3 solveInteract, AtomicInert,
4 InertSet, emptyInert, updInertSet, extractUnsolved, solveOne
7 #include "HsVersions.h"
30 import Control.Monad ( when )
39 import qualified Data.Map as Map
42 import Control.Monad( zipWithM, unless )
43 import FastString ( sLit )
47 Note [InertSet invariants]
48 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
50 An InertSet is a bag of canonical constraints, with the following invariants:
52 1 No two constraints react with each other.
54 A tricky case is when there exists a given (solved) dictionary
55 constraint and a wanted identical constraint in the inert set, but do
56 not react because reaction would create loopy dictionary evidence for
57 the wanted. See note [Recursive dictionaries]
59 2 Given equalities form an idempotent substitution [none of the
60 given LHS's occur in any of the given RHS's or reactant parts]
62 3 Wanted equalities also form an idempotent substitution
63 4 The entire set of equalities is acyclic.
65 5 Wanted dictionaries are inert with the top-level axiom set
67 6 Equalities of the form tv1 ~ tv2 always have a touchable variable
68 on the left (if possible).
69 7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints
70 will be marked as solved right before being pushed into the inert set.
71 See note [Touchables and givens].
73 Note that 6 and 7 are /not/ enforced by canonicalization but rather by
74 insertion in the inert list, ie by TcInteract.
76 During the process of solving, the inert set will contain some
77 previously given constraints, some wanted constraints, and some given
78 constraints which have arisen from solving wanted constraints. For
79 now we do not distinguish between given and solved constraints.
81 Note that we must switch wanted inert items to given when going under an
82 implication constraint (when in top-level inference mode).
84 Note [InertSet FlattenSkolemEqClass]
85 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
86 The inert_fsks field of the inert set contains an "inverse map" of all the
87 flatten skolem equalities in the inert set. For instance, if inert_cts looks
94 Then, the inert_fsks fields holds the following map:
95 fsk2 |-> { fsk1, fsk3 }
97 Along with the necessary coercions to convert fsk1 and fsk3 back to fsk2
98 and fsk4 back to fsk5. Hence, the invariants of the inert_fsks field are:
100 (a) All TcTyVars in the domain and range of inert_fsks are flatten skolems
101 (b) All TcTyVars in the domain of inert_fsk occur naked as rhs in some
102 equalities of inert_cts
103 (c) For every mapping fsk1 |-> { (fsk2,co), ... } it must be:
106 The role of the inert_fsks is to make it easy to maintain the equivalence
107 class of each flatten skolem, which is much needed to correctly do spontaneous
108 solving. See Note [Loopy Spontaneous Solving]
111 -- See Note [InertSet invariants]
113 = IS { inert_eqs :: Bag.Bag CanonicalCt -- Equalities only **CTyEqCan**
114 , inert_cts :: Bag.Bag CanonicalCt -- Other constraints
115 , inert_fds :: FDImprovements -- List of pairwise improvements that have kicked in already
116 -- and reside either in the worklist or in the inerts
117 , inert_fsks :: Map.Map TcTyVar [(TcTyVar,Coercion)] }
118 -- See Note [InertSet FlattenSkolemEqClass]
120 type FDImprovement = (PredType,PredType)
121 type FDImprovements = [(PredType,PredType)]
123 instance Outputable InertSet where
124 ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
125 , vcat (map ppr (Bag.bagToList $ inert_cts is))
126 , vcat (map (\(v,rest) -> ppr v <+> text "|->" <+> hsep (map (ppr.fst) rest))
127 (Map.toList $ inert_fsks is)
131 emptyInert :: InertSet
132 emptyInert = IS { inert_eqs = Bag.emptyBag
133 , inert_cts = Bag.emptyBag, inert_fsks = Map.empty, inert_fds = [] }
135 updInertSet :: InertSet -> AtomicInert -> InertSet
136 -- Introduces an element in the inert set for the first time
137 updInertSet (IS { inert_eqs = eqs, inert_cts = cts, inert_fsks = fsks, inert_fds = fdis })
138 item@(CTyEqCan { cc_id = cv
141 | Just tv2 <- tcGetTyVar_maybe xi,
142 FlatSkol {} <- tcTyVarDetails tv1,
143 FlatSkol {} <- tcTyVarDetails tv2
144 = let eqs' = eqs `Bag.snocBag` item
145 fsks' = Map.insertWith (++) tv2 [(tv1, mkCoVarCoercion cv)] fsks
146 -- See Note [InertSet FlattenSkolemEqClass]
147 in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks', inert_fds = fdis }
148 updInertSet (IS { inert_eqs = eqs, inert_cts = cts
149 , inert_fsks = fsks, inert_fds = fdis }) item
151 = let eqs' = eqs `Bag.snocBag` item
152 in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks, inert_fds = fdis }
154 = let cts' = cts `Bag.snocBag` item
155 in IS { inert_eqs = eqs, inert_cts = cts', inert_fsks = fsks, inert_fds = fdis }
157 updInertSetFDImprs :: InertSet -> Maybe FDImprovement -> InertSet
158 updInertSetFDImprs is (Just fdi) = is { inert_fds = fdi : inert_fds is }
159 updInertSetFDImprs is Nothing = is
161 foldISEqCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a
162 -- Fold over the equalities of the inerts
163 foldISEqCtsM k z IS { inert_eqs = eqs }
164 = Bag.foldlBagM k z eqs
166 foldISOtherCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a
167 -- Fold over other constraints in the inerts
168 foldISOtherCtsM k z IS { inert_cts = cts }
169 = Bag.foldlBagM k z cts
171 extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
172 extractUnsolved is@(IS {inert_eqs = eqs, inert_cts = cts, inert_fds = fdis })
173 = let is_init = is { inert_eqs = emptyCCan
174 , inert_cts = solved_cts, inert_fsks = Map.empty, inert_fds = fdis }
175 is_final = Bag.foldlBag updInertSet is_init solved_eqs -- Add equalities carefully
176 in (is_final, unsolved)
177 where (unsolved_cts, solved_cts) = Bag.partitionBag isWantedCt cts
178 (unsolved_eqs, solved_eqs) = Bag.partitionBag isWantedCt eqs
179 unsolved = unsolved_cts `unionBags` unsolved_eqs
182 getFskEqClass :: InertSet -> TcTyVar -> [(TcTyVar,Coercion)]
183 -- Precondition: tv is a FlatSkol. See Note [InertSet FlattenSkolemEqClass]
184 getFskEqClass (IS { inert_cts = cts, inert_fsks = fsks }) tv
185 = case lkpTyEqCanByLhs of
186 Nothing -> fromMaybe [] (Map.lookup tv fsks)
188 case tcGetTyVar_maybe (cc_rhs ceq) of
189 Just tv_rhs | FlatSkol {} <- tcTyVarDetails tv_rhs
190 -> let ceq_co = mkSymCoercion $ mkCoVarCoercion (cc_id ceq)
191 mk_co (v,c) = (v, mkTransCoercion c ceq_co)
192 in (tv_rhs, ceq_co): map mk_co (fromMaybe [] $ Map.lookup tv fsks)
194 where lkpTyEqCanByLhs = Bag.foldlBag lkp Nothing cts
195 lkp :: Maybe CanonicalCt -> CanonicalCt -> Maybe CanonicalCt
196 lkp Nothing ct@(CTyEqCan {cc_tyvar = tv'}) | tv' == tv = Just ct
197 lkp other _ct = other
199 haveBeenImproved :: FDImprovements -> PredType -> PredType -> Bool
200 haveBeenImproved [] _ _ = False
201 haveBeenImproved ((pty1,pty2):fdimprs) pty1' pty2'
202 | tcEqPred pty1 pty1' && tcEqPred pty2 pty2'
204 | tcEqPred pty1 pty2' && tcEqPred pty2 pty1'
207 = haveBeenImproved fdimprs pty1' pty2'
209 getFDImprovements :: InertSet -> FDImprovements
210 -- Return a list of the improvements that have kicked in so far
211 getFDImprovements = inert_fds
215 data Inert = IS { class_inerts :: FiniteMap Class Atomics
216 ip_inerts :: FiniteMap Class Atomics
217 tyfun_inerts :: FiniteMap TyCon Atomics
218 tyvar_inerts :: FiniteMap TyVar Atomics
221 Later should we also separate out givens and wanteds?
226 Note [Touchables and givens]
227 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
228 Touchable variables will never show up in givens which are inputs to
229 the solver. However, touchables may show up in givens generated by the flattener.
244 which can be put in the inert set. Suppose we also have a wanted
248 We cannot rewrite the given G alpha ~g b using the wanted alpha ~w
249 Int. Instead, after reacting alpha ~w Int with the whole inert set,
250 we observe that we can solve it by unifying alpha with Int, so we mark
251 it as solved and put it back in the *work list*. [We also immediately unify
252 alpha := Int, without telling anyone, see trySpontaneousSolve function, to
253 avoid doing this in the end.]
255 Later, because it is solved (given, in effect), we can use it to rewrite
256 G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually,
257 we will dispatch the remaining wanted constraints using the top-level axioms.
259 Finally, note that after reacting a wanted equality with the entire inert set
260 we may end up with something like
264 which we should flip around to generate the solved constraint alpha ~s b.
266 %*********************************************************************
268 * Main Interaction Solver *
270 **********************************************************************
274 1. Canonicalise (unary)
275 2. Pairwise interaction (binary)
276 * Take one from work list
277 * Try all pair-wise interactions with each constraint in inert
279 As an optimisation, we prioritize the equalities both in the
280 worklist and in the inerts.
282 3. Try to solve spontaneously for equalities involving touchables
283 4. Top-level interaction (binary wrt top-level)
284 Superclass decomposition belongs in (4), see note [Superclasses]
287 type AtomicInert = CanonicalCt -- constraint pulled from InertSet
288 type WorkItem = CanonicalCt -- constraint pulled from WorkList
290 -- A mixture of Given, Wanted, and Derived constraints.
291 -- We split between equalities and the rest to process equalities first.
