: TyBinder -> Maybe TyVar
1474 tyBinderVar_maybe (Named tv) = Just $ binderVar tv
1475 tyBinderVar_maybe _ = Nothing
1476
1477 tyBinderType :: TyBinder -> Type
1478 -- Barely used
1479 tyBinderType (Named tvb) = binderKind tvb
1480 tyBinderType (Anon ty) = ty
1481
1482 -- | Extract a relevant type, if there is one.
1483 binderRelevantType_maybe :: TyBinder -> Maybe Type
1484 binderRelevantType_maybe (Named {}) = Nothing
1485 binderRelevantType_maybe (Anon ty) = Just ty
1486
1487 -- | Like 'maybe', but for binders.
1488 caseBinder :: TyBinder -- ^ binder to scrutinize
1489 -> (TyVarBinder -> a) -- ^ named case
1490 -> (Type -> a) -- ^ anonymous case
1491 -> a
1492 caseBinder (Named v) f _ = f v
1493 caseBinder (Anon t) _ d = d t
1494
1495
1496 {-
1497 %************************************************************************
1498 %* *
1499 Pred
1500 * *
1501 ************************************************************************
1502
1503 Predicates on PredType
1504
1505 Note [isPredTy complications]
1506 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1507 You would think that we could define
1508 isPredTy ty = isConstraintKind (typeKind ty)
1509 But there are a number of complications:
1510
1511 * isPredTy is used when printing types, which can happen in debug
1512 printing during type checking of not-fully-zonked types. So it's
1513 not cool to say isConstraintKind (typeKind ty) because, absent
1514 zonking, the type might be ill-kinded, and typeKind crashes. Hence the
1515 rather tiresome story here
1516
1517 * isPredTy must return "True" to *unlifted* coercions, such as (t1 ~# t2)
1518 and (t1 ~R# t2), which are not of kind Constraint! Currently they are
1519 of kind #.
1520
1521 * If we do form the type '(C a => C [a]) => blah', then we'd like to
1522 print it as such. But that means that isPredTy must return True for
1523 (C a => C [a]). Admittedly that type is illegal in Haskell, but we
1524 want to print it nicely in error messages.
1525 -}
1526
1527 -- | Is the type suitable to classify a given/wanted in the typechecker?
1528 isPredTy :: Type -> Bool
1529 -- See Note [isPredTy complications]
1530 isPredTy ty = go ty []
1531 where
1532 go :: Type -> [KindOrType] -> Bool
1533 go (AppTy ty1 ty2) args = go ty1 (ty2 : args)
1534 go (TyVarTy tv) args = go_k (tyVarKind tv) args
1535 go (TyConApp tc tys) args = ASSERT( null args ) -- TyConApp invariant
1536 go_tc tc tys
1537 go (FunTy arg res) []
1538 | isPredTy arg = isPredTy res -- (Eq a => C a)
1539 | otherwise = False -- (Int -> Bool)
1540 go (ForAllTy _ ty) [] = go ty []
1541 go (CastTy _ co) args = go_k (pSnd (coercionKind co)) args
1542 go _ _ = False
1543
1544 go_tc :: TyCon -> [KindOrType] -> Bool
1545 go_tc tc args
1546 | tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1547 = args `lengthIs` 4 -- ~# and ~R# sadly have result kind #
1548 -- not Constraint; but we still want
1549 -- isPredTy to reply True.
1550 | otherwise = go_k (tyConKind tc) args
1551
1552 go_k :: Kind -> [KindOrType] -> Bool
1553 -- True <=> ('k' applied to 'kts') = Constraint
1554 go_k k [] = isConstraintKind k
1555 go_k k (arg:args) = case piResultTy_maybe k arg of
1556 Just k' -> go_k k' args
1557 Nothing -> WARN( True, text "isPredTy" <+> ppr ty )
1558 False
1559 -- This last case shouldn't happen under most circumstances. It can
1560 -- occur if we call isPredTy during kind checking, especially if one
1561 -- of the following happens:
1562 --
1563 -- 1. There is actually a kind error. Example in which this showed up:
1564 -- polykinds/T11399
1565 --
1566 -- 2. A type constructor application appears to be oversaturated. An
1567 -- example of this occurred in GHC Trac #13187:
1568 --
1569 -- {-# LANGUAGE PolyKinds #-}
1570 -- type Const a b = b
1571 -- f :: Const Int (,) Bool Char -> Char
1572 --
1573 -- We call isPredTy (Const k1 k2 Int (,) Bool Char
1574 -- where k1,k2 are unification variables that have been
1575 -- unified to *, and (*->*->*) resp, /but not zonked/.
1576 -- This shows that isPredTy can report a false negative
1577 -- if a constraint is similarly oversaturated, but
1578 -- it's hard to do better than isPredTy currently does without
1579 -- zonking, so we punt on such cases for now. This only happens
1580 -- during debug-printing, so it doesn't matter.
1581
1582 isClassPred, isEqPred, isNomEqPred, isIPPred :: PredType -> Bool
1583 isClassPred ty = case tyConAppTyCon_maybe ty of
1584 Just tyCon | isClassTyCon tyCon -> True
1585 _ -> False
1586 isEqPred ty = case tyConAppTyCon_maybe ty of
1587 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1588 || tyCon `hasKey` eqReprPrimTyConKey
1589 _ -> False
1590
1591 isNomEqPred ty = case tyConAppTyCon_maybe ty of
1592 Just tyCon -> tyCon `hasKey` eqPrimTyConKey
1593 _ -> False
1594
1595 isIPPred ty = case tyConAppTyCon_maybe ty of
1596 Just tc -> isIPTyCon tc
1597 _ -> False
1598
1599 isIPTyCon :: TyCon -> Bool
1600 isIPTyCon tc = tc `hasKey` ipClassKey
1601 -- Class and its corresponding TyCon have the same Unique
1602
1603 isIPClass :: Class -> Bool
1604 isIPClass cls = cls `hasKey` ipClassKey
1605
1606 isCTupleClass :: Class -> Bool
1607 isCTupleClass cls = isTupleTyCon (classTyCon cls)
1608
1609 isIPPred_maybe :: Type -> Maybe (FastString, Type)
1610 isIPPred_maybe ty =
1611 do (tc,[t1,t2]) <- splitTyConApp_maybe ty
1612 guard (isIPTyCon tc)
1613 x <- isStrLitTy t1
1614 return (x,t2)
1615
1616 {-
1617 Make PredTypes
1618
1619 --------------------- Equality types ---------------------------------
1620 -}
1621
1622 -- | Makes a lifted equality predicate at the given role
1623 mkPrimEqPredRole :: Role -> Type -> Type -> PredType
1624 mkPrimEqPredRole Nominal = mkPrimEqPred
1625 mkPrimEqPredRole Representational = mkReprPrimEqPred
1626 mkPrimEqPredRole Phantom = panic "mkPrimEqPredRole phantom"
1627
1628 -- | Creates a primitive type equality predicate.
