Fix and document cloneWC
[ghc.git] / compiler / typecheck / TcFlatten.hs
1 {-# LANGUAGE CPP, ViewPatterns, BangPatterns #-}
2
3 module TcFlatten(
4 FlattenMode(..),
5 flatten, flattenKind, flattenArgsNom,
6
7 unflattenWanteds
8 ) where
9
10 #include "HsVersions.h"
11
12 import GhcPrelude
13
14 import TcRnTypes
15 import TcType
16 import Type
17 import TcEvidence
18 import TyCon
19 import TyCoRep -- performs delicate algorithm on types
20 import Coercion
21 import Var
22 import VarSet
23 import VarEnv
24 import Outputable
25 import TcSMonad as TcS
26 import BasicTypes( SwapFlag(..) )
27
28 import Pair
29 import Util
30 import Bag
31 import Control.Monad
32
33 import Control.Arrow ( first )
34
35 {-
36 Note [The flattening story]
37 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
38 * A CFunEqCan is either of form
39 [G] <F xis> : F xis ~ fsk -- fsk is a FlatSkolTv
40 [W] x : F xis ~ fmv -- fmv is a FlatMetaTv
41 where
42 x is the witness variable
43 xis are function-free
44 fsk/fmv is a flatten skolem;
45 it is always untouchable (level 0)
46
47 * CFunEqCans can have any flavour: [G], [W], [WD] or [D]
48
49 * KEY INSIGHTS:
50
51 - A given flatten-skolem, fsk, is known a-priori to be equal to
52 F xis (the LHS), with <F xis> evidence. The fsk is still a
53 unification variable, but it is "owned" by its CFunEqCan, and
54 is filled in (unflattened) only by unflattenGivens.
55
56 - A unification flatten-skolem, fmv, stands for the as-yet-unknown
57 type to which (F xis) will eventually reduce. It is filled in
58
59
60 - All fsk/fmv variables are "untouchable". To make it simple to test,
61 we simply give them TcLevel=0. This means that in a CTyVarEq, say,
62 fmv ~ Int
63 we NEVER unify fmv.
64
65 - A unification flatten-skolem, fmv, ONLY gets unified when either
66 a) The CFunEqCan takes a step, using an axiom
67 b) By unflattenWanteds
68 They are never unified in any other form of equality.
69 For example [W] ffmv ~ Int is stuck; it does not unify with fmv.
70
71 * We *never* substitute in the RHS (i.e. the fsk/fmv) of a CFunEqCan.
72 That would destroy the invariant about the shape of a CFunEqCan,
73 and it would risk wanted/wanted interactions. The only way we
74 learn information about fsk is when the CFunEqCan takes a step.
75
76 However we *do* substitute in the LHS of a CFunEqCan (else it
77 would never get to fire!)
78
79 * Unflattening:
80 - We unflatten Givens when leaving their scope (see unflattenGivens)
81 - We unflatten Wanteds at the end of each attempt to simplify the
82 wanteds; see unflattenWanteds, called from solveSimpleWanteds.
83
84 * Ownership of fsk/fmv. Each canonical [G], [W], or [WD]
85 CFunEqCan x : F xis ~ fsk/fmv
86 "owns" a distinct evidence variable x, and flatten-skolem fsk/fmv.
87 Why? We make a fresh fsk/fmv when the constraint is born;
88 and we never rewrite the RHS of a CFunEqCan.
89
90 In contrast a [D] CFunEqCan /shares/ its fmv with its partner [W],
91 but does not "own" it. If we reduce a [D] F Int ~ fmv, where
92 say type instance F Int = ty, then we don't discharge fmv := ty.
93 Rather we simply generate [D] fmv ~ ty (in TcInteract.reduce_top_fun_eq,
94 and dischargeFmv)
95
96 * Inert set invariant: if F xis1 ~ fsk1, F xis2 ~ fsk2
97 then xis1 /= xis2
98 i.e. at most one CFunEqCan with a particular LHS
99
100 * Function applications can occur in the RHS of a CTyEqCan. No reason
101 not allow this, and it reduces the amount of flattening that must occur.
102
103 * Flattening a type (F xis):
104 - If we are flattening in a Wanted/Derived constraint
105 then create new [W] x : F xis ~ fmv
106 else create new [G] x : F xis ~ fsk
107 with fresh evidence variable x and flatten-skolem fsk/fmv
108
109 - Add it to the work list
110
111 - Replace (F xis) with fsk/fmv in the type you are flattening
112
113 - You can also add the CFunEqCan to the "flat cache", which
114 simply keeps track of all the function applications you
115 have flattened.
116
117 - If (F xis) is in the cache already, just
118 use its fsk/fmv and evidence x, and emit nothing.
119
120 - No need to substitute in the flat-cache. It's not the end
121 of the world if we start with, say (F alpha ~ fmv1) and
122 (F Int ~ fmv2) and then find alpha := Int. Athat will
123 simply give rise to fmv1 := fmv2 via [Interacting rule] below
124
125 * Canonicalising a CFunEqCan [G/W] x : F xis ~ fsk/fmv
126 - Flatten xis (to substitute any tyvars; there are already no functions)
127 cos :: xis ~ flat_xis
128 - New wanted x2 :: F flat_xis ~ fsk/fmv
129 - Add new wanted to flat cache
130 - Discharge x = F cos ; x2
131
132 * [Interacting rule]
133 (inert) [W] x1 : F tys ~ fmv1
134 (work item) [W] x2 : F tys ~ fmv2
135 Just solve one from the other:
136 x2 := x1
137 fmv2 := fmv1
138 This just unites the two fsks into one.
139 Always solve given from wanted if poss.
140
141 * For top-level reductions, see Note [Top-level reductions for type functions]
142 in TcInteract
143
144
145 Why given-fsks, alone, doesn't work
146 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
147 Could we get away with only flatten meta-tyvars, with no flatten-skolems? No.
148
149 [W] w : alpha ~ [F alpha Int]
150
151 ---> flatten
152 w = ...w'...
153 [W] w' : alpha ~ [fsk]
154 [G] <F alpha Int> : F alpha Int ~ fsk
155
156 --> unify (no occurs check)
157 alpha := [fsk]
158
159 But since fsk = F alpha Int, this is really an occurs check error. If
160 that is all we know about alpha, we will succeed in constraint
161 solving, producing a program with an infinite type.
162
163 Even if we did finally get (g : fsk ~ Bool) by solving (F alpha Int ~ fsk)
164 using axiom, zonking would not see it, so (x::alpha) sitting in the
165 tree will get zonked to an infinite type. (Zonking always only does
166 refl stuff.)
167
168 Why flatten-meta-vars, alone doesn't work
169 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
170 Look at Simple13, with unification-fmvs only
171
172 [G] g : a ~ [F a]
173
174 ---> Flatten given
175 g' = g;[x]
176 [G] g' : a ~ [fmv]
177 [W] x : F a ~ fmv
178
179 --> subst a in x
180 g' = g;[x]
181 x = F g' ; x2
182 [W] x2 : F [fmv] ~ fmv
183
184 And now we have an evidence cycle between g' and x!
185
186 If we used a given instead (ie current story)
187
188 [G] g : a ~ [F a]
189
190 ---> Flatten given
191 g' = g;[x]
192 [G] g' : a ~ [fsk]
193 [G] <F a> : F a ~ fsk
194
195 ---> Substitute for a
196 [G] g' : a ~ [fsk]
197 [G] F (sym g'); <F a> : F [fsk] ~ fsk
198
199
200 Why is it right to treat fmv's differently to ordinary unification vars?
201 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
202 f :: forall a. a -> a -> Bool
203 g :: F Int -> F Int -> Bool
204
205 Consider
206 f (x:Int) (y:Bool)
207 This gives alpha~Int, alpha~Bool. There is an inconsistency,
208 but really only one error. SherLoc may tell you which location
209 is most likely, based on other occurrences of alpha.
210
211 Consider
212 g (x:Int) (y:Bool)
213 Here we get (F Int ~ Int, F Int ~ Bool), which flattens to
214 (fmv ~ Int, fmv ~ Bool)
215 But there are really TWO separate errors.
216
217 ** We must not complain about Int~Bool. **
218
219 Moreover these two errors could arise in entirely unrelated parts of
220 the code. (In the alpha case, there must be *some* connection (eg
221 v:alpha in common envt).)
222
223 Note [Unflattening can force the solver to iterate]
224 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
225 Look at Trac #10340:
226 type family Any :: * -- No instances
227 get :: MonadState s m => m s
228 instance MonadState s (State s) where ...
229
230 foo :: State Any Any
231 foo = get
232
233 For 'foo' we instantiate 'get' at types mm ss
234 [WD] MonadState ss mm, [WD] mm ss ~ State Any Any
235 Flatten, and decompose
236 [WD] MonadState ss mm, [WD] Any ~ fmv
237 [WD] mm ~ State fmv, [WD] fmv ~ ss
238 Unify mm := State fmv:
239 [WD] MonadState ss (State fmv)
240 [WD] Any ~ fmv, [WD] fmv ~ ss
241 Now we are stuck; the instance does not match!! So unflatten:
242 fmv := Any
243 ss := Any (*)
244 [WD] MonadState Any (State Any)
245
246 The unification (*) represents progress, so we must do a second
247 round of solving; this time it succeeds. This is done by the 'go'
248 loop in solveSimpleWanteds.
249
250 This story does not feel right but it's the best I can do; and the
251 iteration only happens in pretty obscure circumstances.
252
253
254 ************************************************************************
255 * *
256 * Examples
257 Here is a long series of examples I had to work through
258 * *
259 ************************************************************************
260
261 Simple20
262 ~~~~~~~~
263 axiom F [a] = [F a]
264
265 [G] F [a] ~ a
266 -->
267 [G] fsk ~ a
268 [G] [F a] ~ fsk (nc)
269 -->
270 [G] F a ~ fsk2
271 [G] fsk ~ [fsk2]
272 [G] fsk ~ a
273 -->
274 [G] F a ~ fsk2
275 [G] a ~ [fsk2]
276 [G] fsk ~ a
277
278 ----------------------------------------
279 indexed-types/should_compile/T44984
280
281 [W] H (F Bool) ~ H alpha
282 [W] alpha ~ F Bool
283 -->
284 F Bool ~ fmv0
285 H fmv0 ~ fmv1
286 H alpha ~ fmv2
287
288 fmv1 ~ fmv2
289 fmv0 ~ alpha
290
291 flatten
292 ~~~~~~~
293 fmv0 := F Bool
294 fmv1 := H (F Bool)
295 fmv2 := H alpha
296 alpha := F Bool
297 plus
298 fmv1 ~ fmv2
299
300 But these two are equal under the above assumptions.
301 Solve by Refl.
302
303
304 --- under plan B, namely solve fmv1:=fmv2 eagerly ---
305 [W] H (F Bool) ~ H alpha
306 [W] alpha ~ F Bool
307 -->
308 F Bool ~ fmv0
309 H fmv0 ~ fmv1
310 H alpha ~ fmv2
311
312 fmv1 ~ fmv2
313 fmv0 ~ alpha
314 -->
315 F Bool ~ fmv0
316 H fmv0 ~ fmv1
317 H alpha ~ fmv2 fmv2 := fmv1
318
319 fmv0 ~ alpha
320
321 flatten
322 fmv0 := F Bool
323 fmv1 := H fmv0 = H (F Bool)
324 retain H alpha ~ fmv2
325 because fmv2 has been filled
326 alpha := F Bool
327
328
329 ----------------------------
330 indexed-types/should_failt/T4179
331
332 after solving
333 [W] fmv_1 ~ fmv_2
334 [W] A3 (FCon x) ~ fmv_1 (CFunEqCan)
335 [W] A3 (x (aoa -> fmv_2)) ~ fmv_2 (CFunEqCan)
336
337 ----------------------------------------
338 indexed-types/should_fail/T7729a
339
340 a) [W] BasePrimMonad (Rand m) ~ m1
341 b) [W] tt m1 ~ BasePrimMonad (Rand m)
342
343 ---> process (b) first
344 BasePrimMonad (Ramd m) ~ fmv_atH
345 fmv_atH ~ tt m1
346
347 ---> now process (a)
348 m1 ~ s_atH ~ tt m1 -- An obscure occurs check
349
350
351 ----------------------------------------
352 typecheck/TcTypeNatSimple
353
354 Original constraint
355 [W] x + y ~ x + alpha (non-canonical)
356 ==>
357 [W] x + y ~ fmv1 (CFunEqCan)
358 [W] x + alpha ~ fmv2 (CFuneqCan)
359 [W] fmv1 ~ fmv2 (CTyEqCan)
360
361 (sigh)
362
363 ----------------------------------------
364 indexed-types/should_fail/GADTwrong1
365
366 [G] Const a ~ ()
367 ==> flatten
368 [G] fsk ~ ()
369 work item: Const a ~ fsk
370 ==> fire top rule
371 [G] fsk ~ ()
372 work item fsk ~ ()
373
374 Surely the work item should rewrite to () ~ ()? Well, maybe not;
375 it'a very special case. More generally, our givens look like
376 F a ~ Int, where (F a) is not reducible.
377
378
379 ----------------------------------------
380 indexed_types/should_fail/T8227:
381
382 Why using a different can-rewrite rule in CFunEqCan heads
383 does not work.