292 type WorkList = CanonicalCts
293 type SWorkList = WorkList -- A worklist of solved
295 unionWorkLists :: WorkList -> WorkList -> WorkList
296 unionWorkLists = andCCan
298 isEmptyWorkList :: WorkList -> Bool
299 isEmptyWorkList = isEmptyCCan
301 emptyWorkList :: WorkList
302 emptyWorkList = emptyCCan
304 workListFromCCan :: CanonicalCt -> WorkList
305 workListFromCCan = singleCCan
307 ------------------------
309 = Stop -- Work item is consumed
310 | ContinueWith WorkItem -- Not consumed
312 instance Outputable StopOrContinue where
313 ppr Stop = ptext (sLit "Stop")
314 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
316 -- Results after interacting a WorkItem as far as possible with an InertSet
318 = SR { sr_inerts :: InertSet
319 -- The new InertSet to use (REPLACES the old InertSet)
320 , sr_new_work :: WorkList
321 -- Any new work items generated (should be ADDED to the old WorkList)
323 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
324 -- workitem is inert wrt to sr_inerts
325 , sr_stop :: StopOrContinue
328 instance Outputable StageResult where
329 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
330 = ptext (sLit "SR") <+>
331 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
332 , ptext (sLit "new work =") <+> ppr work <> comma
333 , ptext (sLit "stop =") <+> ppr stop])
335 type SimplifierStage = WorkItem -> InertSet -> TcS StageResult
337 -- Combine a sequence of simplifier 'stages' to create a pipeline
338 runSolverPipeline :: [(String, SimplifierStage)]
339 -> InertSet -> WorkItem
340 -> TcS (InertSet, WorkList)
341 -- Precondition: non-empty list of stages
342 runSolverPipeline pipeline inerts workItem
343 = do { traceTcS "Start solver pipeline" $
344 vcat [ ptext (sLit "work item =") <+> ppr workItem
345 , ptext (sLit "inerts =") <+> ppr inerts]
347 ; let itr_in = SR { sr_inerts = inerts
348 , sr_new_work = emptyWorkList
349 , sr_stop = ContinueWith workItem }
350 ; itr_out <- run_pipeline pipeline itr_in
352 = case sr_stop itr_out of
353 Stop -> sr_inerts itr_out
354 ContinueWith item -> sr_inerts itr_out `updInertSet` item
355 ; return (new_inert, sr_new_work itr_out) }
357 run_pipeline :: [(String, SimplifierStage)]
358 -> StageResult -> TcS StageResult
359 run_pipeline [] itr = return itr
360 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
362 run_pipeline ((name,stage):stages)
363 (SR { sr_new_work = accum_work
365 , sr_stop = ContinueWith work_item })
366 = do { itr <- stage work_item inerts
367 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
368 ; let itr' = itr { sr_new_work = accum_work `unionWorkLists` sr_new_work itr }
369 ; run_pipeline stages itr' }
373 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
374 Reagent: a ~ [b] (given)
376 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
377 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
378 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
381 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
384 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
385 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
389 Inert: {a ~ Int, F Int ~ b} (given)
390 Reagent: F a ~ b (wanted)
392 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
393 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
396 -- Main interaction solver: we fully solve the worklist 'in one go',
397 -- returning an extended inert set.
399 -- See Note [Touchables and givens].
400 solveInteract :: InertSet -> CanonicalCts -> TcS InertSet
401 solveInteract inert ws
402 = do { dyn_flags <- getDynFlags
403 ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert ws
405 solveOne :: InertSet -> WorkItem -> TcS InertSet
406 solveOne inerts workItem
407 = do { dyn_flags <- getDynFlags
408 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
412 solveInteractWithDepth :: (Int, Int, [WorkItem])
413 -> InertSet -> WorkList -> TcS InertSet
414 solveInteractWithDepth ctxt@(max_depth,n,stack) inert ws
419 = solverDepthErrorTcS n stack
422 = do { traceTcS "solveInteractWithDepth" $
423 vcat [ text "Current depth =" <+> ppr n
424 , text "Max depth =" <+> ppr max_depth ]
426 -- Solve equalities first
427 ; let (eqs, non_eqs) = Bag.partitionBag isTyEqCCan ws
428 ; is_from_eqs <- Bag.foldlBagM (solveOneWithDepth ctxt) inert eqs
429 ; Bag.foldlBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }
432 -- Fully interact the given work item with an inert set, and return a
433 -- new inert set which has assimilated the new information.
434 solveOneWithDepth :: (Int, Int, [WorkItem])
435 -> InertSet -> WorkItem -> TcS InertSet
436 solveOneWithDepth (max_depth, n, stack) inert work
437 = do { traceTcS0 (indent ++ "Solving {") (ppr work)
438 ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work
440 ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work)
442 -- Recursively solve the new work generated
443 -- from workItem, with a greater depth
444 ; res_inert <- solveInteractWithDepth (max_depth, n+1, work:stack)
447 ; traceTcS0 (indent ++ "Done }") (ppr work)
450 indent = replicate (2*n) ' '
452 thePipeline :: [(String,SimplifierStage)]
453 thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
454 , ("interact with inerts", interactWithInertsStage)
455 , ("spontaneous solve", spontaneousSolveStage)
456 , ("top-level reactions", topReactionsStage) ]
459 *********************************************************************************
461 The spontaneous-solve Stage
463 *********************************************************************************
465 Note [Efficient Orientation]
466 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
468 There are two cases where we have to be careful about
469 orienting equalities to get better efficiency.
471 Case 2: In Rewriting Equalities (function rewriteEqLHS)
473 When rewriting two equalities with the same LHS:
476 We have a choice of producing work (xi1 ~ xi2) (up-to the
477 canonicalization invariants) However, to prevent the inert items
478 from getting kicked out of the inerts first, we prefer to
479 canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
480 ~ xi1) if (a) comes from the inert set.
482 This choice is implemented using the WhichComesFromInert flag.
484 Case 2: In Spontaneous Solving
486 Inerts: [w1] : D alpha
490 Untouchables = [beta]
491 Then a wanted (beta ~ alpha) comes along.
492 1) While interacting with the inerts it is going to kick w2,w4
494 2) Then, it will spontaneoulsy be solved by (alpha := beta)
495 3) Now (and here is the tricky part), to add him back as
496 solved (alpha ~ beta) is no good because, in the next
497 iteration, it will kick out w1,w3 as well so we will end up
498 with *all* the inert equalities back in the worklist!
500 So it is tempting to just add (beta ~ alpha) instead, that is,
501 maintain the original orietnation of the constraint.
503 But that does not work very well, because it may cause the
504 "double unification problem" (See Note [Avoid double unifications]).
511 At the end of the interaction suppose we spontaneously solve alpha := fsk1
512 but keep [Given] fsk1 ~ alpha. Then, the second time around we see the
513 constraint (fsk2 ~ alpha), and we unify *again* alpha := fsk2, which is wrong.
515 Our conclusion is that, while in some cases (Example 2a), it makes sense to
516 preserve the original orientation, it is hard to do this in a sound way.
517 So we *don't* do this for now, @solveWithIdentity@ outputs a constraint that
518 is oriented with the unified variable on the left.
520 Case 3: Functional Dependencies and IP improvement work
521 TODO. Optimisation not yet implemented there.
524 spontaneousSolveStage :: SimplifierStage
525 spontaneousSolveStage workItem inerts
526 = do { mSolve <- trySpontaneousSolve workItem inerts
528 Nothing -> -- no spontaneous solution for him, keep going
529 return $ SR { sr_new_work = emptyWorkList
531 , sr_stop = ContinueWith workItem }
533 Just (workItem', workList')
534 | not (isGivenCt workItem)
535 -- Original was wanted or derived but we have now made him
536 -- given so we have to interact him with the inerts due to
537 -- its status change. This in turn may produce more work.
538 -- We do this *right now* (rather than just putting workItem'
539 -- back into the work-list) because we've solved
540 -> do { (new_inert, new_work) <- runSolverPipeline
541 [ ("recursive interact with inert eqs", interactWithInertEqsStage)
542 , ("recursive interact with inerts", interactWithInertsStage)
544 ; return $ SR { sr_new_work = new_work `unionWorkLists` workList'
545 , sr_inerts = new_inert -- will include workItem'
549 -> -- Original was given; he must then be inert all right, and
550 -- workList' are all givens from flattening
551 return $ SR { sr_new_work = workList'
552 , sr_inerts = inerts `updInertSet` workItem'
556 -- @trySpontaneousSolve wi@ solves equalities where one side is a
557 -- touchable unification variable. Returns:
558 -- * Nothing if we were not able to solve it
559 -- * Just wi' if we solved it, wi' (now a "given") should be put in the work list.
560 -- See Note [Touchables and givens]
561 -- NB: just passing the inerts through for the skolem equivalence classes
562 trySpontaneousSolve :: WorkItem -> InertSet -> TcS (Maybe (WorkItem, SWorkList))
563 trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi }) inerts
566 | Just tv2 <- tcGetTyVar_maybe xi
567 = do { tch1 <- isTouchableMetaTyVar tv1
568 ; tch2 <- isTouchableMetaTyVar tv2
569 ; case (tch1, tch2) of
570 (True, True) -> trySpontaneousEqTwoWay inerts cv gw tv1 tv2
571 (True, False) -> trySpontaneousEqOneWay inerts cv gw tv1 xi
572 (False, True) -> trySpontaneousEqOneWay inerts cv gw tv2 (mkTyVarTy tv1)
573 _ -> return Nothing }
575 = do { tch1 <- isTouchableMetaTyVar tv1
576 ; if tch1 then trySpontaneousEqOneWay inerts cv gw tv1 xi
577 else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:" (ppr workItem)
582 -- trySpontaneousSolve (CFunEqCan ...) = ...
