bd10ac8cf34b81a118bfb056a17f4c548238bcec
[ghc.git] / compiler / types / TyCoRep.hs
1 {-
2 (c) The University of Glasgow 2006
3 (c) The GRASP/AQUA Project, Glasgow University, 1998
4 \section[TyCoRep]{Type and Coercion - friends' interface}
5
6 Note [The Type-related module hierarchy]
7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
8 Class
9 CoAxiom
10 TyCon imports Class, CoAxiom
11 TyCoRep imports Class, CoAxiom, TyCon
12 TysPrim imports TyCoRep ( including mkTyConTy )
13 Kind imports TysPrim ( mainly for primitive kinds )
14 Type imports Kind
15 Coercion imports Type
16 -}
17
18 -- We expose the relevant stuff from this module via the Type module
19 {-# OPTIONS_HADDOCK hide #-}
20 {-# LANGUAGE CPP, DeriveDataTypeable, MultiWayIf #-}
21
22 module TyCoRep (
23 TyThing(..), tyThingCategory, pprTyThingCategory, pprShortTyThing,
24
25 -- * Types
26 Type(..),
27 TyLit(..),
28 KindOrType, Kind,
29 PredType, ThetaType, -- Synonyms
30 ArgFlag(..),
31
32 -- * Coercions
33 Coercion(..),
34 UnivCoProvenance(..),
35 CoercionHole(..), coHoleCoVar, setCoHoleCoVar,
36 CoercionN, CoercionR, CoercionP, KindCoercion,
37 MCoercion(..), MCoercionR,
38
39 -- * Functions over types
40 mkTyConTy, mkTyVarTy, mkTyVarTys,
41 mkFunTy, mkFunTys, mkForAllTy, mkForAllTys,
42 mkPiTy, mkPiTys,
43 isTYPE, tcIsTYPE,
44 isLiftedTypeKind, isUnliftedTypeKind,
45 isCoercionType, isRuntimeRepTy, isRuntimeRepVar,
46 sameVis,
47
48 -- * Functions over binders
49 TyBinder(..), TyVarBinder,
50 binderVar, binderVars, binderKind, binderArgFlag,
51 delBinderVar,
52 isInvisibleArgFlag, isVisibleArgFlag,
53 isInvisibleBinder, isVisibleBinder,
54
55 -- * Functions over coercions
56 pickLR,
57
58 -- * Pretty-printing
59 pprType, pprParendType, pprPrecType,
60 pprTypeApp, pprTvBndr, pprTvBndrs,
61 pprSigmaType,
62 pprTheta, pprParendTheta, pprForAll, pprUserForAll,
63 pprTyVar, pprTyVars,
64 pprThetaArrowTy, pprClassPred,
65 pprKind, pprParendKind, pprTyLit,
66 PprPrec(..), topPrec, sigPrec, opPrec, funPrec, appPrec, maybeParen,
67 pprDataCons, ppSuggestExplicitKinds,
68
69 pprCo, pprParendCo,
70
71 debugPprType,
72
73 -- * Free variables
74 tyCoVarsOfType, tyCoVarsOfTypeDSet, tyCoVarsOfTypes, tyCoVarsOfTypesDSet,
75 tyCoFVsBndr, tyCoFVsOfType, tyCoVarsOfTypeList,
76 tyCoFVsOfTypes, tyCoVarsOfTypesList,
77 closeOverKindsDSet, closeOverKindsFV, closeOverKindsList,
78 coVarsOfType, coVarsOfTypes,
79 coVarsOfCo, coVarsOfCos,
80 tyCoVarsOfCo, tyCoVarsOfCos,
81 tyCoVarsOfCoDSet,
82 tyCoFVsOfCo, tyCoFVsOfCos,
83 tyCoVarsOfCoList, tyCoVarsOfProv,
84 closeOverKinds,
85 injectiveVarsOfBinder, injectiveVarsOfType,
86
87 noFreeVarsOfType, noFreeVarsOfCo,
88
89 -- * Substitutions
90 TCvSubst(..), TvSubstEnv, CvSubstEnv,
91 emptyTvSubstEnv, emptyCvSubstEnv, composeTCvSubstEnv, composeTCvSubst,
92 emptyTCvSubst, mkEmptyTCvSubst, isEmptyTCvSubst,
93 mkTCvSubst, mkTvSubst,
94 getTvSubstEnv,
95 getCvSubstEnv, getTCvInScope, getTCvSubstRangeFVs,
96 isInScope, notElemTCvSubst,
97 setTvSubstEnv, setCvSubstEnv, zapTCvSubst,
98 extendTCvInScope, extendTCvInScopeList, extendTCvInScopeSet,
99 extendTCvSubst,
100 extendCvSubst, extendCvSubstWithClone,
101 extendTvSubst, extendTvSubstBinderAndInScope, extendTvSubstWithClone,
102 extendTvSubstList, extendTvSubstAndInScope,
103 unionTCvSubst, zipTyEnv, zipCoEnv, mkTyCoInScopeSet,
104 zipTvSubst, zipCvSubst,
105 mkTvSubstPrs,
106
107 substTyWith, substTyWithCoVars, substTysWith, substTysWithCoVars,
108 substCoWith,
109 substTy, substTyAddInScope,
110 substTyUnchecked, substTysUnchecked, substThetaUnchecked,
111 substTyWithUnchecked,
112 substCoUnchecked, substCoWithUnchecked,
113 substTyWithInScope,
114 substTys, substTheta,
115 lookupTyVar, substTyVarBndr,
116 substCo, substCos, substCoVar, substCoVars, lookupCoVar,
117 substCoVarBndr, cloneTyVarBndr, cloneTyVarBndrs,
118 substTyVar, substTyVars,
119 substForAllCoBndr,
120 substTyVarBndrCallback, substForAllCoBndrCallback,
121 checkValidSubst, isValidTCvSubst,
122
123 -- * Tidying type related things up for printing
124 tidyType, tidyTypes,
125 tidyOpenType, tidyOpenTypes,
126 tidyOpenKind,
127 tidyTyCoVarBndr, tidyTyCoVarBndrs, tidyFreeTyCoVars,
128 tidyOpenTyCoVar, tidyOpenTyCoVars,
129 tidyTyVarOcc,
130 tidyTopType,
131 tidyKind,
132 tidyCo, tidyCos,
133 tidyTyVarBinder, tidyTyVarBinders,
134
135 -- * Sizes
136 typeSize, coercionSize, provSize
137 ) where
138
139 #include "HsVersions.h"
140
141 import GhcPrelude
142
143 import {-# SOURCE #-} DataCon( dataConFullSig
144 , dataConUserTyVarBinders
145 , DataCon )
146 import {-# SOURCE #-} Type( isPredTy, isCoercionTy, mkAppTy, mkCastTy
147 , tyCoVarsOfTypeWellScoped
148 , tyCoVarsOfTypesWellScoped
149 , toposortTyVars
150 , coreView, tcView )
151 -- Transitively pulls in a LOT of stuff, better to break the loop
152
153 import {-# SOURCE #-} Coercion
154 import {-# SOURCE #-} ConLike ( ConLike(..), conLikeName )
155 import {-# SOURCE #-} ToIface( toIfaceTypeX, toIfaceTyLit, toIfaceForAllBndr
156 , toIfaceTyCon, toIfaceTcArgs, toIfaceCoercionX )
157
158 -- friends:
159 import IfaceType
160 import Var
161 import VarEnv
162 import VarSet
163 import Name hiding ( varName )
164 import TyCon
165 import Class
166 import CoAxiom
167 import FV
168
169 -- others
170 import BasicTypes ( LeftOrRight(..), PprPrec(..), topPrec, sigPrec, opPrec
171 , funPrec, appPrec, maybeParen, pickLR )
172 import PrelNames
173 import Outputable
174 import DynFlags
175 import FastString
176 import Pair
177 import UniqSupply
178 import Util
179 import UniqFM
180 import UniqSet
181
182 -- libraries
183 import qualified Data.Data as Data hiding ( TyCon )
184 import Data.List
185 import Data.IORef ( IORef ) -- for CoercionHole
186
187 {-
188 %************************************************************************
189 %* *
190 TyThing
191 %* *
192 %************************************************************************
193
194 Despite the fact that DataCon has to be imported via a hi-boot route,
195 this module seems the right place for TyThing, because it's needed for
196 funTyCon and all the types in TysPrim.
197
198 It is also SOURCE-imported into Name.hs
199
200
201 Note [ATyCon for classes]
202 ~~~~~~~~~~~~~~~~~~~~~~~~~
203 Both classes and type constructors are represented in the type environment
204 as ATyCon. You can tell the difference, and get to the class, with
205 isClassTyCon :: TyCon -> Bool
206 tyConClass_maybe :: TyCon -> Maybe Class
207 The Class and its associated TyCon have the same Name.
208 -}
209
210 -- | A global typecheckable-thing, essentially anything that has a name.
211 -- Not to be confused with a 'TcTyThing', which is also a typecheckable
212 -- thing but in the *local* context. See 'TcEnv' for how to retrieve
213 -- a 'TyThing' given a 'Name'.
214 data TyThing
215 = AnId Id
216 | AConLike ConLike
217 | ATyCon TyCon -- TyCons and classes; see Note [ATyCon for classes]
218 | ACoAxiom (CoAxiom Branched)
219
220 instance Outputable TyThing where
221 ppr = pprShortTyThing
222
223 instance NamedThing TyThing where -- Can't put this with the type
224 getName (AnId id) = getName id -- decl, because the DataCon instance
225 getName (ATyCon tc) = getName tc -- isn't visible there
226 getName (ACoAxiom cc) = getName cc
227 getName (AConLike cl) = conLikeName cl
228
229 pprShortTyThing :: TyThing -> SDoc
230 -- c.f. PprTyThing.pprTyThing, which prints all the details
231 pprShortTyThing thing
232 = pprTyThingCategory thing <+> quotes (ppr (getName thing))
233
234 pprTyThingCategory :: TyThing -> SDoc
235 pprTyThingCategory = text . capitalise . tyThingCategory
236
237 tyThingCategory :: TyThing -> String
238 tyThingCategory (ATyCon tc)
239 | isClassTyCon tc = "class"
240 | otherwise = "type constructor"
241 tyThingCategory (ACoAxiom _) = "coercion axiom"
242 tyThingCategory (AnId _) = "identifier"
243 tyThingCategory (AConLike (RealDataCon _)) = "data constructor"
244 tyThingCategory (AConLike (PatSynCon _)) = "pattern synonym"
245
246
247 {- **********************************************************************
248 * *
249 Type
250 * *
251 ********************************************************************** -}
252
253 -- | The key representation of types within the compiler
254
255 type KindOrType = Type -- See Note [Arguments to type constructors]
256
257 -- | The key type representing kinds in the compiler.
258 type Kind = Type
259
260 -- If you edit this type, you may need to update the GHC formalism
261 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
262 data Type
263 -- See Note [Non-trivial definitional equality]
264 = TyVarTy Var -- ^ Vanilla type or kind variable (*never* a coercion variable)
265
266 | AppTy
267 Type
268 Type -- ^ Type application to something other than a 'TyCon'. Parameters:
269 --
270 -- 1) Function: must /not/ be a 'TyConApp' or 'CastTy',
271 -- must be another 'AppTy', or 'TyVarTy'
272 -- See Note [Respecting definitional equality] (EQ1) about the
273 -- no 'CastTy' requirement
274 --
275 -- 2) Argument type
276
277 | TyConApp
278 TyCon
279 [KindOrType] -- ^ Application of a 'TyCon', including newtypes /and/ synonyms.
280 -- Invariant: saturated applications of 'FunTyCon' must
281 -- use 'FunTy' and saturated synonyms must use their own
282 -- constructors. However, /unsaturated/ 'FunTyCon's
283 -- do appear as 'TyConApp's.
284 -- Parameters:
285 --
286 -- 1) Type constructor being applied to.
287 --
288 -- 2) Type arguments. Might not have enough type arguments
289 -- here to saturate the constructor.
290 -- Even type synonyms are not necessarily saturated;
291 -- for example unsaturated type synonyms
292 -- can appear as the right hand side of a type synonym.
293
294 | ForAllTy
295 {-# UNPACK #-} !TyVarBinder
296 Type -- ^ A Π type.
297
298 | FunTy Type Type -- ^ t1 -> t2 Very common, so an important special case
299
300 | LitTy TyLit -- ^ Type literals are similar to type constructors.
301
302 | CastTy
303 Type
304 KindCoercion -- ^ A kind cast. The coercion is always nominal.
305 -- INVARIANT: The cast is never refl.
306 -- INVARIANT: The Type is not a CastTy (use TransCo instead)
307 -- See Note [Respecting definitional equality] (EQ2) and (EQ3)
308
309 | CoercionTy
310 Coercion -- ^ Injection of a Coercion into a type
311 -- This should only ever be used in the RHS of an AppTy,
312 -- in the list of a TyConApp, when applying a promoted
313 -- GADT data constructor
314
315 deriving Data.Data
316
317
318 -- NOTE: Other parts of the code assume that type literals do not contain
319 -- types or type variables.
320 data TyLit
321 = NumTyLit Integer
322 | StrTyLit FastString
323 deriving (Eq, Ord, Data.Data)
324
325 {- Note [Arguments to type constructors]
326 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
327 Because of kind polymorphism, in addition to type application we now
328 have kind instantiation. We reuse the same notations to do so.
329
330 For example:
331
332 Just (* -> *) Maybe
333 Right * Nat Zero
334
335 are represented by:
336
337 TyConApp (PromotedDataCon Just) [* -> *, Maybe]
338 TyConApp (PromotedDataCon Right) [*, Nat, (PromotedDataCon Zero)]
339
340 Important note: Nat is used as a *kind* and not as a type. This can be
341 confusing, since type-level Nat and kind-level Nat are identical. We
342 use the kind of (PromotedDataCon Right) to know if its arguments are
343 kinds or types.
344
345 This kind instantiation only happens in TyConApp currently.
346
347 Note [Non-trivial definitional equality]
348 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
349 Is Int |> <*> the same as Int? YES! In order to reduce headaches,
350 we decide that any reflexive casts in types are just ignored.
351 (Indeed they must be. See Note [Respecting definitional equality].)
352 More generally, the `eqType` function, which defines Core's type equality
353 relation, ignores casts and coercion arguments, as long as the
354 two types have the same kind. This allows us to be a little sloppier
355 in keeping track of coercions, which is a good thing. It also means
356 that eqType does not depend on eqCoercion, which is also a good thing.
357
358 Why is this sensible? That is, why is something different than α-equivalence
359 appropriate for the implementation of eqType?
360
361 Anything smaller than ~ and homogeneous is an appropriate definition for
362 equality. The type safety of FC depends only on ~. Let's say η : τ ~ σ. Any
363 expression of type τ can be transmuted to one of type σ at any point by
364 casting. The same is true of types of type τ. So in some sense, τ and σ are
365 interchangeable.
366
367 But let's be more precise. If we examine the typing rules of FC (say, those in
368 http://www.cis.upenn.edu/~eir/papers/2015/equalities/equalities-extended.pdf)
369 there are several places where the same metavariable is used in two different
370 premises to a rule. (For example, see Ty_App.) There is an implicit equality
371 check here. What definition of equality should we use? By convention, we use
372 α-equivalence. Take any rule with one (or more) of these implicit equality
373 checks. Then there is an admissible rule that uses ~ instead of the implicit
374 check, adding in casts as appropriate.
375
376 The only problem here is that ~ is heterogeneous. To make the kinds work out
377 in the admissible rule that uses ~, it is necessary to homogenize the
378 coercions. That is, if we have η : (τ : κ1) ~ (σ : κ2), then we don't use η;
379 we use η |> kind η, which is homogeneous.
380
381 The effect of this all is that eqType, the implementation of the implicit
382 equality check, can use any homogeneous relation that is smaller than ~, as
383 those rules must also be admissible.
384
385 A more drawn out argument around all of this is presented in Section 7.2 of
386 Richard E's thesis (http://cs.brynmawr.edu/~rae/papers/2016/thesis/eisenberg-thesis.pdf).
387
388 What would go wrong if we insisted on the casts matching? See the beginning of
389 Section 8 in the unpublished paper above. Theoretically, nothing at all goes
390 wrong. But in practical terms, getting the coercions right proved to be
391 nightmarish. And types would explode: during kind-checking, we often produce
392 reflexive kind coercions. When we try to cast by these, mkCastTy just discards
393 them. But if we used an eqType that distinguished between Int and Int |> <*>,
394 then we couldn't discard -- the output of kind-checking would be enormous,
395 and we would need enormous casts with lots of CoherenceCo's to straighten
396 them out.
397
398 Would anything go wrong if eqType respected type families? No, not at all. But
399 that makes eqType rather hard to implement.
400
401 Thus, the guideline for eqType is that it should be the largest
402 easy-to-implement relation that is still smaller than ~ and homogeneous. The
403 precise choice of relation is somewhat incidental, as long as the smart
404 constructors and destructors in Type respect whatever relation is chosen.
405
406 Another helpful principle with eqType is this:
407
408 (EQ) If (t1 `eqType` t2) then I can replace t1 by t2 anywhere.
409
410 This principle also tells us that eqType must relate only types with the
411 same kinds.
412
413 Note [Respecting definitional equality]
414 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
415 Note [Non-trivial definitional equality] introduces the property (EQ).
416 How is this upheld?
417
418 Any function that pattern matches on all the constructors will have to
419 consider the possibility of CastTy. Presumably, those functions will handle
420 CastTy appropriately and we'll be OK.
421
422 More dangerous are the splitXXX functions. Let's focus on splitTyConApp.
423 We don't want it to fail on (T a b c |> co). Happily, if we have
424 (T a b c |> co) `eqType` (T d e f)
425 then co must be reflexive. Why? eqType checks that the kinds are equal, as
426 well as checking that (a `eqType` d), (b `eqType` e), and (c `eqType` f).
427 By the kind check, we know that (T a b c |> co) and (T d e f) have the same
428 kind. So the only way that co could be non-reflexive is for (T a b c) to have
429 a different kind than (T d e f). But because T's kind is closed (all tycon kinds
430 are closed), the only way for this to happen is that one of the arguments has
431 to differ, leading to a contradiction. Thus, co is reflexive.
432
433 Accordingly, by eliminating reflexive casts, splitTyConApp need not worry
434 about outermost casts to uphold (EQ). Eliminating reflexive casts is done
435 in mkCastTy.
436
437 Unforunately, that's not the end of the story. Consider comparing
438 (T a b c) =? (T a b |> (co -> <Type>)) (c |> co)
439 These two types have the same kind (Type), but the left type is a TyConApp
440 while the right type is not. To handle this case, we say that the right-hand
441 type is ill-formed, requiring an AppTy never to have a casted TyConApp
442 on its left. It is easy enough to pull around the coercions to maintain
443 this invariant, as done in Type.mkAppTy. In the example above, trying to
444 form the right-hand type will instead yield (T a b (c |> co |> sym co) |> <Type>).