384
385 Assuming NOT rewriting wanteds with wanteds
386
387 Inert: [W] fsk_aBh ~ fmv_aBk -> fmv_aBk
388 [W] fmv_aBk ~ fsk_aBh
389
390 [G] Scalar fsk_aBg ~ fsk_aBh
391 [G] V a ~ f_aBg
392
393 Worklist includes [W] Scalar fmv_aBi ~ fmv_aBk
394 fmv_aBi, fmv_aBk are flatten unification variables
395
396 Work item: [W] V fsk_aBh ~ fmv_aBi
397
398 Note that the inert wanteds are cyclic, because we do not rewrite
399 wanteds with wanteds.
400
401
402 Then we go into a loop when normalise the work-item, because we
403 use rewriteOrSame on the argument of V.
404
405 Conclusion: Don't make canRewrite context specific; instead use
406 [W] a ~ ty to rewrite a wanted iff 'a' is a unification variable.
407
408
409 ----------------------------------------
410
411 Here is a somewhat similar case:
412
413 type family G a :: *
414
415 blah :: (G a ~ Bool, Eq (G a)) => a -> a
416 blah = error "urk"
417
418 foo x = blah x
419
420 For foo we get
421 [W] Eq (G a), G a ~ Bool
422 Flattening
423 [W] G a ~ fmv, Eq fmv, fmv ~ Bool
424 We can't simplify away the Eq Bool unless we substitute for fmv.
425 Maybe that doesn't matter: we would still be left with unsolved
426 G a ~ Bool.
427
428 --------------------------
429 Trac #9318 has a very simple program leading to
430
431 [W] F Int ~ Int
432 [W] F Int ~ Bool
433
434 We don't want to get "Error Int~Bool". But if fmv's can rewrite
435 wanteds, we will
436
437 [W] fmv ~ Int
438 [W] fmv ~ Bool
439 --->
440 [W] Int ~ Bool
441
442
443 ************************************************************************
444 * *
445 * FlattenEnv & FlatM
446 * The flattening environment & monad
447 * *
448 ************************************************************************
449
450 -}
451
452 type FlatWorkListRef = TcRef [Ct] -- See Note [The flattening work list]
453
454 data FlattenEnv
455 = FE { fe_mode :: !FlattenMode
456 , fe_loc :: !CtLoc -- See Note [Flattener CtLoc]
457 , fe_flavour :: !CtFlavour
458 , fe_eq_rel :: !EqRel -- See Note [Flattener EqRels]
459 , fe_work :: !FlatWorkListRef } -- See Note [The flattening work list]
460
461 data FlattenMode -- Postcondition for all three: inert wrt the type substitution
462 = FM_FlattenAll -- Postcondition: function-free
463 | FM_SubstOnly -- See Note [Flattening under a forall]
464
465 -- | FM_Avoid TcTyVar Bool -- See Note [Lazy flattening]
466 -- -- Postcondition:
467 -- -- * tyvar is only mentioned in result under a rigid path
468 -- -- e.g. [a] is ok, but F a won't happen
469 -- -- * If flat_top is True, top level is not a function application
470 -- -- (but under type constructors is ok e.g. [F a])
471
472 instance Outputable FlattenMode where
473 ppr FM_FlattenAll = text "FM_FlattenAll"
474 ppr FM_SubstOnly = text "FM_SubstOnly"
475
476 eqFlattenMode :: FlattenMode -> FlattenMode -> Bool
477 eqFlattenMode FM_FlattenAll FM_FlattenAll = True
478 eqFlattenMode FM_SubstOnly FM_SubstOnly = True
479 -- FM_Avoid tv1 b1 `eq` FM_Avoid tv2 b2 = tv1 == tv2 && b1 == b2
480 eqFlattenMode _ _ = False
481
482 -- | The 'FlatM' monad is a wrapper around 'TcS' with the following
483 -- extra capabilities: (1) it offers access to a 'FlattenEnv';
484 -- and (2) it maintains the flattening worklist.
485 -- See Note [The flattening work list].
486 newtype FlatM a
487 = FlatM { runFlatM :: FlattenEnv -> TcS a }
488
489 instance Monad FlatM where
490 m >>= k = FlatM $ \env ->
491 do { a <- runFlatM m env
492 ; runFlatM (k a) env }
493
494 instance Functor FlatM where
495 fmap = liftM
496
497 instance Applicative FlatM where
498 pure x = FlatM $ const (pure x)
499 (<*>) = ap
500
501 liftTcS :: TcS a -> FlatM a
502 liftTcS thing_inside
503 = FlatM $ const thing_inside
504
505 emitFlatWork :: Ct -> FlatM ()
506 -- See Note [The flattening work list]
507 emitFlatWork ct = FlatM $ \env -> updTcRef (fe_work env) (ct :)
508
509 -- convenient wrapper when you have a CtEvidence describing
510 -- the flattening operation
511 runFlattenCtEv :: FlattenMode -> CtEvidence -> FlatM a -> TcS a
512 runFlattenCtEv mode ev
513 = runFlatten mode (ctEvLoc ev) (ctEvFlavour ev) (ctEvEqRel ev)
514
515 -- Run thing_inside (which does flattening), and put all
516 -- the work it generates onto the main work list
517 -- See Note [The flattening work list]
518 runFlatten :: FlattenMode -> CtLoc -> CtFlavour -> EqRel -> FlatM a -> TcS a
519 runFlatten mode loc flav eq_rel thing_inside
520 = do { flat_ref <- newTcRef []
521 ; let fmode = FE { fe_mode = mode
522 , fe_loc = loc
523 , fe_flavour = flav
524 , fe_eq_rel = eq_rel
525 , fe_work = flat_ref }
526 ; res <- runFlatM thing_inside fmode
527 ; new_flats <- readTcRef flat_ref
528 ; updWorkListTcS (add_flats new_flats)
529 ; return res }
530 where
531 add_flats new_flats wl
532 = wl { wl_funeqs = add_funeqs new_flats (wl_funeqs wl) }
533
534 add_funeqs [] wl = wl
535 add_funeqs (f:fs) wl = add_funeqs fs (f:wl)
536 -- add_funeqs fs ws = reverse fs ++ ws
537 -- e.g. add_funeqs [f1,f2,f3] [w1,w2,w3,w4]
538 -- = [f3,f2,f1,w1,w2,w3,w4]
539
540 traceFlat :: String -> SDoc -> FlatM ()
541 traceFlat herald doc = liftTcS $ traceTcS herald doc
542
543 getFlatEnvField :: (FlattenEnv -> a) -> FlatM a
544 getFlatEnvField accessor
545 = FlatM $ \env -> return (accessor env)
546
547 getEqRel :: FlatM EqRel
548 getEqRel = getFlatEnvField fe_eq_rel
549
550 getRole :: FlatM Role
551 getRole = eqRelRole <$> getEqRel
552
553 getFlavour :: FlatM CtFlavour
554 getFlavour = getFlatEnvField fe_flavour
555
556 getFlavourRole :: FlatM CtFlavourRole
557 getFlavourRole
558 = do { flavour <- getFlavour
559 ; eq_rel <- getEqRel
560 ; return (flavour, eq_rel) }
561
562 getMode :: FlatM FlattenMode
563 getMode = getFlatEnvField fe_mode
564
565 getLoc :: FlatM CtLoc
566 getLoc = getFlatEnvField fe_loc
567
568 checkStackDepth :: Type -> FlatM ()
569 checkStackDepth ty
570 = do { loc <- getLoc
571 ; liftTcS $ checkReductionDepth loc ty }
572
573 -- | Change the 'EqRel' in a 'FlatM'.
574 setEqRel :: EqRel -> FlatM a -> FlatM a
575 setEqRel new_eq_rel thing_inside
576 = FlatM $ \env ->
577 if new_eq_rel == fe_eq_rel env
578 then runFlatM thing_inside env
579 else runFlatM thing_inside (env { fe_eq_rel = new_eq_rel })
580
581 -- | Change the 'FlattenMode' in a 'FlattenEnv'.
582 setMode :: FlattenMode -> FlatM a -> FlatM a
583 setMode new_mode thing_inside
584 = FlatM $ \env ->
585 if new_mode `eqFlattenMode` fe_mode env
586 then runFlatM thing_inside env
587 else runFlatM thing_inside (env { fe_mode = new_mode })
588
589 -- | Make sure that flattening actually produces a coercion (in other
590 -- words, make sure our flavour is not Derived)
591 -- Note [No derived kind equalities]
592 noBogusCoercions :: FlatM a -> FlatM a
593 noBogusCoercions thing_inside
594 = FlatM $ \env ->
595 -- No new thunk is made if the flavour hasn't changed (note the bang).
596 let !env' = case fe_flavour env of
597 Derived -> env { fe_flavour = Wanted WDeriv }
598 _ -> env
599 in
600 runFlatM thing_inside env'
601
602 bumpDepth :: FlatM a -> FlatM a
603 bumpDepth (FlatM thing_inside)
604 = FlatM $ \env -> do
605 -- bumpDepth can be called a lot during flattening so we force the
606 -- new env to avoid accumulating thunks.
607 { let !env' = env { fe_loc = bumpCtLocDepth (fe_loc env) }
608 ; thing_inside env' }
609
610 {-
611 Note [The flattening work list]
612 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
613 The "flattening work list", held in the fe_work field of FlattenEnv,
614 is a list of CFunEqCans generated during flattening. The key idea
615 is this. Consider flattening (Eq (F (G Int) (H Bool)):
616 * The flattener recursively calls itself on sub-terms before building
617 the main term, so it will encounter the terms in order
618 G Int
619 H Bool
620 F (G Int) (H Bool)
621 flattening to sub-goals
622 w1: G Int ~ fuv0
623 w2: H Bool ~ fuv1
624 w3: F fuv0 fuv1 ~ fuv2
625
626 * Processing w3 first is BAD, because we can't reduce i t,so it'll
627 get put into the inert set, and later kicked out when w1, w2 are
628 solved. In Trac #9872 this led to inert sets containing hundreds
629 of suspended calls.
630
631 * So we want to process w1, w2 first.
632
633 * So you might think that we should just use a FIFO deque for the work-list,
634 so that putting adding goals in order w1,w2,w3 would mean we processed
635 w1 first.
636
637 * BUT suppose we have 'type instance G Int = H Char'. Then processing
638 w1 leads to a new goal
639 w4: H Char ~ fuv0
640 We do NOT want to put that on the far end of a deque! Instead we want
641 to put it at the *front* of the work-list so that we continue to work
642 on it.
643
644 So the work-list structure is this:
645
646 * The wl_funeqs (in TcS) is a LIFO stack; we push new goals (such as w4) on
647 top (extendWorkListFunEq), and take new work from the top
648 (selectWorkItem).
649
650 * When flattening, emitFlatWork pushes new flattening goals (like
651 w1,w2,w3) onto the flattening work list, fe_work, another
652 push-down stack.
653
654 * When we finish flattening, we *reverse* the fe_work stack
655 onto the wl_funeqs stack (which brings w1 to the top).
656
657 The function runFlatten initialises the fe_work stack, and reverses
658 it onto wl_fun_eqs at the end.
659
660 Note [Flattener EqRels]
661 ~~~~~~~~~~~~~~~~~~~~~~~
662 When flattening, we need to know which equality relation -- nominal
663 or representation -- we should be respecting. The only difference is
664 that we rewrite variables by representational equalities when fe_eq_rel
665 is ReprEq, and that we unwrap newtypes when flattening w.r.t.
666 representational equality.
667
668 Note [Flattener CtLoc]
669 ~~~~~~~~~~~~~~~~~~~~~~
670 The flattener does eager type-family reduction.
671 Type families might loop, and we
672 don't want GHC to do so. A natural solution is to have a bounded depth
673 to these processes. A central difficulty is that such a solution isn't
674 quite compositional. For example, say it takes F Int 10 steps to get to Bool.
675 How many steps does it take to get from F Int -> F Int to Bool -> Bool?
676 10? 20? What about getting from Const Char (F Int) to Char? 11? 1? Hard to
677 know and hard to track. So, we punt, essentially. We store a CtLoc in
678 the FlattenEnv and just update the environment when recurring. In the
679 TyConApp case, where there may be multiple type families to flatten,
680 we just copy the current CtLoc into each branch. If any branch hits the
681 stack limit, then the whole thing fails.
682
683 A consequence of this is that setting the stack limits appropriately
684 will be essentially impossible. So, the official recommendation if a
685 stack limit is hit is to disable the check entirely. Otherwise, there
686 will be baffling, unpredictable errors.
687
688 Note [Lazy flattening]
689 ~~~~~~~~~~~~~~~~~~~~~~
690 The idea of FM_Avoid mode is to flatten less aggressively. If we have
691 a ~ [F Int]
692 there seems to be no great merit in lifting out (F Int). But if it was
693 a ~ [G a Int]
694 then we *do* want to lift it out, in case (G a Int) reduces to Bool, say,
695 which gets rid of the occurs-check problem. (For the flat_top Bool, see
696 comments above and at call sites.)
697
698 HOWEVER, the lazy flattening actually seems to make type inference go
699 *slower*, not faster. perf/compiler/T3064 is a case in point; it gets
700 *dramatically* worse with FM_Avoid. I think it may be because
701 floating the types out means we normalise them, and that often makes
702 them smaller and perhaps allows more re-use of previously solved
703 goals. But to be honest I'm not absolutely certain, so I am leaving
704 FM_Avoid in the code base. What I'm removing is the unique place
705 where it is *used*, namely in TcCanonical.canEqTyVar.
706
707 See also Note [Conservative unification check] in TcUnify, which gives
708 other examples where lazy flattening caused problems.
709
710 Bottom line: FM_Avoid is unused for now (Nov 14).
711 Note: T5321Fun got faster when I disabled FM_Avoid
712 T5837 did too, but it's pathalogical anyway
713
714 Note [Phantoms in the flattener]
715 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
716 Suppose we have
717
718 data Proxy p = Proxy
719
720 and we're flattening (Proxy ty) w.r.t. ReprEq. Then, we know that `ty`
721 is really irrelevant -- it will be ignored when solving for representational
722 equality later on. So, we omit flattening `ty` entirely. This may
723 violate the expectation of "xi"s for a bit, but the canonicaliser will
724 soon throw out the phantoms when decomposing a TyConApp. (Or, the
725 canonicaliser will emit an insoluble, in which case the unflattened version
726 yields a better error message anyway.)
727
728 Note [No derived kind equalities]
729 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
730 A kind-level coercion can appear in types, via mkCastTy. So, whenever
731 we are generating a coercion in a dependent context (in other words,
732 in a kind) we need to make sure that our flavour is never Derived
733 (as Derived constraints have no evidence). The noBogusCoercions function
734 changes the flavour from Derived just for this purpose.
735
736 -}
737
738 {- *********************************************************************
739 * *
740 * Externally callable flattening functions *
741 * *
742 * They are all wrapped in runFlatten, so their *
743 * flattening work gets put into the work list *
744 * *
745 ********************************************************************* -}
746
747 flatten :: FlattenMode -> CtEvidence -> TcType
748 -> TcS (Xi, TcCoercion)
749 flatten mode ev ty
750 = do { traceTcS "flatten {" (ppr mode <+> ppr ty)
751 ; (ty', co) <- runFlattenCtEv mode ev (flatten_one ty)
752 ; traceTcS "flatten }" (ppr ty')
753 ; return (ty', co) }
754
755 -- specialized to flattening kinds: never Derived, always Nominal
756 -- See Note [No derived kind equalities]
757 flattenKind :: CtLoc -> CtFlavour -> TcType -> TcS (Xi, TcCoercionN)
758 flattenKind loc flav ty
759 = do { traceTcS "flattenKind {" (ppr flav <+> ppr ty)
760 ; let flav' = case flav of
761 Derived -> Wanted WDeriv -- the WDeriv/WOnly choice matters not
762 _ -> flav
763 ; (ty', co) <- runFlatten FM_FlattenAll loc flav' NomEq (flatten_one ty)
764 ; traceTcS "flattenKind }" (ppr ty' $$ ppr co) -- co is never a panic
765 ; return (ty', co) }
766
767 flattenArgsNom :: CtEvidence -> TyCon -> [TcType] -> TcS ([Xi], [TcCoercion], TcCoercionN)
768 -- Externally-callable, hence runFlatten
769 -- Flatten a vector of types all at once; in fact they are
770 -- always the arguments of type family or class, so
771 -- ctEvFlavour ev = Nominal
772 -- and we want to flatten all at nominal role
773 -- The kind passed in is the kind of the type family or class, call it T
774 -- The last coercion returned has type (typeKind(T xis) ~N typeKind(T tys))
775 flattenArgsNom ev tc tys
776 = do { traceTcS "flatten_args {" (vcat (map ppr tys))
777 ; (tys', cos, kind_co)
778 <- runFlattenCtEv FM_FlattenAll ev (flatten_args_tc tc (repeat Nominal) tys)
779 ; traceTcS "flatten }" (vcat (map ppr tys'))
780 ; return (tys', cos, kind_co) }
781
782
783 {- *********************************************************************
784 * *
785 * The main flattening functions
786 * *
787 ********************************************************************* -}
788
789 {- Note [Flattening]
790 ~~~~~~~~~~~~~~~~~~~~
791 flatten ty ==> (xi, co)
792 where
793 xi has no type functions, unless they appear under ForAlls
794 has no skolems that are mapped in the inert set
795 has no filled-in metavariables
796 co :: xi ~ ty
797
798 Key invariants:
799 (F0) co :: xi ~ zonk(ty)
800 (F1) typeKind(xi) succeeds and returns a fully zonked kind
801 (F2) typeKind(xi) `eqType` zonk(typeKind(ty))
802
803 Note that it is flatten's job to flatten *every type function it sees*.
804 flatten is only called on *arguments* to type functions, by canEqGiven.
805
806 Flattening also:
807 * zonks, removing any metavariables, and
808 * applies the substitution embodied in the inert set
809
810 Because flattening zonks and the returned coercion ("co" above) is also
811 zonked, it's possible that (co :: xi ~ ty) isn't quite true. So, instead,
812 we can rely on this fact:
813
814 (F1) typeKind(xi) succeeds and returns a fully zonked kind
815
816 Note that the left-hand type of co is *always* precisely xi. The right-hand
817 type may or may not be ty, however: if ty has unzonked filled-in metavariables,
818 then the right-hand type of co will be the zonked version of ty.
819 It is for this reason that we
820 occasionally have to explicitly zonk, when (co :: xi ~ ty) is important
821 even before we zonk the whole program. For example, see the FTRNotFollowed
822 case in flattenTyVar.
823
824 Why have these invariants on flattening? Because we sometimes use typeKind
825 during canonicalisation, and we want this kind to be zonked (e.g., see
826 TcCanonical.canEqTyVar).
827
828 Flattening is always homogeneous. That is, the kind of the result of flattening is
829 always the same as the kind of the input, modulo zonking. More formally:
830
831 (F2) typeKind(xi) `eqType` zonk(typeKind(ty))
832
833 This invariant means that the kind of a flattened type might not itself be flat.
834
835 Recall that in comments we use alpha[flat = ty] to represent a
836 flattening skolem variable alpha which has been generated to stand in
837 for ty.
838
839 ----- Example of flattening a constraint: ------
840 flatten (List (F (G Int))) ==> (xi, cc)
841 where
842 xi = List alpha
843 cc = { G Int ~ beta[flat = G Int],
844 F beta ~ alpha[flat = F beta] }
845 Here
846 * alpha and beta are 'flattening skolem variables'.
847 * All the constraints in cc are 'given', and all their coercion terms
848 are the identity.
849
850 NB: Flattening Skolems only occur in canonical constraints, which
851 are never zonked, so we don't need to worry about zonking doing
852 accidental unflattening.
853
854 Note that we prefer to leave type synonyms unexpanded when possible,
855 so when the flattener encounters one, it first asks whether its
856 transitive expansion contains any type function applications. If so,
857 it expands the synonym and proceeds; if not, it simply returns the
858 unexpanded synonym.
859
860 Note [flatten_args performance]
861 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
862 In programs with lots of type-level evaluation, flatten_args becomes
863 part of a tight loop. For example, see test perf/compiler/T9872a, which
864 calls flatten_args a whopping 7,106,808 times. It is thus important
865 that flatten_args be efficient.
866
867 Performance testing showed that the current implementation is indeed
868 efficient. It's critically important that zipWithAndUnzipM be
869 specialized to TcS, and it's also quite helpful to actually `inline`
870 it. On test T9872a, here are the allocation stats (Dec 16, 2014):
871
872 * Unspecialized, uninlined: 8,472,613,440 bytes allocated in the heap
873 * Specialized, uninlined: 6,639,253,488 bytes allocated in the heap
874 * Specialized, inlined: 6,281,539,792 bytes allocated in the heap
875
876 To improve performance even further, flatten_args_nom is split off
877 from flatten_args, as nominal equality is the common case. This would
878 be natural to write using mapAndUnzipM, but even inlined, that function
879 is not as performant as a hand-written loop.
880
881 * mapAndUnzipM, inlined: 7,463,047,432 bytes allocated in the heap
882 * hand-written recursion: 5,848,602,848 bytes allocated in the heap
883
884 If you make any change here, pay close attention to the T9872{a,b,c} tests
885 and T5321Fun.
886
887 If we need to make this yet more performant, a possible way forward is to
888 duplicate the flattener code for the nominal case, and make that case
889 faster. This doesn't seem quite worth it, yet.
890
891 Note [flatten_args]
892 ~~~~~~~~~~~~~~~~~~~
893 Invariant (F2) of Note [Flattening] says that flattening is homogeneous.
894 This causes some trouble when flattening a function applied to a telescope
895 of arguments, perhaps with dependency. For example, suppose
896
897 type family F :: forall (j :: Type) (k :: Type). Maybe j -> Either j k -> Bool -> [k]
898
899 and we wish to flatten the args of (with kind applications explicit)
900
901 F a b (Just a c) (Right a b d) False
902
903 where all variables are skolems and
904
905 a :: Type
906 b :: Type
907 c :: a
908 d :: k
909
910 [G] aco :: a ~ fa
911 [G] bco :: b ~ fb
912 [G] cco :: c ~ fc
913 [G] dco :: d ~ fd
914
915 We process the args in left-to-right order. The first two args are easy:
916
917 (sym aco, fa) <- flatten a
918 (sym bco, fb) <- flatten b
919
920 But now consider flattening (Just a c :: Maybe a). Regardless of how this
921 flattens, the result will have kind (Maybe a), due to (F2). And yet, when
922 we build the application (F fa fb ...), we need this argument to have kind
923 (Maybe fa), not (Maybe a). Suppose (Just a c) flattens to f3 (the "3" is
924 because it's the 3rd argument). We know f3 :: Maybe a. In order to get f3
925 to have kind Maybe fa, we must cast it. The coercion to use is determined
926 by the kind of F: we see in F's kind that the third argument has kind
927 Maybe j. Critically, we also know that the argument corresponding to j
928 (in our example, a) flattened with a coercion (sym aco). We can thus
929 know the coercion needed for the 3rd argument is (Maybe aco).
930
931 More generally, we must use the Lifting Lemma, as implemented in
932 Coercion.liftCoSubst. As we work left-to-right, any variable that is a
933 dependent parameter (j and k, in our example) gets mapped in a lifting context
934 to the coercion that is output from flattening the corresponding argument (aco
935 and bco, in our example). Then, after flattening later arguments, we lift the
936 kind of these arguments in the lifting context that we've be building up.
937 This coercion is then used to keep the result of flattening well-kinded.
938
939 Working through our example, this is what happens:
940
941 1. Flatten a, getting (sym aco, fa). Extend the (empty) LC with [j |-> sym aco]
942
943 2. Flatten b, getting (sym bco, fb). Extend the LC with [k |-> sym bco].
944
945 3. Flatten (Just a c), getting (co3, f3). Lifting the kind (Maybe j) with our LC
946 yields lco3 :: Maybe fa ~ Maybe a. Use (f3 |> sym lco3) as the argument to
947 F.
948
949 4. Flatten (Right a b d), getting (co4, f4). Lifting the kind (Either j k) with our LC
950 yields lco4 :: Either fa fb ~ Either a b. Use (f4 |> sym lco4) as the 4th
951 argument to F.
952
953 5. Flatten False, getting (<False>, False). We lift Bool with our LC, getting <Bool>;
954 casting has no effect. (Indeed we lifted and casted with no effect for steps 1 and 2, as well.)
955
956 We're now almost done, but the new application (F fa fb (f3 |> sym lco3) (f4
957 |> sym lco4) False) has the wrong kind. Its kind is [fb], instead of the original [b].
958 So we must use our LC one last time to lift the result kind [k], getting res_co :: [fb] ~ [b], and
959 we cast our result.
960
961 Accordingly, the final result is
962
963 F fa fb (Just fa (fc |> aco) |> Maybe (sym aco) |> sym (Maybe (sym aco)))
964 (Right fa fb (fd |> bco) |> Either (sym aco) (sym bco) |> sym (Either (sym aco) (sym bco)))
965 False
966 |> [sym bco]
967
968 The res_co is returned as the third return value from flatten_args.
969
970 Note [Last case in flatten_args]
971 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
972 In writing flatten_args's `go`, we know here that tys cannot be empty,
973 because that case is first. We've run out of
974 binders. But perhaps inner_ki is a tyvar that has been instantiated with a
975 Π-type. I believe this, today, this Π-type must be an ordinary function.
976 But tomorrow, we may allow, say, visible type application in types. And
977 it's best to be prepared.
978
979 Here is an example.
980
981 a :: forall (k :: Type). k -> k
982 type family Star
983 Proxy :: forall j. j -> Type
984 axStar :: Star ~ Type
985 type family NoWay :: Bool
986 axNoWay :: NoWay ~ False
987 bo :: Type
988 [G] bc :: bo ~ Bool (in inert set)
989
990 co :: (forall j. j -> Type) ~ (forall (j :: Star). (j |> axStar) -> Star)
991 co = forall (j :: sym axStar). (<j> -> sym axStar)
992
993 We are flattening:
994 a (forall (j :: Star). (j |> axStar) -> Star) -- 1
995 (Proxy |> co) -- 2
996 (bo |> sym axStar) -- 3
997 (NoWay |> sym bc) -- 4
998 :: Star
999
1000 Flattening (1) gives us
1001 (forall j. j -> Type)
1002 co1 :: (forall j. j -> Type) ~ (forall (j :: Star). (j |> axStar) -> Star)
1003 We also extend the lifting context with
1004 k |-> co1
1005
1006 Flattening (2) gives us
1007 (Proxy |> co)
1008 But building (a (forall j. j -> Type) Proxy) would be ill-kinded. So we cast the
1009 result of flattening by sym co1, to get
1010 (Proxy |> co |> sym co1)
1011 Happily, co and co1 cancel each other out, leaving us with
1012 Proxy
1013 co2 :: Proxy ~ (Proxy |> co)
1014
1015 Now we need to flatten (3). After flattening, should we tack on a homogenizing
1016 coercion? The way we normally tell is to look at the kind of `a`. (See Note
1017 [flatten_args].) Here, the remainder of the kind of `a` that we're left with
1018 after processing two arguments is just `k`.
1019
1020 The way forward is look up k in the lifting context, getting co1. If we're at
1021 all well-typed, co1 will be a coercion between Π-types, with enough binders on
1022 both sides to accommodate any remaining arguments in flatten_args. So, let's
1023 decompose co1 with decomposePiCos. This decomposition needs arguments to use
1024 to instantiate any kind parameters. Look at the type of co1. If we just
1025 decomposed it, we would end up with coercions whose types include j, which is
1026 out of scope here. Accordingly, decomposePiCos takes a list of types whose
1027 kinds are the *right-hand* types in the decomposed coercion. (See comments on
1028 decomposePiCos, which also reverses the orientation of the coercions.)
1029 The right-hand types are the unflattened ones -- conveniently what we have to
1030 hand.
1031
1032 So we now call
1033
1034 decomposePiCos (forall j. j -> Type)
1035 [bo |> sym axStar, NoWay |> sym bc]
1036 co1
1037
1038 to get
1039
1040 co3 :: Star ~ Type
1041 co4 :: (j |> axStar) ~ (j |> co3), substituted to
1042 (bo |> sym axStar |> axStar) ~ (bo |> sym axStar |> co3)
1043 == bo ~ bo
1044 res_co :: Type ~ Star -- this one's not reversed in decomposePiCos
1045
1046 We then use these casts on (3) and (4) to get
1047
1048 (bo |> sym axStar |> co3 :: Type) -- (C3)
1049 (NoWay |> sym bc |> co4 :: bo) -- (C4)
1050
1051 We can simplify to
1052
1053 bo -- (C3)
1054 (NoWay |> sym bc :: bo) -- (C4)
1055
1056 Now, to flatten (C3) and (C4), we still need to keep track of dependency.
1057 We know the type of the function applied to (C3) and (C4) must be
1058 (forall j. j -> Type), the flattened type
1059 associated with k (the final type in the kind of `a`.) (We discard the lifting
1060 context up to this point; as we've already substituted k, the domain of the
1061 lifting context we used for (1) and (2), away.)
1062
1063 We now flatten (C3) to get
1064 Bool -- F3
1065 co5 :: Bool ~ bo
1066 and flatten (C4) to get
1067 (False |> sym bc)
1068 Like we did when flattening (2), we need to cast the result of flattening
1069 (4), by lifting the type j with a lifting context containing
1070 [j |-> co5]. This lifting yields co5.
1071 We cast the result of flattening (C4) by sym co5 (this is the normal
1072 cast-after-flattening; see Note [flatten_args]):
1073 (False |> sym bc |> sym co5)
1074 which is really just
1075 False -- F4
1076 co4 :: False ~ (NoWay |> sym bc)
1077
1078 Now, we build up the result
1079
1080 a (forall j. j -> Type)
1081 Proxy
1082 Bool
1083 False
1084 |> res_co
1085
1086 Let's check whether this is well-typed. We know
1087
1088 a :: forall (k :: Type). k -> k
1089
1090 a (forall j. j -> Type) :: (forall j. j -> Type) -> forall j. j -> Type
1091
1092 a (forall j. j -> Type)
1093 Proxy
1094 :: forall j. j -> Type
1095
1096 a (forall j. j -> Type)
1097 Proxy
1098 Bool
1099 :: Bool -> Type
1100
1101 a (forall j. j -> Type)
1102 Proxy
1103 Bool
1104 False
1105 :: Type
1106
1107 a (forall j. j -> Type)
1108 Proxy
1109 Bool
1110 False
1111 |> res_co
1112 :: Star
1113
1114 as desired. (Why do we want Star? Because we started with something of kind Star!)
1115
1116 Whew.
1117
1118 Note [flatten_exact_fam_app_fully performance]
1119 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1120
1121 The refactor of GRefl seems to cause performance trouble for T9872x: the allocation of flatten_exact_fam_app_fully_performance increased. See note [Generalized reflexive coercion] in TyCoRep for more information about GRefl and Trac #15192 for the current state.
1122
1123 The explicit pattern match in homogenise_result helps with T9872a, b, c.
1124
1125 Still, it increases the expected allocation of T9872d by ~2%.
1126
1127 TODO: a step-by-step replay of the refactor to analyze the performance.
1128
1129 -}
1130
1131 {-# INLINE flatten_args_tc #-}
1132 flatten_args_tc :: TyCon
1133 -> [Role]
1134 -> [Type]
1135 -> FlatM ([Xi], [Coercion], CoercionN)
1136 flatten_args_tc tc = flatten_args all_bndrs any_named_bndrs inner_ki emptyVarSet
1137 -- NB: TyCon kinds are always closed
1138 where
1139 (bndrs, named)
1140 = ty_con_binders_ty_binders' (tyConBinders tc)
1141 -- it's possible that the result kind has arrows (for, e.g., a type family)
1142 -- so we must split it
1143 (inner_bndrs, inner_ki, inner_named) = split_pi_tys' (tyConResKind tc)
1144 !all_bndrs = bndrs `chkAppend` inner_bndrs
1145 !any_named_bndrs = named || inner_named
1146 -- NB: Those bangs there drop allocations in T9872{a,c,d} by 8%.
1147
1148 {-# INLINE flatten_args #-}
1149 flatten_args :: [TyBinder] -> Bool -- Binders, and True iff any of them are
1150 -- named.
1151 -> Kind -> TcTyCoVarSet -- function kind; kind's free vars
1152 -> [Role] -> [Type] -- these are in 1-to-1 correspondence
1153 -> FlatM ([Xi], [Coercion], CoercionN)
1154 -- Coercions :: Xi ~ Type, at roles given
1155 -- Third coercion :: typeKind(fun xis) ~N typeKind(fun tys)
1156 -- That is, the third coercion relates the kind of some function (whose kind is
1157 -- passed as the first parameter) instantiated at xis to the kind of that
1158 -- function instantiated at the tys. This is useful in keeping flattening
1159 -- homoegeneous. The list of roles must be at least as long as the list of
1160 -- types.
1161 -- See Note [flatten_args]
1162 flatten_args orig_binders
1163 any_named_bndrs
1164 orig_inner_ki
1165 orig_fvs
1166 orig_roles
1167 orig_tys
1168 = if any_named_bndrs
1169 then flatten_args_slow orig_binders
1170 orig_inner_ki
1171 orig_fvs
1172 orig_roles
1173 orig_tys
1174 else flatten_args_fast orig_binders orig_inner_ki orig_roles orig_tys
1175
1176 {-# INLINE flatten_args_fast #-}
1177 -- | fast path flatten_args, in which none of the binders are named and
1178 -- therefore we can avoid tracking a lifting context.
1179 -- There are many bang patterns in here. It's been observed that they
1180 -- greatly improve performance of an optimized build.
1181 -- The T9872 test cases are good witnesses of this fact.
1182 flatten_args_fast :: [TyBinder]
1183 -> Kind
1184 -> [Role]
1185 -> [Type]
1186 -> FlatM ([Xi], [Coercion], CoercionN)
1187 flatten_args_fast orig_binders orig_inner_ki orig_roles orig_tys
1188 = fmap finish (iterate orig_tys orig_roles orig_binders)
1189 where
1190
1191 iterate :: [Type]
1192 -> [Role]
1193 -> [TyBinder]
1194 -> FlatM ([Xi], [Coercion], [TyBinder])
1195 iterate (ty:tys) (role:roles) (_:binders) = do
1196 (xi, co) <- go role ty
1197 (xis, cos, binders) <- iterate tys roles binders
1198 pure (xi : xis, co : cos, binders)
1199 iterate [] _ binders = pure ([], [], binders)
1200 iterate _ _ _ = pprPanic
1201 "flatten_args wandered into deeper water than usual" (vcat [])
1202 -- This debug information is commented out because leaving it in
1203 -- causes a ~2% increase in allocations in T9872{a,c,d}.
1204 {-
1205 (vcat [ppr orig_binders,
1206 ppr orig_inner_ki,
1207 ppr (take 10 orig_roles), -- often infinite!
1208 ppr orig_tys])
1209 -}
1210
1211 {-# INLINE go #-}
1212 go :: Role
1213 -> Type
1214 -> FlatM (Xi, Coercion)
1215 go role ty
1216 = case role of
1217 -- In the slow path we bind the Xi and Coercion from the recursive
1218 -- call and then use it such
1219 --
1220 -- let kind_co = mkTcSymCo $ mkReflCo Nominal (tyBinderType binder)
1221 -- casted_xi = xi `mkCastTy` kind_co
1222 -- casted_co = xi |> kind_co ~r xi ; co
1223 --
1224 -- but this isn't necessary:
1225 -- mkTcSymCo (Refl a b) = Refl a b,
1226 -- mkCastTy x (Refl _ _) = x
1227 -- mkTcGReflLeftCo _ ty (Refl _ _) `mkTransCo` co = co
1228 --
1229 -- Also, no need to check isAnonTyBinder or isNamedTyBinder, since
1230 -- we've already established that they're all anonymous.
1231 Nominal -> setEqRel NomEq $ flatten_one ty
1232 Representational -> setEqRel ReprEq $ flatten_one ty
1233 Phantom -> -- See Note [Phantoms in the flattener]
1234 do { ty <- liftTcS $ zonkTcType ty
1235 ; return (ty, mkReflCo Phantom ty) }
1236
1237
1238 {-# INLINE finish #-}
1239 finish :: ([Xi], [Coercion], [TyBinder]) -> ([Xi], [Coercion], CoercionN)
1240 finish (xis, cos, binders) = (xis, cos, kind_co)
1241 where
1242 final_kind = mkPiTys binders orig_inner_ki
1243 kind_co = mkNomReflCo final_kind
1244
1245 {-# INLINE flatten_args_slow #-}
1246 -- | Slow path, compared to flatten_args_fast, because this one must track
1247 -- a lifting context.
1248 flatten_args_slow :: [TyBinder] -> Kind -> TcTyCoVarSet
1249 -> [Role] -> [Type]
1250 -> FlatM ([Xi], [Coercion], CoercionN)
1251 flatten_args_slow orig_binders orig_inner_ki orig_fvs orig_roles orig_tys
1252 = go [] [] orig_lc orig_binders orig_inner_ki orig_roles orig_tys
1253 where
1254 orig_lc = emptyLiftingContext $ mkInScopeSet $ orig_fvs
1255
1256 go :: [Xi] -- Xis accumulator, in reverse order
1257 -> [Coercion] -- Coercions accumulator, in reverse order
1258 -- These are in 1-to-1 correspondence
1259 -> LiftingContext -- mapping from tyvars to flattening coercions
1260 -> [TyBinder] -- Unsubsted binders of function's kind
1261 -> Kind -- Unsubsted result kind of function (not a Pi-type)
1262 -> [Role] -- Roles at which to flatten these ...
1263 -> [Type] -- ... unflattened types
1264 -> FlatM ([Xi], [Coercion], CoercionN)
1265 go acc_xis acc_cos lc binders inner_ki _ []
1266 = return (reverse acc_xis, reverse acc_cos, kind_co)
1267 where
1268 final_kind = mkPiTys binders inner_ki
1269 kind_co = liftCoSubst Nominal lc final_kind
1270
1271 go acc_xis acc_cos lc (binder:binders) inner_ki (role:roles) (ty:tys)
1272 = do { (xi, co) <- case role of
1273 Nominal -> setEqRel NomEq $
1274 if isNamedTyBinder binder
1275 then noBogusCoercions $ flatten_one ty
1276 else flatten_one ty
1277
1278 Representational -> ASSERT( isAnonTyBinder binder )
1279 setEqRel ReprEq $ flatten_one ty
1280
1281 Phantom -> -- See Note [Phantoms in the flattener]
1282 ASSERT( isAnonTyBinder binder )
1283 do { ty <- liftTcS $ zonkTcType ty
1284 ; return (ty, mkReflCo Phantom ty) }
1285
1286 -- By Note [Flattening] invariant (F2),
1287 -- typeKind(xi) = typeKind(ty). But, it's possible that xi will be
1288 -- used as an argument to a function whose kind is different, if
1289 -- earlier arguments have been flattened to new types. We thus
1290 -- need a coercion (kind_co :: old_kind ~ new_kind).
1291 --
1292 -- The bangs here have been observed to improve performance
1293 -- significantly in optimized builds.
1294 ; let kind_co = mkTcSymCo $
1295 liftCoSubst Nominal lc (tyBinderType binder)
1296 !casted_xi = xi `mkCastTy` kind_co
1297 casted_co = mkTcCoherenceLeftCo role xi kind_co co
1298
1299 -- now, extend the lifting context with the new binding
1300 !new_lc | Just tv <- tyBinderVar_maybe binder
1301 = extendLiftingContextAndInScope lc tv casted_co
1302 | otherwise
1303 = lc
1304
1305 ; go (casted_xi : acc_xis)
1306 (casted_co : acc_cos)
1307 new_lc
1308 binders
1309 inner_ki
1310 roles
1311 tys
1312 }
1313
1314 -- See Note [Last case in flatten_args]
1315 go acc_xis acc_cos lc [] inner_ki roles tys
1316 | Just k <- tcGetTyVar_maybe inner_ki
1317 , Just co1 <- liftCoSubstTyVar lc Nominal k
1318 = do { let co1_kind = coercionKind co1
1319 (arg_cos, res_co) = decomposePiCos co1 co1_kind tys
1320 casted_tys = ASSERT2( equalLength tys arg_cos
1321 , ppr tys $$ ppr arg_cos )
1322 zipWith mkCastTy tys arg_cos
1323 -- In general decomposePiCos can return fewer cos than tys,
1324 -- but not here; see "If we're at all well-typed..."
1325 -- in Note [Last case in flatten_args]. Hence the ASSERT.
1326 zapped_lc = zapLiftingContext lc
1327 Pair flattened_kind _ = co1_kind
1328 (bndrs, new_inner) = splitPiTys flattened_kind
1329
1330 ; (xis_out, cos_out, res_co_out)
1331 <- go acc_xis acc_cos zapped_lc bndrs new_inner roles casted_tys
1332 -- cos_out :: xis_out ~ casted_tys
1333 -- we need to return cos :: xis_out ~ tys
1334 ; let cos = zipWith3 mkTcGReflRightCo
1335 roles
1336 casted_tys
1337 (map mkTcSymCo arg_cos)
1338 cos' = zipWith mkTransCo cos_out cos
1339
1340 ; return (xis_out, cos', res_co_out `mkTcTransCo` res_co) }
1341
1342 go _ _ _ _ _ _ _ = pprPanic
1343 "flatten_args wandered into deeper water than usual" (vcat [])
1344 -- This debug information is commented out because leaving it in
1345 -- causes a ~2% increase in allocations in T9872d.
1346 -- That's independent of the analagous case in flatten_args_fast:
1347 -- each of these causes a 2% increase on its own, so commenting them
1348 -- both out gives a 4% decrease in T9872d.
1349 {-
1350
1351 (vcat [ppr orig_binders,
1352 ppr orig_inner_ki,
1353 ppr (take 10 orig_roles), -- often infinite!
1354 ppr orig_tys])
1355 -}
1356
1357 ------------------
1358 flatten_one :: TcType -> FlatM (Xi, Coercion)
1359 -- Flatten a type to get rid of type function applications, returning
1360 -- the new type-function-free type, and a collection of new equality
1361 -- constraints. See Note [Flattening] for more detail.
1362 --
1363 -- Postcondition: Coercion :: Xi ~ TcType
1364 -- The role on the result coercion matches the EqRel in the FlattenEnv
1365
1366 flatten_one xi@(LitTy {})
1367 = do { role <- getRole
1368 ; return (xi, mkReflCo role xi) }
1369
1370 flatten_one (TyVarTy tv)
1371 = flattenTyVar tv
1372
1373 flatten_one (AppTy ty1 ty2)
1374 = flatten_app_tys ty1 [ty2]
1375
1376 flatten_one (TyConApp tc tys)
1377 -- Expand type synonyms that mention type families
1378 -- on the RHS; see Note [Flattening synonyms]
1379 | Just (tenv, rhs, tys') <- expandSynTyCon_maybe tc tys
1380 , let expanded_ty = mkAppTys (substTy (mkTvSubstPrs tenv) rhs) tys'
1381 = do { mode <- getMode
1382 ; case mode of
1383 FM_FlattenAll | not (isFamFreeTyCon tc)
1384 -> flatten_one expanded_ty
1385 _ -> flatten_ty_con_app tc tys }
1386
1387 -- Otherwise, it's a type function application, and we have to
1388 -- flatten it away as well, and generate a new given equality constraint
1389 -- between the application and a newly generated flattening skolem variable.
1390 | isTypeFamilyTyCon tc
1391 = flatten_fam_app tc tys
1392
1393 -- For * a normal data type application
1394 -- * data family application
1395 -- we just recursively flatten the arguments.
1396 | otherwise
1397 -- FM_Avoid stuff commented out; see Note [Lazy flattening]
1398 -- , let fmode' = case fmode of -- Switch off the flat_top bit in FM_Avoid
1399 -- FE { fe_mode = FM_Avoid tv _ }
1400 -- -> fmode { fe_mode = FM_Avoid tv False }
1401 -- _ -> fmode
1402 = flatten_ty_con_app tc tys
1403
1404 flatten_one (FunTy ty1 ty2)
1405 = do { (xi1,co1) <- flatten_one ty1
1406 ; (xi2,co2) <- flatten_one ty2
1407 ; role <- getRole
1408 ; return (mkFunTy xi1 xi2, mkFunCo role co1 co2) }
1409
1410 flatten_one ty@(ForAllTy {})
1411 -- TODO (RAE): This is inadequate, as it doesn't flatten the kind of
1412 -- the bound tyvar. Doing so will require carrying around a substitution
1413 -- and the usual substTyVarBndr-like silliness. Argh.
1414
1415 -- We allow for-alls when, but only when, no type function
1416 -- applications inside the forall involve the bound type variables.
1417 = do { let (bndrs, rho) = tcSplitForAllTyVarBndrs ty
1418 tvs = binderVars bndrs
1419 ; (rho', co) <- setMode FM_SubstOnly $ flatten_one rho
1420 -- Substitute only under a forall
1421 -- See Note [Flattening under a forall]
1422 ; return (mkForAllTys bndrs rho', mkHomoForAllCos tvs co) }
1423
1424 flatten_one (CastTy ty g)
1425 = do { (xi, co) <- flatten_one ty
1426 ; (g', _) <- flatten_co g
1427
1428 ; role <- getRole
1429 ; return (mkCastTy xi g', castCoercionKind co role xi ty g' g) }
1430
1431 flatten_one (CoercionTy co) = first mkCoercionTy <$> flatten_co co
1432
1433 -- | "Flatten" a coercion. Really, just zonk it so we can uphold
1434 -- (F1) of Note [Flattening]
1435 flatten_co :: Coercion -> FlatM (Coercion, Coercion)
1436 flatten_co co
1437 = do { co <- liftTcS $ zonkCo co
1438 ; env_role <- getRole
1439 ; let co' = mkTcReflCo env_role (mkCoercionTy co)
1440 ; return (co, co') }
1441
1442 -- flatten (nested) AppTys
1443 flatten_app_tys :: Type -> [Type] -> FlatM (Xi, Coercion)
1444 -- commoning up nested applications allows us to look up the function's kind
1445 -- only once. Without commoning up like this, we would spend a quadratic amount
1446 -- of time looking up functions' types
1447 flatten_app_tys (AppTy ty1 ty2) tys = flatten_app_tys ty1 (ty2:tys)
1448 flatten_app_tys fun_ty arg_tys
1449 = do { (fun_xi, fun_co) <- flatten_one fun_ty
1450 ; flatten_app_ty_args fun_xi fun_co arg_tys }
1451
1452 -- Given a flattened function (with the coercion produced by flattening) and
1453 -- a bunch of unflattened arguments, flatten the arguments and apply.
1454 -- The coercion argument's role matches the role stored in the FlatM monad.
1455 --
1456 -- The bang patterns used here were observed to improve performance. If you
1457 -- wish to remove them, be sure to check for regeressions in allocations.
1458 flatten_app_ty_args :: Xi -> Coercion -> [Type] -> FlatM (Xi, Coercion)
1459 flatten_app_ty_args fun_xi fun_co []
1460 -- this will be a common case when called from flatten_fam_app, so shortcut
1461 = return (fun_xi, fun_co)
1462 flatten_app_ty_args fun_xi fun_co arg_tys
1463 = do { (xi, co, kind_co) <- case tcSplitTyConApp_maybe fun_xi of
1464 Just (tc, xis) ->
1465 do { let tc_roles = tyConRolesRepresentational tc
1466 arg_roles = dropList xis tc_roles
1467 ; (arg_xis, arg_cos, kind_co)
1468 <- flatten_vector (typeKind fun_xi) arg_roles arg_tys
1469
1470 -- Here, we have fun_co :: T xi1 xi2 ~ ty
1471 -- and we need to apply fun_co to the arg_cos. The problem is
1472 -- that using mkAppCo is wrong because that function expects
1473 -- its second coercion to be Nominal, and the arg_cos might
1474 -- not be. The solution is to use transitivity:
1475 -- T <xi1> <xi2> arg_cos ;; fun_co <arg_tys>
1476 ; eq_rel <- getEqRel
1477 ; let app_xi = mkTyConApp tc (xis ++ arg_xis)
1478 app_co = case eq_rel of
1479 NomEq -> mkAppCos fun_co arg_cos
1480 ReprEq -> mkTcTyConAppCo Representational tc
1481 (zipWith mkReflCo tc_roles xis ++ arg_cos)
1482 `mkTcTransCo`
1483 mkAppCos fun_co (map mkNomReflCo arg_tys)
1484 ; return (app_xi, app_co, kind_co) }
1485 Nothing ->
1486 do { (arg_xis, arg_cos, kind_co)
1487 <- flatten_vector (typeKind fun_xi) (repeat Nominal) arg_tys
1488 ; let arg_xi = mkAppTys fun_xi arg_xis
1489 arg_co = mkAppCos fun_co arg_cos
1490 ; return (arg_xi, arg_co, kind_co) }
1491
1492 ; role <- getRole
1493 ; return (homogenise_result xi co role kind_co) }
1494
1495 flatten_ty_con_app :: TyCon -> [TcType] -> FlatM (Xi, Coercion)
1496 flatten_ty_con_app tc tys
1497 = do { role <- getRole
1498 ; (xis, cos, kind_co) <- flatten_args_tc tc (tyConRolesX role tc) tys
1499 ; let tyconapp_xi = mkTyConApp tc xis
1500 tyconapp_co = mkTyConAppCo role tc cos
1501 ; return (homogenise_result tyconapp_xi tyconapp_co role kind_co) }
1502
1503 -- Make the result of flattening homogeneous (Note [Flattening] (F2))
1504 homogenise_result :: Xi -- a flattened type
1505 -> Coercion -- :: xi ~r original ty
1506 -> Role -- r
1507 -> CoercionN -- kind_co :: typeKind(xi) ~N typeKind(ty)
1508 -> (Xi, Coercion) -- (xi |> kind_co, (xi |> kind_co)
1509 -- ~r original ty)
1510 homogenise_result xi co r kind_co
1511 -- the explicit pattern match here improves the performance of T9872a, b, c by
1512 -- ~2%
1513 | isGReflCo kind_co = (xi `mkCastTy` kind_co, co)
1514 | otherwise = (xi `mkCastTy` kind_co
1515 , (mkSymCo $ GRefl r xi (MCo kind_co)) `mkTransCo` co)
1516 {-# INLINE homogenise_result #-}
1517
1518 -- Flatten a vector (list of arguments).
1519 flatten_vector :: Kind -- of the function being applied to these arguments
1520 -> [Role] -- If we're flatten w.r.t. ReprEq, what roles do the
1521 -- args have?
1522 -> [Type] -- the args to flatten
1523 -> FlatM ([Xi], [Coercion], CoercionN)
1524 flatten_vector ki roles tys
1525 = do { eq_rel <- getEqRel
1526 ; case eq_rel of
1527 NomEq -> flatten_args bndrs
1528 any_named_bndrs
1529 inner_ki
1530 fvs
1531 (repeat Nominal)
1532 tys
1533 ReprEq -> flatten_args bndrs
1534 any_named_bndrs
1535 inner_ki
1536 fvs
1537 roles
1538 tys
1539 }
1540 where
1541 (bndrs, inner_ki, any_named_bndrs) = split_pi_tys' ki
1542 fvs = tyCoVarsOfType ki
1543 {-# INLINE flatten_vector #-}
1544
1545 {-
1546 Note [Flattening synonyms]
1547 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1548 Not expanding synonyms aggressively improves error messages, and
1549 keeps types smaller. But we need to take care.
1550
1551 Suppose
1552 type T a = a -> a
1553 and we want to flatten the type (T (F a)). Then we can safely flatten
1554 the (F a) to a skolem, and return (T fsk). We don't need to expand the
1555 synonym. This works because TcTyConAppCo can deal with synonyms
1556 (unlike TyConAppCo), see Note [TcCoercions] in TcEvidence.
1557
1558 But (Trac #8979) for
1559 type T a = (F a, a) where F is a type function
1560 we must expand the synonym in (say) T Int, to expose the type function
1561 to the flattener.
1562
1563
1564 Note [Flattening under a forall]
1565 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1566 Under a forall, we
1567 (a) MUST apply the inert substitution
1568 (b) MUST NOT flatten type family applications
1569 Hence FMSubstOnly.
1570
1571 For (a) consider c ~ a, a ~ T (forall b. (b, [c]))
1572 If we don't apply the c~a substitution to the second constraint
1573 we won't see the occurs-check error.
1574
1575 For (b) consider (a ~ forall b. F a b), we don't want to flatten
1576 to (a ~ forall b.fsk, F a b ~ fsk)
1577 because now the 'b' has escaped its scope. We'd have to flatten to
1578 (a ~ forall b. fsk b, forall b. F a b ~ fsk b)
1579 and we have not begun to think about how to make that work!
1580
1581 ************************************************************************
1582 * *
1583 Flattening a type-family application
1584 * *
1585 ************************************************************************
1586 -}
1587
1588 flatten_fam_app :: TyCon -> [TcType] -> FlatM (Xi, Coercion)
1589 -- flatten_fam_app can be over-saturated
1590 -- flatten_exact_fam_app is exactly saturated
1591 -- flatten_exact_fam_app_fully lifts out the application to top level
1592 -- Postcondition: Coercion :: Xi ~ F tys
1593 flatten_fam_app tc tys -- Can be over-saturated
1594 = ASSERT2( tys `lengthAtLeast` tyConArity tc
1595 , ppr tc $$ ppr (tyConArity tc) $$ ppr tys)
1596
1597 do { mode <- getMode
1598 ; case mode of
1599 { FM_SubstOnly -> flatten_ty_con_app tc tys
1600 ; FM_FlattenAll ->
1601
1602 -- Type functions are saturated
1603 -- The type function might be *over* saturated
1604 -- in which case the remaining arguments should
1605 -- be dealt with by AppTys
1606 do { let (tys1, tys_rest) = splitAt (tyConArity tc) tys
1607 ; (xi1, co1) <- flatten_exact_fam_app_fully tc tys1
1608 -- co1 :: xi1 ~ F tys1
1609
1610 ; flatten_app_ty_args xi1 co1 tys_rest } } }
1611
1612 -- the [TcType] exactly saturate the TyCon
1613 -- See note [flatten_exact_fam_app_fully performance]
1614 flatten_exact_fam_app_fully :: TyCon -> [TcType] -> FlatM (Xi, Coercion)
1615 flatten_exact_fam_app_fully tc tys
1616 -- See Note [Reduce type family applications eagerly]
1617 -- the following typeKind should never be evaluated, as it's just used in
1618 -- casting, and casts by refl are dropped
1619 = do { let reduce_co = mkNomReflCo (typeKind (mkTyConApp tc tys))
1620 ; mOut <- try_to_reduce_nocache tc tys reduce_co id
1621 ; case mOut of
1622 Just out -> pure out
1623 Nothing -> do
1624 { -- First, flatten the arguments
1625 ; (xis, cos, kind_co)
1626 <- setEqRel NomEq $ -- just do this once, instead of for
1627 -- each arg
1628 flatten_args_tc tc (repeat Nominal) tys
1629 -- kind_co :: typeKind(F xis) ~N typeKind(F tys)
1630 ; eq_rel <- getEqRel
1631 ; cur_flav <- getFlavour
1632 ; let role = eqRelRole eq_rel
1633 ret_co = mkTyConAppCo role tc cos
1634 -- ret_co :: F xis ~ F tys; might be heterogeneous
1635
1636 -- Now, look in the cache
1637 ; mb_ct <- liftTcS $ lookupFlatCache tc xis
1638 ; case mb_ct of
1639 Just (co, rhs_ty, flav) -- co :: F xis ~ fsk
1640 -- flav is [G] or [WD]
1641 -- See Note [Type family equations] in TcSMonad
1642 | (NotSwapped, _) <- flav `funEqCanDischargeF` cur_flav
1643 -> -- Usable hit in the flat-cache
1644 do { traceFlat "flatten/flat-cache hit" $
1645 (ppr tc <+> ppr xis $$ ppr rhs_ty)
1646 ; (fsk_xi, fsk_co) <- flatten_one rhs_ty
1647 -- The fsk may already have been unified, so
1648 -- flatten it
1649 -- fsk_co :: fsk_xi ~ fsk
1650 ; let xi = fsk_xi `mkCastTy` kind_co
1651 co' = mkTcCoherenceLeftCo role fsk_xi kind_co fsk_co
1652 `mkTransCo`
1653 maybeSubCo eq_rel (mkSymCo co)
1654 `mkTransCo` ret_co
1655 ; return (xi, co')
1656 }
1657 -- :: fsk_xi ~ F xis
1658
1659 -- Try to reduce the family application right now
1660 -- See Note [Reduce type family applications eagerly]
1661 _ -> do { mOut <- try_to_reduce tc
1662 xis
1663 kind_co
1664 (`mkTransCo` ret_co)
1665 ; case mOut of
1666 Just out -> pure out
1667 Nothing -> do
1668 { loc <- getLoc
1669 ; (ev, co, fsk) <- liftTcS $
1670 newFlattenSkolem cur_flav loc tc xis
1671
1672 -- The new constraint (F xis ~ fsk) is not
1673 -- necessarily inert (e.g. the LHS may be a
1674 -- redex) so we must put it in the work list
1675 ; let ct = CFunEqCan { cc_ev = ev
1676 , cc_fun = tc
1677 , cc_tyargs = xis
1678 , cc_fsk = fsk }
1679 ; emitFlatWork ct
1680
1681 ; traceFlat "flatten/flat-cache miss" $
1682 (ppr tc <+> ppr xis $$ ppr fsk $$ ppr ev)
1683
1684 -- NB: fsk's kind is already flattened because
1685 -- the xis are flattened
1686 ; let fsk_ty = mkTyVarTy fsk
1687 xi = fsk_ty `mkCastTy` kind_co
1688 co' = mkTcCoherenceLeftCo role fsk_ty kind_co (maybeSubCo eq_rel (mkSymCo co))
1689 `mkTransCo` ret_co
1690 ; return (xi, co')
1691 }
1692 }
1693 }
1694 }
1695
1696 where
1697
1698 -- try_to_reduce and try_to_reduce_nocache (below) could be unified into
1699 -- a more general definition, but it was observed that separating them
1700 -- gives better performance (lower allocation numbers in T9872x).
1701
1702 try_to_reduce :: TyCon -- F, family tycon
1703 -> [Type] -- args, not necessarily flattened
1704 -> CoercionN -- kind_co :: typeKind(F args) ~N
1705 -- typeKind(F orig_args)
1706 -- where
1707 -- orig_args is what was passed to the outer
1708 -- function
1709 -> ( Coercion -- :: (xi |> kind_co) ~ F args
1710 -> Coercion ) -- what to return from outer function
1711 -> FlatM (Maybe (Xi, Coercion))
1712 try_to_reduce tc tys kind_co update_co
1713 = do { checkStackDepth (mkTyConApp tc tys)
1714 ; mb_match <- liftTcS $ matchFam tc tys
1715 ; case mb_match of
1716 -- NB: norm_co will always be homogeneous. All type families
1717 -- are homogeneous.
1718 Just (norm_co, norm_ty)
1719 -> do { traceFlat "Eager T.F. reduction success" $
1720 vcat [ ppr tc, ppr tys, ppr norm_ty
1721 , ppr norm_co <+> dcolon
1722 <+> ppr (coercionKind norm_co)
1723 ]
1724 ; (xi, final_co) <- bumpDepth $ flatten_one norm_ty
1725 ; eq_rel <- getEqRel
1726 ; let co = maybeSubCo eq_rel norm_co
1727 `mkTransCo` mkSymCo final_co
1728 ; flavour <- getFlavour
1729 -- NB: only extend cache with nominal equalities
1730 ; when (eq_rel == NomEq) $
1731 liftTcS $
1732 extendFlatCache tc tys ( co, xi, flavour )
1733 ; let role = eqRelRole eq_rel
1734 xi' = xi `mkCastTy` kind_co
1735 co' = update_co $
1736 mkTcCoherenceLeftCo role xi kind_co (mkSymCo co)
1737 ; return $ Just (xi', co') }
1738 Nothing -> pure Nothing }
1739
1740 try_to_reduce_nocache :: TyCon -- F, family tycon
1741 -> [Type] -- args, not necessarily flattened
1742 -> CoercionN -- kind_co :: typeKind(F args)
1743 -- ~N typeKind(F orig_args)
1744 -- where
1745 -- orig_args is what was passed to the
1746 -- outer function
1747 -> ( Coercion -- :: (xi |> kind_co) ~ F args
1748 -> Coercion ) -- what to return from outer
1749 -- function
1750 -> FlatM (Maybe (Xi, Coercion))
1751 try_to_reduce_nocache tc tys kind_co update_co
1752 = do { checkStackDepth (mkTyConApp tc tys)
1753 ; mb_match <- liftTcS $ matchFam tc tys
1754 ; case mb_match of
1755 -- NB: norm_co will always be homogeneous. All type families
1756 -- are homogeneous.
1757 Just (norm_co, norm_ty)
1758 -> do { (xi, final_co) <- bumpDepth $ flatten_one norm_ty
1759 ; eq_rel <- getEqRel
1760 ; let co = maybeSubCo eq_rel norm_co
1761 `mkTransCo` mkSymCo final_co
1762 role = eqRelRole eq_rel
1763 xi' = xi `mkCastTy` kind_co
1764 co' = update_co $
1765 mkTcCoherenceLeftCo role xi kind_co (mkSymCo co)
1766 ; return $ Just (xi', co') }
1767 Nothing -> pure Nothing }
1768
1769 {- Note [Reduce type family applications eagerly]
1770 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1771 If we come across a type-family application like (Append (Cons x Nil) t),
1772 then, rather than flattening to a skolem etc, we may as well just reduce
1773 it on the spot to (Cons x t). This saves a lot of intermediate steps.
1774 Examples that are helped are tests T9872, and T5321Fun.
1775
1776 Performance testing indicates that it's best to try this *twice*, once
1777 before flattening arguments and once after flattening arguments.
1778 Adding the extra reduction attempt before flattening arguments cut
1779 the allocation amounts for the T9872{a,b,c} tests by half.
1780
1781 An example of where the early reduction appears helpful:
1782
1783 type family Last x where
1784 Last '[x] = x
1785 Last (h ': t) = Last t
1786
1787 workitem: (x ~ Last '[1,2,3,4,5,6])
1788
1789 Flattening the argument never gets us anywhere, but trying to flatten
1790 it at every step is quadratic in the length of the list. Reducing more
1791 eagerly makes simplifying the right-hand type linear in its length.
1792
1793 Testing also indicated that the early reduction should *not* use the
1794 flat-cache, but that the later reduction *should*. (Although the
1795 effect was not large.) Hence the Bool argument to try_to_reduce. To
1796 me (SLPJ) this seems odd; I get that eager reduction usually succeeds;
1797 and if don't use the cache for eager reduction, we will miss most of
1798 the opportunities for using it at all. More exploration would be good
1799 here.
1800
1801 At the end, once we've got a flat rhs, we extend the flatten-cache to record
1802 the result. Doing so can save lots of work when the same redex shows up more
1803 than once. Note that we record the link from the redex all the way to its
1804 *final* value, not just the single step reduction. Interestingly, using the
1805 flat-cache for the first reduction resulted in an increase in allocations
1806 of about 3% for the four T9872x tests. However, using the flat-cache in
1807 the later reduction is a similar gain. I (Richard E) don't currently (Dec '14)
1808 have any knowledge as to *why* these facts are true.
1809
1810 ************************************************************************
1811 * *
1812 Flattening a type variable
1813 * *
1814 ********************************************************************* -}
1815
1816 -- | The result of flattening a tyvar "one step".
1817 data FlattenTvResult
1818 = FTRNotFollowed
1819 -- ^ The inert set doesn't make the tyvar equal to anything else
1820
1821 | FTRFollowed TcType Coercion
1822 -- ^ The tyvar flattens to a not-necessarily flat other type.
1823 -- co :: new type ~r old type, where the role is determined by
1824 -- the FlattenEnv
1825
1826 flattenTyVar :: TyVar -> FlatM (Xi, Coercion)
1827 flattenTyVar tv
1828 = do { mb_yes <- flatten_tyvar1 tv
1829 ; case mb_yes of
1830 FTRFollowed ty1 co1 -- Recur
1831 -> do { (ty2, co2) <- flatten_one ty1
1832 -- ; traceFlat "flattenTyVar2" (ppr tv $$ ppr ty2)
1833 ; return (ty2, co2 `mkTransCo` co1) }
1834
1835 FTRNotFollowed -- Done, but make sure the kind is zonked
1836 -- Note [Flattening] invariant (F1)
1837 -> do { tv' <- liftTcS $ updateTyVarKindM zonkTcType tv
1838 ; role <- getRole
1839 ; let ty' = mkTyVarTy tv'
1840 ; return (ty', mkTcReflCo role ty') } }
1841
1842 flatten_tyvar1 :: TcTyVar -> FlatM FlattenTvResult
1843 -- "Flattening" a type variable means to apply the substitution to it
1844 -- Specifically, look up the tyvar in
1845 -- * the internal MetaTyVar box
1846 -- * the inerts
1847 -- See also the documentation for FlattenTvResult
1848
1849 flatten_tyvar1 tv
1850 = do { mb_ty <- liftTcS $ isFilledMetaTyVar_maybe tv
1851 ; case mb_ty of
1852 Just ty -> do { traceFlat "Following filled tyvar"
1853 (ppr tv <+> equals <+> ppr ty)
1854 ; role <- getRole
1855 ; return (FTRFollowed ty (mkReflCo role ty)) } ;
1856 Nothing -> do { traceFlat "Unfilled tyvar" (ppr tv)
1857 ; fr <- getFlavourRole
1858 ; flatten_tyvar2 tv fr } }
1859
1860 flatten_tyvar2 :: TcTyVar -> CtFlavourRole -> FlatM FlattenTvResult
1861 -- The tyvar is not a filled-in meta-tyvar
1862 -- Try in the inert equalities
1863 -- See Definition [Applying a generalised substitution] in TcSMonad
1864 -- See Note [Stability of flattening] in TcSMonad
1865
1866 flatten_tyvar2 tv fr@(_, eq_rel)
1867 = do { ieqs <- liftTcS $ getInertEqs
1868 ; mode <- getMode
1869 ; case lookupDVarEnv ieqs tv of
1870 Just (ct:_) -- If the first doesn't work,
1871 -- the subsequent ones won't either
1872 | CTyEqCan { cc_ev = ctev, cc_tyvar = tv
1873 , cc_rhs = rhs_ty, cc_eq_rel = ct_eq_rel } <- ct
1874 , let ct_fr = (ctEvFlavour ctev, ct_eq_rel)
1875 , ct_fr `eqCanRewriteFR` fr -- This is THE key call of eqCanRewriteFR
1876 -> do { traceFlat "Following inert tyvar"
1877 (ppr mode <+>
1878 ppr tv <+>
1879 equals <+>
1880 ppr rhs_ty $$ ppr ctev)
1881 ; let rewrite_co1 = mkSymCo (ctEvCoercion ctev)
1882 rewrite_co = case (ct_eq_rel, eq_rel) of
1883 (ReprEq, _rel) -> ASSERT( _rel == ReprEq )
1884 -- if this ASSERT fails, then
1885 -- eqCanRewriteFR answered incorrectly
1886 rewrite_co1
1887 (NomEq, NomEq) -> rewrite_co1
1888 (NomEq, ReprEq) -> mkSubCo rewrite_co1
1889
1890 ; return (FTRFollowed rhs_ty rewrite_co) }
1891 -- NB: ct is Derived then fmode must be also, hence
1892 -- we are not going to touch the returned coercion
1893 -- so ctEvCoercion is fine.