583 -- See Note [No touchables as FunEq RHS] in TcSMonad
584 trySpontaneousSolve _ _ = return Nothing
587 trySpontaneousEqOneWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> Xi
588 -> TcS (Maybe (WorkItem,SWorkList))
589 -- tv is a MetaTyVar, not untouchable
590 trySpontaneousEqOneWay inerts cv gw tv xi
591 | not (isSigTyVar tv) || isTyVarTy xi
592 = do { kxi <- zonkTcTypeTcS xi >>= return . typeKind -- Must look through the TcTyBinds
593 -- hence kxi and not typeKind xi
594 -- See Note [Kind Errors]
595 ; if kxi `isSubKind` tyVarKind tv then
596 solveWithIdentity inerts cv gw tv xi
597 else if tyVarKind tv `isSubKind` kxi then
598 return Nothing -- kinds are compatible but we can't solveWithIdentity this way
599 -- This case covers the a_touchable :: * ~ b_untouchable :: ??
600 -- which has to be deferred or floated out for someone else to solve
601 -- it in a scope where 'b' is no longer untouchable.
602 else kindErrorTcS gw (mkTyVarTy tv) xi -- See Note [Kind errors]
604 | otherwise -- Still can't solve, sig tyvar and non-variable rhs
608 trySpontaneousEqTwoWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> TcTyVar
609 -> TcS (Maybe (WorkItem,SWorkList))
610 -- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
611 trySpontaneousEqTwoWay inerts cv gw tv1 tv2
613 , nicer_to_update_tv2 = solveWithIdentity inerts cv gw tv2 (mkTyVarTy tv1)
615 = solveWithIdentity inerts cv gw tv1 (mkTyVarTy tv2)
616 | otherwise -- None is a subkind of the other, but they are both touchable!
617 = kindErrorTcS gw (mkTyVarTy tv1) (mkTyVarTy tv2) -- See Note [Kind errors]
621 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
625 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
626 Consider the wanted problem:
627 alpha ~ (# Int, Int #)
628 where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
629 but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
630 simply returns @Nothing@ then that wanted constraint is going to propagate all the way and
631 get quantified over in inference mode. That's bad because we do know at this point that the
632 constraint is insoluble. Instead, we call 'kindErrorTcS' here, which immediately fails.
634 The same applies in canonicalization code in case of kind errors in the givens.
636 However, when we canonicalize givens we only check for compatibility (@compatKind@).
637 If there were a kind error in the givens, this means some form of inconsistency or dead code.
639 When we spontaneously solve wanteds we may have to look through the bindings, hence we
640 call zonkTcTypeTcS above. The reason is that maybe xi is @alpha@ where alpha :: ? and
641 a previous spontaneous solving has set (alpha := f) with (f :: *). The reason that xi is
642 still alpha and not f is becasue the solved constraint may be oriented as (f ~ alpha) instead
643 of (alpha ~ f). Then we should be using @xi@s "real" kind, which is * and not ?, when we try
644 to detect whether spontaneous solving is possible.
647 Note [Spontaneous solving and kind compatibility]
648 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
650 Note that our canonical constraints insist that only *given* equalities (tv ~ xi)
651 or (F xis ~ rhs) require the LHS and the RHS to have exactly the same kinds.
653 - We have to require this because:
654 Given equalities can be freely used to rewrite inside
655 other types or constraints.
656 - We do not have to do the same for wanteds because:
657 First, wanted equations (tv ~ xi) where tv is a touchable
658 unification variable may have kinds that do not agree (the
659 kind of xi must be a sub kind of the kind of tv). Second, any
660 potential kind mismatch will result in the constraint not
661 being soluble, which will be reported anyway. This is the
662 reason that @trySpontaneousOneWay@ and @trySpontaneousTwoWay@
663 will perform a kind compatibility check, and only then will
664 they proceed to @solveWithIdentity@.
667 - Givens from higher-rank, such as:
668 type family T b :: * -> * -> *
669 type instance T Bool = (->)
671 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
673 Whereas we would be able to apply the type instance, we would not be able to
674 use the given (T Bool ~ (->)) in the body of 'flop'
676 Note [Loopy Spontaneous Solving]
677 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
679 Example 1: [The problem of loopy spontaneous solving]
681 Consider the original wanted:
682 wanted : Maybe (E alpha) ~ alpha
683 where E is a type family, such that E (T x) = x. After canonicalization,
684 as a result of flattening, we will get:
685 given : E alpha ~ fsk
686 wanted : alpha ~ Maybe fsk
687 where (fsk := E alpha, on the side). Now, if we spontaneously *solve*
688 (alpha := Maybe fsk) we are in trouble! Instead, we should refrain from solving
689 it and keep it as wanted. In inference mode we'll end up quantifying over
690 (alpha ~ Maybe (E alpha))
691 Hence, 'solveWithIdentity' performs a small occurs check before
692 actually solving. But this occurs check *must look through* flatten skolems.
694 However, it may be the case that the flatten skolem in hand is equal to some other
695 flatten skolem whith *does not* mention our unification variable. Here's a typical example:
697 Example 2: [The need of keeping track of flatten skolem equivalence classes]
702 After canonicalization:
707 After some reactions:
712 At this point, we will try to spontaneously solve (alpha ~ f2) which remains as yet unsolved.
713 We will look inside f2, which immediately mentions (F alpha), so it's not good to unify! However
714 by looking at the equivalence class of the flatten skolems, we can see that it is fine to
715 unify (alpha ~ f1) which solves our goals!
717 Example 3: [The need of looking through TyBinds for already spontaneously solved variables]
719 A similar problem happens because of other spontaneous solving. Suppose we have the
720 following wanteds, arriving in this exact order:
721 (first) w: beta ~ alpha
722 (second) w: alpha ~ fsk
723 (third) g: F beta ~ fsk
724 Then, we first spontaneously solve the first constraint, making (beta := alpha), and having
725 (beta ~ alpha) as given. *Then* we encounter the second wanted (alpha ~ fsk). "fsk" does not
726 obviously mention alpha, so naively we can also spontaneously solve (alpha := fsk). But
727 that is wrong since fsk mentions beta, which has already secretly been unified to alpha!
729 To avoid this problem, the same occurs check must unveil rewritings that can happen because
730 of spontaneously having solved other constraints.
732 Example 4: [Orientation of (tv ~ xi) equalities]
734 We orient equalities (tv ~ xi) so that flatten skolems appear on the left, if possible. Here
735 is an example of why this is needed:
737 [Wanted] w1: alpha ~ fsk
738 [Given] g1: F alpha ~ fsk
740 Flatten skolem equivalence class = []
742 Assume that g2 is *not* oriented properly, as shown above. Then we would like to spontaneously
743 solve w1 but we can't set alpha := fsk, since fsk hides the type F alpha. However, by using
744 the equation g2 it would be possible to solve w1 by setting alpha := b. In other words, it is
745 not enough to look at a flatten skolem equivalence class to try to find alternatives to unify
746 with. We may have to go to other variables.
748 By orienting the equalities so that flatten skolems are in the LHS we are eliminating them
749 as much as possible from the RHS of other wanted equalities, and hence it suffices to look
750 in their flatten skolem equivalence classes.
752 NB: This situation appears in the IndTypesPerf test case, inside indexed-types/.
754 Caveat: You may wonder if we should be doing this for unification variables as well.
755 However, Note [Efficient Orientation], Case 2, demonstrates that this is not possible
756 at least for touchable unification variables which we have to keep oriented with the
757 touchable on the LHS to be able to eliminate it. So then, what about untouchables?
761 Untouchable = beta, Touchable = alpha
763 [Wanted] w1: alpha ~ fsk
764 [Given] g1: F alpha ~ fsk
765 [Given] g2: beta ~ fsk
766 Flatten skolem equivalence class = []
768 Should we be able to unify alpha := beta to solve the constraint? Arguably yes, but
769 that implies that an *untouchable* unification variable (beta) is in the same equivalence
770 class as a flatten skolem that mentions @alpha@. I.e. g2 means that:
772 But I do not think that there is any way to produce evidence for such a constraint from
773 the outside other than beta := F alpha, which violates the OutsideIn-ness.
777 Note [Avoid double unifications]
778 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
779 The spontaneous solver has to return a given which mentions the unified unification
780 variable *on the left* of the equality. Here is what happens if not:
781 Original wanted: (a ~ alpha), (alpha ~ Int)
782 We spontaneously solve the first wanted, without changing the order!
783 given : a ~ alpha [having unified alpha := a]
784 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
785 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
787 We avoid this problem by orienting the given so that the unification
788 variable is on the left. [Note that alternatively we could attempt to
789 enforce this at canonicalization]
791 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
792 double unifications is the main reason we disallow touchable
793 unification variables as RHS of type family equations: F xis ~ alpha.
797 solveWithIdentity :: InertSet
798 -> CoVar -> CtFlavor -> TcTyVar -> Xi
799 -> TcS (Maybe (WorkItem, SWorkList))
800 -- Solve with the identity coercion
801 -- Precondition: kind(xi) is a sub-kind of kind(tv)
802 -- Precondition: CtFlavor is Wanted or Derived
803 -- See [New Wanted Superclass Work] to see why solveWithIdentity
804 -- must work for Derived as well as Wanted
805 -- Returns: (workItem, workList) where
806 -- workItem = the new Given constraint
807 -- workList = some additional work that may have been produced as a result of flattening
808 -- in case we did some chasing through flatten skolem equivalence classes.
809 solveWithIdentity inerts cv gw tv xi
810 = do { tybnds <- getTcSTyBindsMap
811 ; case occurCheck tybnds inerts tv xi of
812 Nothing -> return Nothing
813 Just (xi_unflat,coi) -> solve_with xi_unflat coi }
815 solve_with xi_unflat coi -- coi : xi_unflat ~ xi
816 = do { traceTcS "Sneaky unification:" $
817 vcat [text "Coercion variable: " <+> ppr gw,
818 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
819 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
820 text "Right Kind is : " <+> ppr (typeKind xi)
823 ; setWantedTyBind tv xi_unflat -- Set tv := xi_unflat
824 ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi_unflat xi_unflat
825 ; let flav = mkGivenFlavor gw UnkSkol
826 ; (ct,cts, co) <- case coi of
827 ACo co -> do { (cc,ccs) <- canEqLeafTyVarLeft flav cv_given tv xi_unflat
828 ; return (cc, ccs, co) }
829 IdCo co -> return $ (CTyEqCan { cc_id = cv_given
830 , cc_flavor = mkGivenFlavor gw UnkSkol
831 , cc_tyvar = tv, cc_rhs = xi }
832 -- xi, *not* xi_unflat because
833 -- xi_unflat may require flattening!