1629 -- Invariant: the types are not Coercions
1630 mkPrimEqPred :: Type -> Type -> Type
1631 mkPrimEqPred ty1 ty2
1632 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1633 where
1634 k1 = typeKind ty1
1635 k2 = typeKind ty2
1636
1637 -- | Creates a primite type equality predicate with explicit kinds
1638 mkHeteroPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1639 mkHeteroPrimEqPred k1 k2 ty1 ty2 = TyConApp eqPrimTyCon [k1, k2, ty1, ty2]
1640
1641 -- | Creates a primitive representational type equality predicate
1642 -- with explicit kinds
1643 mkHeteroReprPrimEqPred :: Kind -> Kind -> Type -> Type -> Type
1644 mkHeteroReprPrimEqPred k1 k2 ty1 ty2
1645 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1646
1647 -- | Try to split up a coercion type into the types that it coerces
1648 splitCoercionType_maybe :: Type -> Maybe (Type, Type)
1649 splitCoercionType_maybe ty
1650 = do { (tc, [_, _, ty1, ty2]) <- splitTyConApp_maybe ty
1651 ; guard $ tc `hasKey` eqPrimTyConKey || tc `hasKey` eqReprPrimTyConKey
1652 ; return (ty1, ty2) }
1653
1654 mkReprPrimEqPred :: Type -> Type -> Type
1655 mkReprPrimEqPred ty1 ty2
1656 = TyConApp eqReprPrimTyCon [k1, k2, ty1, ty2]
1657 where
1658 k1 = typeKind ty1
1659 k2 = typeKind ty2
1660
1661 equalityTyCon :: Role -> TyCon
1662 equalityTyCon Nominal = eqPrimTyCon
1663 equalityTyCon Representational = eqReprPrimTyCon
1664 equalityTyCon Phantom = eqPhantPrimTyCon
1665
1666 -- --------------------- Dictionary types ---------------------------------
1667
1668 mkClassPred :: Class -> [Type] -> PredType
1669 mkClassPred clas tys = TyConApp (classTyCon clas) tys
1670
1671 isDictTy :: Type -> Bool
1672 isDictTy = isClassPred
1673
1674 isDictLikeTy :: Type -> Bool
1675 -- Note [Dictionary-like types]
1676 isDictLikeTy ty | Just ty' <- coreView ty = isDictLikeTy ty'
1677 isDictLikeTy ty = case splitTyConApp_maybe ty of
1678 Just (tc, tys) | isClassTyCon tc -> True
1679 | isTupleTyCon tc -> all isDictLikeTy tys
1680 _other -> False
1681
1682 {-
1683 Note [Dictionary-like types]
1684 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1685 Being "dictionary-like" means either a dictionary type or a tuple thereof.
1686 In GHC 6.10 we build implication constraints which construct such tuples,
1687 and if we land up with a binding
1688 t :: (C [a], Eq [a])
1689 t = blah
1690 then we want to treat t as cheap under "-fdicts-cheap" for example.
1691 (Implication constraints are normally inlined, but sadly not if the
1692 occurrence is itself inside an INLINE function! Until we revise the
1693 handling of implication constraints, that is.) This turned out to
1694 be important in getting good arities in DPH code. Example:
1695
1696 class C a
1697 class D a where { foo :: a -> a }
1698 instance C a => D (Maybe a) where { foo x = x }
1699
1700 bar :: (C a, C b) => a -> b -> (Maybe a, Maybe b)
1701 {-# INLINE bar #-}
1702 bar x y = (foo (Just x), foo (Just y))
1703
1704 Then 'bar' should jolly well have arity 4 (two dicts, two args), but
1705 we ended up with something like
1706 bar = __inline_me__ (\d1,d2. let t :: (D (Maybe a), D (Maybe b)) = ...
1707 in \x,y. <blah>)
1708
1709 This is all a bit ad-hoc; eg it relies on knowing that implication
1710 constraints build tuples.
1711
1712
1713 Decomposing PredType
1714 -}
1715
1716 -- | A choice of equality relation. This is separate from the type 'Role'
1717 -- because 'Phantom' does not define a (non-trivial) equality relation.