445 Both the casts there are reflexive and will be dropped. Huzzah.
446
447 This idea of pulling coercions to the right works for splitAppTy as well.
448
449 However, there is one hiccup: it's possible that a coercion doesn't relate two
450 Pi-types. For example, if we have @type family Fun a b where Fun a b = a -> b@,
451 then we might have (T :: Fun Type Type) and (T |> axFun) Int. That axFun can't
452 be pulled to the right. But we don't need to pull it: (T |> axFun) Int is not
453 `eqType` to any proper TyConApp -- thus, leaving it where it is doesn't violate
454 our (EQ) property.
455
456 Lastly, in order to detect reflexive casts reliably, we must make sure not
457 to have nested casts: we update (t |> co1 |> co2) to (t |> (co1 `TransCo` co2)).
458
459 In sum, in order to uphold (EQ), we need the following three invariants:
460
461 (EQ1) No decomposable CastTy to the left of an AppTy, where a decomposable
462 cast is one that relates either a FunTy to a FunTy or a
463 ForAllTy to a ForAllTy.
464 (EQ2) No reflexive casts in CastTy.
465 (EQ3) No nested CastTys.
466
467 These invariants are all documented above, in the declaration for Type.
468
469 -}
470
471 {- **********************************************************************
472 * *
473 TyBinder and ArgFlag
474 * *
475 ********************************************************************** -}
476
477 -- | A 'TyBinder' represents an argument to a function. TyBinders can be dependent
478 -- ('Named') or nondependent ('Anon'). They may also be visible or not.
479 -- See Note [TyBinders]
480 data TyBinder
481 = Named TyVarBinder -- A type-lambda binder
482 | Anon Type -- A term-lambda binder
483 -- Visibility is determined by the type (Constraint vs. *)
484 deriving Data.Data
485
486 -- | Remove the binder's variable from the set, if the binder has
487 -- a variable.
488 delBinderVar :: VarSet -> TyVarBinder -> VarSet
489 delBinderVar vars (TvBndr tv _) = vars `delVarSet` tv
490
491 -- | Does this binder bind an invisible argument?
492 isInvisibleBinder :: TyBinder -> Bool
493 isInvisibleBinder (Named (TvBndr _ vis)) = isInvisibleArgFlag vis
494 isInvisibleBinder (Anon ty) = isPredTy ty
495
496 -- | Does this binder bind a visible argument?
497 isVisibleBinder :: TyBinder -> Bool
498 isVisibleBinder = not . isInvisibleBinder
499
500
501 {- Note [TyBinders]
502 ~~~~~~~~~~~~~~~~~~~
503 A ForAllTy contains a TyVarBinder. But a type can be decomposed
504 to a telescope consisting of a [TyBinder]
505
506 A TyBinder represents the type of binders -- that is, the type of an
507 argument to a Pi-type. GHC Core currently supports two different
508 Pi-types:
509
510 * A non-dependent function type,
511 written with ->, e.g. ty1 -> ty2
512 represented as FunTy ty1 ty2. These are
513 lifted to Coercions with the corresponding FunCo.
514
515 * A dependent compile-time-only polytype,
516 written with forall, e.g. forall (a:*). ty
517 represented as ForAllTy (TvBndr a v) ty
518
519 Both Pi-types classify terms/types that take an argument. In other
520 words, if `x` is either a function or a polytype, `x arg` makes sense
521 (for an appropriate `arg`).
522
523
524 Note [TyVarBndrs, TyVarBinders, TyConBinders, and visibility]
525 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
526 * A ForAllTy (used for both types and kinds) contains a TyVarBinder.
527 Each TyVarBinder
528 TvBndr a tvis
529 is equipped with tvis::ArgFlag, which says whether or not arguments
530 for this binder should be visible (explicit) in source Haskell.
531
532 * A TyCon contains a list of TyConBinders. Each TyConBinder
533 TvBndr a cvis
534 is equipped with cvis::TyConBndrVis, which says whether or not type
535 and kind arguments for this TyCon should be visible (explicit) in
536 source Haskell.
537
538 This table summarises the visibility rules:
539 ---------------------------------------------------------------------------------------
540 | Occurrences look like this
541 | GHC displays type as in Haskell source code
542 |-----------------------------------------------------------------------
543 | TvBndr a tvis :: TyVarBinder, in the binder of ForAllTy for a term
544 | tvis :: ArgFlag
545 | tvis = Inferred: f :: forall {a}. type Arg not allowed: f
546 | tvis = Specified: f :: forall a. type Arg optional: f or f @Int
547 | tvis = Required: T :: forall k -> type Arg required: T *
548 | This last form is illegal in terms: See Note [No Required TyBinder in terms]
549 |
550 | TvBndr k cvis :: TyConBinder, in the TyConBinders of a TyCon
551 | cvis :: TyConBndrVis
552 | cvis = AnonTCB: T :: kind -> kind Required: T *
553 | cvis = NamedTCB Inferred: T :: forall {k}. kind Arg not allowed: T
554 | cvis = NamedTCB Specified: T :: forall k. kind Arg not allowed[1]: T
555 | cvis = NamedTCB Required: T :: forall k -> kind Required: T *
556 ---------------------------------------------------------------------------------------
557
558 [1] In types, in the Specified case, it would make sense to allow
559 optional kind applications, thus (T @*), but we have not
560 yet implemented that
561
562 ---- Examples of where the different visibilities come from -----
563
564 In term declarations:
565
566 * Inferred. Function defn, with no signature: f1 x = x
567 We infer f1 :: forall {a}. a -> a, with 'a' Inferred
568 It's Inferred because it doesn't appear in any
569 user-written signature for f1
570
571 * Specified. Function defn, with signature (implicit forall):
572 f2 :: a -> a; f2 x = x
573 So f2 gets the type f2 :: forall a. a->a, with 'a' Specified
574 even though 'a' is not bound in the source code by an explicit forall
575
576 * Specified. Function defn, with signature (explicit forall):
577 f3 :: forall a. a -> a; f3 x = x
578 So f3 gets the type f3 :: forall a. a->a, with 'a' Specified
579
580 * Inferred/Specified. Function signature with inferred kind polymorphism.
581 f4 :: a b -> Int
582 So 'f4' gets the type f4 :: forall {k} (a:k->*) (b:k). a b -> Int
583 Here 'k' is Inferred (it's not mentioned in the type),
584 but 'a' and 'b' are Specified.
585
586 * Specified. Function signature with explicit kind polymorphism
587 f5 :: a (b :: k) -> Int
588 This time 'k' is Specified, because it is mentioned explicitly,
589 so we get f5 :: forall (k:*) (a:k->*) (b:k). a b -> Int
590
591 * Similarly pattern synonyms:
592 Inferred - from inferred types (e.g. no pattern type signature)
593 - or from inferred kind polymorphism
594
595 In type declarations:
596
597 * Inferred (k)
598 data T1 a b = MkT1 (a b)
599 Here T1's kind is T1 :: forall {k:*}. (k->*) -> k -> *
600 The kind variable 'k' is Inferred, since it is not mentioned
601
602 Note that 'a' and 'b' correspond to /Anon/ TyBinders in T1's kind,
603 and Anon binders don't have a visibility flag. (Or you could think
604 of Anon having an implicit Required flag.)
605
606 * Specified (k)
607 data T2 (a::k->*) b = MkT (a b)
608 Here T's kind is T :: forall (k:*). (k->*) -> k -> *
609 The kind variable 'k' is Specified, since it is mentioned in
610 the signature.
611
612 * Required (k)
613 data T k (a::k->*) b = MkT (a b)
614 Here T's kind is T :: forall k:* -> (k->*) -> k -> *
615 The kind is Required, since it bound in a positional way in T's declaration
616 Every use of T must be explicitly applied to a kind
617
618 * Inferred (k1), Specified (k)
619 data T a b (c :: k) = MkT (a b) (Proxy c)
620 Here T's kind is T :: forall {k1:*} (k:*). (k1->*) -> k1 -> k -> *
621 So 'k' is Specified, because it appears explicitly,
622 but 'k1' is Inferred, because it does not
623
624 ---- Printing -----
625
626 We print forall types with enough syntax to tell you their visibility
627 flag. But this is not source Haskell, and these types may not all
628 be parsable.
629
630 Specified: a list of Specified binders is written between `forall` and `.`:
631 const :: forall a b. a -> b -> a
632
633 Inferred: with -fprint-explicit-foralls, Inferred binders are written
634 in braces:
635 f :: forall {k} (a:k). S k a -> Int
636 Otherwise, they are printed like Specified binders.
637
638 Required: binders are put between `forall` and `->`:
639 T :: forall k -> *
640
641 ---- Other points -----
642
643 * In classic Haskell, all named binders (that is, the type variables in
644 a polymorphic function type f :: forall a. a -> a) have been Inferred.
645
646 * Inferred variables correspond to "generalized" variables from the
647 Visible Type Applications paper (ESOP'16).
648
649 Note [No Required TyBinder in terms]
650 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
651 We don't allow Required foralls for term variables, including pattern
652 synonyms and data constructors. Why? Because then an application
653 would need a /compulsory/ type argument (possibly without an "@"?),
654 thus (f Int); and we don't have concrete syntax for that.
655
656 We could change this decision, but Required, Named TyBinders are rare
657 anyway. (Most are Anons.)
658 -}
659
660
661 {- **********************************************************************
662 * *
663 PredType
664 * *
665 ********************************************************************** -}
666
667
668 -- | A type of the form @p@ of kind @Constraint@ represents a value whose type is
669 -- the Haskell predicate @p@, where a predicate is what occurs before
670 -- the @=>@ in a Haskell type.
671 --
672 -- We use 'PredType' as documentation to mark those types that we guarantee to have
673 -- this kind.
674 --
675 -- It can be expanded into its representation, but:
676 --
677 -- * The type checker must treat it as opaque
678 --
679 -- * The rest of the compiler treats it as transparent
680 --
681 -- Consider these examples:
682 --
683 -- > f :: (Eq a) => a -> Int
684 -- > g :: (?x :: Int -> Int) => a -> Int
685 -- > h :: (r\l) => {r} => {l::Int | r}
686 --
687 -- Here the @Eq a@ and @?x :: Int -> Int@ and @r\l@ are all called \"predicates\"
688 type PredType = Type
689
690 -- | A collection of 'PredType's
691 type ThetaType = [PredType]
692
693 {-
694 (We don't support TREX records yet, but the setup is designed
695 to expand to allow them.)
696
697 A Haskell qualified type, such as that for f,g,h above, is
698 represented using
699 * a FunTy for the double arrow
700 * with a type of kind Constraint as the function argument
701
702 The predicate really does turn into a real extra argument to the
703 function. If the argument has type (p :: Constraint) then the predicate p is
704 represented by evidence of type p.
705
706
707 %************************************************************************
708 %* *
709 Simple constructors
710 %* *
711 %************************************************************************
712
713 These functions are here so that they can be used by TysPrim,
714 which in turn is imported by Type
715 -}
716
717 -- named with "Only" to prevent naive use of mkTyVarTy
718 mkTyVarTy :: TyVar -> Type
719 mkTyVarTy v = ASSERT2( isTyVar v, ppr v <+> dcolon <+> ppr (tyVarKind v) )
720 TyVarTy v
721
722 mkTyVarTys :: [TyVar] -> [Type]
723 mkTyVarTys = map mkTyVarTy -- a common use of mkTyVarTy
724
725 infixr 3 `mkFunTy` -- Associates to the right
726 -- | Make an arrow type
727 mkFunTy :: Type -> Type -> Type
728 mkFunTy arg res = FunTy arg res
729
730 -- | Make nested arrow types
731 mkFunTys :: [Type] -> Type -> Type
732 mkFunTys tys ty = foldr mkFunTy ty tys
733
734 mkForAllTy :: TyVar -> ArgFlag -> Type -> Type
735 mkForAllTy tv vis ty = ForAllTy (TvBndr tv vis) ty
736
737 -- | Wraps foralls over the type using the provided 'TyVar's from left to right
738 mkForAllTys :: [TyVarBinder] -> Type -> Type
739 mkForAllTys tyvars ty = foldr ForAllTy ty tyvars
740
741 mkPiTy :: TyBinder -> Type -> Type
742 mkPiTy (Anon ty1) ty2 = FunTy ty1 ty2
743 mkPiTy (Named tvb) ty = ForAllTy tvb ty
744
745 mkPiTys :: [TyBinder] -> Type -> Type
746 mkPiTys tbs ty = foldr mkPiTy ty tbs
747
748 -- | Does this type classify a core (unlifted) Coercion?
749 -- At either role nominal or representational
750 -- (t1 ~# t2) or (t1 ~R# t2)
751 isCoercionType :: Type -> Bool
752 isCoercionType (TyConApp tc tys)
753 | (tc `hasKey` eqPrimTyConKey) || (tc `hasKey` eqReprPrimTyConKey)
754 , tys `lengthIs` 4
755 = True
756 isCoercionType _ = False
757
758
759 -- | Create the plain type constructor type which has been applied to no type arguments at all.
760 mkTyConTy :: TyCon -> Type
761 mkTyConTy tycon = TyConApp tycon []
762
763 {-
764 Some basic functions, put here to break loops eg with the pretty printer
765 -}
766
767 -- | If a type is @'TYPE' r@ for some @r@, run the predicate argument on @r@.
768 -- Otherwise, return 'False'.
769 --
770 -- This function does not distinguish between 'Constraint' and 'Type'. For a
771 -- version which does distinguish between the two, see 'tcIsTYPE'.
772 isTYPE :: ( Type -- the single argument to TYPE; not a synonym
773 -> Bool ) -- what to return
774 -> Kind -> Bool
775 isTYPE f ki | Just ki' <- coreView ki = isTYPE f ki'
776 isTYPE f (TyConApp tc [arg])
777 | tc `hasKey` tYPETyConKey
778 = go arg
779 where
780 go ty | Just ty' <- coreView ty = go ty'
781 go ty = f ty
782 isTYPE _ _ = False
783
784 -- | If a type is @'TYPE' r@ for some @r@, run the predicate argument on @r@.
785 -- Otherwise, return 'False'.
786 --
787 -- This function distinguishes between 'Constraint' and 'Type' (and will return
788 -- 'False' for 'Constraint'). For a version which does not distinguish between
789 -- the two, see 'isTYPE'.
790 tcIsTYPE :: ( Type -- the single argument to TYPE; not a synonym
791 -> Bool ) -- what to return
792 -> Kind -> Bool
793 tcIsTYPE f ki | Just ki' <- tcView ki = tcIsTYPE f ki'
794 tcIsTYPE f (TyConApp tc [arg])
795 | tc `hasKey` tYPETyConKey
796 = go arg
797 where
798 go ty | Just ty' <- tcView ty = go ty'
799 go ty = f ty
800 tcIsTYPE _ _ = False
801
802 -- | This version considers Constraint to be the same as *. Returns True
803 -- if the argument is equivalent to Type/Constraint and False otherwise.
804 isLiftedTypeKind :: Kind -> Bool
805 isLiftedTypeKind = isTYPE is_lifted
806 where
807 is_lifted (TyConApp lifted_rep []) = lifted_rep `hasKey` liftedRepDataConKey
808 is_lifted _ = False
809
810 -- | Returns True if the kind classifies unlifted types and False otherwise.
811 -- Note that this returns False for levity-polymorphic kinds, which may
812 -- be specialized to a kind that classifies unlifted types.
813 isUnliftedTypeKind :: Kind -> Bool
814 isUnliftedTypeKind = isTYPE is_unlifted
815 where
816 is_unlifted (TyConApp rr _args) = elem (getUnique rr) unliftedRepDataConKeys
817 is_unlifted _ = False
818
819 -- | Is this the type 'RuntimeRep'?
820 isRuntimeRepTy :: Type -> Bool
821 isRuntimeRepTy ty | Just ty' <- coreView ty = isRuntimeRepTy ty'
822 isRuntimeRepTy (TyConApp tc []) = tc `hasKey` runtimeRepTyConKey
823 isRuntimeRepTy _ = False
824
825 -- | Is a tyvar of type 'RuntimeRep'?
826 isRuntimeRepVar :: TyVar -> Bool
827 isRuntimeRepVar = isRuntimeRepTy . tyVarKind
828
829 {-
830 %************************************************************************
831 %* *
832 Coercions
833 %* *
834 %************************************************************************
835 -}
836
837 -- | A 'Coercion' is concrete evidence of the equality/convertibility
838 -- of two types.
839
840 -- If you edit this type, you may need to update the GHC formalism
841 -- See Note [GHC Formalism] in coreSyn/CoreLint.hs
842 data Coercion
843 -- Each constructor has a "role signature", indicating the way roles are
844 -- propagated through coercions.
845 -- - P, N, and R stand for coercions of the given role
846 -- - e stands for a coercion of a specific unknown role
847 -- (think "role polymorphism")
848 -- - "e" stands for an explicit role parameter indicating role e.
849 -- - _ stands for a parameter that is not a Role or Coercion.
850
851 -- These ones mirror the shape of types
852 = -- Refl :: "e" -> _ -> e
853 Refl Role Type -- See Note [Refl invariant]
854 -- Invariant: applications of (Refl T) to a bunch of identity coercions
855 -- always show up as Refl.
856 -- For example (Refl T) (Refl a) (Refl b) shows up as (Refl (T a b)).
857
858 -- Applications of (Refl T) to some coercions, at least one of
859 -- which is NOT the identity, show up as TyConAppCo.
860 -- (They may not be fully saturated however.)
861 -- ConAppCo coercions (like all coercions other than Refl)
862 -- are NEVER the identity.
863
864 -- Use (Refl Representational _), not (SubCo (Refl Nominal _))
865
866 -- These ones simply lift the correspondingly-named
867 -- Type constructors into Coercions
868
869 -- TyConAppCo :: "e" -> _ -> ?? -> e
870 -- See Note [TyConAppCo roles]
871 | TyConAppCo Role TyCon [Coercion] -- lift TyConApp
872 -- The TyCon is never a synonym;
873 -- we expand synonyms eagerly
874 -- But it can be a type function
875
876 | AppCo Coercion CoercionN -- lift AppTy
877 -- AppCo :: e -> N -> e
878
879 -- See Note [Forall coercions]
880 | ForAllCo TyVar KindCoercion Coercion
881 -- ForAllCo :: _ -> N -> e -> e
882
883 | FunCo Role Coercion Coercion -- lift FunTy
884 -- FunCo :: "e" -> e -> e -> e
885
886 -- These are special
887 | CoVarCo CoVar -- :: _ -> (N or R)
888 -- result role depends on the tycon of the variable's type
889
890 -- AxiomInstCo :: e -> _ -> [N] -> e
891 | AxiomInstCo (CoAxiom Branched) BranchIndex [Coercion]
892 -- See also [CoAxiom index]
893 -- The coercion arguments always *precisely* saturate
894 -- arity of (that branch of) the CoAxiom. If there are
895 -- any left over, we use AppCo.
896 -- See [Coercion axioms applied to coercions]
897
898 | AxiomRuleCo CoAxiomRule [Coercion]
899 -- AxiomRuleCo is very like AxiomInstCo, but for a CoAxiomRule
900 -- The number coercions should match exactly the expectations
901 -- of the CoAxiomRule (i.e., the rule is fully saturated).