836 Wanted {} -> setWantedCoBind cv co
837 Derived {} -> setDerivedCoBind cv co
838 _ -> pprPanic "Can't spontaneously solve *given*" empty
839 -- See Note [Avoid double unifications]
840 ; return $ Just (ct,cts)
843 -- ; let flav = mkGivenFlavor gw UnkSkol
844 -- ; (cts, co) <- case coi of
845 -- -- TODO: Optimise this, along the way it used to be
846 -- ACo co -> do { cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi_unflat xi_unflat
847 -- ; setWantedTyBind tv xi_unflat
848 -- ; can_eqs <- canEq flav cv_given (mkTyVarTy tv) xi_unflat
849 -- ; return (can_eqs, co) }
850 -- IdCo co -> do { cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi xi
851 -- ; setWantedTyBind tv xi
852 -- ; can_eqs <- canEq flav cv_given (mkTyVarTy tv) xi
853 -- ; return (can_eqs, co) }
855 -- Wanted {} -> setWantedCoBind cv co
856 -- Derived {} -> setDerivedCoBind cv co
857 -- _ -> pprPanic "Can't spontaneously solve *given*" empty
858 -- -- See Note [Avoid double unifications]
859 -- ; return $ Just cts }
861 occurCheck :: VarEnv (TcTyVar, TcType) -> InertSet
862 -> TcTyVar -> TcType -> Maybe (TcType,CoercionI)
863 -- Traverse @ty@ to make sure that @tv@ does not appear under some flatten skolem.
864 -- If it appears under some flatten skolem look in that flatten skolem equivalence class
865 -- (see Note [InertSet FlattenSkolemEqClass], [Loopy Spontaneous Solving]) to see if you
866 -- can find a different flatten skolem to use, that is, one that does not mention @tv@.
868 -- Postcondition: Just (ty', coi) = occurCheck binds inerts tv ty
870 -- NB: The returned type ty' may not be flat!
872 occurCheck ty_binds inerts the_tv the_ty
873 = ok emptyVarSet the_ty
875 -- If (fsk `elem` bad) then tv occurs in any rendering
876 -- of the type under the expansion of fsk
877 ok bad this_ty@(TyConApp tc tys)
878 | Just tys_cois <- allMaybes (map (ok bad) tys)
879 , (tys',cois') <- unzip tys_cois
880 = Just (TyConApp tc tys', mkTyConAppCoI tc cois')
881 | isSynTyCon tc, Just ty_expanded <- tcView this_ty
882 = ok bad ty_expanded -- See Note [Type synonyms and the occur check] in TcUnify
884 | Just (sty',coi) <- ok_pred bad sty
885 = Just (PredTy sty', coi)
886 ok bad (FunTy arg res)
887 | Just (arg', coiarg) <- ok bad arg, Just (res', coires) <- ok bad res
888 = Just (FunTy arg' res', mkFunTyCoI coiarg coires)
889 ok bad (AppTy fun arg)
890 | Just (fun', coifun) <- ok bad fun, Just (arg', coiarg) <- ok bad arg
891 = Just (AppTy fun' arg', mkAppTyCoI coifun coiarg)
892 ok bad (ForAllTy tv1 ty1)
893 -- WARNING: What if it is a (t1 ~ t2) => t3? It's not handled properly at the moment.
894 | Just (ty1', coi) <- ok bad ty1
895 = Just (ForAllTy tv1 ty1', mkForAllTyCoI tv1 coi)
898 ok bad this_ty@(TyVarTy tv)
899 | tv == the_tv = Nothing -- Occurs check error
900 | not (isTcTyVar tv) = Just (this_ty, IdCo this_ty) -- Bound var
901 | FlatSkol zty <- tcTyVarDetails tv = ok_fsk bad tv zty
902 | Just (_,ty) <- lookupVarEnv ty_binds tv = ok bad ty
903 | otherwise = Just (this_ty, IdCo this_ty)
905 -- Check if there exists a ty bind already, as a result of sneaky unification.
907 ok _bad _ty = Nothing
910 ok_pred bad (ClassP cn tys)
911 | Just tys_cois <- allMaybes $ map (ok bad) tys
912 = let (tys', cois') = unzip tys_cois
913 in Just (ClassP cn tys', mkClassPPredCoI cn cois')
914 ok_pred bad (IParam nm ty)
915 | Just (ty',co') <- ok bad ty
916 = Just (IParam nm ty', mkIParamPredCoI nm co')
917 ok_pred bad (EqPred ty1 ty2)
918 | Just (ty1',coi1) <- ok bad ty1, Just (ty2',coi2) <- ok bad ty2
919 = Just (EqPred ty1' ty2', mkEqPredCoI coi1 coi2)
920 ok_pred _ _ = Nothing
924 | fsk `elemVarSet` bad
925 -- We are already trying to find a rendering of fsk,
926 -- and to do that it seems we need a rendering, so fail
929 = firstJusts (ok new_bad zty : map (go_under_fsk new_bad) fsk_equivs)
931 fsk_equivs = getFskEqClass inerts fsk
932 new_bad = bad `extendVarSetList` (fsk : map fst fsk_equivs)
935 go_under_fsk bad_tvs (fsk,co)
936 | FlatSkol zty <- tcTyVarDetails fsk
937 = case ok bad_tvs zty of
939 Just (ty,coi') -> Just (ty, mkTransCoI coi' (ACo co))
940 | otherwise = pprPanic "go_down_equiv" (ppr fsk)
944 *********************************************************************************
946 The interact-with-inert Stage
948 *********************************************************************************
951 -- Interaction result of WorkItem <~> AtomicInert
953 = IR { ir_stop :: StopOrContinue
955 -- => Reagent (work item) consumed.
956 -- ContinueWith new_reagent
957 -- => Reagent transformed but keep gathering interactions.
958 -- The transformed item remains inert with respect
959 -- to any previously encountered inerts.
961 , ir_inert_action :: InertAction
962 -- Whether the inert item should remain in the InertSet.
964 , ir_new_work :: WorkList
965 -- new work items to add to the WorkList
967 , ir_improvement :: Maybe FDImprovement -- In case improvement kicked in
970 -- What to do with the inert reactant.
971 data InertAction = KeepInert | DropInert
974 mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
975 mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork Nothing
977 mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
978 mkIRStop keep newWork = return $ IR Stop keep newWork Nothing
980 mkIRStop_RecordImprovement :: Monad m => InertAction -> WorkList -> FDImprovement -> m InteractResult
981 mkIRStop_RecordImprovement keep newWork fdimpr = return $ IR Stop keep newWork (Just fdimpr)
984 dischargeWorkItem :: Monad m => m InteractResult
985 dischargeWorkItem = mkIRStop KeepInert emptyWorkList
987 noInteraction :: Monad m => WorkItem -> m InteractResult
988 noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList
990 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
991 -- See Note [Efficient Orientation, Case 2]
994 ---------------------------------------------------
995 -- Interact a single WorkItem with the equalities of an inert set as far as possible, i.e. until we
996 -- get a Stop result from an individual reaction (i.e. when the WorkItem is consumed), or until we've
997 -- interact the WorkItem with the entire equalities of the InertSet
999 interactWithInertEqsStage :: SimplifierStage
1000 interactWithInertEqsStage workItem inert
1001 = foldISEqCtsM interactNext initITR inert
1002 where initITR = SR { sr_inerts = IS { inert_eqs = emptyCCan -- We will fold over the equalities
1003 , inert_fsks = Map.empty -- which will generate those two again
1004 , inert_cts = inert_cts inert
1005 , inert_fds = inert_fds inert
1007 , sr_new_work = emptyWorkList
1008 , sr_stop = ContinueWith workItem }
1011 ---------------------------------------------------
1012 -- Interact a single WorkItem with *non-equality* constraints in the inert set.
1013 -- Precondition: equality interactions must have already happened, hence we have
1014 -- to pick up some information from the incoming inert, before folding over the
1015 -- "Other" constraints it contains!
1016 interactWithInertsStage :: SimplifierStage
1017 interactWithInertsStage workItem inert
1018 = foldISOtherCtsM interactNext initITR inert
1020 initITR = SR { -- Pick up: (1) equations, (2) FD improvements, (3) FlatSkol equiv. classes
1021 sr_inerts = IS { inert_eqs = inert_eqs inert
1022 , inert_cts = emptyCCan
1023 , inert_fds = inert_fds inert
1024 , inert_fsks = inert_fsks inert }
1025 , sr_new_work = emptyWorkList
1026 , sr_stop = ContinueWith workItem }
1028 interactNext :: StageResult -> AtomicInert -> TcS StageResult
1029 interactNext it inert
1030 | ContinueWith workItem <- sr_stop it
1031 = do { let inerts = sr_inerts it
1032 fdimprs_old = getFDImprovements inerts
1034 ; ir <- interactWithInert fdimprs_old inert workItem
1036 -- New inerts depend on whether we KeepInert or not and must
1037 -- be updated with FD improvement information from the interaction result (ir)
1038 ; let inerts_new = updInertSetFDImprs upd_inert (ir_improvement ir)
1039 upd_inert = if ir_inert_action ir == KeepInert
1040 then inerts `updInertSet` inert else inerts
1042 ; return $ SR { sr_inerts = inerts_new
1043 , sr_new_work = sr_new_work it `unionWorkLists` ir_new_work ir
1044 , sr_stop = ir_stop ir } }
1046 = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
1048 -- Do a single interaction of two constraints.
1049 interactWithInert :: FDImprovements -> AtomicInert -> WorkItem -> TcS InteractResult
1050 interactWithInert fdimprs inert workitem
1051 = do { ctxt <- getTcSContext
1052 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workitem
1053 inert_ev = cc_id inert
1054 work_ev = cc_id workitem
1056 -- Never interact a wanted and a derived where the derived's evidence
1057 -- mentions the wanted evidence in an unguarded way.
1058 -- See Note [Superclasses and recursive dictionaries]
1059 -- and Note [New Wanted Superclass Work]
1060 -- We don't have to do this for givens, as we fully know the evidence for them.