1718 data EqRel = NomEq | ReprEq
1719 deriving (Eq, Ord)
1720
1721 instance Outputable EqRel where
1722 ppr NomEq = text "nominal equality"
1723 ppr ReprEq = text "representational equality"
1724
1725 eqRelRole :: EqRel -> Role
1726 eqRelRole NomEq = Nominal
1727 eqRelRole ReprEq = Representational
1728
1729 data PredTree = ClassPred Class [Type]
1730 | EqPred EqRel Type Type
1731 | IrredPred PredType
1732 -- NB: There is no TuplePred case
1733 -- Tuple predicates like (Eq a, Ord b) are just treated
1734 -- as ClassPred, as if we had a tuple class with two superclasses
1735 -- class (c1, c2) => (%,%) c1 c2
1736
1737 classifyPredType :: PredType -> PredTree
1738 classifyPredType ev_ty = case splitTyConApp_maybe ev_ty of
1739 Just (tc, [_, _, ty1, ty2])
1740 | tc `hasKey` eqReprPrimTyConKey -> EqPred ReprEq ty1 ty2
1741 | tc `hasKey` eqPrimTyConKey -> EqPred NomEq ty1 ty2
1742 Just (tc, tys)
1743 | Just clas <- tyConClass_maybe tc -> ClassPred clas tys
1744 _ -> IrredPred ev_ty
1745
1746 getClassPredTys :: HasDebugCallStack => PredType -> (Class, [Type])
1747 getClassPredTys ty = case getClassPredTys_maybe ty of
1748 Just (clas, tys) -> (clas, tys)
1749 Nothing -> pprPanic "getClassPredTys" (ppr ty)
1750
1751 getClassPredTys_maybe :: PredType -> Maybe (Class, [Type])
1752 getClassPredTys_maybe ty = case splitTyConApp_maybe ty of
1753 Just (tc, tys) | Just clas <- tyConClass_maybe tc -> Just (clas, tys)
1754 _ -> Nothing
1755
1756 getEqPredTys :: PredType -> (Type, Type)
1757 getEqPredTys ty
1758 = case splitTyConApp_maybe ty of
1759 Just (tc, [_, _, ty1, ty2])
1760 | tc `hasKey` eqPrimTyConKey
1761 || tc `hasKey` eqReprPrimTyConKey
1762 -> (ty1, ty2)
1763 _ -> pprPanic "getEqPredTys" (ppr ty)
1764
1765 getEqPredTys_maybe :: PredType -> Maybe (Role, Type, Type)
1766 getEqPredTys_maybe ty
1767 = case splitTyConApp_maybe ty of
1768 Just (tc, [_, _, ty1, ty2])
1769 | tc `hasKey` eqPrimTyConKey -> Just (Nominal, ty1, ty2)
1770 | tc `hasKey` eqReprPrimTyConKey -> Just (Representational, ty1, ty2)
1771 _ -> Nothing
1772
1773 getEqPredRole :: PredType -> Role
1774 getEqPredRole ty = eqRelRole (predTypeEqRel ty)
1775
1776 -- | Get the equality relation relevant for a pred type.
1777 predTypeEqRel :: PredType -> EqRel
1778 predTypeEqRel ty
1779 | Just (tc, _) <- splitTyConApp_maybe ty
1780 , tc `hasKey` eqReprPrimTyConKey
1781 = ReprEq
1782 | otherwise
1783 = NomEq
1784
1785 {-
1786 %************************************************************************
1787 %* *
1788 Well-scoped tyvars
1789 * *
1790 ************************************************************************
1791 -}
1792
1793 -- | Do a topological sort on a list of tyvars,
1794 -- so that binders occur before occurrences
1795 -- E.g. given [ a::k, k::*, b::k ]
1796 -- it'll return a well-scoped list [ k::*, a::k, b::k ]
1797 --
1798 -- This is a deterministic sorting operation
1799 -- (that is, doesn't depend on Uniques).
1800 toposortTyVars :: [TyCoVar] -> [TyCoVar]
1801 toposortTyVars tvs = reverse $
1802 [ node_payload node | node <- topologicalSortG $
1803 graphFromEdgedVerticesOrd nodes ]
1804 where
1805 var_ids :: VarEnv Int
1806 var_ids = mkVarEnv (zip tvs [1..])
1807
1808 nodes :: [ Node Int TyVar ]
1809 nodes = [ DigraphNode
1810 tv
1811 (lookupVarEnv_NF var_ids tv)
1812 (mapMaybe (lookupVarEnv var_ids)
1813 (tyCoVarsOfTypeList (tyVarKind tv)))
1814 | tv <- tvs ]
1815
1816 -- | Extract a well-scoped list of variables from a deterministic set of
1817 -- variables. The result is deterministic.
1818 -- NB: There used to exist varSetElemsWellScoped :: VarSet -> [Var] which
1819 -- took a non-deterministic set and produced a non-deterministic
1820 -- well-scoped list. If you care about the list being well-scoped you also
1821 -- most likely care about it being in deterministic order.
1822 dVarSetElemsWellScoped :: DVarSet -> [Var]
1823 dVarSetElemsWellScoped = toposortTyVars . dVarSetElems
1824
1825 -- | Get the free vars of a type in scoped order
1826 tyCoVarsOfTypeWellScoped :: Type -> [TyVar]
1827 tyCoVarsOfTypeWellScoped = toposortTyVars . tyCoVarsOfTypeList
1828
1829 -- | Get the free vars of types in scoped order
1830 tyCoVarsOfTypesWellScoped :: [Type] -> [TyVar]
1831 tyCoVarsOfTypesWellScoped = toposortTyVars . tyCoVarsOfTypesList
1832
1833 {-
1834 ************************************************************************
1835 * *
1836 \subsection{Type families}
1837 * *
1838 ************************************************************************
1839 -}
1840
1841 mkFamilyTyConApp :: TyCon -> [Type] -> Type
1842 -- ^ Given a family instance TyCon and its arg types, return the
1843 -- corresponding family type. E.g:
1844 --
1845 -- > data family T a
1846 -- > data instance T (Maybe b) = MkT b
1847 --
1848 -- Where the instance tycon is :RTL, so:
1849 --
1850 -- > mkFamilyTyConApp :RTL Int = T (Maybe Int)
1851 mkFamilyTyConApp tc tys
1852 | Just (fam_tc, fam_tys) <- tyConFamInst_maybe tc
1853 , let tvs = tyConTyVars tc
1854 fam_subst = ASSERT2( tvs `equalLength` tys, ppr tc <+> ppr tys )
1855 zipTvSubst tvs tys
1856 = mkTyConApp fam_tc (substTys fam_subst fam_tys)
1857 | otherwise
1858 = mkTyConApp tc tys
1859
1860 -- | Get the type on the LHS of a coercion induced by a type/data
1861 -- family instance.
1862 coAxNthLHS :: CoAxiom br -> Int -> Type
1863 coAxNthLHS ax ind =
1864 mkTyConApp (coAxiomTyCon ax) (coAxBranchLHS (coAxiomNthBranch ax ind))
1865
1866 -- | Pretty prints a 'TyCon', using the family instance in case of a
1867 -- representation tycon. For example:
1868 --
1869 -- > data T [a] = ...