902
903 | UnivCo UnivCoProvenance Role Type Type
904 -- :: _ -> "e" -> _ -> _ -> e
905
906 | SymCo Coercion -- :: e -> e
907 | TransCo Coercion Coercion -- :: e -> e -> e
908
909 | NthCo Role Int Coercion -- Zero-indexed; decomposes (T t0 ... tn)
910 -- :: "e" -> _ -> e0 -> e (inverse of TyConAppCo, see Note [TyConAppCo roles])
911 -- Using NthCo on a ForAllCo gives an N coercion always
912 -- See Note [NthCo and newtypes]
913 --
914 -- Invariant: (NthCo r i co), it is always the case that r = role of (Nth i co)
915 -- That is: the role of the entire coercion is redundantly cached here.
916 -- See Note [NthCo Cached Roles]
917
918 | LRCo LeftOrRight CoercionN -- Decomposes (t_left t_right)
919 -- :: _ -> N -> N
920 | InstCo Coercion CoercionN
921 -- :: e -> N -> e
922 -- See Note [InstCo roles]
923
924 -- Coherence applies a coercion to the left-hand type of another coercion
925 -- See Note [Coherence]
926 | CoherenceCo Coercion KindCoercion
927 -- :: e -> N -> e
928
929 -- Extract a kind coercion from a (heterogeneous) type coercion
930 -- NB: all kind coercions are Nominal
931 | KindCo Coercion
932 -- :: e -> N
933
934 | SubCo CoercionN -- Turns a ~N into a ~R
935 -- :: N -> R
936
937 | HoleCo CoercionHole -- ^ See Note [Coercion holes]
938 -- Only present during typechecking
939 deriving Data.Data
940
941 type CoercionN = Coercion -- always nominal
942 type CoercionR = Coercion -- always representational
943 type CoercionP = Coercion -- always phantom
944 type KindCoercion = CoercionN -- always nominal
945
946 -- | A semantically more meaningful type to represent what may or may not be a
947 -- useful 'Coercion'.
948 data MCoercion
949 = MRefl
950 -- A trivial Reflexivity coercion
951 | MCo Coercion
952 -- Other coercions
953 type MCoercionR = MCoercion
954
955 {-
956 Note [Refl invariant]
957 ~~~~~~~~~~~~~~~~~~~~~
958 Invariant 1:
959
960 Coercions have the following invariant
961 Refl is always lifted as far as possible.
962
963 You might think that a consequencs is:
964 Every identity coercions has Refl at the root
965
966 But that's not quite true because of coercion variables. Consider
967 g where g :: Int~Int
968 Left h where h :: Maybe Int ~ Maybe Int
969 etc. So the consequence is only true of coercions that
970 have no coercion variables.
971
972 Note [Coercion axioms applied to coercions]
973 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
974 The reason coercion axioms can be applied to coercions and not just
975 types is to allow for better optimization. There are some cases where
976 we need to be able to "push transitivity inside" an axiom in order to
977 expose further opportunities for optimization.
978
979 For example, suppose we have
980
981 C a : t[a] ~ F a
982 g : b ~ c
983
984 and we want to optimize
985
986 sym (C b) ; t[g] ; C c
987
988 which has the kind
989
990 F b ~ F c
991
992 (stopping through t[b] and t[c] along the way).
993
994 We'd like to optimize this to just F g -- but how? The key is
995 that we need to allow axioms to be instantiated by *coercions*,
996 not just by types. Then we can (in certain cases) push
997 transitivity inside the axiom instantiations, and then react
998 opposite-polarity instantiations of the same axiom. In this
999 case, e.g., we match t[g] against the LHS of (C c)'s kind, to
1000 obtain the substitution a |-> g (note this operation is sort
1001 of the dual of lifting!) and hence end up with
1002
1003 C g : t[b] ~ F c
1004
1005 which indeed has the same kind as t[g] ; C c.
1006
1007 Now we have
1008
1009 sym (C b) ; C g
1010
1011 which can be optimized to F g.
1012
1013 Note [CoAxiom index]
1014 ~~~~~~~~~~~~~~~~~~~~
1015 A CoAxiom has 1 or more branches. Each branch has contains a list
1016 of the free type variables in that branch, the LHS type patterns,
1017 and the RHS type for that branch. When we apply an axiom to a list
1018 of coercions, we must choose which branch of the axiom we wish to
1019 use, as the different branches may have different numbers of free
1020 type variables. (The number of type patterns is always the same
1021 among branches, but that doesn't quite concern us here.)
1022
1023 The Int in the AxiomInstCo constructor is the 0-indexed number
1024 of the chosen branch.
1025
1026 Note [Forall coercions]
1027 ~~~~~~~~~~~~~~~~~~~~~~~
1028 Constructing coercions between forall-types can be a bit tricky,
1029 because the kinds of the bound tyvars can be different.
1030
1031 The typing rule is:
1032
1033
1034 kind_co : k1 ~ k2
1035 tv1:k1 |- co : t1 ~ t2
1036 -------------------------------------------------------------------
1037 ForAllCo tv1 kind_co co : all tv1:k1. t1 ~
1038 all tv1:k2. (t2[tv1 |-> tv1 |> sym kind_co])
1039
1040 First, the TyVar stored in a ForAllCo is really an optimisation: this field
1041 should be a Name, as its kind is redundant. Thinking of the field as a Name
1042 is helpful in understanding what a ForAllCo means.
1043
1044 The idea is that kind_co gives the two kinds of the tyvar. See how, in the
1045 conclusion, tv1 is assigned kind k1 on the left but kind k2 on the right.
1046
1047 Of course, a type variable can't have different kinds at the same time. So,
1048 we arbitrarily prefer the first kind when using tv1 in the inner coercion
1049 co, which shows that t1 equals t2.
1050
1051 The last wrinkle is that we need to fix the kinds in the conclusion. In
1052 t2, tv1 is assumed to have kind k1, but it has kind k2 in the conclusion of
1053 the rule. So we do a kind-fixing substitution, replacing (tv1:k1) with
1054 (tv1:k2) |> sym kind_co. This substitution is slightly bizarre, because it
1055 mentions the same name with different kinds, but it *is* well-kinded, noting
1056 that `(tv1:k2) |> sym kind_co` has kind k1.
1057
1058 This all really would work storing just a Name in the ForAllCo. But we can't
1059 add Names to, e.g., VarSets, and there generally is just an impedance mismatch
1060 in a bunch of places. So we use tv1. When we need tv2, we can use
1061 setTyVarKind.
1062
1063 Note [Coherence]
1064 ~~~~~~~~~~~~~~~~
1065 The Coherence typing rule is thus:
1066
1067 g1 : s ~ t s : k1 g2 : k1 ~ k2
1068 ------------------------------------
1069 CoherenceCo g1 g2 : (s |> g2) ~ t
1070
1071 While this looks (and is) unsymmetric, a combination of other coercion
1072 combinators can make the symmetric version.
1073
1074 For role information, see Note [Roles and kind coercions].
1075
1076 Note [Predicate coercions]
1077 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1078 Suppose we have
1079 g :: a~b
1080 How can we coerce between types
1081 ([c]~a) => [a] -> c
1082 and
1083 ([c]~b) => [b] -> c
1084 where the equality predicate *itself* differs?
1085
1086 Answer: we simply treat (~) as an ordinary type constructor, so these
1087 types really look like
1088
1089 ((~) [c] a) -> [a] -> c
1090 ((~) [c] b) -> [b] -> c
1091
1092 So the coercion between the two is obviously
1093
1094 ((~) [c] g) -> [g] -> c
1095
1096 Another way to see this to say that we simply collapse predicates to
1097 their representation type (see Type.coreView and Type.predTypeRep).
1098
1099 This collapse is done by mkPredCo; there is no PredCo constructor
1100 in Coercion. This is important because we need Nth to work on
1101 predicates too:
1102 Nth 1 ((~) [c] g) = g
1103 See Simplify.simplCoercionF, which generates such selections.
1104
1105 Note [Roles]
1106 ~~~~~~~~~~~~
1107 Roles are a solution to the GeneralizedNewtypeDeriving problem, articulated
1108 in Trac #1496. The full story is in docs/core-spec/core-spec.pdf. Also, see
1109 http://ghc.haskell.org/trac/ghc/wiki/RolesImplementation
1110
1111 Here is one way to phrase the problem:
1112
1113 Given:
1114 newtype Age = MkAge Int
1115 type family F x
1116 type instance F Age = Bool
1117 type instance F Int = Char
1118
1119 This compiles down to:
1120 axAge :: Age ~ Int
1121 axF1 :: F Age ~ Bool
1122 axF2 :: F Int ~ Char
1123
1124 Then, we can make:
1125 (sym (axF1) ; F axAge ; axF2) :: Bool ~ Char
1126
1127 Yikes!
1128
1129 The solution is _roles_, as articulated in "Generative Type Abstraction and
1130 Type-level Computation" (POPL 2010), available at
1131 http://www.seas.upenn.edu/~sweirich/papers/popl163af-weirich.pdf
1132
1133 The specification for roles has evolved somewhat since that paper. For the
1134 current full details, see the documentation in docs/core-spec. Here are some
1135 highlights.
1136
1137 We label every equality with a notion of type equivalence, of which there are
1138 three options: Nominal, Representational, and Phantom. A ground type is
1139 nominally equivalent only with itself. A newtype (which is considered a ground
1140 type in Haskell) is representationally equivalent to its representation.
1141 Anything is "phantomly" equivalent to anything else. We use "N", "R", and "P"
1142 to denote the equivalences.
1143
1144 The axioms above would be:
1145 axAge :: Age ~R Int
1146 axF1 :: F Age ~N Bool
1147 axF2 :: F Age ~N Char
1148
1149 Then, because transitivity applies only to coercions proving the same notion
1150 of equivalence, the above construction is impossible.
1151
1152 However, there is still an escape hatch: we know that any two types that are
1153 nominally equivalent are representationally equivalent as well. This is what
1154 the form SubCo proves -- it "demotes" a nominal equivalence into a
1155 representational equivalence. So, it would seem the following is possible:
1156
1157 sub (sym axF1) ; F axAge ; sub axF2 :: Bool ~R Char -- WRONG
1158
1159 What saves us here is that the arguments to a type function F, lifted into a
1160 coercion, *must* prove nominal equivalence. So, (F axAge) is ill-formed, and
1161 we are safe.
1162
1163 Roles are attached to parameters to TyCons. When lifting a TyCon into a
1164 coercion (through TyConAppCo), we need to ensure that the arguments to the
1165 TyCon respect their roles. For example:
1166
1167 data T a b = MkT a (F b)
1168
1169 If we know that a1 ~R a2, then we know (T a1 b) ~R (T a2 b). But, if we know
1170 that b1 ~R b2, we know nothing about (T a b1) and (T a b2)! This is because
1171 the type function F branches on b's *name*, not representation. So, we say
1172 that 'a' has role Representational and 'b' has role Nominal. The third role,
1173 Phantom, is for parameters not used in the type's definition. Given the
1174 following definition
1175
1176 data Q a = MkQ Int
1177
1178 the Phantom role allows us to say that (Q Bool) ~R (Q Char), because we
1179 can construct the coercion Bool ~P Char (using UnivCo).
1180
1181 See the paper cited above for more examples and information.
1182
1183 Note [TyConAppCo roles]
1184 ~~~~~~~~~~~~~~~~~~~~~~~
1185 The TyConAppCo constructor has a role parameter, indicating the role at
1186 which the coercion proves equality. The choice of this parameter affects
1187 the required roles of the arguments of the TyConAppCo. To help explain
1188 it, assume the following definition:
1189
1190 type instance F Int = Bool -- Axiom axF : F Int ~N Bool
1191 newtype Age = MkAge Int -- Axiom axAge : Age ~R Int
1192 data Foo a = MkFoo a -- Role on Foo's parameter is Representational
1193
1194 TyConAppCo Nominal Foo axF : Foo (F Int) ~N Foo Bool
1195 For (TyConAppCo Nominal) all arguments must have role Nominal. Why?
1196 So that Foo Age ~N Foo Int does *not* hold.
1197
1198 TyConAppCo Representational Foo (SubCo axF) : Foo (F Int) ~R Foo Bool
1199 TyConAppCo Representational Foo axAge : Foo Age ~R Foo Int
1200 For (TyConAppCo Representational), all arguments must have the roles
1201 corresponding to the result of tyConRoles on the TyCon. This is the
1202 whole point of having roles on the TyCon to begin with. So, we can
1203 have Foo Age ~R Foo Int, if Foo's parameter has role R.
1204
1205 If a Representational TyConAppCo is over-saturated (which is otherwise fine),
1206 the spill-over arguments must all be at Nominal. This corresponds to the
1207 behavior for AppCo.
1208
1209 TyConAppCo Phantom Foo (UnivCo Phantom Int Bool) : Foo Int ~P Foo Bool
1210 All arguments must have role Phantom. This one isn't strictly
1211 necessary for soundness, but this choice removes ambiguity.
1212
1213 The rules here dictate the roles of the parameters to mkTyConAppCo
1214 (should be checked by Lint).
1215
1216 Note [NthCo and newtypes]
1217 ~~~~~~~~~~~~~~~~~~~~~~~~~
1218 Suppose we have
1219
1220 newtype N a = MkN Int
1221 type role N representational
1222
1223 This yields axiom
1224
1225 NTCo:N :: forall a. N a ~R Int
1226
1227 We can then build
1228
1229 co :: forall a b. N a ~R N b
1230 co = NTCo:N a ; sym (NTCo:N b)
1231
1232 for any `a` and `b`. Because of the role annotation on N, if we use
1233 NthCo, we'll get out a representational coercion. That is:
1234
1235 NthCo r 0 co :: forall a b. a ~R b
1236
1237 Yikes! Clearly, this is terrible. The solution is simple: forbid
1238 NthCo to be used on newtypes if the internal coercion is representational.
1239
1240 This is not just some corner case discovered by a segfault somewhere;
1241 it was discovered in the proof of soundness of roles and described
1242 in the "Safe Coercions" paper (ICFP '14).
1243
1244 Note [NthCo Cached Roles]
1245 ~~~~~~~~~~~~~~~~~~~~~~~~~
1246 Why do we cache the role of NthCo in the NthCo constructor?
1247 Because computing role(Nth i co) involves figuring out that
1248
1249 co :: T tys1 ~ T tys2
1250
1251 using coercionKind, and finding (coercionRole co), and then looking
1252 at the tyConRoles of T. Avoiding bad asymptotic behaviour here means
1253 we have to compute the kind and role of a coercion simultaneously,
1254 which makes the code complicated and inefficient.
1255
1256 This only happens for NthCo. Caching the role solves the problem, and
1257 allows coercionKind and coercionRole to be simple.
1258
1259 See Trac #11735
1260
1261 Note [InstCo roles]
1262 ~~~~~~~~~~~~~~~~~~~
1263 Here is (essentially) the typing rule for InstCo:
1264
1265 g :: (forall a. t1) ~r (forall a. t2)
1266 w :: s1 ~N s2
1267 ------------------------------- InstCo
1268 InstCo g w :: (t1 [a |-> s1]) ~r (t2 [a |-> s2])
1269
1270 Note that the Coercion w *must* be nominal. This is necessary
1271 because the variable a might be used in a "nominal position"
1272 (that is, a place where role inference would require a nominal
1273 role) in t1 or t2. If we allowed w to be representational, we
1274 could get bogus equalities.
1275
1276 A more nuanced treatment might be able to relax this condition
1277 somewhat, by checking if t1 and/or t2 use their bound variables
1278 in nominal ways. If not, having w be representational is OK.
1279
1280
1281 %************************************************************************
1282 %* *
1283 UnivCoProvenance
1284 %* *
1285 %************************************************************************
1286
1287 A UnivCo is a coercion whose proof does not directly express its role
1288 and kind (indeed for some UnivCos, like UnsafeCoerceProv, there /is/
1289 no proof).
1290
1291 The different kinds of UnivCo are described by UnivCoProvenance. Really
1292 each is entirely separate, but they all share the need to represent their
1293 role and kind, which is done in the UnivCo constructor.
1294
1295 -}
1296
1297 -- | For simplicity, we have just one UnivCo that represents a coercion from
1298 -- some type to some other type, with (in general) no restrictions on the
1299 -- type. The UnivCoProvenance specifies more exactly what the coercion really
1300 -- is and why a program should (or shouldn't!) trust the coercion.
1301 -- It is reasonable to consider each constructor of 'UnivCoProvenance'
1302 -- as a totally independent coercion form; their only commonality is
1303 -- that they don't tell you what types they coercion between. (That info
1304 -- is in the 'UnivCo' constructor of 'Coercion'.
1305 data UnivCoProvenance
1306 = UnsafeCoerceProv -- ^ From @unsafeCoerce#@. These are unsound.
1307
1308 | PhantomProv KindCoercion -- ^ See Note [Phantom coercions]. Only in Phantom
1309 -- roled coercions
1310
1311 | ProofIrrelProv KindCoercion -- ^ From the fact that any two coercions are
1312 -- considered equivalent. See Note [ProofIrrelProv].
1313 -- Can be used in Nominal or Representational coercions
1314
1315 | PluginProv String -- ^ From a plugin, which asserts that this coercion
1316 -- is sound. The string is for the use of the plugin.
1317
1318 deriving Data.Data
1319
1320 instance Outputable UnivCoProvenance where
1321 ppr UnsafeCoerceProv = text "(unsafeCoerce#)"
1322 ppr (PhantomProv _) = text "(phantom)"
1323 ppr (ProofIrrelProv _) = text "(proof irrel.)"
1324 ppr (PluginProv str) = parens (text "plugin" <+> brackets (text str))
1325
1326 -- | A coercion to be filled in by the type-checker. See Note [Coercion holes]
1327 data CoercionHole
1328 = CoercionHole { ch_co_var :: CoVar
1329 -- See Note [CoercionHoles and coercion free variables]
1330
1331 , ch_ref :: IORef (Maybe Coercion)
1332 }
1333
1334 coHoleCoVar :: CoercionHole -> CoVar
1335 coHoleCoVar = ch_co_var
1336
1337 setCoHoleCoVar :: CoercionHole -> CoVar -> CoercionHole
1338 setCoHoleCoVar h cv = h { ch_co_var = cv }
1339
1340 instance Data.Data CoercionHole where
1341 -- don't traverse?
1342 toConstr _ = abstractConstr "CoercionHole"
1343 gunfold _ _ = error "gunfold"
1344 dataTypeOf _ = mkNoRepType "CoercionHole"
1345
1346 instance Outputable CoercionHole where
1347 ppr (CoercionHole { ch_co_var = cv }) = braces (ppr cv)
1348
1349
1350 {- Note [Phantom coercions]
1351 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
1352 Consider
1353 data T a = T1 | T2
1354 Then we have
1355 T s ~R T t
1356 for any old s,t. The witness for this is (TyConAppCo T Rep co),
1357 where (co :: s ~P t) is a phantom coercion built with PhantomProv.
1358 The role of the UnivCo is always Phantom. The Coercion stored is the
1359 (nominal) kind coercion between the types
1360 kind(s) ~N kind (t)
1361
1362 Note [Coercion holes]
1363 ~~~~~~~~~~~~~~~~~~~~~~~~
1364 During typechecking, constraint solving for type classes works by
1365 - Generate an evidence Id, d7 :: Num a
1366 - Wrap it in a Wanted constraint, [W] d7 :: Num a
1367 - Use the evidence Id where the evidence is needed
1368 - Solve the constraint later
1369 - When solved, add an enclosing let-binding let d7 = .... in ....