1062 case (cc_flavor inert, cc_flavor workitem) of
1063 (Wanted loc, Derived {}) -> isGoodRecEv work_ev (WantedEvVar inert_ev loc)
1064 (Derived {}, Wanted loc) -> isGoodRecEv inert_ev (WantedEvVar work_ev loc)
1067 ; if is_allowed && rec_ev_ok then
1068 doInteractWithInert fdimprs inert workitem
1070 noInteraction workitem
1073 allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
1074 -- Allowed interactions
1075 allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
1076 allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
1077 allowedInteraction _ _ _ = True
1079 --------------------------------------------
1080 doInteractWithInert :: FDImprovements -> CanonicalCt -> CanonicalCt -> TcS InteractResult
1081 -- Identical class constraints.
1083 doInteractWithInert fdimprs
1084 (CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
1085 workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
1086 | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
1087 = solveOneFromTheOther (d1,fl1) workItem
1089 | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
1090 = -- See Note [When improvement happens]
1091 do { let pty1 = ClassP cls1 tys1
1092 pty2 = ClassP cls2 tys2
1093 work_item_pred_loc = (pty2, ppr d2)
1094 inert_pred_loc = (pty1, ppr d1)
1095 loc = combineCtLoc fl1 fl2
1096 eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc
1098 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
1099 ; fd_work <- canWanteds wevvars
1100 -- See Note [Generating extra equalities]
1101 ; traceTcS "Checking if improvements existed." (ppr fdimprs)
1102 ; if isEmptyWorkList fd_work || haveBeenImproved fdimprs pty1 pty2 then
1104 mkIRContinue workItem KeepInert fd_work
1105 else do { traceTcS "Recording improvement and throwing item back in worklist." (ppr (pty1,pty2))
1106 ; mkIRStop_RecordImprovement KeepInert
1107 (fd_work `unionWorkLists` workListFromCCan workItem) (pty1,pty2)
1109 -- See Note [FunDep Reactions]
1112 -- Class constraint and given equality: use the equality to rewrite
1113 -- the class constraint.
1114 doInteractWithInert _fdimprs
1115 (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1116 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
1117 | ifl `canRewrite` wfl
1118 , tv `elemVarSet` tyVarsOfTypes xis
1119 = if isDerivedSC wfl then
1120 mkIRStop KeepInert $ emptyWorkList -- See Note [Adding Derived Superclasses]
1121 else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
1122 -- Continue with rewritten Dictionary because we can only be in the
1123 -- interactWithEqsStage, so the dictionary is inert.
1124 ; mkIRContinue rewritten_dict KeepInert emptyWorkList }
1126 doInteractWithInert _fdimprs
1127 (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
1128 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1129 | wfl `canRewrite` ifl
1130 , tv `elemVarSet` tyVarsOfTypes xis
1131 = if isDerivedSC ifl then
1132 mkIRContinue workItem DropInert emptyWorkList -- No need to do any rewriting,
1133 -- see Note [Adding Derived Superclasses]
1134 else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
1135 ; mkIRContinue workItem DropInert (workListFromCCan rewritten_dict) }
1137 -- Class constraint and given equality: use the equality to rewrite
1138 -- the class constraint.
1139 doInteractWithInert _fdimprs
1140 (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1141 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
1142 | ifl `canRewrite` wfl
1143 , tv `elemVarSet` tyVarsOfType ty
1144 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
1145 ; mkIRContinue rewritten_ip KeepInert emptyWorkList }
1147 doInteractWithInert _fdimprs
1148 (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
1149 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1150 | wfl `canRewrite` ifl
1151 , tv `elemVarSet` tyVarsOfType ty
1152 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
1153 ; mkIRContinue workItem DropInert (workListFromCCan rewritten_ip) }
1155 -- Two implicit parameter constraints. If the names are the same,
1156 -- but their types are not, we generate a wanted type equality
1157 -- that equates the type (this is "improvement").
1158 -- However, we don't actually need the coercion evidence,
1159 -- so we just generate a fresh coercion variable that isn't used anywhere.
1160 doInteractWithInert _fdimprs
1161 (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
1162 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
1163 | nm1 == nm2 && isGiven wfl && isGiven ifl
1164 = -- See Note [Overriding implicit parameters]
1165 -- Dump the inert item, override totally with the new one
1166 -- Do not require type equality
1167 mkIRContinue workItem DropInert emptyWorkList
1169 | nm1 == nm2 && ty1 `tcEqType` ty2
1170 = solveOneFromTheOther (id1,ifl) workItem
1173 = -- See Note [When improvement happens]
1174 do { co_var <- newWantedCoVar ty1 ty2
1175 ; let flav = Wanted (combineCtLoc ifl wfl)
1176 ; cans <- mkCanonical flav co_var
1177 ; mkIRContinue workItem KeepInert cans }
1180 -- Inert: equality, work item: function equality
1182 -- Never rewrite a given with a wanted equality, and a type function
1183 -- equality can never rewrite an equality. Note also that if we have
1184 -- F x1 ~ x2 and a ~ x3, and a occurs in x2, we don't rewrite it. We
1185 -- can wait until F x1 ~ x2 matches another F x1 ~ x4, and only then
1186 -- we will ``expose'' x2 and x4 to rewriting.
1188 -- Otherwise, we can try rewriting the type function equality with the equality.
1189 doInteractWithInert _fdimprs
1190 (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
1191 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
1192 , cc_tyargs = args, cc_rhs = xi2 })
1193 | ifl `canRewrite` wfl
1194 , tv `elemVarSet` tyVarsOfTypes args
1195 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
1196 ; mkIRStop KeepInert (workListFromCCan rewritten_funeq) }
1197 -- must Stop here, because we may no longer be inert after the rewritting.
1199 -- Inert: function equality, work item: equality
1200 doInteractWithInert _fdimprs
1201 (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
1202 , cc_tyargs = args, cc_rhs = xi1 })
1203 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
1204 | wfl `canRewrite` ifl
1205 , tv `elemVarSet` tyVarsOfTypes args
1206 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
1207 ; mkIRContinue workItem DropInert (workListFromCCan rewritten_funeq) }
1209 doInteractWithInert _fdimprs
1210 (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
1211 , cc_tyargs = args1, cc_rhs = xi1 })
1212 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
1213 , cc_tyargs = args2, cc_rhs = xi2 })
1214 | fl1 `canSolve` fl2 && lhss_match
1215 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1216 ; mkIRStop KeepInert cans }
1217 | fl2 `canSolve` fl1 && lhss_match
1218 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1219 ; mkIRContinue workItem DropInert cans }
1221 lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
1223 doInteractWithInert _fdimprs
1224 inert@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1225 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
1226 -- Check for matching LHS
1227 | fl1 `canSolve` fl2 && tv1 == tv2
1228 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1229 ; mkIRStop KeepInert cans }
1231 | fl2 `canSolve` fl1 && tv1 == tv2
1232 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1233 ; mkIRContinue workItem DropInert cans }
1235 -- Check for rewriting RHS
1236 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1237 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1238 ; mkIRStop KeepInert rewritten_eq }
1239 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1240 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1241 ; mkIRContinue workItem DropInert rewritten_eq }
1243 -- Finally, if workitem is a Flatten Equivalence Class constraint and the
1244 -- inert is a wanted constraint, even when the workitem cannot rewrite the
1245 -- inert, drop the inert out because you may have to reconsider solving the
1246 -- inert *using* the equivalence class you created. See note [Loopy Spontaneous Solving]
1247 -- and [InertSet FlattenSkolemEqClass]
1249 | not $ isGiven fl1, -- The inert is wanted or derived
1250 isMetaTyVar tv1, -- and has a unification variable lhs
1251 FlatSkol {} <- tcTyVarDetails tv2, -- And workitem is a flatten skolem equality
1252 Just tv2' <- tcGetTyVar_maybe xi2, FlatSkol {} <- tcTyVarDetails tv2'
1253 = mkIRContinue workItem DropInert (workListFromCCan inert)
1256 -- Fall-through case for all other situations
1257 doInteractWithInert _fdimprs _ workItem = noInteraction workItem
1259 -------------------------
1260 -- Equational Rewriting
1261 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1262 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1263 = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
1264 args = substTysWith [tv] [xi] xis
1266 dict_co = mkTyConCoercion con cos
1267 ; dv' <- newDictVar cl args
1269 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
1270 _given_or_derived -> setDictBind dv' (EvCast dv dict_co)
1271 ; return (CDictCan { cc_id = dv'
1274 , cc_tyargs = args }) }
1276 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1277 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1278 = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi]
1279 ty' = substTyWith [tv] [xi] ty
1280 ; ipid' <- newIPVar nm ty'
1282 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co))
1283 _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co)
1284 ; return (CIPCan { cc_id = ipid'
1287 , cc_ip_ty = ty' }) }
1289 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1290 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2)
1291 = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
1292 args' = substTysWith [tv] [xi1] args
1293 fun_co = mkTyConCoercion tc arg_cos
1294 ; cv2' <- case gw of
1295 Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2
1296 ; setWantedCoBind cv2 $
1297 mkTransCoercion fun_co (mkCoVarCoercion cv2')
1299 _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2 $
1300 mkTransCoercion (mkSymCoercion fun_co) (mkCoVarCoercion cv2)
1301 ; return (CFunEqCan { cc_id = cv2'
1308 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
1309 -- Use the first equality to rewrite the second, flavors already checked.