1870 --
1871 -- In that case we want to print @T [a]@, where @T@ is the family 'TyCon'
1872 pprSourceTyCon :: TyCon -> SDoc
1873 pprSourceTyCon tycon
1874 | Just (fam_tc, tys) <- tyConFamInst_maybe tycon
1875 = ppr $ fam_tc `TyConApp` tys -- can't be FunTyCon
1876 | otherwise
1877 = ppr tycon
1878
1879 -- @isTauTy@ tests if a type has no foralls
1880 isFamFreeTy :: Type -> Bool
1881 isFamFreeTy ty | Just ty' <- coreView ty = isFamFreeTy ty'
1882 isFamFreeTy (TyVarTy _) = True
1883 isFamFreeTy (LitTy {}) = True
1884 isFamFreeTy (TyConApp tc tys) = all isFamFreeTy tys && isFamFreeTyCon tc
1885 isFamFreeTy (AppTy a b) = isFamFreeTy a && isFamFreeTy b
1886 isFamFreeTy (FunTy a b) = isFamFreeTy a && isFamFreeTy b
1887 isFamFreeTy (ForAllTy _ ty) = isFamFreeTy ty
1888 isFamFreeTy (CastTy ty _) = isFamFreeTy ty
1889 isFamFreeTy (CoercionTy _) = False -- Not sure about this
1890
1891 {-
1892 ************************************************************************
1893 * *
1894 \subsection{Liftedness}
1895 * *
1896 ************************************************************************
1897 -}
1898
1899 -- | Returns Just True if this type is surely lifted, Just False
1900 -- if it is surely unlifted, Nothing if we can't be sure (i.e., it is
1901 -- levity polymorphic), and panics if the kind does not have the shape
1902 -- TYPE r.
1903 isLiftedType_maybe :: HasDebugCallStack => Type -> Maybe Bool
1904 isLiftedType_maybe ty = go (getRuntimeRep ty)
1905 where
1906 go rr | Just rr' <- coreView rr = go rr'
1907 go (TyConApp lifted_rep [])
1908 | lifted_rep `hasKey` liftedRepDataConKey = Just True
1909 go (TyConApp {}) = Just False -- everything else is unlifted
1910 go _ = Nothing -- levity polymorphic
1911
1912 -- | See "Type#type_classification" for what an unlifted type is.
1913 -- Panics on levity polymorphic types.
1914 isUnliftedType :: HasDebugCallStack => Type -> Bool
1915 -- isUnliftedType returns True for forall'd unlifted types:
1916 -- x :: forall a. Int#
1917 -- I found bindings like these were getting floated to the top level.
1918 -- They are pretty bogus types, mind you. It would be better never to
1919 -- construct them
1920 isUnliftedType ty
1921 = not (isLiftedType_maybe ty `orElse`
1922 pprPanic "isUnliftedType" (ppr ty <+> dcolon <+> ppr (typeKind ty)))
1923
1924 -- | Is this a type of kind RuntimeRep? (e.g. LiftedRep)
1925 isRuntimeRepKindedTy :: Type -> Bool
1926 isRuntimeRepKindedTy = isRuntimeRepTy . typeKind
1927
1928 -- | Drops prefix of RuntimeRep constructors in 'TyConApp's. Useful for e.g.
1929 -- dropping 'LiftedRep arguments of unboxed tuple TyCon applications:
1930 --
1931 -- dropRuntimeRepArgs [ 'LiftedRep, 'IntRep
1932 -- , String, Int# ] == [String, Int#]
1933 --
1934 dropRuntimeRepArgs :: [Type] -> [Type]
1935 dropRuntimeRepArgs = dropWhile isRuntimeRepKindedTy
1936
1937 -- | Extract the RuntimeRep classifier of a type. For instance,
1938 -- @getRuntimeRep_maybe Int = LiftedRep@. Returns 'Nothing' if this is not
1939 -- possible.
1940 getRuntimeRep_maybe :: HasDebugCallStack
1941 => Type -> Maybe Type
1942 getRuntimeRep_maybe = getRuntimeRepFromKind_maybe . typeKind
1943
1944 -- | Extract the RuntimeRep classifier of a type. For instance,
1945 -- @getRuntimeRep_maybe Int = LiftedRep@. Panics if this is not possible.
1946 getRuntimeRep :: HasDebugCallStack => Type -> Type
1947 getRuntimeRep ty
1948 = case getRuntimeRep_maybe ty of
1949 Just r -> r
1950 Nothing -> pprPanic "getRuntimeRep" (ppr ty <+> dcolon <+> ppr (typeKind ty))
1951
1952 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1953 -- @getRuntimeRepFromKind * = LiftedRep@; Panics if this is not possible.
1954 getRuntimeRepFromKind :: HasDebugCallStack
1955 => Type -> Type
1956 getRuntimeRepFromKind k =
1957 case getRuntimeRepFromKind_maybe k of
1958 Just r -> r
1959 Nothing -> pprPanic "getRuntimeRepFromKind"
1960 (ppr k <+> dcolon <+> ppr (typeKind k))
1961
1962 -- | Extract the RuntimeRep classifier of a type from its kind. For example,
1963 -- @getRuntimeRepFromKind * = LiftedRep@; Returns 'Nothing' if this is not
1964 -- possible.
1965 getRuntimeRepFromKind_maybe :: HasDebugCallStack
1966 => Type -> Maybe Type
1967 getRuntimeRepFromKind_maybe = go
1968 where
1969 go k | Just k' <- coreView k = go k'
1970 go k
1971 | Just (_tc, [arg]) <- splitTyConApp_maybe k
1972 = ASSERT2( _tc `hasKey` tYPETyConKey, ppr k )
1973 Just arg
1974 go _ = Nothing
1975
1976 isUnboxedTupleType :: Type -> Bool
1977 isUnboxedTupleType ty
1978 = tyConAppTyCon (getRuntimeRep ty) `hasKey` tupleRepDataConKey
1979 -- NB: Do not use typePrimRep, as that can't tell the difference between
1980 -- unboxed tuples and unboxed sums
1981
1982
1983 isUnboxedSumType :: Type -> Bool
1984 isUnboxedSumType ty
1985 = tyConAppTyCon (getRuntimeRep ty) `hasKey` sumRepDataConKey
1986
1987 -- | See "Type#type_classification" for what an algebraic type is.
1988 -- Should only be applied to /types/, as opposed to e.g. partially
1989 -- saturated type constructors
1990 isAlgType :: Type -> Bool
1991 isAlgType ty
1992 = case splitTyConApp_maybe ty of
1993 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
1994 isAlgTyCon tc
1995 _other -> False
1996
1997 -- | Check whether a type is a data family type
1998 isDataFamilyAppType :: Type -> Bool
1999 isDataFamilyAppType ty = case tyConAppTyCon_maybe ty of
2000 Just tc -> isDataFamilyTyCon tc
2001 _ -> False
2002
2003 -- | Computes whether an argument (or let right hand side) should
2004 -- be computed strictly or lazily, based only on its type.