1894
1895 _other -> return FTRNotFollowed }
1896
1897 {-
1898 Note [An alternative story for the inert substitution]
1899 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1900 (This entire note is just background, left here in case we ever want
1901 to return the previous state of affairs)
1902
1903 We used (GHC 7.8) to have this story for the inert substitution inert_eqs
1904
1905 * 'a' is not in fvs(ty)
1906 * They are *inert* in the weaker sense that there is no infinite chain of
1907 (i1 `eqCanRewrite` i2), (i2 `eqCanRewrite` i3), etc
1908
1909 This means that flattening must be recursive, but it does allow
1910 [G] a ~ [b]
1911 [G] b ~ Maybe c
1912
1913 This avoids "saturating" the Givens, which can save a modest amount of work.
1914 It is easy to implement, in TcInteract.kick_out, by only kicking out an inert
1915 only if (a) the work item can rewrite the inert AND
1916 (b) the inert cannot rewrite the work item
1917
1918 This is significantly harder to think about. It can save a LOT of work
1919 in occurs-check cases, but we don't care about them much. Trac #5837
1920 is an example; all the constraints here are Givens
1921
1922 [G] a ~ TF (a,Int)
1923 -->
1924 work TF (a,Int) ~ fsk
1925 inert fsk ~ a
1926
1927 --->
1928 work fsk ~ (TF a, TF Int)
1929 inert fsk ~ a
1930
1931 --->
1932 work a ~ (TF a, TF Int)
1933 inert fsk ~ a
1934
1935 ---> (attempting to flatten (TF a) so that it does not mention a
1936 work TF a ~ fsk2
1937 inert a ~ (fsk2, TF Int)
1938 inert fsk ~ (fsk2, TF Int)
1939
1940 ---> (substitute for a)
1941 work TF (fsk2, TF Int) ~ fsk2
1942 inert a ~ (fsk2, TF Int)
1943 inert fsk ~ (fsk2, TF Int)
1944
1945 ---> (top-level reduction, re-orient)
1946 work fsk2 ~ (TF fsk2, TF Int)
1947 inert a ~ (fsk2, TF Int)
1948 inert fsk ~ (fsk2, TF Int)
1949
1950 ---> (attempt to flatten (TF fsk2) to get rid of fsk2
1951 work TF fsk2 ~ fsk3
1952 work fsk2 ~ (fsk3, TF Int)
1953 inert a ~ (fsk2, TF Int)
1954 inert fsk ~ (fsk2, TF Int)
1955
1956 --->
1957 work TF fsk2 ~ fsk3
1958 inert fsk2 ~ (fsk3, TF Int)
1959 inert a ~ ((fsk3, TF Int), TF Int)
1960 inert fsk ~ ((fsk3, TF Int), TF Int)
1961
1962 Because the incoming given rewrites all the inert givens, we get more and
1963 more duplication in the inert set. But this really only happens in pathalogical
1964 casee, so we don't care.
1965
1966
1967 ************************************************************************
1968 * *
1969 Unflattening
1970 * *
1971 ************************************************************************
1972
1973 An unflattening example:
1974 [W] F a ~ alpha
1975 flattens to
1976 [W] F a ~ fmv (CFunEqCan)
1977 [W] fmv ~ alpha (CTyEqCan)
1978 We must solve both!
1979 -}
1980
1981 unflattenWanteds :: Cts -> Cts -> TcS Cts
1982 unflattenWanteds tv_eqs funeqs
1983 = do { tclvl <- getTcLevel
1984
1985 ; traceTcS "Unflattening" $ braces $
1986 vcat [ text "Funeqs =" <+> pprCts funeqs
1987 , text "Tv eqs =" <+> pprCts tv_eqs ]
1988
1989 -- Step 1: unflatten the CFunEqCans, except if that causes an occurs check
1990 -- Occurs check: consider [W] alpha ~ [F alpha]
1991 -- ==> (flatten) [W] F alpha ~ fmv, [W] alpha ~ [fmv]
1992 -- ==> (unify) [W] F [fmv] ~ fmv
1993 -- See Note [Unflatten using funeqs first]
1994 ; funeqs <- foldrBagM unflatten_funeq emptyCts funeqs
1995 ; traceTcS "Unflattening 1" $ braces (pprCts funeqs)
1996
1997 -- Step 2: unify the tv_eqs, if possible
1998 ; tv_eqs <- foldrBagM (unflatten_eq tclvl) emptyCts tv_eqs
1999 ; traceTcS "Unflattening 2" $ braces (pprCts tv_eqs)
2000
2001 -- Step 3: fill any remaining fmvs with fresh unification variables
2002 ; funeqs <- mapBagM finalise_funeq funeqs
2003 ; traceTcS "Unflattening 3" $ braces (pprCts funeqs)
2004
2005 -- Step 4: remove any tv_eqs that look like ty ~ ty
2006 ; tv_eqs <- foldrBagM finalise_eq emptyCts tv_eqs
2007
2008 ; let all_flat = tv_eqs `andCts` funeqs
2009 ; traceTcS "Unflattening done" $ braces (pprCts all_flat)
2010
2011 ; return all_flat }
2012 where
2013 ----------------
2014 unflatten_funeq :: Ct -> Cts -> TcS Cts
2015 unflatten_funeq ct@(CFunEqCan { cc_fun = tc, cc_tyargs = xis
2016 , cc_fsk = fmv, cc_ev = ev }) rest
2017 = do { -- fmv should be an un-filled flatten meta-tv;
2018 -- we now fix its final value by filling it, being careful
2019 -- to observe the occurs check. Zonking will eliminate it
2020 -- altogether in due course
2021 rhs' <- zonkTcType (mkTyConApp tc xis)
2022 ; case occCheckExpand [fmv] rhs' of
2023 Just rhs'' -- Normal case: fill the tyvar
2024 -> do { setReflEvidence ev NomEq rhs''
2025 ; unflattenFmv fmv rhs''
2026 ; return rest }
2027
2028 Nothing -> -- Occurs check
2029 return (ct `consCts` rest) }
2030
2031 unflatten_funeq other_ct _
2032 = pprPanic "unflatten_funeq" (ppr other_ct)
2033
2034 ----------------
2035 finalise_funeq :: Ct -> TcS Ct
2036 finalise_funeq (CFunEqCan { cc_fsk = fmv, cc_ev = ev })
2037 = do { demoteUnfilledFmv fmv
2038 ; return (mkNonCanonical ev) }
2039 finalise_funeq ct = pprPanic "finalise_funeq" (ppr ct)
2040
2041 ----------------
2042 unflatten_eq :: TcLevel -> Ct -> Cts -> TcS Cts
2043 unflatten_eq tclvl ct@(CTyEqCan { cc_ev = ev, cc_tyvar = tv
2044 , cc_rhs = rhs, cc_eq_rel = eq_rel }) rest
2045
2046 | NomEq <- eq_rel -- See Note [Do not unify representational equalities]
2047 -- in TcInteract
2048 , isFmvTyVar tv -- Previously these fmvs were untouchable,
2049 -- but now they are touchable
2050 -- NB: unlike unflattenFmv, filling a fmv here /does/
2051 -- bump the unification count; it is "improvement"
2052 -- Note [Unflattening can force the solver to iterate]
2053 = ASSERT2( tyVarKind tv `eqType` typeKind rhs, ppr ct )
2054 -- CTyEqCan invariant should ensure this is true
2055 do { is_filled <- isFilledMetaTyVar tv
2056 ; elim <- case is_filled of
2057 False -> do { traceTcS "unflatten_eq 2" (ppr ct)
2058 ; tryFill ev tv rhs }
2059 True -> do { traceTcS "unflatten_eq 3" (ppr ct)
2060 ; try_fill_rhs ev tclvl tv rhs }
2061 ; if elim
2062 then do { setReflEvidence ev eq_rel (mkTyVarTy tv)
2063 ; return rest }
2064 else return (ct `consCts` rest) }
2065
2066 | otherwise
2067 = return (ct `consCts` rest)
2068
2069 unflatten_eq _ ct _ = pprPanic "unflatten_irred" (ppr ct)
2070
2071 ----------------
2072 try_fill_rhs ev tclvl lhs_tv rhs
2073 -- Constraint is lhs_tv ~ rhs_tv,
2074 -- and lhs_tv is filled, so try RHS
2075 | Just (rhs_tv, co) <- getCastedTyVar_maybe rhs
2076 -- co :: kind(rhs_tv) ~ kind(lhs_tv)
2077 , isFmvTyVar rhs_tv || (isTouchableMetaTyVar tclvl rhs_tv
2078 && not (isSigTyVar rhs_tv))
2079 -- LHS is a filled fmv, and so is a type
2080 -- family application, which a SigTv should
2081 -- not unify with
2082 = do { is_filled <- isFilledMetaTyVar rhs_tv
2083 ; if is_filled then return False
2084 else tryFill ev rhs_tv
2085 (mkTyVarTy lhs_tv `mkCastTy` mkSymCo co) }
2086
2087 | otherwise
2088 = return False
2089
2090 ----------------
2091 finalise_eq :: Ct -> Cts -> TcS Cts
2092 finalise_eq (CTyEqCan { cc_ev = ev, cc_tyvar = tv
2093 , cc_rhs = rhs, cc_eq_rel = eq_rel }) rest
2094 | isFmvTyVar tv
2095 = do { ty1 <- zonkTcTyVar tv
2096 ; rhs' <- zonkTcType rhs
2097 ; if ty1 `tcEqType` rhs'
2098 then do { setReflEvidence ev eq_rel rhs'
2099 ; return rest }
2100 else return (mkNonCanonical ev `consCts` rest) }
2101
2102 | otherwise
2103 = return (mkNonCanonical ev `consCts` rest)
2104
2105 finalise_eq ct _ = pprPanic "finalise_irred" (ppr ct)
2106
2107 tryFill :: CtEvidence -> TcTyVar -> TcType -> TcS Bool
2108 -- (tryFill tv rhs ev) assumes 'tv' is an /un-filled/ MetaTv
2109 -- If tv does not appear in 'rhs', it set tv := rhs,
2110 -- binds the evidence (which should be a CtWanted) to Refl<rhs>
2111 -- and return True. Otherwise returns False
2112 tryFill ev tv rhs
2113 = ASSERT2( not (isGiven ev), ppr ev )
2114 do { rhs' <- zonkTcType rhs
2115 ; case () of
2116 _ | Just tv' <- tcGetTyVar_maybe rhs'
2117 , tv == tv' -- tv == rhs
2118 -> return True
2119
2120 _ | Just rhs'' <- occCheckExpand [tv] rhs'
2121 -> do { -- Fill the tyvar
2122 unifyTyVar tv rhs''
2123 ; return True }
2124
2125 _ | otherwise -- Occurs check
2126 -> return False
2127 }
2128
2129 setReflEvidence :: CtEvidence -> EqRel -> TcType -> TcS ()
2130 setReflEvidence ev eq_rel rhs
2131 = setEvBindIfWanted ev (evCoercion refl_co)
2132 where
2133 refl_co = mkTcReflCo (eqRelRole eq_rel) rhs
2134
2135 {-
2136 Note [Unflatten using funeqs first]
2137 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2138 [W] G a ~ Int
2139 [W] F (G a) ~ G a
2140
2141 do not want to end up with
2142 [W] F Int ~ Int
2143 because that might actually hold! Better to end up with the two above
2144 unsolved constraints. The flat form will be
2145
2146 G a ~ fmv1 (CFunEqCan)
2147 F fmv1 ~ fmv2 (CFunEqCan)
2148 fmv1 ~ Int (CTyEqCan)
2149 fmv1 ~ fmv2 (CTyEqCan)
2150
2151 Flatten using the fun-eqs first.
2152 -}
2153
2154 -- | Like 'splitPiTys'' but comes with a 'Bool' which is 'True' iff there is at
2155 -- least one named binder.
2156 split_pi_tys' :: Type -> ([TyBinder], Type, Bool)
2157 split_pi_tys' ty = split ty ty
2158 where
2159 split orig_ty ty | Just ty' <- coreView ty = split orig_ty ty'
2160 split _ (ForAllTy b res) = let (bs, ty, _) = split res res
2161 in (Named b : bs, ty, True)
2162 split _ (FunTy arg res) = let (bs, ty, named) = split res res
2163 in (Anon arg : bs, ty, named)
2164 split orig_ty _ = ([], orig_ty, False)
2165 {-# INLINE split_pi_tys' #-}
2166
2167 -- | Like 'tyConBindersTyBinders' but you also get a 'Bool' which is true iff
2168 -- there is at least one named binder.
2169 ty_con_binders_ty_binders' :: [TyConBinder] -> ([TyBinder], Bool)
2170 ty_con_binders_ty_binders' = foldr go ([], False)
2171 where
2172 go (TvBndr tv (NamedTCB vis)) (bndrs, _)
2173 = (Named (TvBndr tv vis) : bndrs, True)
2174 go (TvBndr tv AnonTCB) (bndrs, n)
2175 = (Anon (tyVarKind tv) : bndrs, n)
2176 {-# INLINE go #-}
2177 {-# INLINE ty_con_binders_ty_binders' #-}