1310 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1311 -- rewrites c2 to give
1312 -- c2' : tv2 ~ xi2[xi1/tv1]
1313 -- We must do an occurs check to sure the new constraint is canonical
1314 -- So we might return an empty bag
1315 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1316 | Just tv2' <- tcGetTyVar_maybe xi2'
1317 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1318 = do { when (isWanted gw) (setWantedCoBind cv2 (mkSymCoercion co2'))
1319 ; return emptyCCan }
1324 -> do { cv2' <- newWantedCoVar (mkTyVarTy tv2) xi2'
1325 ; setWantedCoBind cv2 $
1326 mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion co2'
1329 -> newGivOrDerCoVar (mkTyVarTy tv2) xi2' $
1330 mkCoVarCoercion cv2 `mkTransCoercion` co2'
1332 ; xi2'' <- canOccursCheck gw tv2 xi2' -- we know xi2' is *not* tv2
1333 ; canEq gw cv2' (mkTyVarTy tv2) xi2''
1336 xi2' = substTyWith [tv1] [xi1] xi2
1337 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1340 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
1341 -- Used to ineract two equalities of the following form:
1342 -- First Equality: co1: (XXX ~ xi1)
1343 -- Second Equality: cv2: (XXX ~ xi2)
1344 -- Where the cv1 `canSolve` cv2 equality
1345 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1),
1346 -- See Note [Efficient Orientation] for that
1347 rewriteEqLHS which (co1,xi1) (cv2,gw,xi2)
1348 = do { cv2' <- case (isWanted gw, which) of
1349 (True,LeftComesFromInert) ->
1350 do { cv2' <- newWantedCoVar xi2 xi1
1351 ; setWantedCoBind cv2 $
1352 co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
1354 (True,RightComesFromInert) ->
1355 do { cv2' <- newWantedCoVar xi1 xi2
1356 ; setWantedCoBind cv2 $
1357 co1 `mkTransCoercion` mkCoVarCoercion cv2'
1359 (False,LeftComesFromInert) ->
1360 newGivOrDerCoVar xi2 xi1 $
1361 mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
1362 (False,RightComesFromInert) ->
1363 newGivOrDerCoVar xi1 xi2 $
1364 mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
1365 ; mkCanonical gw cv2'
1368 solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult
1369 -- First argument inert, second argument workitem. They both represent
1370 -- wanted/given/derived evidence for the *same* predicate so we try here to
1371 -- discharge one directly from the other.
1373 -- Precondition: value evidence only (implicit parameters, classes)
1375 solveOneFromTheOther (iid,ifl) workItem
1376 -- Both derived needs a special case. You might think that we do not need
1377 -- two evidence terms for the same claim. But, since the evidence is partial,
1378 -- either evidence may do in some cases; see TcSMonad.isGoodRecEv.
1379 -- See also Example 3 in Note [Superclasses and recursive dictionaries]
1380 | isDerived ifl && isDerived wfl
1381 = noInteraction workItem
1383 | ifl `canSolve` wfl
1384 = do { unless (isGiven wfl) $ setEvBind wid (EvId iid)
1385 -- Overwrite the binding, if one exists
1386 -- For Givens, which are lambda-bound, nothing to overwrite,
1387 ; dischargeWorkItem }
1389 | otherwise -- wfl `canSolve` ifl
1390 = do { unless (isGiven ifl) $ setEvBind iid (EvId wid)
1391 ; mkIRContinue workItem DropInert emptyWorkList }
1394 wfl = cc_flavor workItem
1395 wid = cc_id workItem
1398 Note [Superclasses and recursive dictionaries]
1399 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1400 Overlaps with Note [SUPERCLASS-LOOP 1]
1401 Note [SUPERCLASS-LOOP 2]
1402 Note [Recursive instances and superclases]
1403 ToDo: check overlap and delete redundant stuff
1405 Right before adding a given into the inert set, we must
1406 produce some more work, that will bring the superclasses
1407 of the given into scope. The superclass constraints go into
1410 When we simplify a wanted constraint, if we first see a matching
1411 instance, we may produce new wanted work. To (1) avoid doing this work
1412 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1413 this item as solved (in effect, given) into our inert set and with that add
1414 its superclass constraints (as given) in our worklist.
1416 But now we have added partially solved constraints to the worklist which may
1417 interact with other wanteds. Consider the example:
1421 class Eq b => Foo a b --- 0-th selector
1422 instance Eq a => Foo [a] a --- fooDFun
1424 and wanted (Foo [t] t). We are first going to see that the instance matches
1425 and create an inert set that includes the solved (Foo [t] t) and its
1427 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1428 d2 :_g Eq t d2 := EvSuperClass d1 0
1429 Our work list is going to contain a new *wanted* goal
1431 It is wrong to react the wanted (Eq t) with the given (Eq t) because that would
1432 construct loopy evidence. Hence the check isGoodRecEv in doInteractWithInert.
1434 OK, so we have ruled out bad behaviour, but how do we ge recursive dictionaries,
1439 data D r = ZeroD | SuccD (r (D r));
1441 instance (Eq (r (D r))) => Eq (D r) where
1442 ZeroD == ZeroD = True
1443 (SuccD a) == (SuccD b) = a == b
1446 equalDC :: D [] -> D [] -> Bool;
1449 We need to prove (Eq (D [])). Here's how we go:
1453 by instance decl, holds if
1457 *BUT* we have an inert set which gives us (no superclasses):
1459 By the instance declaration of Eq we can show the 'd2' goal if
1461 where d2 = dfEqList d3
1463 Now, however this wanted can interact with our inert d1 to set:
1465 and solve the goal. Why was this interaction OK? Because, if we chase the
1466 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1468 d3 := dfEqD2 (dfEqList d3)
1469 which is FINE because the use of d3 is protected by the instance function
1472 So, our strategy is to try to put solved wanted dictionaries into the
1473 inert set along with their superclasses (when this is meaningful,
1474 i.e. when new wanted goals are generated) but solve a wanted dictionary
1475 from a given only in the case where the evidence variable of the
1476 wanted is mentioned in the evidence of the given (recursively through
1477 the evidence binds) in a protected way: more instance function applications
1478 than superclass selectors.
1480 Here are some more examples from GHC's previous type checker
1484 This code arises in the context of "Scrap Your Boilerplate with Class"
1488 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1489 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1491 class Data Maybe a => Foo a
1493 instance Foo t => Sat (Maybe t) -- dfunSat
1495 instance Data Maybe a => Foo a -- dfunFoo1
1496 instance Foo a => Foo [a] -- dfunFoo2
1497 instance Foo [Char] -- dfunFoo3
1499 Consider generating the superclasses of the instance declaration
1500 instance Foo a => Foo [a]
1502 So our problem is this
1504 d1 :_w Data Maybe [t]
1506 We may add the given in the inert set, along with its superclasses
1507 [assuming we don't fail because there is a matching instance, see
1508 tryTopReact, given case ]
1512 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1513 d1 :_w Data Maybe [t]
1514 Then d2 can readily enter the inert, and we also do solving of the wanted
1517 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1519 d2 :_w Sat (Maybe [t])
1521 d01 :_g Data Maybe t
1522 Now, we may simplify d2 more:
1525 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1526 d1 :_g Data Maybe [t]
1527 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1531 d01 :_g Data Maybe t
1533 Now, we can just solve d3.
1536 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1537 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1540 d01 :_g Data Maybe t
1541 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1544 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1545 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1546 d4 :_g Foo [t] d4 := dfunFoo2 d5
1549 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1550 d01 :_g Data Maybe t
1551 Now, d5 can be solved! (and its superclass enter scope)
1554 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1555 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1556 d4 :_g Foo [t] d4 := dfunFoo2 d5
1557 d5 :_g Foo t d5 := dfunFoo1 d7
1560 d6 :_g Data Maybe [t]
1561 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1562 d01 :_g Data Maybe t
1565 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1566 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1567 that must not be used (look at case interactInert where both inert and workitem
1568 are givens). So we have several options:
1569 - Drop the workitem always (this will drop d8)
1570 This feels very unsafe -- what if the work item was the "good" one
1571 that should be used later to solve another wanted?
1572 - Don't drop anyone: the inert set may contain multiple givens!
1573 [This is currently implemented]
1575 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1576 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1577 d7. Now the [isRecDictEv] function in the ineration solver
1578 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1579 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1581 So, no interaction happens there. Then we meet d01 and there is no recursion
1582 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1584 Note [SUPERCLASS-LOOP 1]
1585 ~~~~~~~~~~~~~~~~~~~~~~~~
1586 We have to be very, very careful when generating superclasses, lest we
1587 accidentally build a loop. Here's an example:
1591 class S a => C a where { opc :: a -> a }
1592 class S b => D b where { opd :: b -> b }
1594 instance C Int where
1597 instance D Int where
1600 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1601 Simplifying, we may well get:
1602 $dfCInt = :C ds1 (opd dd)
1605 Notice that we spot that we can extract ds1 from dd.
1607 Alas! Alack! We can do the same for (instance D Int):
1609 $dfDInt = :D ds2 (opc dc)
1613 And now we've defined the superclass in terms of itself.
1614 Two more nasty cases are in
1619 - Satisfy the superclass context *all by itself*
1620 (tcSimplifySuperClasses)
1621 - And do so completely; i.e. no left-over constraints
1622 to mix with the constraints arising from method declarations
1625 Note [SUPERCLASS-LOOP 2]
1626 ~~~~~~~~~~~~~~~~~~~~~~~~
1627 We need to be careful when adding "the constaint we are trying to prove".
1628 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1630 class Ord a => C a where
1631 instance Ord [a] => C [a] where ...
1633 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1634 superclasses of C [a] to avails. But we must not overwrite the binding
1635 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1638 Here's another variant, immortalised in tcrun020
1639 class Monad m => C1 m
1640 class C1 m => C2 m x
1641 instance C2 Maybe Bool
1642 For the instance decl we need to build (C1 Maybe), and it's no good if
1643 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1644 before we search for C1 Maybe.
1646 Here's another example
1647 class Eq b => Foo a b
1648 instance Eq a => Foo [a] a
1652 we'll first deduce that it holds (via the instance decl). We must not
1653 then overwrite the Eq t constraint with a superclass selection!
1655 At first I had a gross hack, whereby I simply did not add superclass constraints
1656 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1657 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1658 I found a very obscure program (now tcrun021) in which improvement meant the
1659 simplifier got two bites a the cherry... so something seemed to be an Stop
1660 first time, but reducible next time.
1662 Now we implement the Right Solution, which is to check for loops directly
1663 when adding superclasses. It's a bit like the occurs check in unification.