2005 -- Currently, it's just 'isUnliftedType'. Panics on levity-polymorphic types.
2006 isStrictType :: HasDebugCallStack => Type -> Bool
2007 isStrictType = isUnliftedType
2008
2009 isPrimitiveType :: Type -> Bool
2010 -- ^ Returns true of types that are opaque to Haskell.
2011 isPrimitiveType ty = case splitTyConApp_maybe ty of
2012 Just (tc, ty_args) -> ASSERT( ty_args `lengthIs` tyConArity tc )
2013 isPrimTyCon tc
2014 _ -> False
2015
2016 {-
2017 ************************************************************************
2018 * *
2019 \subsection{Join points}
2020 * *
2021 ************************************************************************
2022 -}
2023
2024 -- | Determine whether a type could be the type of a join point of given total
2025 -- arity, according to the polymorphism rule. A join point cannot be polymorphic
2026 -- in its return type, since given
2027 -- join j @a @b x y z = e1 in e2,
2028 -- the types of e1 and e2 must be the same, and a and b are not in scope for e2.
2029 -- (See Note [The polymorphism rule of join points] in CoreSyn.) Returns False
2030 -- also if the type simply doesn't have enough arguments.
2031 --
2032 -- Note that we need to know how many arguments (type *and* value) the putative
2033 -- join point takes; for instance, if
2034 -- j :: forall a. a -> Int
2035 -- then j could be a binary join point returning an Int, but it could *not* be a
2036 -- unary join point returning a -> Int.
2037 --
2038 -- TODO: See Note [Excess polymorphism and join points]
2039 isValidJoinPointType :: JoinArity -> Type -> Bool
2040 isValidJoinPointType arity ty
2041 = valid_under emptyVarSet arity ty
2042 where
2043 valid_under tvs arity ty
2044 | arity == 0
2045 = isEmptyVarSet (tvs `intersectVarSet` tyCoVarsOfType ty)
2046 | Just (t, ty') <- splitForAllTy_maybe ty
2047 = valid_under (tvs `extendVarSet` t) (arity-1) ty'
2048 | Just (_, res_ty) <- splitFunTy_maybe ty
2049 = valid_under tvs (arity-1) res_ty
2050 | otherwise
2051 = False
2052
2053 {- Note [Excess polymorphism and join points]
2054 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2055 In principle, if a function would be a join point except that it fails
2056 the polymorphism rule (see Note [The polymorphism rule of join points] in
2057 CoreSyn), it can still be made a join point with some effort. This is because
2058 all tail calls must return the same type (they return to the same context!), and
2059 thus if the return type depends on an argument, that argument must always be the
2060 same.
2061
2062 For instance, consider:
2063
2064 let f :: forall a. a -> Char -> [a]
2065 f @a x c = ... f @a y 'a' ...
2066 in ... f @Int 1 'b' ... f @Int 2 'c' ...
2067
2068 (where the calls are tail calls). `f` fails the polymorphism rule because its
2069 return type is [a], where [a] is bound. But since the type argument is always
2070 'Int', we can rewrite it as:
2071
2072 let f' :: Int -> Char -> [Int]
2073 f' x c = ... f' y 'a' ...
2074 in ... f' 1 'b' ... f 2 'c' ...
2075
2076 and now we can make f' a join point:
2077
2078 join f' :: Int -> Char -> [Int]
2079 f' x c = ... jump f' y 'a' ...
2080 in ... jump f' 1 'b' ... jump f' 2 'c' ...
2081
2082 It's not clear that this comes up often, however. TODO: Measure how often and
2083 add this analysis if necessary. See Trac #14620.
2084
2085
2086 ************************************************************************
2087 * *
2088 \subsection{Sequencing on types}
2089 * *
2090 ************************************************************************
2091 -}
2092
2093 seqType :: Type -> ()
2094 seqType (LitTy n) = n `seq` ()
2095 seqType (TyVarTy tv) = tv `seq` ()
2096 seqType (AppTy t1 t2) = seqType t1 `seq` seqType t2
2097 seqType (FunTy t1 t2) = seqType t1 `seq` seqType t2
2098 seqType (TyConApp tc tys) = tc `seq` seqTypes tys
2099 seqType (ForAllTy (TvBndr tv _) ty) = seqType (tyVarKind tv) `seq` seqType ty
2100 seqType (CastTy ty co) = seqType ty `seq` seqCo co
2101 seqType (CoercionTy co) = seqCo co
2102
2103 seqTypes :: [Type] -> ()
2104 seqTypes [] = ()
2105 seqTypes (ty:tys) = seqType ty `seq` seqTypes tys
2106
2107 {-
2108 ************************************************************************
2109 * *
2110 Comparison for types
2111 (We don't use instances so that we know where it happens)
2112 * *
2113 ************************************************************************
2114
2115 Note [Equality on AppTys]
2116 ~~~~~~~~~~~~~~~~~~~~~~~~~
2117 In our cast-ignoring equality, we want to say that the following two
2118 are equal:
2119
2120 (Maybe |> co) (Int |> co') ~? Maybe Int
2121
2122 But the left is an AppTy while the right is a TyConApp. The solution is
2123 to use repSplitAppTy_maybe to break up the TyConApp into its pieces and
2124 then continue. Easy to do, but also easy to forget to do.
2125
2126 -}
2127
2128 eqType :: Type -> Type -> Bool
2129 -- ^ Type equality on source types. Does not look through @newtypes@ or
2130 -- 'PredType's, but it does look through type synonyms.
2131 -- This first checks that the kinds of the types are equal and then
2132 -- checks whether the types are equal, ignoring casts and coercions.
2133 -- (The kind check is a recursive call, but since all kinds have type
2134 -- @Type@, there is no need to check the types of kinds.)
2135 -- See also Note [Non-trivial definitional equality] in TyCoRep.
2136 eqType t1 t2 = isEqual $ nonDetCmpType t1 t2
2137 -- It's OK to use nonDetCmpType here and eqType is deterministic,
2138 -- nonDetCmpType does equality deterministically
2139
2140 -- | Compare types with respect to a (presumably) non-empty 'RnEnv2'.