1370 which actually binds d7 to the (Num a) evidence
1371
1372 For equality constraints we use a different strategy. See Note [The
1373 equality types story] in TysPrim for background on equality constraints.
1374 - For /boxed/ equality constraints, (t1 ~N t2) and (t1 ~R t2), it's just
1375 like type classes above. (Indeed, boxed equality constraints *are* classes.)
1376 - But for /unboxed/ equality constraints (t1 ~R# t2) and (t1 ~N# t2)
1377 we use a different plan
1378
1379 For unboxed equalities:
1380 - Generate a CoercionHole, a mutable variable just like a unification
1381 variable
1382 - Wrap the CoercionHole in a Wanted constraint; see TcRnTypes.TcEvDest
1383 - Use the CoercionHole in a Coercion, via HoleCo
1384 - Solve the constraint later
1385 - When solved, fill in the CoercionHole by side effect, instead of
1386 doing the let-binding thing
1387
1388 The main reason for all this is that there may be no good place to let-bind
1389 the evidence for unboxed equalities:
1390
1391 - We emit constraints for kind coercions, to be used to cast a
1392 type's kind. These coercions then must be used in types. Because
1393 they might appear in a top-level type, there is no place to bind
1394 these (unlifted) coercions in the usual way.
1395
1396 - A coercion for (forall a. t1) ~ (forall a. t2) will look like
1397 forall a. (coercion for t1~t2)
1398 But the coercion for (t1~t2) may mention 'a', and we don't have
1399 let-bindings within coercions. We could add them, but coercion
1400 holes are easier.
1401
1402 - Moreover, nothing is lost from the lack of let-bindings. For
1403 dicionaries want to achieve sharing to avoid recomoputing the
1404 dictionary. But coercions are entirely erased, so there's little
1405 benefit to sharing. Indeed, even if we had a let-binding, we
1406 always inline types and coercions at every use site and drop the
1407 binding.
1408
1409 Other notes about HoleCo:
1410
1411 * INVARIANT: CoercionHole and HoleCo are used only during type checking,
1412 and should never appear in Core. Just like unification variables; a Type
1413 can contain a TcTyVar, but only during type checking. If, one day, we
1414 use type-level information to separate out forms that can appear during
1415 type-checking vs forms that can appear in core proper, holes in Core will
1416 be ruled out.
1417
1418 * See Note [CoercionHoles and coercion free variables]
1419
1420 * Coercion holes can be compared for equality like other coercions:
1421 by looking at the types coerced.
1422
1423
1424 Note [CoercionHoles and coercion free variables]
1425 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1426 Why does a CoercionHole contain a CoVar, as well as reference to
1427 fill in? Because we want to treat that CoVar as a free variable of
1428 the coercion. See Trac #14584, and Note [What prevents a
1429 constraint from floating] in TcSimplify, item (4):
1430
1431 forall k. [W] co1 :: t1 ~# t2 |> co2
1432 [W] co2 :: k ~# *
1433
1434 Here co2 is a CoercionHole. But we /must/ know that it is free in
1435 co1, because that's all that stops it floating outside the
1436 implication.
1437
1438
1439 Note [ProofIrrelProv]
1440 ~~~~~~~~~~~~~~~~~~~~~
1441 A ProofIrrelProv is a coercion between coercions. For example:
1442
1443 data G a where
1444 MkG :: G Bool
1445
1446 In core, we get
1447
1448 G :: * -> *
1449 MkG :: forall (a :: *). (a ~ Bool) -> G a
1450
1451 Now, consider 'MkG -- that is, MkG used in a type -- and suppose we want
1452 a proof that ('MkG co1 a1) ~ ('MkG co2 a2). This will have to be
1453
1454 TyConAppCo Nominal MkG [co3, co4]
1455 where
1456 co3 :: co1 ~ co2
1457 co4 :: a1 ~ a2
1458
1459 Note that
1460 co1 :: a1 ~ Bool
1461 co2 :: a2 ~ Bool
1462
1463 Here,
1464 co3 = UnivCo (ProofIrrelProv co5) Nominal (CoercionTy co1) (CoercionTy co2)
1465 where
1466 co5 :: (a1 ~ Bool) ~ (a2 ~ Bool)
1467 co5 = TyConAppCo Nominal (~) [<*>, <*>, co4, <Bool>]
1468
1469
1470 %************************************************************************
1471 %* *
1472 Free variables of types and coercions
1473 %* *
1474 %************************************************************************
1475 -}
1476
1477 {- Note [Free variables of types]
1478 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1479 The family of functions tyCoVarsOfType, tyCoVarsOfTypes etc, returns
1480 a VarSet that is closed over the types of its variables. More precisely,
1481 if S = tyCoVarsOfType( t )
1482 and (a:k) is in S
1483 then tyCoVarsOftype( k ) is a subset of S
1484
1485 Example: The tyCoVars of this ((a:* -> k) Int) is {a, k}.
1486
1487 We could /not/ close over the kinds of the variable occurrences, and
1488 instead do so at call sites, but it seems that we always want to do
1489 so, so it's easiest to do it here.
1490 -}
1491
1492
1493 -- | Returns free variables of a type, including kind variables as
1494 -- a non-deterministic set. For type synonyms it does /not/ expand the
1495 -- synonym.
1496 tyCoVarsOfType :: Type -> TyCoVarSet
1497 -- See Note [Free variables of types]
1498 tyCoVarsOfType ty = fvVarSet $ tyCoFVsOfType ty
1499
1500 -- | `tyCoFVsOfType` that returns free variables of a type in a deterministic
1501 -- set. For explanation of why using `VarSet` is not deterministic see
1502 -- Note [Deterministic FV] in FV.
1503 tyCoVarsOfTypeDSet :: Type -> DTyCoVarSet
1504 -- See Note [Free variables of types]
1505 tyCoVarsOfTypeDSet ty = fvDVarSet $ tyCoFVsOfType ty
1506
1507 -- | `tyCoFVsOfType` that returns free variables of a type in deterministic
1508 -- order. For explanation of why using `VarSet` is not deterministic see
1509 -- Note [Deterministic FV] in FV.
1510 tyCoVarsOfTypeList :: Type -> [TyCoVar]
1511 -- See Note [Free variables of types]
1512 tyCoVarsOfTypeList ty = fvVarList $ tyCoFVsOfType ty
1513
1514 -- | The worker for `tyCoFVsOfType` and `tyCoFVsOfTypeList`.
1515 -- The previous implementation used `unionVarSet` which is O(n+m) and can
1516 -- make the function quadratic.
1517 -- It's exported, so that it can be composed with
1518 -- other functions that compute free variables.
1519 -- See Note [FV naming conventions] in FV.
1520 --
1521 -- Eta-expanded because that makes it run faster (apparently)
1522 -- See Note [FV eta expansion] in FV for explanation.
1523 tyCoFVsOfType :: Type -> FV
1524 -- See Note [Free variables of types]
1525 tyCoFVsOfType (TyVarTy v) a b c = (unitFV v `unionFV` tyCoFVsOfType (tyVarKind v)) a b c
1526 tyCoFVsOfType (TyConApp _ tys) a b c = tyCoFVsOfTypes tys a b c
1527 tyCoFVsOfType (LitTy {}) a b c = emptyFV a b c
1528 tyCoFVsOfType (AppTy fun arg) a b c = (tyCoFVsOfType fun `unionFV` tyCoFVsOfType arg) a b c
1529 tyCoFVsOfType (FunTy arg res) a b c = (tyCoFVsOfType arg `unionFV` tyCoFVsOfType res) a b c
1530 tyCoFVsOfType (ForAllTy bndr ty) a b c = tyCoFVsBndr bndr (tyCoFVsOfType ty) a b c
1531 tyCoFVsOfType (CastTy ty co) a b c = (tyCoFVsOfType ty `unionFV` tyCoFVsOfCo co) a b c
1532 tyCoFVsOfType (CoercionTy co) a b c = tyCoFVsOfCo co a b c
1533
1534 tyCoFVsBndr :: TyVarBinder -> FV -> FV
1535 -- Free vars of (forall b. <thing with fvs>)
1536 tyCoFVsBndr (TvBndr tv _) fvs = (delFV tv fvs)
1537 `unionFV` tyCoFVsOfType (tyVarKind tv)
1538
1539 -- | Returns free variables of types, including kind variables as
1540 -- a non-deterministic set. For type synonyms it does /not/ expand the
1541 -- synonym.
1542 tyCoVarsOfTypes :: [Type] -> TyCoVarSet
1543 -- See Note [Free variables of types]
1544 tyCoVarsOfTypes tys = fvVarSet $ tyCoFVsOfTypes tys
1545
1546 -- | Returns free variables of types, including kind variables as
1547 -- a non-deterministic set. For type synonyms it does /not/ expand the
1548 -- synonym.
1549 tyCoVarsOfTypesSet :: TyVarEnv Type -> TyCoVarSet
1550 -- See Note [Free variables of types]
1551 tyCoVarsOfTypesSet tys = fvVarSet $ tyCoFVsOfTypes $ nonDetEltsUFM tys
1552 -- It's OK to use nonDetEltsUFM here because we immediately forget the
1553 -- ordering by returning a set
1554
1555 -- | Returns free variables of types, including kind variables as
1556 -- a deterministic set. For type synonyms it does /not/ expand the
1557 -- synonym.
1558 tyCoVarsOfTypesDSet :: [Type] -> DTyCoVarSet
1559 -- See Note [Free variables of types]
1560 tyCoVarsOfTypesDSet tys = fvDVarSet $ tyCoFVsOfTypes tys
1561
1562 -- | Returns free variables of types, including kind variables as
1563 -- a deterministically ordered list. For type synonyms it does /not/ expand the
1564 -- synonym.
1565 tyCoVarsOfTypesList :: [Type] -> [TyCoVar]
1566 -- See Note [Free variables of types]
1567 tyCoVarsOfTypesList tys = fvVarList $ tyCoFVsOfTypes tys
1568
1569 tyCoFVsOfTypes :: [Type] -> FV
1570 -- See Note [Free variables of types]
1571 tyCoFVsOfTypes (ty:tys) fv_cand in_scope acc = (tyCoFVsOfType ty `unionFV` tyCoFVsOfTypes tys) fv_cand in_scope acc
1572 tyCoFVsOfTypes [] fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1573
1574 tyCoVarsOfCo :: Coercion -> TyCoVarSet
1575 -- See Note [Free variables of types]
1576 tyCoVarsOfCo co = fvVarSet $ tyCoFVsOfCo co
1577
1578 -- | Get a deterministic set of the vars free in a coercion
1579 tyCoVarsOfCoDSet :: Coercion -> DTyCoVarSet
1580 -- See Note [Free variables of types]
1581 tyCoVarsOfCoDSet co = fvDVarSet $ tyCoFVsOfCo co
1582
1583 tyCoVarsOfCoList :: Coercion -> [TyCoVar]
1584 -- See Note [Free variables of types]
1585 tyCoVarsOfCoList co = fvVarList $ tyCoFVsOfCo co
1586
1587 tyCoFVsOfCo :: Coercion -> FV
1588 -- Extracts type and coercion variables from a coercion
1589 -- See Note [Free variables of types]
1590 tyCoFVsOfCo (Refl _ ty) fv_cand in_scope acc = tyCoFVsOfType ty fv_cand in_scope acc
1591 tyCoFVsOfCo (TyConAppCo _ _ cos) fv_cand in_scope acc = tyCoFVsOfCos cos fv_cand in_scope acc
1592 tyCoFVsOfCo (AppCo co arg) fv_cand in_scope acc
1593 = (tyCoFVsOfCo co `unionFV` tyCoFVsOfCo arg) fv_cand in_scope acc
1594 tyCoFVsOfCo (ForAllCo tv kind_co co) fv_cand in_scope acc
1595 = (delFV tv (tyCoFVsOfCo co) `unionFV` tyCoFVsOfCo kind_co) fv_cand in_scope acc
1596 tyCoFVsOfCo (FunCo _ co1 co2) fv_cand in_scope acc
1597 = (tyCoFVsOfCo co1 `unionFV` tyCoFVsOfCo co2) fv_cand in_scope acc
1598 tyCoFVsOfCo (CoVarCo v) fv_cand in_scope acc
1599 = tyCoFVsOfCoVar v fv_cand in_scope acc
1600 tyCoFVsOfCo (HoleCo h) fv_cand in_scope acc
1601 = tyCoFVsOfCoVar (coHoleCoVar h) fv_cand in_scope acc
1602 -- See Note [CoercionHoles and coercion free variables]
1603 tyCoFVsOfCo (AxiomInstCo _ _ cos) fv_cand in_scope acc = tyCoFVsOfCos cos fv_cand in_scope acc
1604 tyCoFVsOfCo (UnivCo p _ t1 t2) fv_cand in_scope acc
1605 = (tyCoFVsOfProv p `unionFV` tyCoFVsOfType t1
1606 `unionFV` tyCoFVsOfType t2) fv_cand in_scope acc
1607 tyCoFVsOfCo (SymCo co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1608 tyCoFVsOfCo (TransCo co1 co2) fv_cand in_scope acc = (tyCoFVsOfCo co1 `unionFV` tyCoFVsOfCo co2) fv_cand in_scope acc
1609 tyCoFVsOfCo (NthCo _ _ co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1610 tyCoFVsOfCo (LRCo _ co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1611 tyCoFVsOfCo (InstCo co arg) fv_cand in_scope acc = (tyCoFVsOfCo co `unionFV` tyCoFVsOfCo arg) fv_cand in_scope acc
1612 tyCoFVsOfCo (CoherenceCo c1 c2) fv_cand in_scope acc = (tyCoFVsOfCo c1 `unionFV` tyCoFVsOfCo c2) fv_cand in_scope acc
1613 tyCoFVsOfCo (KindCo co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1614 tyCoFVsOfCo (SubCo co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1615 tyCoFVsOfCo (AxiomRuleCo _ cs) fv_cand in_scope acc = tyCoFVsOfCos cs fv_cand in_scope acc
1616
1617 tyCoFVsOfCoVar :: CoVar -> FV
1618 tyCoFVsOfCoVar v fv_cand in_scope acc
1619 = (unitFV v `unionFV` tyCoFVsOfType (varType v)) fv_cand in_scope acc
1620
1621 tyCoVarsOfProv :: UnivCoProvenance -> TyCoVarSet
1622 tyCoVarsOfProv prov = fvVarSet $ tyCoFVsOfProv prov
1623
1624 tyCoFVsOfProv :: UnivCoProvenance -> FV
1625 tyCoFVsOfProv UnsafeCoerceProv fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1626 tyCoFVsOfProv (PhantomProv co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1627 tyCoFVsOfProv (ProofIrrelProv co) fv_cand in_scope acc = tyCoFVsOfCo co fv_cand in_scope acc
1628 tyCoFVsOfProv (PluginProv _) fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1629
1630 tyCoVarsOfCos :: [Coercion] -> TyCoVarSet
1631 tyCoVarsOfCos cos = fvVarSet $ tyCoFVsOfCos cos
1632
1633 tyCoVarsOfCosSet :: CoVarEnv Coercion -> TyCoVarSet
1634 tyCoVarsOfCosSet cos = fvVarSet $ tyCoFVsOfCos $ nonDetEltsUFM cos
1635 -- It's OK to use nonDetEltsUFM here because we immediately forget the
1636 -- ordering by returning a set
1637
1638 tyCoFVsOfCos :: [Coercion] -> FV
1639 tyCoFVsOfCos [] fv_cand in_scope acc = emptyFV fv_cand in_scope acc
1640 tyCoFVsOfCos (co:cos) fv_cand in_scope acc = (tyCoFVsOfCo co `unionFV` tyCoFVsOfCos cos) fv_cand in_scope acc
1641
1642 coVarsOfType :: Type -> CoVarSet
1643 coVarsOfType (TyVarTy v) = coVarsOfType (tyVarKind v)
1644 coVarsOfType (TyConApp _ tys) = coVarsOfTypes tys
1645 coVarsOfType (LitTy {}) = emptyVarSet
1646 coVarsOfType (AppTy fun arg) = coVarsOfType fun `unionVarSet` coVarsOfType arg
1647 coVarsOfType (FunTy arg res) = coVarsOfType arg `unionVarSet` coVarsOfType res
1648 coVarsOfType (ForAllTy (TvBndr tv _) ty)
1649 = (coVarsOfType ty `delVarSet` tv)
1650 `unionVarSet` coVarsOfType (tyVarKind tv)
1651 coVarsOfType (CastTy ty co) = coVarsOfType ty `unionVarSet` coVarsOfCo co
1652 coVarsOfType (CoercionTy co) = coVarsOfCo co
1653
1654 coVarsOfTypes :: [Type] -> TyCoVarSet
1655 coVarsOfTypes tys = mapUnionVarSet coVarsOfType tys
1656
1657 coVarsOfCo :: Coercion -> CoVarSet
1658 -- Extract *coercion* variables only. Tiresome to repeat the code, but easy.
1659 coVarsOfCo (Refl _ ty) = coVarsOfType ty
1660 coVarsOfCo (TyConAppCo _ _ args) = coVarsOfCos args
1661 coVarsOfCo (AppCo co arg) = coVarsOfCo co `unionVarSet` coVarsOfCo arg
1662 coVarsOfCo (ForAllCo tv kind_co co)
1663 = coVarsOfCo co `delVarSet` tv `unionVarSet` coVarsOfCo kind_co
1664 coVarsOfCo (FunCo _ co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
1665 coVarsOfCo (CoVarCo v) = coVarsOfCoVar v
1666 coVarsOfCo (HoleCo h) = coVarsOfCoVar (coHoleCoVar h)
1667 -- See Note [CoercionHoles and coercion free variables]
1668 coVarsOfCo (AxiomInstCo _ _ as) = coVarsOfCos as
1669 coVarsOfCo (UnivCo p _ t1 t2) = coVarsOfProv p `unionVarSet` coVarsOfTypes [t1, t2]
1670 coVarsOfCo (SymCo co) = coVarsOfCo co
1671 coVarsOfCo (TransCo co1 co2) = coVarsOfCo co1 `unionVarSet` coVarsOfCo co2
1672 coVarsOfCo (NthCo _ _ co) = coVarsOfCo co
1673 coVarsOfCo (LRCo _ co) = coVarsOfCo co
1674 coVarsOfCo (InstCo co arg) = coVarsOfCo co `unionVarSet` coVarsOfCo arg
1675 coVarsOfCo (CoherenceCo c1 c2) = coVarsOfCos [c1, c2]
1676 coVarsOfCo (KindCo co) = coVarsOfCo co
1677 coVarsOfCo (SubCo co) = coVarsOfCo co
1678 coVarsOfCo (AxiomRuleCo _ cs) = coVarsOfCos cs
1679
1680 coVarsOfCoVar :: CoVar -> CoVarSet
1681 coVarsOfCoVar v = unitVarSet v `unionVarSet` coVarsOfType (varType v)
1682
1683 coVarsOfProv :: UnivCoProvenance -> CoVarSet
1684 coVarsOfProv UnsafeCoerceProv = emptyVarSet
1685 coVarsOfProv (PhantomProv co) = coVarsOfCo co
1686 coVarsOfProv (ProofIrrelProv co) = coVarsOfCo co
1687 coVarsOfProv (PluginProv _) = emptyVarSet
1688
1689 coVarsOfCos :: [Coercion] -> CoVarSet
1690 coVarsOfCos cos = mapUnionVarSet coVarsOfCo cos
1691
1692 -- | Add the kind variables free in the kinds of the tyvars in the given set.
1693 -- Returns a non-deterministic set.
1694 closeOverKinds :: TyVarSet -> TyVarSet
1695 closeOverKinds = fvVarSet . closeOverKindsFV . nonDetEltsUniqSet
1696 -- It's OK to use nonDetEltsUniqSet here because we immediately forget
1697 -- about the ordering by returning a set.
1698
1699 -- | Given a list of tyvars returns a deterministic FV computation that
1700 -- returns the given tyvars with the kind variables free in the kinds of the
1701 -- given tyvars.
1702 closeOverKindsFV :: [TyVar] -> FV
1703 closeOverKindsFV tvs =
1704 mapUnionFV (tyCoFVsOfType . tyVarKind) tvs `unionFV` mkFVs tvs
1705
1706 -- | Add the kind variables free in the kinds of the tyvars in the given set.
1707 -- Returns a deterministically ordered list.
1708 closeOverKindsList :: [TyVar] -> [TyVar]
1709 closeOverKindsList tvs = fvVarList $ closeOverKindsFV tvs
1710
1711 -- | Add the kind variables free in the kinds of the tyvars in the given set.
1712 -- Returns a deterministic set.
1713 closeOverKindsDSet :: DTyVarSet -> DTyVarSet
1714 closeOverKindsDSet = fvDVarSet . closeOverKindsFV . dVarSetElems
1715
1716 -- | Returns the free variables of a 'TyConBinder' that are in injective
1717 -- positions. (See @Note [Kind annotations on TyConApps]@ in "TcSplice" for an
1718 -- explanation of what an injective position is.)
1719 injectiveVarsOfBinder :: TyConBinder -> FV
1720 injectiveVarsOfBinder (TvBndr tv vis) =
1721 case vis of
1722 AnonTCB -> injectiveVarsOfType (tyVarKind tv)
1723 NamedTCB Required -> unitFV tv `unionFV`
1724 injectiveVarsOfType (tyVarKind tv)
1725 NamedTCB _ -> emptyFV
1726
1727 -- | Returns the free variables of a 'Type' that are in injective positions.
1728 -- (See @Note [Kind annotations on TyConApps]@ in "TcSplice" for an explanation
1729 -- of what an injective position is.)
1730 injectiveVarsOfType :: Type -> FV
1731 injectiveVarsOfType = go
1732 where
1733 go ty | Just ty' <- coreView ty
1734 = go ty'
1735 go (TyVarTy v) = unitFV v `unionFV` go (tyVarKind v)
1736 go (AppTy f a) = go f `unionFV` go a
1737 go (FunTy ty1 ty2) = go ty1 `unionFV` go ty2
1738 go (TyConApp tc tys) =
1739 case tyConInjectivityInfo tc of
1740 NotInjective -> emptyFV
1741 Injective inj -> mapUnionFV go $
1742 filterByList (inj ++ repeat True) tys
1743 -- Oversaturated arguments to a tycon are
1744 -- always injective, hence the repeat True
1745 go (ForAllTy tvb ty) = tyCoFVsBndr tvb $ go (tyVarKind (binderVar tvb))
1746 `unionFV` go ty
1747 go LitTy{} = emptyFV
1748 go (CastTy ty _) = go ty
1749 go CoercionTy{} = emptyFV
1750
1751 -- | Returns True if this type has no free variables. Should be the same as
1752 -- isEmptyVarSet . tyCoVarsOfType, but faster in the non-forall case.
1753 noFreeVarsOfType :: Type -> Bool
1754 noFreeVarsOfType (TyVarTy _) = False
1755 noFreeVarsOfType (AppTy t1 t2) = noFreeVarsOfType t1 && noFreeVarsOfType t2
1756 noFreeVarsOfType (TyConApp _ tys) = all noFreeVarsOfType tys
1757 noFreeVarsOfType ty@(ForAllTy {}) = isEmptyVarSet (tyCoVarsOfType ty)
1758 noFreeVarsOfType (FunTy t1 t2) = noFreeVarsOfType t1 && noFreeVarsOfType t2
1759 noFreeVarsOfType (LitTy _) = True
1760 noFreeVarsOfType (CastTy ty co) = noFreeVarsOfType ty && noFreeVarsOfCo co
1761 noFreeVarsOfType (CoercionTy co) = noFreeVarsOfCo co
1762
1763 -- | Returns True if this coercion has no free variables. Should be the same as
1764 -- isEmptyVarSet . tyCoVarsOfCo, but faster in the non-forall case.
1765 noFreeVarsOfCo :: Coercion -> Bool
1766 noFreeVarsOfCo (Refl _ ty) = noFreeVarsOfType ty
1767 noFreeVarsOfCo (TyConAppCo _ _ args) = all noFreeVarsOfCo args
1768 noFreeVarsOfCo (AppCo c1 c2) = noFreeVarsOfCo c1 && noFreeVarsOfCo c2
1769 noFreeVarsOfCo co@(ForAllCo {}) = isEmptyVarSet (tyCoVarsOfCo co)
1770 noFreeVarsOfCo (FunCo _ c1 c2) = noFreeVarsOfCo c1 && noFreeVarsOfCo c2
1771 noFreeVarsOfCo (CoVarCo _) = False
1772 noFreeVarsOfCo (HoleCo {}) = True -- I'm unsure; probably never happens
1773 noFreeVarsOfCo (AxiomInstCo _ _ args) = all noFreeVarsOfCo args
1774 noFreeVarsOfCo (UnivCo p _ t1 t2) = noFreeVarsOfProv p &&
1775 noFreeVarsOfType t1 &&
1776 noFreeVarsOfType t2
1777 noFreeVarsOfCo (SymCo co) = noFreeVarsOfCo co
1778 noFreeVarsOfCo (TransCo co1 co2) = noFreeVarsOfCo co1 && noFreeVarsOfCo co2
1779 noFreeVarsOfCo (NthCo _ _ co) = noFreeVarsOfCo co
1780 noFreeVarsOfCo (LRCo _ co) = noFreeVarsOfCo co
1781 noFreeVarsOfCo (InstCo co1 co2) = noFreeVarsOfCo co1 && noFreeVarsOfCo co2
1782 noFreeVarsOfCo (CoherenceCo co1 co2) = noFreeVarsOfCo co1 && noFreeVarsOfCo co2
1783 noFreeVarsOfCo (KindCo co) = noFreeVarsOfCo co
1784 noFreeVarsOfCo (SubCo co) = noFreeVarsOfCo co
1785 noFreeVarsOfCo (AxiomRuleCo _ cs) = all noFreeVarsOfCo cs
1786
1787 -- | Returns True if this UnivCoProv has no free variables. Should be the same as
1788 -- isEmptyVarSet . tyCoVarsOfProv, but faster in the non-forall case.
1789 noFreeVarsOfProv :: UnivCoProvenance -> Bool
1790 noFreeVarsOfProv UnsafeCoerceProv = True
1791 noFreeVarsOfProv (PhantomProv co) = noFreeVarsOfCo co
1792 noFreeVarsOfProv (ProofIrrelProv co) = noFreeVarsOfCo co
1793 noFreeVarsOfProv (PluginProv {}) = True
1794
1795 {-
1796 %************************************************************************
1797 %* *
1798 Substitutions
1799 Data type defined here to avoid unnecessary mutual recursion
1800 %* *
1801 %************************************************************************
1802 -}
1803
1804 -- | Type & coercion substitution
1805 --
1806 -- #tcvsubst_invariant#
1807 -- The following invariants must hold of a 'TCvSubst':
1808 --
1809 -- 1. The in-scope set is needed /only/ to
1810 -- guide the generation of fresh uniques
1811 --
1812 -- 2. In particular, the /kind/ of the type variables in
1813 -- the in-scope set is not relevant
1814 --
1815 -- 3. The substitution is only applied ONCE! This is because
1816 -- in general such application will not reach a fixed point.
1817 data TCvSubst
1818 = TCvSubst InScopeSet -- The in-scope type and kind variables
1819 TvSubstEnv -- Substitutes both type and kind variables
1820 CvSubstEnv -- Substitutes coercion variables
1821 -- See Note [Substitutions apply only once]
1822 -- and Note [Extending the TvSubstEnv]
1823 -- and Note [Substituting types and coercions]
1824 -- and Note [The substitution invariant]
1825
1826 -- | A substitution of 'Type's for 'TyVar's
1827 -- and 'Kind's for 'KindVar's
1828 type TvSubstEnv = TyVarEnv Type
1829 -- NB: A TvSubstEnv is used
1830 -- both inside a TCvSubst (with the apply-once invariant
1831 -- discussed in Note [Substitutions apply only once],
1832 -- and also independently in the middle of matching,
1833 -- and unification (see Types.Unify).
1834 -- So you have to look at the context to know if it's idempotent or
1835 -- apply-once or whatever
1836
1837 -- | A substitution of 'Coercion's for 'CoVar's
1838 type CvSubstEnv = CoVarEnv Coercion
1839
1840 {- Note [The substitution invariant]
1841 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1842 When calling (substTy subst ty) it should be the case that
1843 the in-scope set in the substitution is a superset of both:
1844
1845 (SIa) The free vars of the range of the substitution
1846 (SIb) The free vars of ty minus the domain of the substitution
1847
1848 The same rules apply to other substitutions (notably CoreSubst.Subst)
1849
1850 * Reason for (SIa). Consider
1851 substTy [a :-> Maybe b] (forall b. b->a)
1852 we must rename the forall b, to get
1853 forall b2. b2 -> Maybe b
1854 Making 'b' part of the in-scope set forces this renaming to
1855 take place.
1856
1857 * Reason for (SIb). Consider
1858 substTy [a :-> Maybe b] (forall b. (a,b,x))
1859 Then if we use the in-scope set {b}, satisfying (SIa), there is
1860 a danger we will rename the forall'd variable to 'x' by mistake,
1861 getting this:
1862 forall x. (List b, x, x)
1863 Breaking (SIb) caused the bug from #11371.
1864
1865 Note: if the free vars of the range of the substitution are freshly created,
1866 then the problems of (SIa) can't happen, and so it would be sound to
1867 ignore (SIa).
1868
1869 Note [Substitutions apply only once]
1870 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1871 We use TCvSubsts to instantiate things, and we might instantiate
1872 forall a b. ty
1873 with the types
1874 [a, b], or [b, a].
1875 So the substitution might go [a->b, b->a]. A similar situation arises in Core
1876 when we find a beta redex like
1877 (/\ a /\ b -> e) b a
1878 Then we also end up with a substitution that permutes type variables. Other
1879 variations happen to; for example [a -> (a, b)].
1880
1881 ********************************************************
1882 *** So a substitution must be applied precisely once ***
1883 ********************************************************
1884
1885 A TCvSubst is not idempotent, but, unlike the non-idempotent substitution
1886 we use during unifications, it must not be repeatedly applied.
1887
1888 Note [Extending the TvSubstEnv]
1889 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1890 See #tcvsubst_invariant# for the invariants that must hold.
1891
1892 This invariant allows a short-cut when the subst envs are empty:
1893 if the TvSubstEnv and CvSubstEnv are empty --- i.e. (isEmptyTCvSubst subst)
1894 holds --- then (substTy subst ty) does nothing.
1895
1896 For example, consider:
1897 (/\a. /\b:(a~Int). ...b..) Int
1898 We substitute Int for 'a'. The Unique of 'b' does not change, but
1899 nevertheless we add 'b' to the TvSubstEnv, because b's kind does change
1900
1901 This invariant has several crucial consequences:
1902
1903 * In substTyVarBndr, we need extend the TvSubstEnv
1904 - if the unique has changed
1905 - or if the kind has changed
1906
1907 * In substTyVar, we do not need to consult the in-scope set;
1908 the TvSubstEnv is enough
1909
1910 * In substTy, substTheta, we can short-circuit when the TvSubstEnv is empty
1911
1912 Note [Substituting types and coercions]
1913 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1914 Types and coercions are mutually recursive, and either may have variables
1915 "belonging" to the other. Thus, every time we wish to substitute in a
1916 type, we may also need to substitute in a coercion, and vice versa.
1917 However, the constructor used to create type variables is distinct from
1918 that of coercion variables, so we carry two VarEnvs in a TCvSubst. Note
1919 that it would be possible to use the CoercionTy constructor to combine
1920 these environments, but that seems like a false economy.
1921
1922 Note that the TvSubstEnv should *never* map a CoVar (built with the Id
1923 constructor) and the CvSubstEnv should *never* map a TyVar. Furthermore,
1924 the range of the TvSubstEnv should *never* include a type headed with
1925 CoercionTy.
1926 -}
1927
1928 emptyTvSubstEnv :: TvSubstEnv
1929 emptyTvSubstEnv = emptyVarEnv
1930
1931 emptyCvSubstEnv :: CvSubstEnv
1932 emptyCvSubstEnv = emptyVarEnv
1933
1934 composeTCvSubstEnv :: InScopeSet
1935 -> (TvSubstEnv, CvSubstEnv)
1936 -> (TvSubstEnv, CvSubstEnv)
1937 -> (TvSubstEnv, CvSubstEnv)
1938 -- ^ @(compose env1 env2)(x)@ is @env1(env2(x))@; i.e. apply @env2@ then @env1@.
1939 -- It assumes that both are idempotent.
1940 -- Typically, @env1@ is the refinement to a base substitution @env2@
1941 composeTCvSubstEnv in_scope (tenv1, cenv1) (tenv2, cenv2)
1942 = ( tenv1 `plusVarEnv` mapVarEnv (substTy subst1) tenv2
1943 , cenv1 `plusVarEnv` mapVarEnv (substCo subst1) cenv2 )
1944 -- First apply env1 to the range of env2
1945 -- Then combine the two, making sure that env1 loses if
1946 -- both bind the same variable; that's why env1 is the
1947 -- *left* argument to plusVarEnv, because the right arg wins
1948 where
1949 subst1 = TCvSubst in_scope tenv1 cenv1
1950
1951 -- | Composes two substitutions, applying the second one provided first,
1952 -- like in function composition.
1953 composeTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
1954 composeTCvSubst (TCvSubst is1 tenv1 cenv1) (TCvSubst is2 tenv2 cenv2)
1955 = TCvSubst is3 tenv3 cenv3
1956 where
1957 is3 = is1 `unionInScope` is2
1958 (tenv3, cenv3) = composeTCvSubstEnv is3 (tenv1, cenv1) (tenv2, cenv2)
1959
1960 emptyTCvSubst :: TCvSubst
1961 emptyTCvSubst = TCvSubst emptyInScopeSet emptyTvSubstEnv emptyCvSubstEnv
1962
1963 mkEmptyTCvSubst :: InScopeSet -> TCvSubst
1964 mkEmptyTCvSubst is = TCvSubst is emptyTvSubstEnv emptyCvSubstEnv
1965
1966 isEmptyTCvSubst :: TCvSubst -> Bool
1967 -- See Note [Extending the TvSubstEnv]
1968 isEmptyTCvSubst (TCvSubst _ tenv cenv) = isEmptyVarEnv tenv && isEmptyVarEnv cenv
1969
1970 mkTCvSubst :: InScopeSet -> (TvSubstEnv, CvSubstEnv) -> TCvSubst
1971 mkTCvSubst in_scope (tenv, cenv) = TCvSubst in_scope tenv cenv
1972
1973 mkTvSubst :: InScopeSet -> TvSubstEnv -> TCvSubst
1974 -- ^ Make a TCvSubst with specified tyvar subst and empty covar subst
1975 mkTvSubst in_scope tenv = TCvSubst in_scope tenv emptyCvSubstEnv
1976
1977 getTvSubstEnv :: TCvSubst -> TvSubstEnv
1978 getTvSubstEnv (TCvSubst _ env _) = env
1979
1980 getCvSubstEnv :: TCvSubst -> CvSubstEnv
1981 getCvSubstEnv (TCvSubst _ _ env) = env
1982
1983 getTCvInScope :: TCvSubst -> InScopeSet
1984 getTCvInScope (TCvSubst in_scope _ _) = in_scope
1985
1986 -- | Returns the free variables of the types in the range of a substitution as
1987 -- a non-deterministic set.
1988 getTCvSubstRangeFVs :: TCvSubst -> VarSet
1989 getTCvSubstRangeFVs (TCvSubst _ tenv cenv)
1990 = unionVarSet tenvFVs cenvFVs
1991 where
1992 tenvFVs = tyCoVarsOfTypesSet tenv
1993 cenvFVs = tyCoVarsOfCosSet cenv
1994
1995 isInScope :: Var -> TCvSubst -> Bool
1996 isInScope v (TCvSubst in_scope _ _) = v `elemInScopeSet` in_scope
1997
1998 notElemTCvSubst :: Var -> TCvSubst -> Bool
1999 notElemTCvSubst v (TCvSubst _ tenv cenv)
2000 | isTyVar v
2001 = not (v `elemVarEnv` tenv)
2002 | otherwise
2003 = not (v `elemVarEnv` cenv)
2004
2005 setTvSubstEnv :: TCvSubst -> TvSubstEnv -> TCvSubst
2006 setTvSubstEnv (TCvSubst in_scope _ cenv) tenv = TCvSubst in_scope tenv cenv
2007
2008 setCvSubstEnv :: TCvSubst -> CvSubstEnv -> TCvSubst
2009 setCvSubstEnv (TCvSubst in_scope tenv _) cenv = TCvSubst in_scope tenv cenv
2010
2011 zapTCvSubst :: TCvSubst -> TCvSubst
2012 zapTCvSubst (TCvSubst in_scope _ _) = TCvSubst in_scope emptyVarEnv emptyVarEnv
2013
2014 extendTCvInScope :: TCvSubst -> Var -> TCvSubst
2015 extendTCvInScope (TCvSubst in_scope tenv cenv) var
2016 = TCvSubst (extendInScopeSet in_scope var) tenv cenv
2017
2018 extendTCvInScopeList :: TCvSubst -> [Var] -> TCvSubst
2019 extendTCvInScopeList (TCvSubst in_scope tenv cenv) vars
2020 = TCvSubst (extendInScopeSetList in_scope vars) tenv cenv
2021
2022 extendTCvInScopeSet :: TCvSubst -> VarSet -> TCvSubst
2023 extendTCvInScopeSet (TCvSubst in_scope tenv cenv) vars
2024 = TCvSubst (extendInScopeSetSet in_scope vars) tenv cenv
2025
2026 extendTCvSubst :: TCvSubst -> TyCoVar -> Type -> TCvSubst
2027 extendTCvSubst subst v ty
2028 | isTyVar v
2029 = extendTvSubst subst v ty
2030 | CoercionTy co <- ty
2031 = extendCvSubst subst v co
2032 | otherwise
2033 = pprPanic "extendTCvSubst" (ppr v <+> text "|->" <+> ppr ty)
2034
2035 extendTvSubst :: TCvSubst -> TyVar -> Type -> TCvSubst
2036 extendTvSubst (TCvSubst in_scope tenv cenv) tv ty
2037 = TCvSubst in_scope (extendVarEnv tenv tv ty) cenv
2038
2039 extendTvSubstBinderAndInScope :: TCvSubst -> TyBinder -> Type -> TCvSubst
2040 extendTvSubstBinderAndInScope subst (Named bndr) ty
2041 = extendTvSubstAndInScope subst (binderVar bndr) ty
2042 extendTvSubstBinderAndInScope subst (Anon _) _
2043 = subst
2044
2045 extendTvSubstWithClone :: TCvSubst -> TyVar -> TyVar -> TCvSubst
2046 -- Adds a new tv -> tv mapping, /and/ extends the in-scope set
2047 extendTvSubstWithClone (TCvSubst in_scope tenv cenv) tv tv'
2048 = TCvSubst (extendInScopeSetSet in_scope new_in_scope)
2049 (extendVarEnv tenv tv (mkTyVarTy tv'))
2050 cenv
2051 where
2052 new_in_scope = tyCoVarsOfType (tyVarKind tv') `extendVarSet` tv'
2053
2054 extendCvSubst :: TCvSubst -> CoVar -> Coercion -> TCvSubst
2055 extendCvSubst (TCvSubst in_scope tenv cenv) v co
2056 = TCvSubst in_scope tenv (extendVarEnv cenv v co)
2057
2058 extendCvSubstWithClone :: TCvSubst -> CoVar -> CoVar -> TCvSubst
2059 extendCvSubstWithClone (TCvSubst in_scope tenv cenv) cv cv'
2060 = TCvSubst (extendInScopeSetSet in_scope new_in_scope)
2061 tenv
2062 (extendVarEnv cenv cv (mkCoVarCo cv'))
2063 where
2064 new_in_scope = tyCoVarsOfType (varType cv') `extendVarSet` cv'
2065
2066 extendTvSubstAndInScope :: TCvSubst -> TyVar -> Type -> TCvSubst
2067 -- Also extends the in-scope set
2068 extendTvSubstAndInScope (TCvSubst in_scope tenv cenv) tv ty
2069 = TCvSubst (in_scope `extendInScopeSetSet` tyCoVarsOfType ty)
2070 (extendVarEnv tenv tv ty)
2071 cenv
2072
2073 extendTvSubstList :: TCvSubst -> [Var] -> [Type] -> TCvSubst
2074 extendTvSubstList subst tvs tys
2075 = foldl2 extendTvSubst subst tvs tys
2076
2077 unionTCvSubst :: TCvSubst -> TCvSubst -> TCvSubst
2078 -- Works when the ranges are disjoint
2079 unionTCvSubst (TCvSubst in_scope1 tenv1 cenv1) (TCvSubst in_scope2 tenv2 cenv2)
2080 = ASSERT( not (tenv1 `intersectsVarEnv` tenv2)
2081 && not (cenv1 `intersectsVarEnv` cenv2) )
2082 TCvSubst (in_scope1 `unionInScope` in_scope2)
2083 (tenv1 `plusVarEnv` tenv2)
2084 (cenv1 `plusVarEnv` cenv2)
2085
2086 -- mkTvSubstPrs and zipTvSubst generate the in-scope set from
2087 -- the types given; but it's just a thunk so with a bit of luck
2088 -- it'll never be evaluated
2089
2090 -- | Generates an in-scope set from the free variables in a list of types
2091 -- and a list of coercions
2092 mkTyCoInScopeSet :: [Type] -> [Coercion] -> InScopeSet
2093 mkTyCoInScopeSet tys cos
2094 = mkInScopeSet (tyCoVarsOfTypes tys `unionVarSet` tyCoVarsOfCos cos)
2095
2096 -- | Generates the in-scope set for the 'TCvSubst' from the types in the incoming
2097 -- environment. No CoVars, please!
2098 zipTvSubst :: [TyVar] -> [Type] -> TCvSubst
2099 zipTvSubst tvs tys
2100 | debugIsOn
2101 , not (all isTyVar tvs) || neLength tvs tys
2102 = pprTrace "zipTvSubst" (ppr tvs $$ ppr tys) emptyTCvSubst
2103 | otherwise
2104 = mkTvSubst (mkInScopeSet (tyCoVarsOfTypes tys)) tenv
2105 where
2106 tenv = zipTyEnv tvs tys
2107
2108 -- | Generates the in-scope set for the 'TCvSubst' from the types in the incoming
2109 -- environment. No TyVars, please!
2110 zipCvSubst :: [CoVar] -> [Coercion] -> TCvSubst
2111 zipCvSubst cvs cos
2112 | debugIsOn
2113 , not (all isCoVar cvs) || neLength cvs cos
2114 = pprTrace "zipCvSubst" (ppr cvs $$ ppr cos) emptyTCvSubst
2115 | otherwise
2116 = TCvSubst (mkInScopeSet (tyCoVarsOfCos cos)) emptyTvSubstEnv cenv
2117 where
2118 cenv = zipCoEnv cvs cos
2119
2120 -- | Generates the in-scope set for the 'TCvSubst' from the types in the
2121 -- incoming environment. No CoVars, please!
2122 mkTvSubstPrs :: [(TyVar, Type)] -> TCvSubst
2123 mkTvSubstPrs prs =
2124 ASSERT2( onlyTyVarsAndNoCoercionTy, text "prs" <+> ppr prs )
2125 mkTvSubst in_scope tenv
2126 where tenv = mkVarEnv prs
2127 in_scope = mkInScopeSet $ tyCoVarsOfTypes $ map snd prs
2128 onlyTyVarsAndNoCoercionTy =
2129 and [ isTyVar tv && not (isCoercionTy ty)
2130 | (tv, ty) <- prs ]
2131
2132 zipTyEnv :: [TyVar] -> [Type] -> TvSubstEnv
2133 zipTyEnv tyvars tys
2134 = ASSERT( all (not . isCoercionTy) tys )
2135 mkVarEnv (zipEqual "zipTyEnv" tyvars tys)
2136 -- There used to be a special case for when
2137 -- ty == TyVarTy tv
2138 -- (a not-uncommon case) in which case the substitution was dropped.
2139 -- But the type-tidier changes the print-name of a type variable without
2140 -- changing the unique, and that led to a bug. Why? Pre-tidying, we had
2141 -- a type {Foo t}, where Foo is a one-method class. So Foo is really a newtype.
2142 -- And it happened that t was the type variable of the class. Post-tiding,
2143 -- it got turned into {Foo t2}. The ext-core printer expanded this using
2144 -- sourceTypeRep, but that said "Oh, t == t2" because they have the same unique,
2145 -- and so generated a rep type mentioning t not t2.
2146 --
2147 -- Simplest fix is to nuke the "optimisation"
2148
2149 zipCoEnv :: [CoVar] -> [Coercion] -> CvSubstEnv
2150 zipCoEnv cvs cos = mkVarEnv (zipEqual "zipCoEnv" cvs cos)
2151
2152 instance Outputable TCvSubst where
2153 ppr (TCvSubst ins tenv cenv)
2154 = brackets $ sep[ text "TCvSubst",
2155 nest 2 (text "In scope:" <+> ppr ins),
2156 nest 2 (text "Type env:" <+> ppr tenv),
2157 nest 2 (text "Co env:" <+> ppr cenv) ]
2158
2159 {-
2160 %************************************************************************
2161 %* *
2162 Performing type or kind substitutions
2163 %* *
2164 %************************************************************************
2165
2166 Note [Sym and ForAllCo]
2167 ~~~~~~~~~~~~~~~~~~~~~~~
2168 In OptCoercion, we try to push "sym" out to the leaves of a coercion. But,
2169 how do we push sym into a ForAllCo? It's a little ugly.
2170
2171 Here is the typing rule:
2172
2173 h : k1 ~# k2
2174 (tv : k1) |- g : ty1 ~# ty2
2175 ----------------------------
2176 ForAllCo tv h g : (ForAllTy (tv : k1) ty1) ~#
2177 (ForAllTy (tv : k2) (ty2[tv |-> tv |> sym h]))
2178
2179 Here is what we want:
2180
2181 ForAllCo tv h' g' : (ForAllTy (tv : k2) (ty2[tv |-> tv |> sym h])) ~#
2182 (ForAllTy (tv : k1) ty1)
2183
2184
2185 Because the kinds of the type variables to the right of the colon are the kinds
2186 coerced by h', we know (h' : k2 ~# k1). Thus, (h' = sym h).
2187
2188 Now, we can rewrite ty1 to be (ty1[tv |-> tv |> sym h' |> h']). We thus want
2189
2190 ForAllCo tv h' g' :
2191 (ForAllTy (tv : k2) (ty2[tv |-> tv |> h'])) ~#
2192 (ForAllTy (tv : k1) (ty1[tv |-> tv |> h'][tv |-> tv |> sym h']))
2193
2194 We thus see that we want
2195
2196 g' : ty2[tv |-> tv |> h'] ~# ty1[tv |-> tv |> h']
2197
2198 and thus g' = sym (g[tv |-> tv |> h']).
2199
2200 Putting it all together, we get this:
2201
2202 sym (ForAllCo tv h g)
2203 ==>
2204 ForAllCo tv (sym h) (sym g[tv |-> tv |> sym h])
2205
2206 -}
2207
2208 -- | Type substitution, see 'zipTvSubst'
2209 substTyWith :: HasCallStack => [TyVar] -> [Type] -> Type -> Type
2210 -- Works only if the domain of the substitution is a
2211 -- superset of the type being substituted into
2212 substTyWith tvs tys = {-#SCC "substTyWith" #-}
2213 ASSERT( tvs `equalLength` tys )
2214 substTy (zipTvSubst tvs tys)
2215
2216 -- | Type substitution, see 'zipTvSubst'. Disables sanity checks.
2217 -- The problems that the sanity checks in substTy catch are described in
2218 -- Note [The substitution invariant].
2219 -- The goal of #11371 is to migrate all the calls of substTyUnchecked to
2220 -- substTy and remove this function. Please don't use in new code.
2221 substTyWithUnchecked :: [TyVar] -> [Type] -> Type -> Type
2222 substTyWithUnchecked tvs tys
2223 = ASSERT( tvs `equalLength` tys )
2224 substTyUnchecked (zipTvSubst tvs tys)
2225
2226 -- | Substitute tyvars within a type using a known 'InScopeSet'.
2227 -- Pre-condition: the 'in_scope' set should satisfy Note [The substitution
2228 -- invariant]; specifically it should include the free vars of 'tys',
2229 -- and of 'ty' minus the domain of the subst.
2230 substTyWithInScope :: InScopeSet -> [TyVar] -> [Type] -> Type -> Type
2231 substTyWithInScope in_scope tvs tys ty =
2232 ASSERT( tvs `equalLength` tys )
2233 substTy (mkTvSubst in_scope tenv) ty
2234 where tenv = zipTyEnv tvs tys
2235
2236 -- | Coercion substitution, see 'zipTvSubst'
2237 substCoWith :: HasCallStack => [TyVar] -> [Type] -> Coercion -> Coercion
2238 substCoWith tvs tys = ASSERT( tvs `equalLength` tys )
2239 substCo (zipTvSubst tvs tys)
2240
2241 -- | Coercion substitution, see 'zipTvSubst'. Disables sanity checks.
2242 -- The problems that the sanity checks in substCo catch are described in
2243 -- Note [The substitution invariant].
2244 -- The goal of #11371 is to migrate all the calls of substCoUnchecked to
2245 -- substCo and remove this function. Please don't use in new code.
2246 substCoWithUnchecked :: [TyVar] -> [Type] -> Coercion -> Coercion
2247 substCoWithUnchecked tvs tys
2248 = ASSERT( tvs `equalLength` tys )
2249 substCoUnchecked (zipTvSubst tvs tys)
2250
2251
2252
2253 -- | Substitute covars within a type
2254 substTyWithCoVars :: [CoVar] -> [Coercion] -> Type -> Type
2255 substTyWithCoVars cvs cos = substTy (zipCvSubst cvs cos)
2256
2257 -- | Type substitution, see 'zipTvSubst'
2258 substTysWith :: [TyVar] -> [Type] -> [Type] -> [Type]
2259 substTysWith tvs tys = ASSERT( tvs `equalLength` tys )
2260 substTys (zipTvSubst tvs tys)
2261
2262 -- | Type substitution, see 'zipTvSubst'
2263 substTysWithCoVars :: [CoVar] -> [Coercion] -> [Type] -> [Type]
2264 substTysWithCoVars cvs cos = ASSERT( cvs `equalLength` cos )
2265 substTys (zipCvSubst cvs cos)
2266
2267 -- | Substitute within a 'Type' after adding the free variables of the type
2268 -- to the in-scope set. This is useful for the case when the free variables
2269 -- aren't already in the in-scope set or easily available.
2270 -- See also Note [The substitution invariant].
2271 substTyAddInScope :: TCvSubst -> Type -> Type
2272 substTyAddInScope subst ty =
2273 substTy (extendTCvInScopeSet subst $ tyCoVarsOfType ty) ty
2274
2275 -- | When calling `substTy` it should be the case that the in-scope set in
2276 -- the substitution is a superset of the free vars of the range of the
2277 -- substitution.
2278 -- See also Note [The substitution invariant].
2279 isValidTCvSubst :: TCvSubst -> Bool
2280 isValidTCvSubst (TCvSubst in_scope tenv cenv) =
2281 (tenvFVs `varSetInScope` in_scope) &&
2282 (cenvFVs `varSetInScope` in_scope)
2283 where
2284 tenvFVs = tyCoVarsOfTypesSet tenv
2285 cenvFVs = tyCoVarsOfCosSet cenv
2286
2287 -- | This checks if the substitution satisfies the invariant from
2288 -- Note [The substitution invariant].
2289 checkValidSubst :: HasCallStack => TCvSubst -> [Type] -> [Coercion] -> a -> a
2290 checkValidSubst subst@(TCvSubst in_scope tenv cenv) tys cos a
2291 -- TODO (RAE): Change back to ASSERT
2292 = WARN( not ({-#SCC "isValidTCvSubst" #-} isValidTCvSubst subst),
2293 text "in_scope" <+> ppr in_scope $$
2294 text "tenv" <+> ppr tenv $$
2295 text "tenvFVs"
2296 <+> ppr (tyCoVarsOfTypesSet tenv) $$
2297 text "cenv" <+> ppr cenv $$
2298 text "cenvFVs"
2299 <+> ppr (tyCoVarsOfCosSet cenv) $$
2300 text "tys" <+> ppr tys $$
2301 text "cos" <+> ppr cos )
2302 WARN( not ({-#SCC "tysCosFVsInScope" #-} tysCosFVsInScope),
2303 text "in_scope" <+> ppr in_scope $$
2304 text "tenv" <+> ppr tenv $$
2305 text "cenv" <+> ppr cenv $$
2306 text "tys" <+> ppr tys $$
2307 text "cos" <+> ppr cos $$
2308 text "needInScope" <+> ppr needInScope )
2309 a
2310 where
2311 substDomain = nonDetKeysUFM tenv ++ nonDetKeysUFM cenv
2312 -- It's OK to use nonDetKeysUFM here, because we only use this list to
2313 -- remove some elements from a set
2314 needInScope = (tyCoVarsOfTypes tys `unionVarSet` tyCoVarsOfCos cos)
2315 `delListFromUniqSet_Directly` substDomain
2316 tysCosFVsInScope = needInScope `varSetInScope` in_scope
2317
2318
2319 -- | Substitute within a 'Type'
2320 -- The substitution has to satisfy the invariants described in
2321 -- Note [The substitution invariant].
2322 substTy :: HasCallStack => TCvSubst -> Type -> Type
2323 substTy subst ty
2324 | isEmptyTCvSubst subst = ty
2325 | otherwise = checkValidSubst subst [ty] [] $
2326 subst_ty subst ty
2327
2328 -- | Substitute within a 'Type' disabling the sanity checks.
2329 -- The problems that the sanity checks in substTy catch are described in
2330 -- Note [The substitution invariant].
2331 -- The goal of #11371 is to migrate all the calls of substTyUnchecked to
2332 -- substTy and remove this function. Please don't use in new code.
2333 substTyUnchecked :: TCvSubst -> Type -> Type
2334 substTyUnchecked subst ty
2335 | isEmptyTCvSubst subst = ty
2336 | otherwise = subst_ty subst ty
2337
2338 -- | Substitute within several 'Type's
2339 -- The substitution has to satisfy the invariants described in
2340 -- Note [The substitution invariant].
2341 substTys :: HasCallStack => TCvSubst -> [Type] -> [Type]
2342 substTys subst tys
2343 | isEmptyTCvSubst subst = tys
2344 | otherwise = checkValidSubst subst tys [] $ map (subst_ty subst) tys
2345
2346 -- | Substitute within several 'Type's disabling the sanity checks.
2347 -- The problems that the sanity checks in substTys catch are described in
2348 -- Note [The substitution invariant].
2349 -- The goal of #11371 is to migrate all the calls of substTysUnchecked to
2350 -- substTys and remove this function. Please don't use in new code.
2351 substTysUnchecked :: TCvSubst -> [Type] -> [Type]
2352 substTysUnchecked subst tys
2353 | isEmptyTCvSubst subst = tys
2354 | otherwise = map (subst_ty subst) tys
2355
2356 -- | Substitute within a 'ThetaType'
2357 -- The substitution has to satisfy the invariants described in
2358 -- Note [The substitution invariant].
2359 substTheta :: HasCallStack => TCvSubst -> ThetaType -> ThetaType
2360 substTheta = substTys
2361
2362 -- | Substitute within a 'ThetaType' disabling the sanity checks.
2363 -- The problems that the sanity checks in substTys catch are described in
2364 -- Note [The substitution invariant].
2365 -- The goal of #11371 is to migrate all the calls of substThetaUnchecked to
2366 -- substTheta and remove this function. Please don't use in new code.
2367 substThetaUnchecked :: TCvSubst -> ThetaType -> ThetaType
2368 substThetaUnchecked = substTysUnchecked
2369
2370
2371 subst_ty :: TCvSubst -> Type -> Type
2372 -- subst_ty is the main workhorse for type substitution
2373 --
2374 -- Note that the in_scope set is poked only if we hit a forall
2375 -- so it may often never be fully computed
2376 subst_ty subst ty
2377 = go ty
2378 where
2379 go (TyVarTy tv) = substTyVar subst tv
2380 go (AppTy fun arg) = mkAppTy (go fun) $! (go arg)
2381 -- The mkAppTy smart constructor is important
2382 -- we might be replacing (a Int), represented with App
2383 -- by [Int], represented with TyConApp
2384 go (TyConApp tc tys) = let args = map go tys
2385 in args `seqList` TyConApp tc args
2386 go (FunTy arg res) = (FunTy $! go arg) $! go res
2387 go (ForAllTy (TvBndr tv vis) ty)
2388 = case substTyVarBndrUnchecked subst tv of
2389 (subst', tv') ->
2390 (ForAllTy $! ((TvBndr $! tv') vis)) $!
2391 (subst_ty subst' ty)
2392 go (LitTy n) = LitTy $! n
2393 go (CastTy ty co) = (mkCastTy $! (go ty)) $! (subst_co subst co)
2394 go (CoercionTy co) = CoercionTy $! (subst_co subst co)
2395
2396 substTyVar :: TCvSubst -> TyVar -> Type
2397 substTyVar (TCvSubst _ tenv _) tv
2398 = ASSERT( isTyVar tv )
2399 case lookupVarEnv tenv tv of
2400 Just ty -> ty
2401 Nothing -> TyVarTy tv
2402
2403 substTyVars :: TCvSubst -> [TyVar] -> [Type]
2404 substTyVars subst = map $ substTyVar subst
2405
2406 lookupTyVar :: TCvSubst -> TyVar -> Maybe Type
2407 -- See Note [Extending the TCvSubst]
2408 lookupTyVar (TCvSubst _ tenv _) tv
2409 = ASSERT( isTyVar tv )
2410 lookupVarEnv tenv tv
2411
2412 -- | Substitute within a 'Coercion'
2413 -- The substitution has to satisfy the invariants described in
2414 -- Note [The substitution invariant].
2415 substCo :: HasCallStack => TCvSubst -> Coercion -> Coercion
2416 substCo subst co
2417 | isEmptyTCvSubst subst = co
2418 | otherwise = checkValidSubst subst [] [co] $ subst_co subst co
2419
2420 -- | Substitute within a 'Coercion' disabling sanity checks.
2421 -- The problems that the sanity checks in substCo catch are described in
2422 -- Note [The substitution invariant].
2423 -- The goal of #11371 is to migrate all the calls of substCoUnchecked to
2424 -- substCo and remove this function. Please don't use in new code.
2425 substCoUnchecked :: TCvSubst -> Coercion -> Coercion
2426 substCoUnchecked subst co
2427 | isEmptyTCvSubst subst = co
2428 | otherwise = subst_co subst co
2429
2430 -- | Substitute within several 'Coercion's
2431 -- The substitution has to satisfy the invariants described in
2432 -- Note [The substitution invariant].
2433 substCos :: HasCallStack => TCvSubst -> [Coercion] -> [Coercion]
2434 substCos subst cos
2435 | isEmptyTCvSubst subst = cos
2436 | otherwise = checkValidSubst subst [] cos $ map (subst_co subst) cos
2437
2438 subst_co :: TCvSubst -> Coercion -> Coercion
2439 subst_co subst co
2440 = go co
2441 where
2442 go_ty :: Type -> Type
2443 go_ty = subst_ty subst
2444
2445 go :: Coercion -> Coercion
2446 go (Refl r ty) = mkReflCo r $! go_ty ty
2447 go (TyConAppCo r tc args)= let args' = map go args
2448 in args' `seqList` mkTyConAppCo r tc args'
2449 go (AppCo co arg) = (mkAppCo $! go co) $! go arg
2450 go (ForAllCo tv kind_co co)
2451 = case substForAllCoBndrUnchecked subst tv kind_co of { (subst', tv', kind_co') ->
2452 ((mkForAllCo $! tv') $! kind_co') $! subst_co subst' co }
2453 go (FunCo r co1 co2) = (mkFunCo r $! go co1) $! go co2
2454 go (CoVarCo cv) = substCoVar subst cv
2455 go (AxiomInstCo con ind cos) = mkAxiomInstCo con ind $! map go cos
2456 go (UnivCo p r t1 t2) = (((mkUnivCo $! go_prov p) $! r) $!
2457 (go_ty t1)) $! (go_ty t2)
2458 go (SymCo co) = mkSymCo $! (go co)
2459 go (TransCo co1 co2) = (mkTransCo $! (go co1)) $! (go co2)
2460 go (NthCo r d co) = mkNthCo r d $! (go co)
2461 go (LRCo lr co) = mkLRCo lr $! (go co)
2462 go (InstCo co arg) = (mkInstCo $! (go co)) $! go arg
2463 go (CoherenceCo co1 co2) = (mkCoherenceCo $! (go co1)) $! (go co2)
2464 go (KindCo co) = mkKindCo $! (go co)
2465 go (SubCo co) = mkSubCo $! (go co)
2466 go (AxiomRuleCo c cs) = let cs1 = map go cs
2467 in cs1 `seqList` AxiomRuleCo c cs1
2468 go (HoleCo h) = HoleCo h
2469 -- NB: this last case is a little suspicious, but we need it. Originally,
2470 -- there was a panic here, but it triggered from deeplySkolemise. Because
2471 -- we only skolemise tyvars that are manually bound, this operation makes
2472 -- sense, even over a coercion with holes. We don't need to substitute
2473 -- in the type of the coHoleCoVar because it wouldn't makes sense to have
2474 -- forall a. ....(ty |> {hole_cv::a})....
2475
2476 go_prov UnsafeCoerceProv = UnsafeCoerceProv
2477 go_prov (PhantomProv kco) = PhantomProv (go kco)
2478 go_prov (ProofIrrelProv kco) = ProofIrrelProv (go kco)
2479 go_prov p@(PluginProv _) = p
2480
2481 substForAllCoBndr :: TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion)
2482 substForAllCoBndr subst
2483 = substForAllCoBndrCallback False (substCo subst) subst
2484
2485 -- | Like 'substForAllCoBndr', but disables sanity checks.
2486 -- The problems that the sanity checks in substCo catch are described in
2487 -- Note [The substitution invariant].
2488 -- The goal of #11371 is to migrate all the calls of substCoUnchecked to
2489 -- substCo and remove this function. Please don't use in new code.
2490 substForAllCoBndrUnchecked :: TCvSubst -> TyVar -> Coercion -> (TCvSubst, TyVar, Coercion)
2491 substForAllCoBndrUnchecked subst
2492 = substForAllCoBndrCallback False (substCoUnchecked subst) subst
2493
2494 -- See Note [Sym and ForAllCo]
2495 substForAllCoBndrCallback :: Bool -- apply sym to binder?
2496 -> (Coercion -> Coercion) -- transformation to kind co
2497 -> TCvSubst -> TyVar -> Coercion
2498 -> (TCvSubst, TyVar, Coercion)
2499 substForAllCoBndrCallback sym sco (TCvSubst in_scope tenv cenv)
2500 old_var old_kind_co
2501 = ( TCvSubst (in_scope `extendInScopeSet` new_var) new_env cenv
2502 , new_var, new_kind_co )
2503 where
2504 new_env | no_change && not sym = delVarEnv tenv old_var
2505 | sym = extendVarEnv tenv old_var $
2506 TyVarTy new_var `CastTy` new_kind_co
2507 | otherwise = extendVarEnv tenv old_var (TyVarTy new_var)
2508
2509 no_kind_change = noFreeVarsOfCo old_kind_co
2510 no_change = no_kind_change && (new_var == old_var)
2511
2512 new_kind_co | no_kind_change = old_kind_co
2513 | otherwise = sco old_kind_co
2514
2515 Pair new_ki1 _ = coercionKind new_kind_co
2516
2517 new_var = uniqAway in_scope (setTyVarKind old_var new_ki1)
2518
2519 substCoVar :: TCvSubst -> CoVar -> Coercion
2520 substCoVar (TCvSubst _ _ cenv) cv
2521 = case lookupVarEnv cenv cv of
2522 Just co -> co
2523 Nothing -> CoVarCo cv
2524
2525 substCoVars :: TCvSubst -> [CoVar] -> [Coercion]
2526 substCoVars subst cvs = map (substCoVar subst) cvs
2527
2528 lookupCoVar :: TCvSubst -> Var -> Maybe Coercion
2529 lookupCoVar (TCvSubst _ _ cenv) v = lookupVarEnv cenv v
2530
2531 substTyVarBndr :: HasCallStack => TCvSubst -> TyVar -> (TCvSubst, TyVar)
2532 substTyVarBndr = substTyVarBndrCallback substTy
2533
2534 -- | Like 'substTyVarBndr' but disables sanity checks.
2535 -- The problems that the sanity checks in substTy catch are described in
2536 -- Note [The substitution invariant].
2537 -- The goal of #11371 is to migrate all the calls of substTyUnchecked to
2538 -- substTy and remove this function. Please don't use in new code.
2539 substTyVarBndrUnchecked :: TCvSubst -> TyVar -> (TCvSubst, TyVar)
2540 substTyVarBndrUnchecked = substTyVarBndrCallback substTyUnchecked
2541
2542 -- | Substitute a tyvar in a binding position, returning an
2543 -- extended subst and a new tyvar.
2544 substTyVarBndrCallback :: (TCvSubst -> Type -> Type) -- ^ the subst function
2545 -> TCvSubst -> TyVar -> (TCvSubst, TyVar)
2546 substTyVarBndrCallback subst_fn subst@(TCvSubst in_scope tenv cenv) old_var
2547 = ASSERT2( _no_capture, pprTyVar old_var $$ pprTyVar new_var $$ ppr subst )
2548 ASSERT( isTyVar old_var )
2549 (TCvSubst (in_scope `extendInScopeSet` new_var) new_env cenv, new_var)
2550 where
2551 new_env | no_change = delVarEnv tenv old_var
2552 | otherwise = extendVarEnv tenv old_var (TyVarTy new_var)
2553
2554 _no_capture = not (new_var `elemVarSet` tyCoVarsOfTypesSet tenv)
2555 -- Assertion check that we are not capturing something in the substitution
2556
2557 old_ki = tyVarKind old_var
2558 no_kind_change = noFreeVarsOfType old_ki -- verify that kind is closed
2559 no_change = no_kind_change && (new_var == old_var)
2560 -- no_change means that the new_var is identical in
2561 -- all respects to the old_var (same unique, same kind)
2562 -- See Note [Extending the TCvSubst]
2563 --
2564 -- In that case we don't need to extend the substitution
2565 -- to map old to new. But instead we must zap any
2566 -- current substitution for the variable. For example:
2567 -- (\x.e) with id_subst = [x |-> e']
2568 -- Here we must simply zap the substitution for x
2569
2570 new_var | no_kind_change = uniqAway in_scope old_var
2571 | otherwise = uniqAway in_scope $
2572 setTyVarKind old_var (subst_fn subst old_ki)
2573 -- The uniqAway part makes sure the new variable is not already in scope
2574
2575 substCoVarBndr :: TCvSubst -> CoVar -> (TCvSubst, CoVar)
2576 substCoVarBndr subst@(TCvSubst in_scope tenv cenv) old_var
2577 = ASSERT( isCoVar old_var )
2578 (TCvSubst (in_scope `extendInScopeSet` new_var) tenv new_cenv, new_var)
2579 where
2580 new_co = mkCoVarCo new_var
2581 no_kind_change = all noFreeVarsOfType [t1, t2]
2582 no_change = new_var == old_var && no_kind_change
2583
2584 new_cenv | no_change = delVarEnv cenv old_var
2585 | otherwise = extendVarEnv cenv old_var new_co
2586
2587 new_var = uniqAway in_scope subst_old_var
2588 subst_old_var = mkCoVar (varName old_var) new_var_type
2589
2590 (_, _, t1, t2, role) = coVarKindsTypesRole old_var
2591 t1' = substTy subst t1
2592 t2' = substTy subst t2
2593 new_var_type = mkCoercionType role t1' t2'
2594 -- It's important to do the substitution for coercions,
2595 -- because they can have free type variables
2596
2597 cloneTyVarBndr :: TCvSubst -> TyVar -> Unique -> (TCvSubst, TyVar)
2598 cloneTyVarBndr subst@(TCvSubst in_scope tv_env cv_env) tv uniq
2599 = ASSERT2( isTyVar tv, ppr tv ) -- I think it's only called on TyVars
2600 (TCvSubst (extendInScopeSet in_scope tv')
2601 (extendVarEnv tv_env tv (mkTyVarTy tv')) cv_env, tv')
2602 where
2603 old_ki = tyVarKind tv
2604 no_kind_change = noFreeVarsOfType old_ki -- verify that kind is closed
2605
2606 tv1 | no_kind_change = tv
2607 | otherwise = setTyVarKind tv (substTy subst old_ki)
2608
2609 tv' = setVarUnique tv1 uniq
2610
2611 cloneTyVarBndrs :: TCvSubst -> [TyVar] -> UniqSupply -> (TCvSubst, [TyVar])
2612 cloneTyVarBndrs subst [] _usupply = (subst, [])
2613 cloneTyVarBndrs subst (t:ts) usupply = (subst'', tv:tvs)
2614 where
2615 (uniq, usupply') = takeUniqFromSupply usupply
2616 (subst' , tv ) = cloneTyVarBndr subst t uniq
2617 (subst'', tvs) = cloneTyVarBndrs subst' ts usupply'
2618
2619 {-
2620 %************************************************************************
2621 %* *
2622 Pretty-printing types
2623
2624 Defined very early because of debug printing in assertions
2625 %* *
2626 %************************************************************************
2627
2628 @pprType@ is the standard @Type@ printer; the overloaded @ppr@ function is
2629 defined to use this. @pprParendType@ is the same, except it puts
2630 parens around the type, except for the atomic cases. @pprParendType@
2631 works just by setting the initial context precedence very high.
2632
2633 See Note [Precedence in types] in BasicTypes.
2634 -}
2635
2636 ------------------
2637
2638 pprType, pprParendType :: Type -> SDoc
2639 pprType = pprPrecType topPrec
2640 pprParendType = pprPrecType appPrec
2641
2642 pprPrecType :: PprPrec -> Type -> SDoc
2643 pprPrecType prec ty
2644 = getPprStyle $ \sty ->
2645 if debugStyle sty -- Use pprDebugType when in
2646 then debug_ppr_ty prec ty -- when in debug-style
2647 else pprPrecIfaceType prec (tidyToIfaceTypeSty ty sty)
2648
2649 pprTyLit :: TyLit -> SDoc
2650 pprTyLit = pprIfaceTyLit . toIfaceTyLit
2651
2652 pprKind, pprParendKind :: Kind -> SDoc
2653 pprKind = pprType
2654 pprParendKind = pprParendType
2655
2656 tidyToIfaceTypeSty :: Type -> PprStyle -> IfaceType
2657 tidyToIfaceTypeSty ty sty
2658 | userStyle sty = tidyToIfaceType ty
2659 | otherwise = toIfaceTypeX (tyCoVarsOfType ty) ty
2660 -- in latter case, don't tidy, as we'll be printing uniques.
2661
2662 tidyToIfaceType :: Type -> IfaceType
2663 -- It's vital to tidy before converting to an IfaceType
2664 -- or nested binders will become indistinguishable!
2665 --
2666 -- Also for the free type variables, tell toIfaceTypeX to
2667 -- leave them as IfaceFreeTyVar. This is super-important
2668 -- for debug printing.
2669 tidyToIfaceType ty = toIfaceTypeX (mkVarSet free_tcvs) (tidyType env ty)
2670 where
2671 env = tidyFreeTyCoVars emptyTidyEnv free_tcvs
2672 free_tcvs = tyCoVarsOfTypeWellScoped ty
2673
2674 ------------
2675 pprCo, pprParendCo :: Coercion -> SDoc
2676 pprCo co = getPprStyle $ \ sty -> pprIfaceCoercion (tidyToIfaceCoSty co sty)
2677 pprParendCo co = getPprStyle $ \ sty -> pprParendIfaceCoercion (tidyToIfaceCoSty co sty)
2678
2679 tidyToIfaceCoSty :: Coercion -> PprStyle -> IfaceCoercion
2680 tidyToIfaceCoSty co sty
2681 | userStyle sty = tidyToIfaceCo co
2682 | otherwise = toIfaceCoercionX (tyCoVarsOfCo co) co
2683 -- in latter case, don't tidy, as we'll be printing uniques.
2684
2685 tidyToIfaceCo :: Coercion -> IfaceCoercion
2686 -- It's vital to tidy before converting to an IfaceType
2687 -- or nested binders will become indistinguishable!
2688 --
2689 -- Also for the free type variables, tell toIfaceCoercionX to
2690 -- leave them as IfaceFreeCoVar. This is super-important
2691 -- for debug printing.
2692 tidyToIfaceCo co = toIfaceCoercionX (mkVarSet free_tcvs) (tidyCo env co)
2693 where
2694 env = tidyFreeTyCoVars emptyTidyEnv free_tcvs
2695 free_tcvs = toposortTyVars $ tyCoVarsOfCoList co
2696
2697 ------------
2698 pprClassPred :: Class -> [Type] -> SDoc
2699 pprClassPred clas tys = pprTypeApp (classTyCon clas) tys
2700
2701 ------------
2702 pprTheta :: ThetaType -> SDoc
2703 pprTheta = pprIfaceContext topPrec . map tidyToIfaceType
2704
2705 pprParendTheta :: ThetaType -> SDoc
2706 pprParendTheta = pprIfaceContext appPrec . map tidyToIfaceType
2707
2708 pprThetaArrowTy :: ThetaType -> SDoc
2709 pprThetaArrowTy = pprIfaceContextArr . map tidyToIfaceType
2710
2711 ------------------
2712 instance Outputable Type where
2713 ppr ty = pprType ty
2714
2715 instance Outputable TyLit where
2716 ppr = pprTyLit
2717
2718 ------------------
2719 pprSigmaType :: Type -> SDoc
2720 pprSigmaType = pprIfaceSigmaType ShowForAllWhen . tidyToIfaceType
2721
2722 pprForAll :: [TyVarBinder] -> SDoc
2723 pprForAll tvs = pprIfaceForAll (map toIfaceForAllBndr tvs)
2724
2725 -- | Print a user-level forall; see Note [When to print foralls]
2726 pprUserForAll :: [TyVarBinder] -> SDoc
2727 pprUserForAll = pprUserIfaceForAll . map toIfaceForAllBndr
2728
2729 pprTvBndrs :: [TyVarBinder] -> SDoc
2730 pprTvBndrs tvs = sep (map pprTvBndr tvs)
2731
2732 pprTvBndr :: TyVarBinder -> SDoc
2733 pprTvBndr = pprTyVar . binderVar
2734
2735 pprTyVars :: [TyVar] -> SDoc
2736 pprTyVars tvs = sep (map pprTyVar tvs)
2737
2738 pprTyVar :: TyVar -> SDoc
2739 -- Print a type variable binder with its kind (but not if *)
2740 -- Here we do not go via IfaceType, because the duplication with
2741 -- pprIfaceTvBndr is minimal, and the loss of uniques etc in
2742 -- debug printing is disastrous
2743 pprTyVar tv
2744 | isLiftedTypeKind kind = ppr tv
2745 | otherwise = parens (ppr tv <+> dcolon <+> ppr kind)
2746 where
2747 kind = tyVarKind tv
2748
2749 instance Outputable TyBinder where
2750 ppr (Anon ty) = text "[anon]" <+> ppr ty
2751 ppr (Named (TvBndr v Required)) = ppr v
2752 ppr (Named (TvBndr v Specified)) = char '@' <> ppr v
2753 ppr (Named (TvBndr v Inferred)) = braces (ppr v)
2754
2755 -----------------
2756 instance Outputable Coercion where -- defined here to avoid orphans
2757 ppr = pprCo
2758
2759 debugPprType :: Type -> SDoc
2760 -- ^ debugPprType is a simple pretty printer that prints a type
2761 -- without going through IfaceType. It does not format as prettily
2762 -- as the normal route, but it's much more direct, and that can
2763 -- be useful for debugging. E.g. with -dppr-debug it prints the
2764 -- kind on type-variable /occurrences/ which the normal route
2765 -- fundamentally cannot do.
2766 debugPprType ty = debug_ppr_ty topPrec ty
2767
2768 debug_ppr_ty :: PprPrec -> Type -> SDoc
2769 debug_ppr_ty _ (LitTy l)
2770 = ppr l
2771
2772 debug_ppr_ty _ (TyVarTy tv)
2773 = ppr tv -- With -dppr-debug we get (tv :: kind)
2774
2775 debug_ppr_ty prec (FunTy arg res)
2776 = maybeParen prec funPrec $
2777 sep [debug_ppr_ty funPrec arg, arrow <+> debug_ppr_ty prec res]
2778
2779 debug_ppr_ty prec (TyConApp tc tys)
2780 | null tys = ppr tc
2781 | otherwise = maybeParen prec appPrec $
2782 hang (ppr tc) 2 (sep (map (debug_ppr_ty appPrec) tys))
2783
2784 debug_ppr_ty prec (AppTy t1 t2)
2785 = hang (debug_ppr_ty prec t1)
2786 2 (debug_ppr_ty appPrec t2)
2787
2788 debug_ppr_ty prec (CastTy ty co)
2789 = maybeParen prec topPrec $
2790 hang (debug_ppr_ty topPrec ty)
2791 2 (text "|>" <+> ppr co)
2792
2793 debug_ppr_ty _ (CoercionTy co)
2794 = parens (text "CO" <+> ppr co)
2795
2796 debug_ppr_ty prec ty@(ForAllTy {})
2797 | (tvs, body) <- split ty
2798 = maybeParen prec funPrec $
2799 hang (text "forall" <+> fsep (map ppr tvs) <> dot)
2800 -- The (map ppr tvs) will print kind-annotated
2801 -- tvs, because we are (usually) in debug-style
2802 2 (ppr body)
2803 where
2804 split ty | ForAllTy tv ty' <- ty
2805 , (tvs, body) <- split ty'
2806 = (tv:tvs, body)
2807 | otherwise
2808 = ([], ty)
2809
2810 {-
2811 Note [When to print foralls]
2812 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2813 Mostly we want to print top-level foralls when (and only when) the user specifies
2814 -fprint-explicit-foralls. But when kind polymorphism is at work, that suppresses
2815 too much information; see Trac #9018.
2816
2817 So I'm trying out this rule: print explicit foralls if
2818 a) User specifies -fprint-explicit-foralls, or
2819 b) Any of the quantified type variables has a kind
2820 that mentions a kind variable
2821
2822 This catches common situations, such as a type siguature
2823 f :: m a
2824 which means
2825 f :: forall k. forall (m :: k->*) (a :: k). m a
2826 We really want to see both the "forall k" and the kind signatures
2827 on m and a. The latter comes from pprTvBndr.
2828
2829 Note [Infix type variables]
2830 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
2831 With TypeOperators you can say
2832
2833 f :: (a ~> b) -> b
2834
2835 and the (~>) is considered a type variable. However, the type
2836 pretty-printer in this module will just see (a ~> b) as
2837
2838 App (App (TyVarTy "~>") (TyVarTy "a")) (TyVarTy "b")
2839
2840 So it'll print the type in prefix form. To avoid confusion we must
2841 remember to parenthesise the operator, thus
2842
2843 (~>) a b -> b
2844
2845 See Trac #2766.
2846 -}
2847
2848 pprDataCons :: TyCon -> SDoc
2849 pprDataCons = sepWithVBars . fmap pprDataConWithArgs . tyConDataCons
2850 where
2851 sepWithVBars [] = empty
2852 sepWithVBars docs = sep (punctuate (space <> vbar) docs)
2853
2854 pprDataConWithArgs :: DataCon -> SDoc
2855 pprDataConWithArgs dc = sep [forAllDoc, thetaDoc, ppr dc <+> argsDoc]
2856 where
2857 (_univ_tvs, _ex_tvs, _eq_spec, theta, arg_tys, _res_ty) = dataConFullSig dc
2858 user_bndrs = dataConUserTyVarBinders dc
2859 forAllDoc = pprUserForAll user_bndrs
2860 thetaDoc = pprThetaArrowTy theta
2861 argsDoc = hsep (fmap pprParendType arg_tys)
2862
2863
2864 pprTypeApp :: TyCon -> [Type] -> SDoc
2865 pprTypeApp tc tys
2866 = pprIfaceTypeApp topPrec (toIfaceTyCon tc)
2867 (toIfaceTcArgs tc tys)
2868 -- TODO: toIfaceTcArgs seems rather wasteful here
2869
2870 ------------------
2871 ppSuggestExplicitKinds :: SDoc
2872 -- Print a helpful suggstion about -fprint-explicit-kinds,
2873 -- if it is not already on
2874 ppSuggestExplicitKinds
2875 = sdocWithDynFlags $ \ dflags ->
2876 ppUnless (gopt Opt_PrintExplicitKinds dflags) $
2877 text "Use -fprint-explicit-kinds to see the kind arguments"
2878
2879 {-
2880 %************************************************************************
2881 %* *
2882 \subsection{TidyType}
2883 %* *
2884 %************************************************************************
2885 -}
2886
2887 -- | This tidies up a type for printing in an error message, or in
2888 -- an interface file.
2889 --
2890 -- It doesn't change the uniques at all, just the print names.
2891 tidyTyCoVarBndrs :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
2892 tidyTyCoVarBndrs (occ_env, subst) tvs
2893 = mapAccumL tidyTyCoVarBndr tidy_env' tvs
2894 where
2895 -- Seed the occ_env with clashes among the names, see
2896 -- Node [Tidying multiple names at once] in OccName
2897 -- Se still go through tidyTyCoVarBndr so that each kind variable is tidied
2898 -- with the correct tidy_env
2899 occs = map getHelpfulOccName tvs
2900 tidy_env' = (avoidClashesOccEnv occ_env occs, subst)
2901
2902 tidyTyCoVarBndr :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
2903 tidyTyCoVarBndr tidy_env@(occ_env, subst) tyvar
2904 = case tidyOccName occ_env (getHelpfulOccName tyvar) of
2905 (occ_env', occ') -> ((occ_env', subst'), tyvar')
2906 where
2907 subst' = extendVarEnv subst tyvar tyvar'
2908 tyvar' = setTyVarKind (setTyVarName tyvar name') kind'
2909 kind' = tidyKind tidy_env (tyVarKind tyvar)
2910 name' = tidyNameOcc name occ'
2911 name = tyVarName tyvar
2912
2913 getHelpfulOccName :: TyCoVar -> OccName
2914 getHelpfulOccName tyvar = occ1
2915 where
2916 name = tyVarName tyvar
2917 occ = getOccName name
2918 -- A TcTyVar with a System Name is probably a unification variable;
2919 -- when we tidy them we give them a trailing "0" (or 1 etc)
2920 -- so that they don't take precedence for the un-modified name
2921 -- Plus, indicating a unification variable in this way is a
2922 -- helpful clue for users
2923 occ1 | isSystemName name
2924 , isTcTyVar tyvar
2925 = mkTyVarOcc (occNameString occ ++ "0")
2926 | otherwise
2927 = occ
2928
2929 tidyTyVarBinder :: TidyEnv -> TyVarBndr TyVar vis
2930 -> (TidyEnv, TyVarBndr TyVar vis)
2931 tidyTyVarBinder tidy_env (TvBndr tv vis)
2932 = (tidy_env', TvBndr tv' vis)
2933 where
2934 (tidy_env', tv') = tidyTyCoVarBndr tidy_env tv
2935
2936 tidyTyVarBinders :: TidyEnv -> [TyVarBndr TyVar vis]
2937 -> (TidyEnv, [TyVarBndr TyVar vis])
2938 tidyTyVarBinders = mapAccumL tidyTyVarBinder
2939
2940 ---------------
2941 tidyFreeTyCoVars :: TidyEnv -> [TyCoVar] -> TidyEnv
2942 -- ^ Add the free 'TyVar's to the env in tidy form,
2943 -- so that we can tidy the type they are free in
2944 tidyFreeTyCoVars (full_occ_env, var_env) tyvars
2945 = fst (tidyOpenTyCoVars (full_occ_env, var_env) tyvars)
2946
2947 ---------------
2948 tidyOpenTyCoVars :: TidyEnv -> [TyCoVar] -> (TidyEnv, [TyCoVar])
2949 tidyOpenTyCoVars env tyvars = mapAccumL tidyOpenTyCoVar env tyvars
2950
2951 ---------------
2952 tidyOpenTyCoVar :: TidyEnv -> TyCoVar -> (TidyEnv, TyCoVar)
2953 -- ^ Treat a new 'TyCoVar' as a binder, and give it a fresh tidy name
2954 -- using the environment if one has not already been allocated. See
2955 -- also 'tidyTyCoVarBndr'
2956 tidyOpenTyCoVar env@(_, subst) tyvar
2957 = case lookupVarEnv subst tyvar of
2958 Just tyvar' -> (env, tyvar') -- Already substituted
2959 Nothing ->
2960 let env' = tidyFreeTyCoVars env (tyCoVarsOfTypeList (tyVarKind tyvar))
2961 in tidyTyCoVarBndr env' tyvar -- Treat it as a binder
2962
2963 ---------------
2964 tidyTyVarOcc :: TidyEnv -> TyVar -> TyVar
2965 tidyTyVarOcc env@(_, subst) tv
2966 = case lookupVarEnv subst tv of
2967 Nothing -> updateTyVarKind (tidyType env) tv
2968 Just tv' -> tv'
2969
2970 ---------------
2971 tidyTypes :: TidyEnv -> [Type] -> [Type]
2972 tidyTypes env tys = map (tidyType env) tys
2973
2974 ---------------
2975 tidyType :: TidyEnv -> Type -> Type
2976 tidyType _ (LitTy n) = LitTy n
2977 tidyType env (TyVarTy tv) = TyVarTy (tidyTyVarOcc env tv)
2978 tidyType env (TyConApp tycon tys) = let args = tidyTypes env tys
2979 in args `seqList` TyConApp tycon args
2980 tidyType env (AppTy fun arg) = (AppTy $! (tidyType env fun)) $! (tidyType env arg)
2981 tidyType env (FunTy fun arg) = (FunTy $! (tidyType env fun)) $! (tidyType env arg)
2982 tidyType env (ty@(ForAllTy{})) = mkForAllTys' (zip tvs' vis) $! tidyType env' body_ty
2983 where
2984 (tvs, vis, body_ty) = splitForAllTys' ty
2985 (env', tvs') = tidyTyCoVarBndrs env tvs
2986 tidyType env (CastTy ty co) = (CastTy $! tidyType env ty) $! (tidyCo env co)
2987 tidyType env (CoercionTy co) = CoercionTy $! (tidyCo env co)
2988
2989
2990 -- The following two functions differ from mkForAllTys and splitForAllTys in that
2991 -- they expect/preserve the ArgFlag argument. Thes belong to types/Type.hs, but
2992 -- how should they be named?
2993 mkForAllTys' :: [(TyVar, ArgFlag)] -> Type -> Type
2994 mkForAllTys' tvvs ty = foldr strictMkForAllTy ty tvvs
2995 where
2996 strictMkForAllTy (tv,vis) ty = (ForAllTy $! ((TvBndr $! tv) $! vis)) $! ty
2997
2998 splitForAllTys' :: Type -> ([TyVar], [ArgFlag], Type)
2999 splitForAllTys' ty = go ty [] []
3000 where
3001 go (ForAllTy (TvBndr tv vis) ty) tvs viss = go ty (tv:tvs) (vis:viss)
3002 go ty tvs viss = (reverse tvs, reverse viss, ty)
3003
3004
3005 ---------------
3006 -- | Grabs the free type variables, tidies them
3007 -- and then uses 'tidyType' to work over the type itself
3008 tidyOpenTypes :: TidyEnv -> [Type] -> (TidyEnv, [Type])
3009 tidyOpenTypes env tys
3010 = (env', tidyTypes (trimmed_occ_env, var_env) tys)
3011 where
3012 (env'@(_, var_env), tvs') = tidyOpenTyCoVars env $
3013 tyCoVarsOfTypesWellScoped tys
3014 trimmed_occ_env = initTidyOccEnv (map getOccName tvs')
3015 -- The idea here was that we restrict the new TidyEnv to the
3016 -- _free_ vars of the types, so that we don't gratuitously rename
3017 -- the _bound_ variables of the types.
3018
3019 ---------------
3020 tidyOpenType :: TidyEnv -> Type -> (TidyEnv, Type)
3021 tidyOpenType env ty = let (env', [ty']) = tidyOpenTypes env [ty] in
3022 (env', ty')
3023
3024 ---------------
3025 -- | Calls 'tidyType' on a top-level type (i.e. with an empty tidying environment)
3026 tidyTopType :: Type -> Type
3027 tidyTopType ty = tidyType emptyTidyEnv ty
3028
3029 ---------------
3030 tidyOpenKind :: TidyEnv -> Kind -> (TidyEnv, Kind)
3031 tidyOpenKind = tidyOpenType
3032
3033 tidyKind :: TidyEnv -> Kind -> Kind
3034 tidyKind = tidyType
3035
3036 ----------------
3037 tidyCo :: TidyEnv -> Coercion -> Coercion
3038 tidyCo env@(_, subst) co
3039 = go co
3040 where
3041 go (Refl r ty) = Refl r (tidyType env ty)
3042 go (TyConAppCo r tc cos) = let args = map go cos
3043 in args `seqList` TyConAppCo r tc args
3044 go (AppCo co1 co2) = (AppCo $! go co1) $! go co2
3045 go (ForAllCo tv h co) = ((ForAllCo $! tvp) $! (go h)) $! (tidyCo envp co)
3046 where (envp, tvp) = tidyTyCoVarBndr env tv
3047 -- the case above duplicates a bit of work in tidying h and the kind
3048 -- of tv. But the alternative is to use coercionKind, which seems worse.
3049 go (FunCo r co1 co2) = (FunCo r $! go co1) $! go co2
3050 go (CoVarCo cv) = case lookupVarEnv subst cv of
3051 Nothing -> CoVarCo cv
3052 Just cv' -> CoVarCo cv'
3053 go (HoleCo h) = HoleCo h
3054 go (AxiomInstCo con ind cos) = let args = map go cos
3055 in args `seqList` AxiomInstCo con ind args
3056 go (UnivCo p r t1 t2) = (((UnivCo $! (go_prov p)) $! r) $!
3057 tidyType env t1) $! tidyType env t2
3058 go (SymCo co) = SymCo $! go co
3059 go (TransCo co1 co2) = (TransCo $! go co1) $! go co2
3060 go (NthCo r d co) = NthCo r d $! go co
3061 go (LRCo lr co) = LRCo lr $! go co
3062 go (InstCo co ty) = (InstCo $! go co) $! go ty
3063 go (CoherenceCo co1 co2) = (CoherenceCo $! go co1) $! go co2
3064 go (KindCo co) = KindCo $! go co
3065 go (SubCo co) = SubCo $! go co
3066 go (AxiomRuleCo ax cos) = let cos1 = tidyCos env cos
3067 in cos1 `seqList` AxiomRuleCo ax cos1
3068
3069 go_prov UnsafeCoerceProv = UnsafeCoerceProv
3070 go_prov (PhantomProv co) = PhantomProv (go co)
3071 go_prov (ProofIrrelProv co) = ProofIrrelProv (go co)
3072 go_prov p@(PluginProv _) = p
3073
3074 tidyCos :: TidyEnv -> [Coercion] -> [Coercion]
3075 tidyCos env = map (tidyCo env)
3076
3077
3078 {- *********************************************************************
3079 * *
3080 typeSize, coercionSize
3081 * *
3082 ********************************************************************* -}
3083
3084 -- NB: We put typeSize/coercionSize here because they are mutually
3085 -- recursive, and have the CPR property. If we have mutual
3086 -- recursion across a hi-boot file, we don't get the CPR property
3087 -- and these functions allocate a tremendous amount of rubbish.
3088 -- It's not critical (because typeSize is really only used in
3089 -- debug mode, but I tripped over an example (T5642) in which
3090 -- typeSize was one of the biggest single allocators in all of GHC.
3091 -- And it's easy to fix, so I did.
3092
3093 -- NB: typeSize does not respect `eqType`, in that two types that
3094 -- are `eqType` may return different sizes. This is OK, because this
3095 -- function is used only in reporting, not decision-making.
3096
3097 typeSize :: Type -> Int
3098 typeSize (LitTy {}) = 1
3099 typeSize (TyVarTy {}) = 1
3100 typeSize (AppTy t1 t2) = typeSize t1 + typeSize t2
3101 typeSize (FunTy t1 t2) = typeSize t1 + typeSize t2
3102 typeSize (ForAllTy (TvBndr tv _) t) = typeSize (tyVarKind tv) + typeSize t
3103 typeSize (TyConApp _ ts) = 1 + sum (map typeSize ts)
3104 typeSize (CastTy ty co) = typeSize ty + coercionSize co
3105 typeSize (CoercionTy co) = coercionSize co
3106
3107 coercionSize :: Coercion -> Int
3108 coercionSize (Refl _ ty) = typeSize ty
3109 coercionSize (TyConAppCo _ _ args) = 1 + sum (map coercionSize args)
3110 coercionSize (AppCo co arg) = coercionSize co + coercionSize arg
3111 coercionSize (ForAllCo _ h co) = 1 + coercionSize co + coercionSize h
3112 coercionSize (FunCo _ co1 co2) = 1 + coercionSize co1 + coercionSize co2
3113 coercionSize (CoVarCo _) = 1
3114 coercionSize (HoleCo _) = 1
3115 coercionSize (AxiomInstCo _ _ args) = 1 + sum (map coercionSize args)
3116 coercionSize (UnivCo p _ t1 t2) = 1 + provSize p + typeSize t1 + typeSize t2
3117 coercionSize (SymCo co) = 1 + coercionSize co
3118 coercionSize (TransCo co1 co2) = 1 + coercionSize co1 + coercionSize co2
3119 coercionSize (NthCo _ _ co) = 1 + coercionSize co
3120 coercionSize (LRCo _ co) = 1 + coercionSize co
3121 coercionSize (InstCo co arg) = 1 + coercionSize co + coercionSize arg
3122 coercionSize (CoherenceCo c1 c2) = 1 + coercionSize c1 + coercionSize c2
3123 coercionSize (KindCo co) = 1 + coercionSize co
3124 coercionSize (SubCo co) = 1 + coercionSize co
3125 coercionSize (AxiomRuleCo _ cs) = 1 + sum (map coercionSize cs)
3126
3127 provSize :: UnivCoProvenance -> Int
3128 provSize UnsafeCoerceProv = 1
3129 provSize (PhantomProv co) = 1 + coercionSize co
3130 provSize (ProofIrrelProv co) = 1 + coercionSize co
3131 provSize (PluginProv _) = 1