1665 Note [Recursive instances and superclases]
1666 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1667 Consider this code, which arises in the context of "Scrap Your
1668 Boilerplate with Class".
1672 instance Sat (ctx Char) => Data ctx Char
1673 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1675 class Data Maybe a => Foo a
1677 instance Foo t => Sat (Maybe t)
1679 instance Data Maybe a => Foo a
1680 instance Foo a => Foo [a]
1683 In the instance for Foo [a], when generating evidence for the superclasses
1684 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1685 Using the instance for Data, we therefore need
1686 (Sat (Maybe [a], Data Maybe a)
1687 But we are given (Foo a), and hence its superclass (Data Maybe a).
1688 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1689 we need (Foo [a]). And that is the very dictionary we are bulding
1690 an instance for! So we must put that in the "givens". So in this
1692 Given: Foo a, Foo [a]
1693 Wanted: Data Maybe [a]
1695 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1696 the givens, which is what 'addGiven' would normally do. Why? Because
1697 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1698 by selecting a superclass from Foo [a], which simply makes a loop.
1700 On the other hand we *must* put the superclasses of (Foo a) in
1701 the givens, as you can see from the derivation described above.
1703 Conclusion: in the very special case of tcSimplifySuperClasses
1704 we have one 'given' (namely the "this" dictionary) whose superclasses
1705 must not be added to 'givens' by addGiven.
1707 There is a complication though. Suppose there are equalities
1708 instance (Eq a, a~b) => Num (a,b)
1709 Then we normalise the 'givens' wrt the equalities, so the original
1710 given "this" dictionary is cast to one of a different type. So it's a
1711 bit trickier than before to identify the "special" dictionary whose
1712 superclasses must not be added. See test
1713 indexed-types/should_run/EqInInstance
1715 We need a persistent property of the dictionary to record this
1716 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1717 but cool), which is maintained by dictionary normalisation.
1718 Specifically, the InstLocOrigin is
1720 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1723 Note [MATCHING-SYNONYMS]
1724 ~~~~~~~~~~~~~~~~~~~~~~~~
1725 When trying to match a dictionary (D tau) to a top-level instance, or a
1726 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1727 we do *not* need to expand type synonyms because the matcher will do that for us.
1730 Note [RHS-FAMILY-SYNONYMS]
1731 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1732 The RHS of a family instance is represented as yet another constructor which is
1733 like a type synonym for the real RHS the programmer declared. Eg:
1734 type instance F (a,a) = [a]
1736 :R32 a = [a] -- internal type synonym introduced
1737 F (a,a) ~ :R32 a -- instance
1739 When we react a family instance with a type family equation in the work list
1740 we keep the synonym-using RHS without expansion.
1743 *********************************************************************************
1745 The top-reaction Stage
1747 *********************************************************************************
1750 -- If a work item has any form of interaction with top-level we get this
1751 data TopInteractResult
1752 = NoTopInt -- No top-level interaction
1754 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1755 -- for superclasses)
1756 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1757 } -- NB: in ``given'' (solved) form if the
1758 -- original was wanted or given and instance match
1759 -- was found, but may also be in wanted form if we
1760 -- only reacted with functional dependencies
1761 -- arising from top-level instances.
1763 topReactionsStage :: SimplifierStage
1764 topReactionsStage workItem inerts
1765 = do { tir <- tryTopReact workItem
1768 return $ SR { sr_inerts = inerts
1769 , sr_new_work = emptyWorkList
1770 , sr_stop = ContinueWith workItem }
1771 SomeTopInt tir_new_work tir_new_inert ->
1772 return $ SR { sr_inerts = inerts
1773 , sr_new_work = tir_new_work
1774 , sr_stop = tir_new_inert
1778 tryTopReact :: WorkItem -> TcS TopInteractResult
1779 tryTopReact workitem
1780 = do { -- A flag controls the amount of interaction allowed
1781 -- See Note [Simplifying RULE lhs constraints]
1782 ctxt <- getTcSContext
1783 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1784 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1785 ; doTopReact workitem }
1786 else return NoTopInt
1789 allowedTopReaction :: Bool -> WorkItem -> Bool
1790 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1791 allowedTopReaction _ _ = True
1794 doTopReact :: WorkItem -> TcS TopInteractResult
1795 -- The work item does not react with the inert set,
1796 -- so try interaction with top-level instances
1798 -- Given dictionary; just add superclasses
1799 -- See Note [Given constraint that matches an instance declaration]
1800 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Given loc
1801 , cc_class = cls, cc_tyargs = xis })
1802 = do { sc_work <- newGivenSCWork dv loc cls xis
1803 ; return $ SomeTopInt sc_work (ContinueWith workItem) }
1805 -- Derived dictionary
1806 -- Do not add any further derived superclasses; their
1807 -- full transitive closure has already been added.
1808 -- But do look for functional dependencies
1809 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Derived loc _
1810 , cc_class = cls, cc_tyargs = xis })
1811 = do { fd_work <- findClassFunDeps dv cls xis loc
1812 ; if isEmptyWorkList fd_work then
1814 else return $ SomeTopInt { tir_new_work = fd_work
1815 , tir_new_inert = ContinueWith workItem } }
1817 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Wanted loc
1818 , cc_class = cls, cc_tyargs = xis })
1819 = do { -- See Note [MATCHING-SYNONYMS]
1820 ; lkp_inst_res <- matchClassInst cls xis loc
1821 ; case lkp_inst_res of
1823 do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1824 ; fd_work <- findClassFunDeps dv cls xis loc
1825 ; if isEmptyWorkList fd_work then
1826 do { sc_work <- newDerivedSCWork dv loc cls xis
1827 -- See Note [Adding Derived Superclasses]
1828 -- NB: workItem is inert, but it isn't solved
1829 -- keep it as inert, although it's not solved
1830 -- because we have now reacted all its
1831 -- top-level fundep-induced equalities!
1832 ; return $ SomeTopInt
1833 { tir_new_work = fd_work `unionWorkLists` sc_work
1834 , tir_new_inert = ContinueWith workItem } }
1836 else -- More fundep work produced, don't do any superclass stuff,
1837 -- just thow him back in the worklist, which will prioritize
1838 -- the solution of fd equalities
1840 { tir_new_work = fd_work `unionWorkLists`
1841 workListFromCCan workItem
1842 , tir_new_inert = Stop } }
1844 GenInst wtvs ev_term -> -- Solved
1845 -- No need to do fundeps stuff here; the instance
1846 -- matches already so we won't get any more info
1847 -- from functional dependencies
1848 do { traceTcS "doTopReact/ found class instance for" (ppr dv)
1849 ; setDictBind dv ev_term
1850 ; inst_work <- canWanteds wtvs
1852 -- Solved in one step and no new wanted work produced.
1853 -- i.e we directly matched a top-level instance
1854 -- No point in caching this in 'inert', nor in adding superclasses
1855 then return $ SomeTopInt { tir_new_work = emptyWorkList
1856 , tir_new_inert = Stop }
1858 -- Solved and new wanted work produced, you may cache the
1859 -- (tentatively solved) dictionary as Derived and its superclasses
1860 else do { let solved = makeSolvedByInst workItem
1861 ; sc_work <- newDerivedSCWork dv loc cls xis
1862 -- See Note [Adding Derived Superclasses]
1863 ; return $ SomeTopInt
1864 { tir_new_work = inst_work `unionWorkLists` sc_work
1865 , tir_new_inert = ContinueWith solved } }
1869 doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
1870 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1871 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1872 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1876 MatchInstSingle (rep_tc, rep_tys)
1877 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1878 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1879 -- Eagerly expand away the type synonym on the
1880 -- RHS of a type function, so that it never
1881 -- appears in an error message
1882 -- See Note [Type synonym families] in TyCon
1883 coe = mkTyConApp coe_tc rep_tys
1885 Wanted {} -> do { cv' <- newWantedCoVar rhs_ty xi
1886 ; setWantedCoBind cv $
1887 coe `mkTransCoercion`
1890 _ -> newGivOrDerCoVar xi rhs_ty $
1891 mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
1893 ; can_cts <- mkCanonical fl cv'
1894 ; return $ SomeTopInt can_cts Stop }
1896 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1900 -- Any other work item does not react with any top-level equations
1901 doTopReact _workItem = return NoTopInt
1903 ----------------------
1904 findClassFunDeps :: EvVar -> Class -> [Xi] -> WantedLoc -> TcS WorkList
1905 -- Look for a fundep reaction beween the wanted item
1906 -- and a top-level instance declaration
1907 findClassFunDeps dv cls xis loc
1908 = do { instEnvs <- getInstEnvs
1909 ; let eqn_pred_locs = improveFromInstEnv (classInstances instEnvs)
1910 (ClassP cls xis, ppr dv)
1911 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
1912 -- NB: fundeps generate some wanted equalities, but
1913 -- we don't use their evidence for anything
1914 ; canWanteds wevvars }
1917 Note [Adding Derived Superclasses]
1918 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1919 Generally speaking, we want to be able to add derived superclasses of
1920 unsolved wanteds, and wanteds that have been partially being solved
1921 via an instance. This is important to be able to simplify the inferred
1922 constraints more (and to allow for recursive dictionaries, less
1923 importantly). Example:
1925 Inferred wanted constraint is (Eq a, Ord a), but we'd only like to
1926 quantify over Ord a, hence we would like to be able to add the
1927 superclass of Ord a as Derived and use it to solve the wanted Eq a.
1929 Hence we will add Derived superclasses in the following two cases:
1930 (1) When we meet an unsolved wanted in top-level reactions
1931 (2) When we partially solve a wanted in top-level reactions using an instance decl.
1933 At that point, we have two options:
1934 (1) Add transitively add *ALL* of the superclasses of the Derived
1935 (2) Add only the immediate ones, but whenever we meet a Derived in
1936 the future, add its own superclasses as Derived.
1938 Option (2) is terrible, because deriveds may be rewritten or kicked
1939 out of the inert set, which will result in slightly rewritten
1940 superclasses being reintroduced in the worklist and the inert set. Eg:
1943 instance Foo a => B [a]
1945 Original constraints:
1947 [Given] co : a ~ Int
1949 We apply the instance to the wanted and put it and its superclasses as
1950 as Deriveds in the inerts:
1953 [Derived] (sel d) : C [a]
1956 [Given] co : a ~ Int
1959 Now, suppose that we interact the Derived with the Given equality, and
1960 kick him out of the inert, the next time around a superclass C [Int]
1961 will be produced -- but we already *have* C [a] in the inerts which
1962 will anyway get rewritten to C [Int].