2141 eqTypeX :: RnEnv2 -> Type -> Type -> Bool
2142 eqTypeX env t1 t2 = isEqual $ nonDetCmpTypeX env t1 t2
2143 -- It's OK to use nonDetCmpType here and eqTypeX is deterministic,
2144 -- nonDetCmpTypeX does equality deterministically
2145
2146 -- | Type equality on lists of types, looking through type synonyms
2147 -- but not newtypes.
2148 eqTypes :: [Type] -> [Type] -> Bool
2149 eqTypes tys1 tys2 = isEqual $ nonDetCmpTypes tys1 tys2
2150 -- It's OK to use nonDetCmpType here and eqTypes is deterministic,
2151 -- nonDetCmpTypes does equality deterministically
2152
2153 eqVarBndrs :: RnEnv2 -> [Var] -> [Var] -> Maybe RnEnv2
2154 -- Check that the var lists are the same length
2155 -- and have matching kinds; if so, extend the RnEnv2
2156 -- Returns Nothing if they don't match
2157 eqVarBndrs env [] []
2158 = Just env
2159 eqVarBndrs env (tv1:tvs1) (tv2:tvs2)
2160 | eqTypeX env (tyVarKind tv1) (tyVarKind tv2)
2161 = eqVarBndrs (rnBndr2 env tv1 tv2) tvs1 tvs2
2162 eqVarBndrs _ _ _= Nothing
2163
2164 -- Now here comes the real worker
2165
2166 {-
2167 Note [nonDetCmpType nondeterminism]
2168 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2169 nonDetCmpType is implemented in terms of nonDetCmpTypeX. nonDetCmpTypeX
2170 uses nonDetCmpTc which compares TyCons by their Unique value. Using Uniques for
2171 ordering leads to nondeterminism. We hit the same problem in the TyVarTy case,
2172 comparing type variables is nondeterministic, note the call to nonDetCmpVar in
2173 nonDetCmpTypeX.
2174 See Note [Unique Determinism] for more details.
2175 -}
2176
2177 nonDetCmpType :: Type -> Type -> Ordering
2178 nonDetCmpType t1 t2
2179 -- we know k1 and k2 have the same kind, because they both have kind *.
2180 = nonDetCmpTypeX rn_env t1 t2
2181 where
2182 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes [t1, t2]))
2183
2184 nonDetCmpTypes :: [Type] -> [Type] -> Ordering
2185 nonDetCmpTypes ts1 ts2 = nonDetCmpTypesX rn_env ts1 ts2
2186 where
2187 rn_env = mkRnEnv2 (mkInScopeSet (tyCoVarsOfTypes (ts1 ++ ts2)))
2188
2189 -- | An ordering relation between two 'Type's (known below as @t1 :: k1@
2190 -- and @t2 :: k2@)
2191 data TypeOrdering = TLT -- ^ @t1 < t2@
2192 | TEQ -- ^ @t1 ~ t2@ and there are no casts in either,
2193 -- therefore we can conclude @k1 ~ k2@
2194 | TEQX -- ^ @t1 ~ t2@ yet one of the types contains a cast so
2195 -- they may differ in kind.
2196 | TGT -- ^ @t1 > t2@
2197 deriving (Eq, Ord, Enum, Bounded)
2198
2199 nonDetCmpTypeX :: RnEnv2 -> Type -> Type -> Ordering -- Main workhorse
2200 -- See Note [Non-trivial definitional equality] in TyCoRep
2201 nonDetCmpTypeX env orig_t1 orig_t2 =
2202 case go env orig_t1 orig_t2 of
2203 -- If there are casts then we also need to do a comparison of the kinds of
2204 -- the types being compared
2205 TEQX -> toOrdering $ go env k1 k2
2206 ty_ordering -> toOrdering ty_ordering
2207 where
2208 k1 = typeKind orig_t1
2209 k2 = typeKind orig_t2
2210
2211 toOrdering :: TypeOrdering -> Ordering
2212 toOrdering TLT = LT
2213 toOrdering TEQ = EQ
2214 toOrdering TEQX = EQ
2215 toOrdering TGT = GT
2216
2217 liftOrdering :: Ordering -> TypeOrdering
2218 liftOrdering LT = TLT
2219 liftOrdering EQ = TEQ
2220 liftOrdering GT = TGT
2221
2222 thenCmpTy :: TypeOrdering -> TypeOrdering -> TypeOrdering
2223 thenCmpTy TEQ rel = rel
2224 thenCmpTy TEQX rel = hasCast rel
2225 thenCmpTy rel _ = rel
2226
2227 hasCast :: TypeOrdering -> TypeOrdering
2228 hasCast TEQ = TEQX
2229 hasCast rel = rel
2230
2231 -- Returns both the resulting ordering relation between the two types
2232 -- and whether either contains a cast.
2233 go :: RnEnv2 -> Type -> Type -> TypeOrdering
2234 go env t1 t2
2235 | Just t1' <- coreView t1 = go env t1' t2
2236 | Just t2' <- coreView t2 = go env t1 t2'
2237
2238 go env (TyVarTy tv1) (TyVarTy tv2)
2239 = liftOrdering $ rnOccL env tv1 `nonDetCmpVar` rnOccR env tv2
2240 go env (ForAllTy (TvBndr tv1 _) t1) (ForAllTy (TvBndr tv2 _) t2)
2241 = go env (tyVarKind tv1) (tyVarKind tv2)
2242 `thenCmpTy` go (rnBndr2 env tv1 tv2) t1 t2
2243 -- See Note [Equality on AppTys]
2244 go env (AppTy s1 t1) ty2
2245 | Just (s2, t2) <- repSplitAppTy_maybe ty2
2246 = go env s1 s2 `thenCmpTy` go env t1 t2
2247 go env ty1 (AppTy s2 t2)
2248 | Just (s1, t1) <- repSplitAppTy_maybe ty1
2249 = go env s1 s2 `thenCmpTy` go env t1 t2
2250 go env (FunTy s1 t1) (FunTy s2 t2)
2251 = go env s1 s2 `thenCmpTy` go env t1 t2
2252 go env (TyConApp tc1 tys1) (TyConApp tc2 tys2)
2253 = liftOrdering (tc1 `nonDetCmpTc` tc2) `thenCmpTy` gos env tys1 tys2
2254 go _ (LitTy l1) (LitTy l2) = liftOrdering (compare l1 l2)
2255 go env (CastTy t1 _) t2 = hasCast $ go env t1 t2
2256 go env t1 (CastTy t2 _) = hasCast $ go env t1 t2
2257
2258 go _ (CoercionTy {}) (CoercionTy {}) = TEQ
2259
2260 -- Deal with the rest: TyVarTy < CoercionTy < AppTy < LitTy < TyConApp < ForAllTy
2261 go _ ty1 ty2
2262 = liftOrdering $ (get_rank ty1) `compare` (get_rank ty2)
2263 where get_rank :: Type -> Int
2264 get_rank (CastTy {})
2265 = pprPanic "nonDetCmpTypeX.get_rank" (ppr [ty1,ty2])
2266 get_rank (TyVarTy {}) = 0
2267 get_rank (CoercionTy {}) = 1
2268 get_rank (AppTy {}) = 3
2269 get_rank (LitTy {}) = 4
2270 get_rank (TyConApp {}) = 5
2271 get_rank (FunTy {}) = 6
2272 get_rank (ForAllTy {}) = 7
2273
2274 gos :: RnEnv2 -> [Type] -> [Type] -> TypeOrdering
2275 gos _ [] [] = TEQ
2276 gos _ [] _ = TLT
2277 gos _ _ [] = TGT
2278 gos env (ty1:tys1) (ty2:tys2) = go env ty1 ty2 `thenCmpTy` gos env tys1 tys2
2279
2280 -------------
2281 nonDetCmpTypesX :: RnEnv2 -> [Type] -> [Type] -> Ordering
2282 nonDetCmpTypesX _ [] [] = EQ
2283 nonDetCmpTypesX env (t1:tys1) (t2:tys2) = nonDetCmpTypeX env t1 t2
2284 `thenCmp` nonDetCmpTypesX env tys1 tys2
2285 nonDetCmpTypesX _ [] _ = LT
2286 nonDetCmpTypesX _ _ [] = GT
2287
2288 -------------
2289 -- | Compare two 'TyCon's. NB: This should /never/ see the "star synonyms",
2290 -- as recognized by Kind.isStarKindSynonymTyCon. See Note
2291 -- [Kind Constraint and kind *] in Kind.
2292 -- See Note [nonDetCmpType nondeterminism]
2293 nonDetCmpTc :: TyCon -> TyCon -> Ordering
2294 nonDetCmpTc tc1 tc2
2295 = ASSERT( not (isStarKindSynonymTyCon tc1) && not (isStarKindSynonymTyCon tc2) )
2296 u1 `nonDetCmpUnique` u2
2297 where
2298 u1 = tyConUnique tc1
2299 u2 = tyConUnique tc2
2300
2301 {-
2302 ************************************************************************
2303 * *
2304 The kind of a type
2305 * *
2306 ************************************************************************
2307 -}
2308
2309 typeKind :: HasDebugCallStack => Type -> Kind
2310 typeKind (TyConApp tc tys) = piResultTys (tyConKind tc) tys
2311 typeKind (AppTy fun arg) = typeKind_apps fun [arg]
2312 typeKind (LitTy l) = typeLiteralKind l
2313 typeKind (FunTy {}) = liftedTypeKind
2314 typeKind (ForAllTy _ ty) = typeKind ty
2315 typeKind (TyVarTy tyvar) = tyVarKind tyvar
2316 typeKind (CastTy _ty co) = pSnd $ coercionKind co
2317 typeKind (CoercionTy co) = coercionType co
2318
2319 typeKind_apps :: HasDebugCallStack => Type -> [Type] -> Kind
2320 -- The sole purpose of the function is to accumulate
2321 -- the type arugments, so we can call piResultTys, rather than
2322 -- a succession of calls to piResultTy (which is asymptotically
2323 -- less efficient as the number of arguments increases)
2324 typeKind_apps (AppTy fun arg) args = typeKind_apps fun (arg:args)
2325 typeKind_apps fun args = piResultTys (typeKind fun) args
2326
2327 --------------------------
2328 typeLiteralKind :: TyLit -> Kind
2329 typeLiteralKind l =
2330 case l of
2331 NumTyLit _ -> typeNatKind
2332 StrTyLit _ -> typeSymbolKind
2333
2334 -- | Returns True if a type is levity polymorphic. Should be the same
2335 -- as (isKindLevPoly . typeKind) but much faster.
2336 -- Precondition: The type has kind (TYPE blah)
2337 isTypeLevPoly :: Type -> Bool
2338 isTypeLevPoly = go
2339 where
2340 go ty@(TyVarTy {}) = check_kind ty
2341 go ty@(AppTy {}) = check_kind ty
2342 go ty@(TyConApp tc _) | not (isTcLevPoly tc) = False
2343 | otherwise = check_kind ty
2344 go (ForAllTy _ ty) = go ty
2345 go (FunTy {}) = False
2346 go (LitTy {}) = False
2347 go ty@(CastTy {}) = check_kind ty
2348 go ty@(CoercionTy {}) = pprPanic "isTypeLevPoly co" (ppr ty)
2349
2350 check_kind = isKindLevPoly . typeKind
2351
2352 -- | Looking past all pi-types, is the end result potentially levity polymorphic?
2353 -- Example: True for (forall r (a :: TYPE r). String -> a)
2354 -- Example: False for (forall r1 r2 (a :: TYPE r1) (b :: TYPE r2). a -> b -> Type)
2355 resultIsLevPoly :: Type -> Bool
2356 resultIsLevPoly = isTypeLevPoly . snd . splitPiTys
2357
2358 {-
2359 %************************************************************************
2360 %* *
2361 Miscellaneous functions
2362 %* *
2363 %************************************************************************
2364
2365 -}
2366 -- | All type constructors occurring in the type; looking through type
2367 -- synonyms, but not newtypes.
2368 -- When it finds a Class, it returns the class TyCon.
2369 tyConsOfType :: Type -> UniqSet TyCon
2370 tyConsOfType ty
2371 = go ty
2372 where
2373 go :: Type -> UniqSet TyCon -- The UniqSet does duplicate elim
2374 go ty | Just ty' <- coreView ty = go ty'
2375 go (TyVarTy {}) = emptyUniqSet
2376 go (LitTy {}) = emptyUniqSet
2377 go (TyConApp tc tys) = go_tc tc `unionUniqSets` go_s tys
2378 go (AppTy a b) = go a `unionUniqSets` go b
2379 go (FunTy a b) = go a `unionUniqSets` go b `unionUniqSets` go_tc funTyCon
2380 go (ForAllTy (TvBndr tv _) ty) = go ty `unionUniqSets` go (tyVarKind tv)
2381 go (CastTy ty co) = go ty `unionUniqSets` go_co co
2382 go (CoercionTy co) = go_co co
2383
2384 go_co (Refl _ ty) = go ty
2385 go_co (TyConAppCo _ tc args) = go_tc tc `unionUniqSets` go_cos args
2386 go_co (AppCo co arg) = go_co co `unionUniqSets` go_co arg
2387 go_co (ForAllCo _ kind_co co) = go_co kind_co `unionUniqSets` go_co co
2388 go_co (FunCo _ co1 co2) = go_co co1 `unionUniqSets` go_co co2
2389 go_co (AxiomInstCo ax _ args) = go_ax ax `unionUniqSets` go_cos args
2390 go_co (UnivCo p _ t1 t2) = go_prov p `unionUniqSets` go t1 `unionUniqSets` go t2
2391 go_co (CoVarCo {}) = emptyUniqSet
2392 go_co (HoleCo {}) = emptyUniqSet
2393 go_co (SymCo co) = go_co co
2394 go_co (TransCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2395 go_co (NthCo _ _ co) = go_co co
2396 go_co (LRCo _ co) = go_co co
2397 go_co (InstCo co arg) = go_co co `unionUniqSets` go_co arg
2398 go_co (CoherenceCo co1 co2) = go_co co1 `unionUniqSets` go_co co2
2399 go_co (KindCo co) = go_co co
2400 go_co (SubCo co) = go_co co
2401 go_co (AxiomRuleCo _ cs) = go_cos cs
2402
2403 go_prov UnsafeCoerceProv = emptyUniqSet
2404 go_prov (PhantomProv co) = go_co co
2405 go_prov (ProofIrrelProv co) = go_co co
2406 go_prov (PluginProv _) = emptyUniqSet
2407 -- this last case can happen from the tyConsOfType used from
2408 -- checkTauTvUpdate
2409
2410 go_s tys = foldr (unionUniqSets . go) emptyUniqSet tys
2411 go_cos cos = foldr (unionUniqSets . go_co) emptyUniqSet cos
2412
2413 go_tc tc = unitUniqSet tc
2414 go_ax ax = go_tc $ coAxiomTyCon ax
2415
2416 -- | Find the result 'Kind' of a type synonym,
2417 -- after applying it to its 'arity' number of type variables
2418 -- Actually this function works fine on data types too,
2419 -- but they'd always return '*', so we never need to ask
2420 synTyConResKind :: TyCon -> Kind
2421 synTyConResKind tycon = piResultTys (tyConKind tycon) (mkTyVarTys (tyConTyVars tycon))
2422
2423 -- | Retrieve the free variables in this type, splitting them based
2424 -- on whether they are used visibly or invisibly. Invisible ones come
2425 -- first.
2426 splitVisVarsOfType :: Type -> Pair TyCoVarSet
2427 splitVisVarsOfType orig_ty = Pair invis_vars vis_vars
2428 where
2429 Pair invis_vars1 vis_vars = go orig_ty
2430 invis_vars = invis_vars1 `minusVarSet` vis_vars
2431
2432 go (TyVarTy tv) = Pair (tyCoVarsOfType $ tyVarKind tv) (unitVarSet tv)
2433 go (AppTy t1 t2) = go t1 `mappend` go t2
2434 go (TyConApp tc tys) = go_tc tc tys
2435 go (FunTy t1 t2) = go t1 `mappend` go t2
2436 go (ForAllTy (TvBndr tv _) ty)
2437 = ((`delVarSet` tv) <$> go ty) `mappend`
2438 (invisible (tyCoVarsOfType $ tyVarKind tv))
2439 go (LitTy {}) = mempty
2440 go (CastTy ty co) = go ty `mappend` invisible (tyCoVarsOfCo co)
2441 go (CoercionTy co) = invisible $ tyCoVarsOfCo co
2442
2443 invisible vs = Pair vs emptyVarSet
2444
2445 go_tc tc tys = let (invis, vis) = partitionInvisibles tc id tys in
2446 invisible (tyCoVarsOfTypes invis) `mappend` foldMap go vis
2447
2448 splitVisVarsOfTypes :: [Type] -> Pair TyCoVarSet
2449 splitVisVarsOfTypes = foldMap splitVisVarsOfType
2450
2451 modifyJoinResTy :: Int -- Number of binders to skip
2452 -> (Type -> Type) -- Function to apply to result type
2453 -> Type -- Type of join point
2454 -> Type -- New type
2455 -- INVARIANT: If any of the first n binders are foralls, those tyvars cannot
2456 -- appear in the original result type. See isValidJoinPointType.
2457 modifyJoinResTy orig_ar f orig_ty
2458 = go orig_ar orig_ty
2459 where
2460 go 0 ty = f ty
2461 go n ty | Just (arg_bndr, res_ty) <- splitPiTy_maybe ty
2462 = mkPiTy arg_bndr (go (n-1) res_ty)
2463 | otherwise
2464 = pprPanic "modifyJoinResTy" (ppr orig_ar <+> ppr orig_ty)
2465
2466 setJoinResTy :: Int -- Number of binders to skip
2467 -> Type -- New result type
2468 -> Type -- Type of join point
2469 -> Type -- New type
2470 -- INVARIANT: Same as for modifyJoinResTy
2471 setJoinResTy ar new_res_ty ty
2472 = modifyJoinResTy ar (const new_res_ty) ty
2473
2474 {-
2475 %************************************************************************
2476 %* *
2477 Pretty-printing
2478 %* *
2479 %************************************************************************
2480
2481 Most pretty-printing is either in TyCoRep or IfaceType.
2482
2483 -}
2484
2485 -- | This variant preserves any use of TYPE in a type, effectively
2486 -- locally setting -fprint-explicit-runtime-reps.
2487 pprWithTYPE :: Type -> SDoc
2488 pprWithTYPE ty = updSDocDynFlags (flip gopt_set Opt_PrintExplicitRuntimeReps) $
2489 ppr ty