1964 So we choose (1), and *never* introduce any more superclass work from
1965 Deriveds. This enables yet another optimisation: If we ever meet an
1966 equality that can rewrite a Derived, if that Derived is a superclass
1967 derived (like C [a] above), i.e. not a partially solved one (like B
1968 [a]) above, we may simply completely *discard* that Derived. The
1969 reason is because somewhere in the inert lies the original wanted, or
1970 partially solved constraint that gave rise to that superclass, and
1971 that constraint *will* be kicked out, and *will* result in the
1972 rewritten superclass to be added in the inerts later on, anyway.
1976 Note [FunDep and implicit parameter reactions]
1977 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1978 Currently, our story of interacting two dictionaries (or a dictionary
1979 and top-level instances) for functional dependencies, and implicit
1980 paramters, is that we simply produce new wanted equalities. So for example
1982 class D a b | a -> b where ...
1988 We generate the extra work item
1990 where 'cv' is currently unused. However, this new item reacts with d2,
1991 discharging it in favour of a new constraint d2' thus:
1993 d2 := d2' |> D Int cv
1994 Now d2' can be discharged from d1
1996 We could be more aggressive and try to *immediately* solve the dictionary
1997 using those extra equalities. With the same inert set and work item we
1998 might dischard d2 directly:
2001 d2 := d1 |> D Int cv
2003 But in general it's a bit painful to figure out the necessary coercion,
2004 so we just take the first approach. Here is a better example. Consider:
2005 class C a b c | a -> b
2007 [Given] d1 : C T Int Char
2008 [Wanted] d2 : C T beta Int
2009 In this case, it's *not even possible* to solve the wanted immediately.
2010 So we should simply output the functional dependency and add this guy
2011 [but NOT its superclasses] back in the worklist. Even worse:
2012 [Given] d1 : C T Int beta
2013 [Wanted] d2: C T beta Int
2014 Then it is solvable, but its very hard to detect this on the spot.
2016 It's exactly the same with implicit parameters, except that the
2017 "aggressive" approach would be much easier to implement.
2019 Note [When improvement happens]
2020 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2021 We fire an improvement rule when
2023 * Two constraints match (modulo the fundep)
2024 e.g. C t1 t2, C t1 t3 where C a b | a->b
2025 The two match because the first arg is identical
2027 * At least one is not Given. If they are both given, we don't fire
2028 the reaction because we have no way of constructing evidence for a
2029 new equality nor does it seem right to create a new wanted goal
2030 (because the goal will most likely contain untouchables, which
2031 can't be solved anyway)!
2033 Note that we *do* fire the improvement if one is Given and one is Derived.
2034 The latter can be a superclass of a wanted goal. Example (tcfail138)
2035 class L a b | a -> b
2036 class (G a, L a b) => C a b
2038 instance C a b' => G (Maybe a)
2039 instance C a b => C (Maybe a) a
2040 instance L (Maybe a) a
2042 When solving the superclasses of the (C (Maybe a) a) instance, we get
2043 Given: C a b ... and hance by superclasses, (G a, L a b)
2045 Use the instance decl to get
2047 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
2048 and now we need improvement between that derived superclass an the Given (L a b)
2050 Note [Overriding implicit parameters]
2051 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2053 f :: (?x::a) -> Bool -> a
2055 g v = let ?x::Int = 3
2056 in (f v, let ?x::Bool = True in f v)
2058 This should probably be well typed, with
2059 g :: Bool -> (Int, Bool)
2061 So the inner binding for ?x::Bool *overrides* the outer one.
2062 Hence a work-item Given overrides an inert-item Given.
2064 Note [Given constraint that matches an instance declaration]
2065 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2066 What should we do when we discover that one (or more) top-level
2067 instances match a given (or solved) class constraint? We have
2070 1. Reject the program. The reason is that there may not be a unique
2071 best strategy for the solver. Example, from the OutsideIn(X) paper:
2072 instance P x => Q [x]
2073 instance (x ~ y) => R [x] y
2075 wob :: forall a b. (Q [b], R b a) => a -> Int
2077 g :: forall a. Q [a] => [a] -> Int
2080 will generate the impliation constraint:
2081 Q [a] => (Q [beta], R beta [a])
2082 If we react (Q [beta]) with its top-level axiom, we end up with a
2083 (P beta), which we have no way of discharging. On the other hand,
2084 if we react R beta [a] with the top-level we get (beta ~ a), which
2085 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
2086 now solvable by the given Q [a].
2088 However, this option is restrictive, for instance [Example 3] from
2089 Note [Recursive dictionaries] will fail to work.
2091 2. Ignore the problem, hoping that the situations where there exist indeed
2092 such multiple strategies are rare: Indeed the cause of the previous
2093 problem is that (R [x] y) yields the new work (x ~ y) which can be
2094 *spontaneously* solved, not using the givens.
2096 We are choosing option 2 below but we might consider having a flag as well.
2099 Note [New Wanted Superclass Work]
2100 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2101 Even in the case of wanted constraints, we add all of its superclasses as
2102 new given work. There are several reasons for this:
2103 a) to minimise error messages;
2104 eg suppose we have wanted (Eq a, Ord a)
2105 then we report only (Ord a) unsoluble
2107 b) to make the smallest number of constraints when *inferring* a type
2108 (same Eq/Ord example)
2110 c) for recursive dictionaries we *must* add the superclasses
2111 so that we can use them when solving a sub-problem
2113 d) To allow FD-like improvement for type families. Assume that
2115 class C a b | a -> b
2116 and we have to solve the implication constraint:
2118 Then, FD improvement can help us to produce a new wanted (beta ~ b)
2120 We want to have the same effect with the type family encoding of
2121 functional dependencies. Namely, consider:
2122 class (F a ~ b) => C a b
2123 Now suppose that we have:
2126 By interacting the given we will get given (F a ~ b) which is not
2127 enough by itself to make us discharge (C a beta). However, we
2128 may create a new derived equality from the super-class of the
2129 wanted constraint (C a beta), namely derived (F a ~ beta).
2130 Now we may interact this with given (F a ~ b) to get:
2132 But 'beta' is a touchable unification variable, and hence OK to
2133 unify it with 'b', replacing the derived evidence with the identity.
2135 This requires trySpontaneousSolve to solve *derived*
2136 equalities that have a touchable in their RHS, *in addition*
2137 to solving wanted equalities.
2139 Here is another example where this is useful.
2143 class (F a ~ b) => C a b
2144 And we are given the wanteds:
2148 We surely do *not* want to quantify over (b ~ c), since if someone provides
2149 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
2150 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
2152 Step 1: We will get new *given* superclass work,
2153 provisionally to our solving of w1 and w2
2155 g1: F a ~ b, g2 : F a ~ c,
2156 w1 : C a b, w2 : C a c, w3 : b ~ c
2158 The evidence for g1 and g2 is a superclass evidence term:
2160 g1 := sc w1, g2 := sc w2
2162 Step 2: The givens will solve the wanted w3, so that
2163 w3 := sym (sc w1) ; sc w2
2165 Step 3: Now, one may naively assume that then w2 can be solve from w1
2166 after rewriting with the (now solved equality) (b ~ c).
2168 But this rewriting is ruled out by the isGoodRectDict!
2170 Conclusion, we will (correctly) end up with the unsolved goals
2173 NB: The desugarer needs be more clever to deal with equalities
2174 that participate in recursive dictionary bindings.
2178 newGivenSCWork :: EvVar -> GivenLoc -> Class -> [Xi] -> TcS WorkList
2179 newGivenSCWork ev loc cls xis
2180 | NoScSkol <- ctLocOrigin loc -- Very important!
2181 = return emptyWorkList
2183 = newImmSCWorkFromFlavored ev (Given loc) cls xis >>= return
2185 newDerivedSCWork :: EvVar -> WantedLoc -> Class -> [Xi] -> TcS WorkList
2186 newDerivedSCWork ev loc cls xis
2187 = do { ims <- newImmSCWorkFromFlavored ev flavor cls xis
2190 rec_sc_work :: CanonicalCts -> TcS CanonicalCts
2192 = do { bg <- mapBagM (\c -> do { ims <- imm_sc_work c
2193 ; recs_ims <- rec_sc_work ims
2194 ; return $ consBag c recs_ims }) cts
2195 ; return $ concatBag bg }
2196 imm_sc_work (CDictCan { cc_id = dv, cc_flavor = fl, cc_class = cls, cc_tyargs = xis })
2197 = newImmSCWorkFromFlavored dv fl cls xis
2198 imm_sc_work _ct = return emptyCCan
2200 flavor = Derived loc DerSC
2202 newImmSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS WorkList
2203 -- Returns immediate superclasses
2204 newImmSCWorkFromFlavored ev flavor cls xis
2205 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
2206 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
2207 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
2208 ; mkCanonicals flavor sc_vars }
2210 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
2213 data LookupInstResult
2215 | GenInst [WantedEvVar] EvTerm
2217 matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
2218 matchClassInst clas tys loc
2219 = do { let pred = mkClassPred clas tys
2220 ; mb_result <- matchClass clas tys
2222 MatchInstNo -> return NoInstance
2223 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
2224 -- we learn more about the reagent
2225 MatchInstSingle (dfun_id, mb_inst_tys) ->
2226 do { checkWellStagedDFun pred dfun_id loc
2228 -- It's possible that not all the tyvars are in
2229 -- the substitution, tenv. For example:
2230 -- instance C X a => D X where ...
2231 -- (presumably there's a functional dependency in class C)
2232 -- Hence mb_inst_tys :: Either TyVar TcType
2234 ; tys <- instDFunTypes mb_inst_tys
2235 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
2236 ; if null theta then
2237 return (GenInst [] (EvDFunApp dfun_id tys []))
2239 { ev_vars <- instDFunConstraints theta
2240 ; let wevs = [WantedEvVar w loc | w <- ev_vars]
2241 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }