3 solveInteract, solveInteractGiven, solveInteractWanted,
4 AtomicInert, tyVarsOfInert,
5 InertSet, emptyInert, updInertSet, extractUnsolved, solveOne,
8 #include "HsVersions.h"
22 import Inst( tyVarsOfEvVar )
36 import qualified Data.Map as Map
38 import Control.Monad( when )
40 import FastString ( sLit )
44 Note [InertSet invariants]
45 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
46 An InertSet is a bag of canonical constraints, with the following invariants:
48 1 No two constraints react with each other.
50 A tricky case is when there exists a given (solved) dictionary
51 constraint and a wanted identical constraint in the inert set, but do
52 not react because reaction would create loopy dictionary evidence for
53 the wanted. See note [Recursive dictionaries]
55 2 Given equalities form an idempotent substitution [none of the
56 given LHS's occur in any of the given RHS's or reactant parts]
58 3 Wanted equalities also form an idempotent substitution
60 4 The entire set of equalities is acyclic.
62 5 Wanted dictionaries are inert with the top-level axiom set
64 6 Equalities of the form tv1 ~ tv2 always have a touchable variable
65 on the left (if possible).
67 7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints
68 will be marked as solved right before being pushed into the inert set.
69 See note [Touchables and givens].
71 8 No Given constraint mentions a touchable unification variable,
74 Note that 6 and 7 are /not/ enforced by canonicalization but rather by
75 insertion in the inert list, ie by TcInteract.
77 During the process of solving, the inert set will contain some
78 previously given constraints, some wanted constraints, and some given
79 constraints which have arisen from solving wanted constraints. For
80 now we do not distinguish between given and solved constraints.
82 Note that we must switch wanted inert items to given when going under an
83 implication constraint (when in top-level inference mode).
87 data CCanMap a = CCanMap { cts_given :: Map.Map a CanonicalCts
88 -- Invariant: all Given
89 , cts_derived :: Map.Map a CanonicalCts
90 -- Invariant: all Derived
91 , cts_wanted :: Map.Map a CanonicalCts }
92 -- Invariant: all Wanted
94 cCanMapToBag :: Ord a => CCanMap a -> CanonicalCts
95 cCanMapToBag cmap = Map.fold unionBags rest_wder (cts_given cmap)
96 where rest_wder = Map.fold unionBags rest_der (cts_wanted cmap)
97 rest_der = Map.fold unionBags emptyCCan (cts_derived cmap)
99 emptyCCanMap :: CCanMap a
100 emptyCCanMap = CCanMap { cts_given = Map.empty
101 , cts_derived = Map.empty, cts_wanted = Map.empty }
103 updCCanMap:: Ord a => (a,CanonicalCt) -> CCanMap a -> CCanMap a
104 updCCanMap (a,ct) cmap
105 = case cc_flavor ct of
107 -> cmap { cts_wanted = Map.insertWith unionBags a this_ct (cts_wanted cmap) }
109 -> cmap { cts_given = Map.insertWith unionBags a this_ct (cts_given cmap) }
111 -> cmap { cts_derived = Map.insertWith unionBags a this_ct (cts_derived cmap) }
112 where this_ct = singleCCan ct
114 getRelevantCts :: Ord a => a -> CCanMap a -> (CanonicalCts, CCanMap a)
115 -- Gets the relevant constraints and returns the rest of the CCanMap
116 getRelevantCts a cmap
117 = let relevant = unionManyBags [ Map.findWithDefault emptyCCan a (cts_wanted cmap)
118 , Map.findWithDefault emptyCCan a (cts_given cmap)
119 , Map.findWithDefault emptyCCan a (cts_derived cmap) ]
120 residual_map = cmap { cts_wanted = Map.delete a (cts_wanted cmap)
121 , cts_given = Map.delete a (cts_given cmap)
122 , cts_derived = Map.delete a (cts_derived cmap) }
123 in (relevant, residual_map)
125 extractUnsolvedCMap :: Ord a => CCanMap a -> (CanonicalCts, CCanMap a)
126 -- Gets the wanted or derived constraints and returns a residual
127 -- CCanMap with only givens.
128 extractUnsolvedCMap cmap =
129 let wntd = Map.fold unionBags emptyCCan (cts_wanted cmap)
130 derd = Map.fold unionBags emptyCCan (cts_derived cmap)
131 in (wntd `unionBags` derd,
132 cmap { cts_wanted = Map.empty, cts_derived = Map.empty })
135 -- See Note [InertSet invariants]
137 = IS { inert_eqs :: CanonicalCts -- Equalities only (CTyEqCan)
138 , inert_dicts :: CCanMap Class -- Dictionaries only
139 , inert_ips :: CCanMap (IPName Name) -- Implicit parameters
140 , inert_frozen :: CanonicalCts
141 , inert_funeqs :: CCanMap TyCon -- Type family equalities only
142 -- This representation allows us to quickly get to the relevant
143 -- inert constraints when interacting a work item with the inert set.
146 tyVarsOfInert :: InertSet -> TcTyVarSet
147 tyVarsOfInert (IS { inert_eqs = eqs
148 , inert_dicts = dictmap
150 , inert_frozen = frozen
151 , inert_funeqs = funeqmap }) = tyVarsOfCanonicals cts
153 cts = eqs `andCCan` frozen `andCCan` cCanMapToBag dictmap
154 `andCCan` cCanMapToBag ipmap `andCCan` cCanMapToBag funeqmap
156 instance Outputable InertSet where
157 ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
158 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_dicts is)))
159 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_ips is)))
160 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_funeqs is)))
161 , vcat (map ppr (Bag.bagToList $ inert_frozen is))
164 emptyInert :: InertSet
165 emptyInert = IS { inert_eqs = Bag.emptyBag
166 , inert_frozen = Bag.emptyBag
167 , inert_dicts = emptyCCanMap
168 , inert_ips = emptyCCanMap
169 , inert_funeqs = emptyCCanMap }
171 updInertSet :: InertSet -> AtomicInert -> InertSet
173 | isCTyEqCan item -- Other equality
174 = let eqs' = inert_eqs is `Bag.snocBag` item
175 in is { inert_eqs = eqs' }
176 | Just cls <- isCDictCan_Maybe item -- Dictionary
177 = is { inert_dicts = updCCanMap (cls,item) (inert_dicts is) }
178 | Just x <- isCIPCan_Maybe item -- IP
179 = is { inert_ips = updCCanMap (x,item) (inert_ips is) }
180 | Just tc <- isCFunEqCan_Maybe item -- Function equality
181 = is { inert_funeqs = updCCanMap (tc,item) (inert_funeqs is) }
183 = is { inert_frozen = inert_frozen is `Bag.snocBag` item }
185 extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
186 -- Postcondition: the returned canonical cts are either Derived, or Wanted.
187 extractUnsolved is@(IS {inert_eqs = eqs})
188 = let is_solved = is { inert_eqs = solved_eqs
189 , inert_dicts = solved_dicts
190 , inert_ips = solved_ips
191 , inert_frozen = emptyCCan
192 , inert_funeqs = solved_funeqs }
193 in (is_solved, unsolved)
195 where (unsolved_eqs, solved_eqs) = Bag.partitionBag (not.isGivenCt) eqs
196 (unsolved_ips, solved_ips) = extractUnsolvedCMap (inert_ips is)
197 (unsolved_dicts, solved_dicts) = extractUnsolvedCMap (inert_dicts is)
198 (unsolved_funeqs, solved_funeqs) = extractUnsolvedCMap (inert_funeqs is)
200 unsolved = unsolved_eqs `unionBags` inert_frozen is `unionBags`
201 unsolved_ips `unionBags` unsolved_dicts `unionBags` unsolved_funeqs
204 %*********************************************************************
206 * Main Interaction Solver *
208 **********************************************************************
212 1. Canonicalise (unary)
213 2. Pairwise interaction (binary)
214 * Take one from work list
215 * Try all pair-wise interactions with each constraint in inert
217 As an optimisation, we prioritize the equalities both in the
218 worklist and in the inerts.
220 3. Try to solve spontaneously for equalities involving touchables
221 4. Top-level interaction (binary wrt top-level)
222 Superclass decomposition belongs in (4), see note [Superclasses]
225 type AtomicInert = CanonicalCt -- constraint pulled from InertSet
226 type WorkItem = CanonicalCt -- constraint pulled from WorkList
228 ------------------------
230 = Stop -- Work item is consumed
231 | ContinueWith WorkItem -- Not consumed
233 instance Outputable StopOrContinue where
234 ppr Stop = ptext (sLit "Stop")
235 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
237 -- Results after interacting a WorkItem as far as possible with an InertSet
239 = SR { sr_inerts :: InertSet
240 -- The new InertSet to use (REPLACES the old InertSet)
241 , sr_new_work :: WorkList
242 -- Any new work items generated (should be ADDED to the old WorkList)
244 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
245 -- workitem is inert wrt to sr_inerts
246 , sr_stop :: StopOrContinue
249 instance Outputable StageResult where
250 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
251 = ptext (sLit "SR") <+>
252 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
253 , ptext (sLit "new work =") <+> ppr work <> comma
254 , ptext (sLit "stop =") <+> ppr stop])
256 type SubGoalDepth = Int -- Starts at zero; used to limit infinite
257 -- recursion of sub-goals
258 type SimplifierStage = SubGoalDepth -> WorkItem -> InertSet -> TcS StageResult
260 -- Combine a sequence of simplifier 'stages' to create a pipeline
261 runSolverPipeline :: SubGoalDepth
262 -> [(String, SimplifierStage)]
263 -> InertSet -> WorkItem
264 -> TcS (InertSet, WorkList)
265 -- Precondition: non-empty list of stages
266 runSolverPipeline depth pipeline inerts workItem
267 = do { traceTcS "Start solver pipeline" $
268 vcat [ ptext (sLit "work item =") <+> ppr workItem
269 , ptext (sLit "inerts =") <+> ppr inerts]
271 ; let itr_in = SR { sr_inerts = inerts
272 , sr_new_work = emptyWorkList
273 , sr_stop = ContinueWith workItem }
274 ; itr_out <- run_pipeline pipeline itr_in
276 = case sr_stop itr_out of
277 Stop -> sr_inerts itr_out
278 ContinueWith item -> sr_inerts itr_out `updInertSet` item
279 ; return (new_inert, sr_new_work itr_out) }
281 run_pipeline :: [(String, SimplifierStage)]
282 -> StageResult -> TcS StageResult
283 run_pipeline [] itr = return itr
284 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
286 run_pipeline ((name,stage):stages)
287 (SR { sr_new_work = accum_work
289 , sr_stop = ContinueWith work_item })
290 = do { itr <- stage depth work_item inerts
291 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
292 ; let itr' = itr { sr_new_work = accum_work `unionWorkList` sr_new_work itr }
293 ; run_pipeline stages itr' }
297 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
298 Reagent: a ~ [b] (given)
300 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
301 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
302 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
305 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
308 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
309 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
313 Inert: {a ~ Int, F Int ~ b} (given)
314 Reagent: F a ~ b (wanted)
316 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
317 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
320 -- Main interaction solver: we fully solve the worklist 'in one go',
321 -- returning an extended inert set.
323 -- See Note [Touchables and givens].
324 solveInteractGiven :: InertSet -> GivenLoc -> [EvVar] -> TcS InertSet
325 solveInteractGiven inert gloc evs
326 = do { (_, inert_ret) <- solveInteract inert $ listToBag $
331 mk_given ev = mkEvVarX ev flav
333 solveInteractWanted :: InertSet -> [WantedEvVar] -> TcS InertSet
334 solveInteractWanted inert wvs
335 = do { (_,inert_ret) <- solveInteract inert $ listToBag $
336 map wantedToFlavored wvs
339 solveInteract :: InertSet -> Bag FlavoredEvVar -> TcS (Bool, InertSet)
340 -- Post: (True, inert_set) means we managed to discharge all constraints
341 -- without actually doing any interactions!
342 -- (False, inert_set) means some interactions occurred
343 solveInteract inert ws
344 = do { dyn_flags <- getDynFlags
345 ; sctx <- getTcSContext
347 ; traceTcS "solveInteract, before clever canonicalization:" $
348 vcat [ text "ws = " <+> ppr (mapBag (\(EvVarX ev ct)
349 -> (ct,evVarPred ev)) ws)
350 , text "inert = " <+> ppr inert ]
352 ; can_ws <- mkCanonicalFEVs ws
355 <- foldrWorkListM (tryPreSolveAndInteract sctx dyn_flags) (True,inert) can_ws
357 ; traceTcS "solveInteract, after clever canonicalization (and interaction):" $
358 vcat [ text "No interaction happened = " <+> ppr flag
359 , text "inert_ret = " <+> ppr inert_ret ]
361 ; return (flag, inert_ret) }
363 tryPreSolveAndInteract :: SimplContext
367 -> TcS (Bool, InertSet)
368 -- Returns: True if it was able to discharge this constraint AND all previous ones
369 tryPreSolveAndInteract sctx dyn_flags ct (all_previous_discharged, inert)
370 = do { let inert_cts = get_inert_cts (evVarPred ev_var)
372 ; this_one_discharged <-
373 if isCFrozenErr ct then
376 dischargeFromCCans inert_cts ev_var fl
378 ; if this_one_discharged
379 then return (all_previous_discharged, inert)
382 { inert_ret <- solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) ct inert
383 ; return (False, inert_ret) } }
389 get_inert_cts (ClassP clas _)
390 | simplEqsOnly sctx = emptyCCan
391 | otherwise = fst (getRelevantCts clas (inert_dicts inert))
392 get_inert_cts (IParam {})
393 = emptyCCan -- We must not do the same thing for IParams, because (contrary
394 -- to dictionaries), work items /must/ override inert items.
395 -- See Note [Overriding implicit parameters] in TcInteract.
396 get_inert_cts (EqPred {})
397 = inert_eqs inert `unionBags` cCanMapToBag (inert_funeqs inert)
399 dischargeFromCCans :: CanonicalCts -> EvVar -> CtFlavor -> TcS Bool
400 -- See if this (pre-canonicalised) work-item is identical to a
401 -- one already in the inert set. Reasons:
402 -- a) Avoid creating superclass constraints for millions of incoming (Num a) constraints
403 -- b) Termination for improve_eqs in TcSimplify.simpl_loop
404 dischargeFromCCans cans ev fl
405 = Bag.foldrBag discharge_ct (return False) cans
407 the_pred = evVarPred ev
409 discharge_ct :: CanonicalCt -> TcS Bool -> TcS Bool
410 discharge_ct ct _rest
411 | evVarPred (cc_id ct) `eqPred` the_pred
412 , cc_flavor ct `canSolve` fl
413 = do { when (isWanted fl) $ setEvBind ev (evVarTerm (cc_id ct))
414 -- Deriveds need no evidence
415 -- For Givens, we already have evidence, and we don't need it twice
418 discharge_ct _ct rest = rest
421 Note [Avoiding the superclass explosion]
422 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
423 This note now is not as significant as it used to be because we no
424 longer add the superclasses of Wanted as Derived, except only if they
425 have equality superclasses or superclasses with functional
426 dependencies. The fear was that hundreds of identical wanteds would
427 give rise each to the same superclass or equality Derived's which
428 would lead to a blo-up in the number of interactions.
430 Instead, what we do with tryPreSolveAndCanon, is when we encounter a
431 new constraint, we very quickly see if it can be immediately
432 discharged by a class constraint in our inert set or the previous
433 canonicals. If so, we add nothing to the returned canonical
437 solveOne :: WorkItem -> InertSet -> TcS InertSet
438 solveOne workItem inerts
439 = do { dyn_flags <- getDynFlags
440 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) workItem inerts
444 solveInteractWithDepth :: (Int, Int, [WorkItem])
445 -> WorkList -> InertSet -> TcS InertSet
446 solveInteractWithDepth ctxt@(max_depth,n,stack) ws inert
451 = solverDepthErrorTcS n stack
454 = do { traceTcS "solveInteractWithDepth" $
455 vcat [ text "Current depth =" <+> ppr n
456 , text "Max depth =" <+> ppr max_depth
457 , text "ws =" <+> ppr ws ]
460 ; foldrWorkListM (solveOneWithDepth ctxt) inert ws }
461 -- use foldr to preserve the order
464 -- Fully interact the given work item with an inert set, and return a
465 -- new inert set which has assimilated the new information.
466 solveOneWithDepth :: (Int, Int, [WorkItem])
467 -> WorkItem -> InertSet -> TcS InertSet
468 solveOneWithDepth (max_depth, depth, stack) work inert
469 = do { traceFireTcS depth (text "Solving {" <+> ppr work)
470 ; (new_inert, new_work) <- runSolverPipeline depth thePipeline inert work
472 -- Recursively solve the new work generated
473 -- from workItem, with a greater depth
474 ; res_inert <- solveInteractWithDepth (max_depth, depth+1, work:stack) new_work new_inert
476 ; traceFireTcS depth (text "Done }" <+> ppr work)
480 thePipeline :: [(String,SimplifierStage)]
481 thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
482 , ("interact with inerts", interactWithInertsStage)
483 , ("spontaneous solve", spontaneousSolveStage)
484 , ("top-level reactions", topReactionsStage) ]
487 *********************************************************************************
489 The spontaneous-solve Stage
491 *********************************************************************************
493 Note [Efficient Orientation]
494 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
496 There are two cases where we have to be careful about
497 orienting equalities to get better efficiency.
499 Case 1: In Rewriting Equalities (function rewriteEqLHS)
501 When rewriting two equalities with the same LHS:
504 We have a choice of producing work (xi1 ~ xi2) (up-to the
505 canonicalization invariants) However, to prevent the inert items
506 from getting kicked out of the inerts first, we prefer to
507 canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
508 ~ xi1) if (a) comes from the inert set.
510 This choice is implemented using the WhichComesFromInert flag.
512 Case 2: Functional Dependencies
513 Again, we should prefer, if possible, the inert variables on the RHS
515 Case 3: IP improvement work
516 We must always rewrite so that the inert type is on the right.
519 spontaneousSolveStage :: SimplifierStage
520 spontaneousSolveStage depth workItem inerts
521 = do { mSolve <- trySpontaneousSolve workItem
524 SPCantSolve -> -- No spontaneous solution for him, keep going
525 return $ SR { sr_new_work = emptyWorkList
527 , sr_stop = ContinueWith workItem }
530 | not (isGivenCt workItem)
531 -- Original was wanted or derived but we have now made him
532 -- given so we have to interact him with the inerts due to
533 -- its status change. This in turn may produce more work.
534 -- We do this *right now* (rather than just putting workItem'
535 -- back into the work-list) because we've solved
536 -> do { bumpStepCountTcS
537 ; traceFireTcS depth (ptext (sLit "Spontaneous (w/d)") <+> ppr workItem)
538 ; (new_inert, new_work) <- runSolverPipeline depth
539 [ ("recursive interact with inert eqs", interactWithInertEqsStage)
540 , ("recursive interact with inerts", interactWithInertsStage)
542 ; return $ SR { sr_new_work = new_work
543 , sr_inerts = new_inert -- will include workItem'
547 -> -- Original was given; he must then be inert all right, and
548 -- workList' are all givens from flattening
549 do { bumpStepCountTcS
550 ; traceFireTcS depth (ptext (sLit "Spontaneous (g)") <+> ppr workItem)
551 ; return $ SR { sr_new_work = emptyWorkList
552 , sr_inerts = inerts `updInertSet` workItem'
554 SPError -> -- Return with no new work
555 return $ SR { sr_new_work = emptyWorkList
560 data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
561 -- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
562 -- SPSolved workItem' gives us a new *given* to go on
563 -- SPError means that it's completely impossible to solve this equality, eg due to a kind error
566 -- @trySpontaneousSolve wi@ solves equalities where one side is a
567 -- touchable unification variable.
568 -- See Note [Touchables and givens]
569 trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
570 trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
573 | Just tv2 <- tcGetTyVar_maybe xi
574 = do { tch1 <- isTouchableMetaTyVar tv1
575 ; tch2 <- isTouchableMetaTyVar tv2
576 ; case (tch1, tch2) of
577 (True, True) -> trySpontaneousEqTwoWay cv gw tv1 tv2
578 (True, False) -> trySpontaneousEqOneWay cv gw tv1 xi
579 (False, True) -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
580 _ -> return SPCantSolve }
582 = do { tch1 <- isTouchableMetaTyVar tv1
583 ; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
584 else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:"
586 ; return SPCantSolve }
590 -- trySpontaneousSolve (CFunEqCan ...) = ...
591 -- See Note [No touchables as FunEq RHS] in TcSMonad
592 trySpontaneousSolve _ = return SPCantSolve
595 trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
596 -- tv is a MetaTyVar, not untouchable
597 trySpontaneousEqOneWay cv gw tv xi
598 | not (isSigTyVar tv) || isTyVarTy xi
599 = do { let kxi = typeKind xi -- NB: 'xi' is fully rewritten according to the inerts
600 -- so we have its more specific kind in our hands
601 ; if kxi `isSubKind` tyVarKind tv then
602 solveWithIdentity cv gw tv xi
603 else return SPCantSolve
605 else if tyVarKind tv `isSubKind` kxi then
606 return SPCantSolve -- kinds are compatible but we can't solveWithIdentity this way
607 -- This case covers the a_touchable :: * ~ b_untouchable :: ??
608 -- which has to be deferred or floated out for someone else to solve
609 -- it in a scope where 'b' is no longer untouchable.
610 else do { addErrorTcS KindError gw (mkTyVarTy tv) xi -- See Note [Kind errors]
614 | otherwise -- Still can't solve, sig tyvar and non-variable rhs
618 trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
619 -- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
620 trySpontaneousEqTwoWay cv gw tv1 tv2
622 , nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
624 = solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
625 | otherwise -- None is a subkind of the other, but they are both touchable!
627 -- do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
628 -- ; return SPError }
632 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
636 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
637 Consider the wanted problem:
638 alpha ~ (# Int, Int #)
639 where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
640 but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
641 simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and
642 get quantified over in inference mode. That's bad because we do know at this point that the
643 constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
645 The same applies in canonicalization code in case of kind errors in the givens.
647 However, when we canonicalize givens we only check for compatibility (@compatKind@).
648 If there were a kind error in the givens, this means some form of inconsistency or dead code.
650 You may think that when we spontaneously solve wanteds we may have to look through the
651 bindings to determine the right kind of the RHS type. E.g one may be worried that xi is
652 @alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
653 But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
654 so this situation can't happen.
656 Note [Spontaneous solving and kind compatibility]
657 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
658 Note that our canonical constraints insist that *all* equalities (tv ~
659 xi) or (F xis ~ rhs) require the LHS and the RHS to have *compatible*
660 the same kinds. ("compatible" means one is a subKind of the other.)
662 - It can't be *equal* kinds, because
663 b) wanted constraints don't necessarily have identical kinds
665 b) a solved wanted constraint becomes a given
667 - SPJ thinks that *given* constraints (tv ~ tau) always have that
668 tau has a sub-kind of tv; and when solving wanted constraints
669 in trySpontaneousEqTwoWay we re-orient to achieve this.
671 - Note that the kind invariant is maintained by rewriting.
672 Eg wanted1 rewrites wanted2; if both were compatible kinds before,
673 wanted2 will be afterwards. Similarly givens.
676 - Givens from higher-rank, such as:
677 type family T b :: * -> * -> *
678 type instance T Bool = (->)
680 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
682 Whereas we would be able to apply the type instance, we would not be able to
683 use the given (T Bool ~ (->)) in the body of 'flop'
686 Note [Avoid double unifications]
687 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
688 The spontaneous solver has to return a given which mentions the unified unification
689 variable *on the left* of the equality. Here is what happens if not:
690 Original wanted: (a ~ alpha), (alpha ~ Int)
691 We spontaneously solve the first wanted, without changing the order!
692 given : a ~ alpha [having unified alpha := a]
693 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
694 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
696 We avoid this problem by orienting the resulting given so that the unification
697 variable is on the left. [Note that alternatively we could attempt to
698 enforce this at canonicalization]
700 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
701 double unifications is the main reason we disallow touchable
702 unification variables as RHS of type family equations: F xis ~ alpha.
707 solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
708 -- Solve with the identity coercion
709 -- Precondition: kind(xi) is a sub-kind of kind(tv)
710 -- Precondition: CtFlavor is Wanted or Derived
711 -- See [New Wanted Superclass Work] to see why solveWithIdentity
712 -- must work for Derived as well as Wanted
713 -- Returns: workItem where
714 -- workItem = the new Given constraint
715 solveWithIdentity cv wd tv xi
716 = do { traceTcS "Sneaky unification:" $
717 vcat [text "Coercion variable: " <+> ppr wd,
718 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
719 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
720 text "Right Kind is : " <+> ppr (typeKind xi)
723 ; setWantedTyBind tv xi
724 ; let refl_xi = mkReflCo xi
725 ; cv_given <- newGivenCoVar (mkTyVarTy tv) xi refl_xi
727 ; when (isWanted wd) (setCoBind cv refl_xi)
728 -- We don't want to do this for Derived, that's why we use 'when (isWanted wd)'
730 ; return $ SPSolved (CTyEqCan { cc_id = cv_given
731 , cc_flavor = mkGivenFlavor wd UnkSkol
732 , cc_tyvar = tv, cc_rhs = xi }) }
736 *********************************************************************************
738 The interact-with-inert Stage
740 *********************************************************************************
742 Note [The Solver Invariant]
743 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
744 We always add Givens first. So you might think that the solver has
747 If the work-item is Given,
748 then the inert item must Given
750 But this isn't quite true. Suppose we have,
751 c1: [W] beta ~ [alpha], c2 : [W] blah, c3 :[W] alpha ~ Int
752 After processing the first two, we get
753 c1: [G] beta ~ [alpha], c2 : [W] blah
754 Now, c3 does not interact with the the given c1, so when we spontaneously
755 solve c3, we must re-react it with the inert set. So we can attempt a
756 reaction between inert c2 [W] and work-item c3 [G].
758 It *is* true that [Solver Invariant]
759 If the work-item is Given,
760 AND there is a reaction
761 then the inert item must Given
763 If the work-item is Given,
764 and the inert item is Wanted/Derived
765 then there is no reaction
768 -- Interaction result of WorkItem <~> AtomicInert
770 = IR { ir_stop :: StopOrContinue
772 -- => Reagent (work item) consumed.
773 -- ContinueWith new_reagent
774 -- => Reagent transformed but keep gathering interactions.
775 -- The transformed item remains inert with respect
776 -- to any previously encountered inerts.
778 , ir_inert_action :: InertAction
779 -- Whether the inert item should remain in the InertSet.
781 , ir_new_work :: WorkList
782 -- new work items to add to the WorkList
784 , ir_fire :: Maybe String -- Tells whether a rule fired, and if so what
787 -- What to do with the inert reactant.
788 data InertAction = KeepInert | DropInert
790 mkIRContinue :: String -> WorkItem -> InertAction -> WorkList -> TcS InteractResult
791 mkIRContinue rule wi keep newWork
792 = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = keep
793 , ir_new_work = newWork, ir_fire = Just rule }
795 mkIRStopK :: String -> WorkList -> TcS InteractResult
796 mkIRStopK rule newWork
797 = return $ IR { ir_stop = Stop, ir_inert_action = KeepInert
798 , ir_new_work = newWork, ir_fire = Just rule }
800 mkIRStopD :: String -> WorkList -> TcS InteractResult
801 mkIRStopD rule newWork
802 = return $ IR { ir_stop = Stop, ir_inert_action = DropInert
803 , ir_new_work = newWork, ir_fire = Just rule }
805 noInteraction :: Monad m => WorkItem -> m InteractResult
807 = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = KeepInert
808 , ir_new_work = emptyWorkList, ir_fire = Nothing }
810 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
811 -- See Note [Efficient Orientation]
814 ---------------------------------------------------
815 -- Interact a single WorkItem with the equalities of an inert set as
816 -- far as possible, i.e. until we get a Stop result from an individual
817 -- reaction (i.e. when the WorkItem is consumed), or until we've
818 -- interact the WorkItem with the entire equalities of the InertSet
820 interactWithInertEqsStage :: SimplifierStage
821 interactWithInertEqsStage depth workItem inert
822 = Bag.foldrBagM (interactNext depth) initITR (inert_eqs inert)
823 -- use foldr to preserve the order
825 initITR = SR { sr_inerts = inert { inert_eqs = emptyCCan }
826 , sr_new_work = emptyWorkList
827 , sr_stop = ContinueWith workItem }
829 ---------------------------------------------------
830 -- Interact a single WorkItem with *non-equality* constraints in the inert set.
831 -- Precondition: equality interactions must have already happened, hence we have
832 -- to pick up some information from the incoming inert, before folding over the
833 -- "Other" constraints it contains!
835 interactWithInertsStage :: SimplifierStage
836 interactWithInertsStage depth workItem inert
837 = let (relevant, inert_residual) = getISRelevant workItem inert
838 initITR = SR { sr_inerts = inert_residual
839 , sr_new_work = emptyWorkList
840 , sr_stop = ContinueWith workItem }
841 in Bag.foldrBagM (interactNext depth) initITR relevant
842 -- use foldr to preserve the order
844 getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet)
845 getISRelevant (CFrozenErr {}) is = (emptyCCan, is)
846 -- Nothing s relevant; we have alread interacted
847 -- it with the equalities in the inert set
849 getISRelevant (CDictCan { cc_class = cls } ) is
850 = let (relevant, residual_map) = getRelevantCts cls (inert_dicts is)
851 in (relevant, is { inert_dicts = residual_map })
852 getISRelevant (CFunEqCan { cc_fun = tc } ) is
853 = let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is)
854 in (relevant, is { inert_funeqs = residual_map })
855 getISRelevant (CIPCan { cc_ip_nm = nm }) is
856 = let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
857 in (relevant, is { inert_ips = residual_map })
858 -- An equality, finally, may kick everything except equalities out
859 -- because we have already interacted the equalities in interactWithInertEqsStage
860 getISRelevant _eq_ct is -- Equality, everything is relevant for this one
861 -- TODO: if we were caching variables, we'd know that only
862 -- some are relevant. Experiment with this for now.
863 = let cts = cCanMapToBag (inert_ips is) `unionBags`
864 cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
865 in (cts, is { inert_dicts = emptyCCanMap
866 , inert_ips = emptyCCanMap
867 , inert_funeqs = emptyCCanMap })
869 interactNext :: SubGoalDepth -> AtomicInert -> StageResult -> TcS StageResult
870 interactNext depth inert it
871 | ContinueWith work_item <- sr_stop it
872 = do { let inerts = sr_inerts it
874 ; IR { ir_new_work = new_work, ir_inert_action = inert_action
875 , ir_fire = fire_info, ir_stop = stop }
876 <- interactWithInert inert work_item
879 = text rule <+> keep_doc
880 <+> vcat [ ptext (sLit "Inert =") <+> ppr inert
881 , ptext (sLit "Work =") <+> ppr work_item
882 , ppUnless (isEmptyWorkList new_work) $
883 ptext (sLit "New =") <+> ppr new_work ]
884 keep_doc = case inert_action of
885 KeepInert -> ptext (sLit "[keep]")
886 DropInert -> ptext (sLit "[drop]")
888 Just rule -> do { bumpStepCountTcS
889 ; traceFireTcS depth (mk_msg rule) }
892 -- New inerts depend on whether we KeepInert or not
893 ; let inerts_new = case inert_action of
894 KeepInert -> inerts `updInertSet` inert
897 ; return $ SR { sr_inerts = inerts_new
898 , sr_new_work = sr_new_work it `unionWorkList` new_work
901 = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
903 -- Do a single interaction of two constraints.
904 interactWithInert :: AtomicInert -> WorkItem -> TcS InteractResult
905 interactWithInert inert workItem
906 = do { ctxt <- getTcSContext
907 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workItem
910 doInteractWithInert inert workItem
912 noInteraction workItem
915 allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
916 -- Allowed interactions
917 allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
918 allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
919 allowedInteraction _ _ _ = True
921 --------------------------------------------
922 doInteractWithInert :: CanonicalCt -> CanonicalCt -> TcS InteractResult
923 -- Identical class constraints.
926 inertItem@(CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
927 workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
928 | cls1 == cls2 && eqTypes tys1 tys2
929 = solveOneFromTheOther "Cls/Cls" (EvId d1,fl1) workItem
931 | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
932 = -- See Note [When improvement happens]
933 do { let pty1 = ClassP cls1 tys1
934 pty2 = ClassP cls2 tys2
935 inert_pred_loc = (pty1, pprFlavorArising fl1)
936 work_item_pred_loc = (pty2, pprFlavorArising fl2)
937 fd_eqns = improveFromAnother
938 inert_pred_loc -- the template
939 work_item_pred_loc -- the one we aim to rewrite
940 -- See Note [Efficient Orientation]
942 ; m <- rewriteWithFunDeps fd_eqns tys2 fl2
944 Nothing -> noInteraction workItem
945 Just (rewritten_tys2, cos2, fd_work)
946 | eqTypes tys1 rewritten_tys2
947 -> -- Solve him on the spot in this case
949 Given {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
950 Derived {} -> mkIRStopK "Cls/Cls fundep (solved)" fd_work
953 -> do { setDictBind d2 (EvCast d1 dict_co)
954 ; let inert_w = inertItem { cc_flavor = fl2 }
955 -- A bit naughty: we take the inert Derived,
956 -- turn it into a Wanted, use it to solve the work-item
957 -- and put it back into the work-list
958 -- Maybe rather than starting again, we could *replace* the
959 -- inert item, but its safe and simple to restart
960 ; mkIRStopD "Cls/Cls fundep (solved)" $
961 workListFromNonEq inert_w `unionWorkList` fd_work }
963 -> do { setDictBind d2 (EvCast d1 dict_co)
964 ; mkIRStopK "Cls/Cls fundep (solved)" fd_work }
967 -> -- We could not quite solve him, but we still rewrite him
968 -- Example: class C a b c | a -> b
969 -- Given: C Int Bool x, Wanted: C Int beta y
970 -- Then rewrite the wanted to C Int Bool y
971 -- but note that is still not identical to the given
972 -- The important thing is that the rewritten constraint is
973 -- inert wrt the given.
974 -- However it is not necessarily inert wrt previous inert-set items.
975 -- class C a b c d | a -> b, b c -> d
976 -- Inert: c1: C b Q R S, c2: C P Q a b
977 -- Work: C P alpha R beta
978 -- Does not react with c1; reacts with c2, with alpha:=Q
979 -- NOW it reacts with c1!
980 -- So we must stop, and put the rewritten constraint back in the work list
981 do { d2' <- newDictVar cls1 rewritten_tys2
983 Given {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
984 Wanted {} -> setDictBind d2 (EvCast d2' dict_co)
985 Derived {} -> return ()
986 ; let workItem' = workItem { cc_id = d2', cc_tyargs = rewritten_tys2 }
987 ; mkIRStopK "Cls/Cls fundep (partial)" $
988 workListFromNonEq workItem' `unionWorkList` fd_work }
991 dict_co = mkTyConAppCo (classTyCon cls1) cos2
994 -- Class constraint and given equality: use the equality to rewrite
995 -- the class constraint.
996 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
997 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
998 | ifl `canRewrite` wfl
999 , tv `elemVarSet` tyVarsOfTypes xis
1000 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
1001 -- Continue with rewritten Dictionary because we can only be in the
1002 -- interactWithEqsStage, so the dictionary is inert.
1003 ; mkIRContinue "Eq/Cls" rewritten_dict KeepInert emptyWorkList }
1005 doInteractWithInert (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
1006 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1007 | wfl `canRewrite` ifl
1008 , tv `elemVarSet` tyVarsOfTypes xis
1009 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
1010 ; mkIRContinue "Cls/Eq" workItem DropInert (workListFromNonEq rewritten_dict) }
1012 -- Class constraint and given equality: use the equality to rewrite
1013 -- the class constraint.
1014 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1015 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
1016 | ifl `canRewrite` wfl
1017 , tv `elemVarSet` tyVarsOfType ty
1018 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
1019 ; mkIRContinue "Eq/IP" rewritten_ip KeepInert emptyWorkList }
1021 doInteractWithInert (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
1022 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1023 | wfl `canRewrite` ifl
1024 , tv `elemVarSet` tyVarsOfType ty
1025 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
1026 ; mkIRContinue "IP/Eq" workItem DropInert (workListFromNonEq rewritten_ip) }
1028 -- Two implicit parameter constraints. If the names are the same,
1029 -- but their types are not, we generate a wanted type equality
1030 -- that equates the type (this is "improvement").
1031 -- However, we don't actually need the coercion evidence,
1032 -- so we just generate a fresh coercion variable that isn't used anywhere.
1033 doInteractWithInert (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
1034 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
1035 | nm1 == nm2 && isGiven wfl && isGiven ifl
1036 = -- See Note [Overriding implicit parameters]
1037 -- Dump the inert item, override totally with the new one
1038 -- Do not require type equality
1039 -- For example, given let ?x::Int = 3 in let ?x::Bool = True in ...
1040 -- we must *override* the outer one with the inner one
1041 mkIRContinue "IP/IP override" workItem DropInert emptyWorkList
1043 | nm1 == nm2 && ty1 `eqType` ty2
1044 = solveOneFromTheOther "IP/IP" (EvId id1,ifl) workItem
1047 = -- See Note [When improvement happens]
1048 do { co_var <- newCoVar ty2 ty1 -- See Note [Efficient Orientation]
1049 ; let flav = Wanted (combineCtLoc ifl wfl)
1050 ; cans <- mkCanonical flav co_var
1052 Given {} -> pprPanic "Unexpected given IP" (ppr workItem)
1053 Derived {} -> pprPanic "Unexpected derived IP" (ppr workItem)
1055 do { setIPBind (cc_id workItem) $
1056 EvCast id1 (mkSymCo (mkCoVarCo co_var))
1057 ; mkIRStopK "IP/IP interaction (solved)" cans }
1060 -- Never rewrite a given with a wanted equality, and a type function
1061 -- equality can never rewrite an equality. We rewrite LHS *and* RHS
1062 -- of function equalities so that our inert set exposes everything that
1063 -- we know about equalities.
1065 -- Inert: equality, work item: function equality
1066 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
1067 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
1068 , cc_tyargs = args, cc_rhs = xi2 })
1069 | ifl `canRewrite` wfl
1070 , tv `elemVarSet` tyVarsOfTypes (xi2:args) -- Rewrite RHS as well
1071 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
1072 ; mkIRStopK "Eq/FunEq" (workListFromEq rewritten_funeq) }
1073 -- Must Stop here, because we may no longer be inert after the rewritting.
1075 -- Inert: function equality, work item: equality
1076 doInteractWithInert (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
1077 , cc_tyargs = args, cc_rhs = xi1 })
1078 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
1079 | wfl `canRewrite` ifl
1080 , tv `elemVarSet` tyVarsOfTypes (xi1:args) -- Rewrite RHS as well
1081 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
1082 ; mkIRContinue "FunEq/Eq" workItem DropInert (workListFromEq rewritten_funeq) }
1083 -- One may think that we could (KeepTransformedInert rewritten_funeq)
1084 -- but that is wrong, because it may end up not being inert with respect
1085 -- to future inerts. Example:
1086 -- Original inert = { F xis ~ [a], b ~ Maybe Int }
1087 -- Work item comes along = a ~ [b]
1088 -- If we keep { F xis ~ [b] } in the inert set we will end up with:
1089 -- { F xis ~ [b], b ~ Maybe Int, a ~ [Maybe Int] }
1090 -- At the end, which is *not* inert. So we should unfortunately DropInert here.
1092 doInteractWithInert (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
1093 , cc_tyargs = args1, cc_rhs = xi1 })
1094 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
1095 , cc_tyargs = args2, cc_rhs = xi2 })
1096 | fl1 `canSolve` fl2 && lhss_match
1097 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCo cv1,xi1) (cv2,fl2,xi2)
1098 ; mkIRStopK "FunEq/FunEq" cans }
1099 | fl2 `canSolve` fl1 && lhss_match
1100 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCo cv2,xi2) (cv1,fl1,xi1)
1101 ; mkIRContinue "FunEq/FunEq" workItem DropInert cans }
1103 lhss_match = tc1 == tc2 && eqTypes args1 args2
1105 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1106 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
1107 -- Check for matching LHS
1108 | fl1 `canSolve` fl2 && tv1 == tv2
1109 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCo cv1,xi1) (cv2,fl2,xi2)
1110 ; mkIRStopK "Eq/Eq lhs" cans }
1112 | fl2 `canSolve` fl1 && tv1 == tv2
1113 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCo cv2,xi2) (cv1,fl1,xi1)
1114 ; mkIRContinue "Eq/Eq lhs" workItem DropInert cans }
1116 -- Check for rewriting RHS
1117 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1118 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1119 ; mkIRStopK "Eq/Eq rhs" rewritten_eq }
1121 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1122 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1123 ; mkIRContinue "Eq/Eq rhs" workItem DropInert rewritten_eq }
1125 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1126 (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
1127 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
1128 = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1129 ; mkIRStopK "Frozen/Eq" rewritten_frozen }
1131 doInteractWithInert (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
1132 workItem@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1133 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
1134 = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1135 ; mkIRContinue "Frozen/Eq" workItem DropInert rewritten_frozen }
1137 -- Fall-through case for all other situations
1138 doInteractWithInert _ workItem = noInteraction workItem
1140 -------------------------
1141 -- Equational Rewriting
1142 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1143 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1144 = do { let cos = map (liftCoSubstWith [tv] [mkCoVarCo cv]) xis -- xis[tv] ~ xis[xi]
1145 args = substTysWith [tv] [xi] xis
1147 dict_co = mkTyConAppCo con cos
1148 ; dv' <- newDictVar cl args
1150 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCo dict_co))
1151 Given {} -> setDictBind dv' (EvCast dv dict_co)
1152 Derived {} -> return () -- Derived dicts we don't set any evidence
1154 ; return (CDictCan { cc_id = dv'
1157 , cc_tyargs = args }) }
1159 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1160 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1161 = do { let ip_co = liftCoSubstWith [tv] [mkCoVarCo cv] ty -- ty[tv] ~ t[xi]
1162 ty' = substTyWith [tv] [xi] ty
1163 ; ipid' <- newIPVar nm ty'
1165 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCo ip_co))
1166 Given {} -> setIPBind ipid' (EvCast ipid ip_co)
1167 Derived {} -> return () -- Derived ips: we don't set any evidence
1169 ; return (CIPCan { cc_id = ipid'
1172 , cc_ip_ty = ty' }) }
1174 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1175 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2) -- cv2 :: F args ~ xi2
1176 = do { let co_subst = liftCoSubstWith [tv] [mkCoVarCo cv1]
1177 arg_cos = map co_subst args
1178 args' = substTysWith [tv] [xi1] args
1179 fun_co = mkTyConAppCo tc arg_cos -- fun_co :: F args ~ F args'
1181 xi2' = substTyWith [tv] [xi1] xi2
1182 xi2_co = co_subst xi2 -- xi2_co :: xi2 ~ xi2'
1184 ; cv2' <- newCoVar (mkTyConApp tc args') xi2'
1186 Wanted {} -> setCoBind cv2 (fun_co `mkTransCo`
1187 mkCoVarCo cv2' `mkTransCo`
1189 Given {} -> setCoBind cv2' (mkSymCo fun_co `mkTransCo`
1190 mkCoVarCo cv2 `mkTransCo`
1192 Derived {} -> return ()
1194 ; return (CFunEqCan { cc_id = cv2'
1198 , cc_rhs = xi2' }) }
1201 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
1202 -- Use the first equality to rewrite the second, flavors already checked.
1203 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1204 -- rewrites c2 to give
1205 -- c2' : tv2 ~ xi2[xi1/tv1]
1206 -- We must do an occurs check to sure the new constraint is canonical
1207 -- So we might return an empty bag
1208 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1209 | Just tv2' <- tcGetTyVar_maybe xi2'
1210 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1211 = do { when (isWanted gw) (setCoBind cv2 (mkSymCo co2'))
1212 ; return emptyWorkList }
1214 = do { cv2' <- newCoVar (mkTyVarTy tv2) xi2'
1216 Wanted {} -> setCoBind cv2 $ mkCoVarCo cv2' `mkTransCo`
1218 Given {} -> setCoBind cv2' $ mkCoVarCo cv2 `mkTransCo`
1220 Derived {} -> return ()
1221 ; canEqToWorkList gw cv2' (mkTyVarTy tv2) xi2' }
1223 xi2' = substTyWith [tv1] [xi1] xi2
1224 co2' = liftCoSubstWith [tv1] [mkCoVarCo cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1226 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
1227 -- Used to ineract two equalities of the following form:
1228 -- First Equality: co1: (XXX ~ xi1)
1229 -- Second Equality: cv2: (XXX ~ xi2)
1230 -- Where the cv1 `canRewrite` cv2 equality
1231 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1),
1232 -- See Note [Efficient Orientation] for that
1233 rewriteEqLHS LeftComesFromInert (co1,xi1) (cv2,gw,xi2)
1234 = do { cv2' <- newCoVar xi2 xi1
1236 Wanted {} -> setCoBind cv2 $
1237 co1 `mkTransCo` mkSymCo (mkCoVarCo cv2')
1238 Given {} -> setCoBind cv2' $
1239 mkSymCo (mkCoVarCo cv2) `mkTransCo` co1
1240 Derived {} -> return ()
1241 ; mkCanonical gw cv2' }
1243 rewriteEqLHS RightComesFromInert (co1,xi1) (cv2,gw,xi2)
1244 = do { cv2' <- newCoVar xi1 xi2
1246 Wanted {} -> setCoBind cv2 $
1247 co1 `mkTransCo` mkCoVarCo cv2'
1248 Given {} -> setCoBind cv2' $
1249 mkSymCo co1 `mkTransCo` mkCoVarCo cv2
1250 Derived {} -> return ()
1251 ; mkCanonical gw cv2' }
1253 rewriteFrozen :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor) -> TcS WorkList
1254 rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1255 = do { cv2' <- newCoVar ty2a' ty2b' -- ty2a[xi1/tv1] ~ ty2b[xi1/tv1]
1257 Wanted {} -> setCoBind cv2 $ co2a' `mkTransCo`
1258 mkCoVarCo cv2' `mkTransCo`
1261 Given {} -> setCoBind cv2' $ mkSymCo co2a' `mkTransCo`
1262 mkCoVarCo cv2 `mkTransCo`
1265 Derived {} -> return ()
1267 ; return (workListFromNonEq $ CFrozenErr { cc_id = cv2', cc_flavor = fl2 }) }
1269 (ty2a, ty2b) = coVarKind cv2 -- cv2 : ty2a ~ ty2b
1270 ty2a' = substTyWith [tv1] [xi1] ty2a
1271 ty2b' = substTyWith [tv1] [xi1] ty2b
1273 co2a' = liftCoSubstWith [tv1] [mkCoVarCo cv1] ty2a -- ty2a ~ ty2a[xi1/tv1]
1274 co2b' = liftCoSubstWith [tv1] [mkCoVarCo cv1] ty2b -- ty2b ~ ty2b[xi1/tv1]
1276 solveOneFromTheOther :: String -> (EvTerm, CtFlavor) -> CanonicalCt -> TcS InteractResult
1277 -- First argument inert, second argument work-item. They both represent
1278 -- wanted/given/derived evidence for the *same* predicate so
1279 -- we can discharge one directly from the other.
1281 -- Precondition: value evidence only (implicit parameters, classes)
1283 solveOneFromTheOther info (ev_term,ifl) workItem
1285 = mkIRStopK ("Solved[DW] " ++ info) emptyWorkList
1287 | isDerived ifl -- The inert item is Derived, we can just throw it away,
1288 -- The workItem is inert wrt earlier inert-set items,
1289 -- so it's safe to continue on from this point
1290 = mkIRContinue ("Solved[DI] " ++ info) workItem DropInert emptyWorkList
1293 = ASSERT( ifl `canSolve` wfl )
1294 -- Because of Note [The Solver Invariant], plus Derived dealt with
1295 do { when (isWanted wfl) $ setEvBind wid ev_term
1296 -- Overwrite the binding, if one exists
1297 -- If both are Given, we already have evidence; no need to duplicate
1298 ; mkIRStopK ("Solved " ++ info) emptyWorkList }
1300 wfl = cc_flavor workItem
1301 wid = cc_id workItem
1304 Note [Superclasses and recursive dictionaries]
1305 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1306 Overlaps with Note [SUPERCLASS-LOOP 1]
1307 Note [SUPERCLASS-LOOP 2]
1308 Note [Recursive instances and superclases]
1309 ToDo: check overlap and delete redundant stuff
1311 Right before adding a given into the inert set, we must
1312 produce some more work, that will bring the superclasses
1313 of the given into scope. The superclass constraints go into
1316 When we simplify a wanted constraint, if we first see a matching
1317 instance, we may produce new wanted work. To (1) avoid doing this work
1318 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1319 this item as given into our inert set WITHOUT adding its superclass constraints,
1320 otherwise we'd be in danger of creating a loop [In fact this was the exact reason
1321 for doing the isGoodRecEv check in an older version of the type checker].
1323 But now we have added partially solved constraints to the worklist which may
1324 interact with other wanteds. Consider the example:
1328 class Eq b => Foo a b --- 0-th selector
1329 instance Eq a => Foo [a] a --- fooDFun
1331 and wanted (Foo [t] t). We are first going to see that the instance matches
1332 and create an inert set that includes the solved (Foo [t] t) but not its superclasses:
1333 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1334 Our work list is going to contain a new *wanted* goal
1337 Ok, so how do we get recursive dictionaries, at all:
1341 data D r = ZeroD | SuccD (r (D r));
1343 instance (Eq (r (D r))) => Eq (D r) where
1344 ZeroD == ZeroD = True
1345 (SuccD a) == (SuccD b) = a == b
1348 equalDC :: D [] -> D [] -> Bool;
1351 We need to prove (Eq (D [])). Here's how we go:
1355 by instance decl, holds if
1359 *BUT* we have an inert set which gives us (no superclasses):
1361 By the instance declaration of Eq we can show the 'd2' goal if
1363 where d2 = dfEqList d3
1365 Now, however this wanted can interact with our inert d1 to set:
1367 and solve the goal. Why was this interaction OK? Because, if we chase the
1368 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1370 d3 := dfEqD2 (dfEqList d3)
1371 which is FINE because the use of d3 is protected by the instance function
1374 So, our strategy is to try to put solved wanted dictionaries into the
1375 inert set along with their superclasses (when this is meaningful,
1376 i.e. when new wanted goals are generated) but solve a wanted dictionary
1377 from a given only in the case where the evidence variable of the
1378 wanted is mentioned in the evidence of the given (recursively through
1379 the evidence binds) in a protected way: more instance function applications
1380 than superclass selectors.
1382 Here are some more examples from GHC's previous type checker
1386 This code arises in the context of "Scrap Your Boilerplate with Class"
1390 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1391 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1393 class Data Maybe a => Foo a
1395 instance Foo t => Sat (Maybe t) -- dfunSat
1397 instance Data Maybe a => Foo a -- dfunFoo1
1398 instance Foo a => Foo [a] -- dfunFoo2
1399 instance Foo [Char] -- dfunFoo3
1401 Consider generating the superclasses of the instance declaration
1402 instance Foo a => Foo [a]
1404 So our problem is this
1406 d1 :_w Data Maybe [t]
1408 We may add the given in the inert set, along with its superclasses
1409 [assuming we don't fail because there is a matching instance, see
1410 tryTopReact, given case ]
1414 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1415 d1 :_w Data Maybe [t]
1416 Then d2 can readily enter the inert, and we also do solving of the wanted
1419 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1421 d2 :_w Sat (Maybe [t])
1423 d01 :_g Data Maybe t
1424 Now, we may simplify d2 more:
1427 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1428 d1 :_g Data Maybe [t]
1429 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1433 d01 :_g Data Maybe t
1435 Now, we can just solve d3.
1438 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1439 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1442 d01 :_g Data Maybe t
1443 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1446 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1447 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1448 d4 :_g Foo [t] d4 := dfunFoo2 d5
1451 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1452 d01 :_g Data Maybe t
1453 Now, d5 can be solved! (and its superclass enter scope)
1456 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1457 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1458 d4 :_g Foo [t] d4 := dfunFoo2 d5
1459 d5 :_g Foo t d5 := dfunFoo1 d7
1462 d6 :_g Data Maybe [t]
1463 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1464 d01 :_g Data Maybe t
1467 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1468 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1469 that must not be used (look at case interactInert where both inert and workitem
1470 are givens). So we have several options:
1471 - Drop the workitem always (this will drop d8)
1472 This feels very unsafe -- what if the work item was the "good" one
1473 that should be used later to solve another wanted?
1474 - Don't drop anyone: the inert set may contain multiple givens!
1475 [This is currently implemented]
1477 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1478 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1479 d7. Now the [isRecDictEv] function in the ineration solver
1480 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1481 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1483 So, no interaction happens there. Then we meet d01 and there is no recursion
1484 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1486 Note [SUPERCLASS-LOOP 1]
1487 ~~~~~~~~~~~~~~~~~~~~~~~~
1488 We have to be very, very careful when generating superclasses, lest we
1489 accidentally build a loop. Here's an example:
1493 class S a => C a where { opc :: a -> a }
1494 class S b => D b where { opd :: b -> b }
1496 instance C Int where
1499 instance D Int where
1502 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1503 Simplifying, we may well get:
1504 $dfCInt = :C ds1 (opd dd)
1507 Notice that we spot that we can extract ds1 from dd.
1509 Alas! Alack! We can do the same for (instance D Int):
1511 $dfDInt = :D ds2 (opc dc)
1515 And now we've defined the superclass in terms of itself.
1516 Two more nasty cases are in
1521 - Satisfy the superclass context *all by itself*
1522 (tcSimplifySuperClasses)
1523 - And do so completely; i.e. no left-over constraints
1524 to mix with the constraints arising from method declarations
1527 Note [SUPERCLASS-LOOP 2]
1528 ~~~~~~~~~~~~~~~~~~~~~~~~
1529 We need to be careful when adding "the constaint we are trying to prove".
1530 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1532 class Ord a => C a where
1533 instance Ord [a] => C [a] where ...
1535 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1536 superclasses of C [a] to avails. But we must not overwrite the binding
1537 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1540 Here's another variant, immortalised in tcrun020
1541 class Monad m => C1 m
1542 class C1 m => C2 m x
1543 instance C2 Maybe Bool
1544 For the instance decl we need to build (C1 Maybe), and it's no good if
1545 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1546 before we search for C1 Maybe.
1548 Here's another example
1549 class Eq b => Foo a b
1550 instance Eq a => Foo [a] a
1554 we'll first deduce that it holds (via the instance decl). We must not
1555 then overwrite the Eq t constraint with a superclass selection!
1557 At first I had a gross hack, whereby I simply did not add superclass constraints
1558 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1559 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1560 I found a very obscure program (now tcrun021) in which improvement meant the
1561 simplifier got two bites a the cherry... so something seemed to be an Stop
1562 first time, but reducible next time.
1564 Now we implement the Right Solution, which is to check for loops directly
1565 when adding superclasses. It's a bit like the occurs check in unification.
1567 Note [Recursive instances and superclases]
1568 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1569 Consider this code, which arises in the context of "Scrap Your
1570 Boilerplate with Class".
1574 instance Sat (ctx Char) => Data ctx Char
1575 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1577 class Data Maybe a => Foo a
1579 instance Foo t => Sat (Maybe t)
1581 instance Data Maybe a => Foo a
1582 instance Foo a => Foo [a]
1585 In the instance for Foo [a], when generating evidence for the superclasses
1586 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1587 Using the instance for Data, we therefore need
1588 (Sat (Maybe [a], Data Maybe a)
1589 But we are given (Foo a), and hence its superclass (Data Maybe a).
1590 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1591 we need (Foo [a]). And that is the very dictionary we are bulding
1592 an instance for! So we must put that in the "givens". So in this
1594 Given: Foo a, Foo [a]
1595 Wanted: Data Maybe [a]
1597 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1598 the givens, which is what 'addGiven' would normally do. Why? Because
1599 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1600 by selecting a superclass from Foo [a], which simply makes a loop.
1602 On the other hand we *must* put the superclasses of (Foo a) in
1603 the givens, as you can see from the derivation described above.
1605 Conclusion: in the very special case of tcSimplifySuperClasses
1606 we have one 'given' (namely the "this" dictionary) whose superclasses
1607 must not be added to 'givens' by addGiven.
1609 There is a complication though. Suppose there are equalities
1610 instance (Eq a, a~b) => Num (a,b)
1611 Then we normalise the 'givens' wrt the equalities, so the original
1612 given "this" dictionary is cast to one of a different type. So it's a
1613 bit trickier than before to identify the "special" dictionary whose
1614 superclasses must not be added. See test
1615 indexed-types/should_run/EqInInstance
1617 We need a persistent property of the dictionary to record this
1618 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1619 but cool), which is maintained by dictionary normalisation.
1620 Specifically, the InstLocOrigin is
1622 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1625 Note [MATCHING-SYNONYMS]
1626 ~~~~~~~~~~~~~~~~~~~~~~~~
1627 When trying to match a dictionary (D tau) to a top-level instance, or a
1628 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1629 we do *not* need to expand type synonyms because the matcher will do that for us.
1632 Note [RHS-FAMILY-SYNONYMS]
1633 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1634 The RHS of a family instance is represented as yet another constructor which is
1635 like a type synonym for the real RHS the programmer declared. Eg:
1636 type instance F (a,a) = [a]
1638 :R32 a = [a] -- internal type synonym introduced
1639 F (a,a) ~ :R32 a -- instance
1641 When we react a family instance with a type family equation in the work list
1642 we keep the synonym-using RHS without expansion.
1645 *********************************************************************************
1647 The top-reaction Stage
1649 *********************************************************************************
1652 -- If a work item has any form of interaction with top-level we get this
1653 data TopInteractResult
1654 = NoTopInt -- No top-level interaction
1655 -- Equivalent to (SomeTopInt emptyWorkList (ContinueWith work_item))
1657 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1658 -- for superclasses)
1659 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1660 } -- NB: in ``given'' (solved) form if the
1661 -- original was wanted or given and instance match
1662 -- was found, but may also be in wanted form if we
1663 -- only reacted with functional dependencies
1664 -- arising from top-level instances.
1666 topReactionsStage :: SimplifierStage
1667 topReactionsStage depth workItem inerts
1668 = do { tir <- tryTopReact workItem
1671 return $ SR { sr_inerts = inerts
1672 , sr_new_work = emptyWorkList
1673 , sr_stop = ContinueWith workItem }
1674 SomeTopInt tir_new_work tir_new_inert ->
1675 do { bumpStepCountTcS
1676 ; traceFireTcS depth (ptext (sLit "Top react")
1677 <+> vcat [ ptext (sLit "Work =") <+> ppr workItem
1678 , ptext (sLit "New =") <+> ppr tir_new_work ])
1679 ; return $ SR { sr_inerts = inerts
1680 , sr_new_work = tir_new_work
1681 , sr_stop = tir_new_inert
1685 tryTopReact :: WorkItem -> TcS TopInteractResult
1686 tryTopReact workitem
1687 = do { -- A flag controls the amount of interaction allowed
1688 -- See Note [Simplifying RULE lhs constraints]
1689 ctxt <- getTcSContext
1690 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1691 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1692 ; doTopReact workitem }
1693 else return NoTopInt
1696 allowedTopReaction :: Bool -> WorkItem -> Bool
1697 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1698 allowedTopReaction _ _ = True
1700 doTopReact :: WorkItem -> TcS TopInteractResult
1701 -- The work item does not react with the inert set, so try interaction with top-level instances
1702 -- NB: The place to add superclasses in *not* in doTopReact stage. Instead superclasses are
1703 -- added in the worklist as part of the canonicalisation process.
1704 -- See Note [Adding superclasses] in TcCanonical.
1707 -- See Note [Given constraint that matches an instance declaration]
1708 doTopReact (CDictCan { cc_flavor = Given {} })
1709 = return NoTopInt -- NB: Superclasses already added since it's canonical
1711 -- Derived dictionary: just look for functional dependencies
1712 doTopReact workItem@(CDictCan { cc_flavor = fl@(Derived loc)
1713 , cc_class = cls, cc_tyargs = xis })
1714 = do { instEnvs <- getInstEnvs
1715 ; let fd_eqns = improveFromInstEnv instEnvs
1716 (ClassP cls xis, pprArisingAt loc)
1717 ; m <- rewriteWithFunDeps fd_eqns xis fl
1719 Nothing -> return NoTopInt
1720 Just (xis',_,fd_work) ->
1721 let workItem' = workItem { cc_tyargs = xis' }
1722 -- Deriveds are not supposed to have identity (cc_id is unused!)
1723 in return $ SomeTopInt { tir_new_work = fd_work
1724 , tir_new_inert = ContinueWith workItem' } }
1726 -- Wanted dictionary
1727 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = fl@(Wanted loc)
1728 , cc_class = cls, cc_tyargs = xis })
1729 = do { -- See Note [MATCHING-SYNONYMS]
1730 ; lkp_inst_res <- matchClassInst cls xis loc
1731 ; case lkp_inst_res of
1733 do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1735 ; instEnvs <- getInstEnvs
1736 ; let fd_eqns = improveFromInstEnv instEnvs
1737 (ClassP cls xis, pprArisingAt loc)
1738 ; m <- rewriteWithFunDeps fd_eqns xis fl
1740 Nothing -> return NoTopInt
1741 Just (xis',cos,fd_work) ->
1742 do { let dict_co = mkTyConAppCo (classTyCon cls) cos
1743 ; dv'<- newDictVar cls xis'
1744 ; setDictBind dv (EvCast dv' dict_co)
1745 ; let workItem' = CDictCan { cc_id = dv', cc_flavor = fl,
1746 cc_class = cls, cc_tyargs = xis' }
1748 SomeTopInt { tir_new_work = workListFromNonEq workItem' `unionWorkList` fd_work
1749 , tir_new_inert = Stop } } }
1751 GenInst wtvs ev_term -- Solved
1752 -- No need to do fundeps stuff here; the instance
1753 -- matches already so we won't get any more info
1754 -- from functional dependencies
1756 -> do { traceTcS "doTopReact/ found nullary class instance for" (ppr dv)
1757 ; setDictBind dv ev_term
1758 -- Solved in one step and no new wanted work produced.
1759 -- i.e we directly matched a top-level instance
1760 -- No point in caching this in 'inert'; hence Stop
1761 ; return $ SomeTopInt { tir_new_work = emptyWorkList
1762 , tir_new_inert = Stop } }
1765 -> do { traceTcS "doTopReact/ found nullary class instance for" (ppr dv)
1766 ; setDictBind dv ev_term
1767 -- Solved and new wanted work produced, you may cache the
1768 -- (tentatively solved) dictionary as Given! (used to be: Derived)
1769 ; let solved = workItem { cc_flavor = given_fl }
1770 given_fl = Given (setCtLocOrigin loc UnkSkol)
1771 ; inst_work <- canWanteds wtvs
1772 ; return $ SomeTopInt { tir_new_work = inst_work
1773 , tir_new_inert = ContinueWith solved } }
1777 doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
1778 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1779 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1780 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1784 MatchInstSingle (rep_tc, rep_tys)
1785 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1786 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1787 -- Eagerly expand away the type synonym on the
1788 -- RHS of a type function, so that it never
1789 -- appears in an error message
1790 -- See Note [Type synonym families] in TyCon
1791 coe = mkAxInstCo coe_tc rep_tys
1793 Wanted {} -> do { cv' <- newCoVar rhs_ty xi
1798 Given {} -> newGivenCoVar xi rhs_ty $
1799 mkSymCo (mkCoVarCo cv) `mkTransCo` coe
1800 Derived {} -> newDerivedId (EqPred xi rhs_ty)
1801 ; can_cts <- mkCanonical fl cv'
1802 ; return $ SomeTopInt can_cts Stop }
1804 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1808 -- Any other work item does not react with any top-level equations
1809 doTopReact _workItem = return NoTopInt
1813 Note [FunDep and implicit parameter reactions]
1814 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1815 Currently, our story of interacting two dictionaries (or a dictionary
1816 and top-level instances) for functional dependencies, and implicit
1817 paramters, is that we simply produce new wanted equalities. So for example
1819 class D a b | a -> b where ...
1825 We generate the extra work item
1827 where 'cv' is currently unused. However, this new item reacts with d2,
1828 discharging it in favour of a new constraint d2' thus:
1830 d2 := d2' |> D Int cv
1831 Now d2' can be discharged from d1
1833 We could be more aggressive and try to *immediately* solve the dictionary
1834 using those extra equalities. With the same inert set and work item we
1835 might dischard d2 directly:
1838 d2 := d1 |> D Int cv
1840 But in general it's a bit painful to figure out the necessary coercion,
1841 so we just take the first approach. Here is a better example. Consider:
1842 class C a b c | a -> b
1844 [Given] d1 : C T Int Char
1845 [Wanted] d2 : C T beta Int
1846 In this case, it's *not even possible* to solve the wanted immediately.
1847 So we should simply output the functional dependency and add this guy
1848 [but NOT its superclasses] back in the worklist. Even worse:
1849 [Given] d1 : C T Int beta
1850 [Wanted] d2: C T beta Int
1851 Then it is solvable, but its very hard to detect this on the spot.
1853 It's exactly the same with implicit parameters, except that the
1854 "aggressive" approach would be much easier to implement.
1856 Note [When improvement happens]
1857 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1858 We fire an improvement rule when
1860 * Two constraints match (modulo the fundep)
1861 e.g. C t1 t2, C t1 t3 where C a b | a->b
1862 The two match because the first arg is identical
1864 * At least one is not Given. If they are both given, we don't fire
1865 the reaction because we have no way of constructing evidence for a
1866 new equality nor does it seem right to create a new wanted goal
1867 (because the goal will most likely contain untouchables, which
1868 can't be solved anyway)!
1870 Note that we *do* fire the improvement if one is Given and one is Derived.
1871 The latter can be a superclass of a wanted goal. Example (tcfail138)
1872 class L a b | a -> b
1873 class (G a, L a b) => C a b
1875 instance C a b' => G (Maybe a)
1876 instance C a b => C (Maybe a) a
1877 instance L (Maybe a) a
1879 When solving the superclasses of the (C (Maybe a) a) instance, we get
1880 Given: C a b ... and hance by superclasses, (G a, L a b)
1882 Use the instance decl to get
1884 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
1885 and now we need improvement between that derived superclass an the Given (L a b)
1887 Note [Overriding implicit parameters]
1888 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1890 f :: (?x::a) -> Bool -> a
1892 g v = let ?x::Int = 3
1893 in (f v, let ?x::Bool = True in f v)
1895 This should probably be well typed, with
1896 g :: Bool -> (Int, Bool)
1898 So the inner binding for ?x::Bool *overrides* the outer one.
1899 Hence a work-item Given overrides an inert-item Given.
1901 Note [Given constraint that matches an instance declaration]
1902 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1903 What should we do when we discover that one (or more) top-level
1904 instances match a given (or solved) class constraint? We have
1907 1. Reject the program. The reason is that there may not be a unique
1908 best strategy for the solver. Example, from the OutsideIn(X) paper:
1909 instance P x => Q [x]
1910 instance (x ~ y) => R [x] y
1912 wob :: forall a b. (Q [b], R b a) => a -> Int
1914 g :: forall a. Q [a] => [a] -> Int
1917 will generate the impliation constraint:
1918 Q [a] => (Q [beta], R beta [a])
1919 If we react (Q [beta]) with its top-level axiom, we end up with a
1920 (P beta), which we have no way of discharging. On the other hand,
1921 if we react R beta [a] with the top-level we get (beta ~ a), which
1922 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
1923 now solvable by the given Q [a].
1925 However, this option is restrictive, for instance [Example 3] from
1926 Note [Recursive dictionaries] will fail to work.
1928 2. Ignore the problem, hoping that the situations where there exist indeed
1929 such multiple strategies are rare: Indeed the cause of the previous
1930 problem is that (R [x] y) yields the new work (x ~ y) which can be
1931 *spontaneously* solved, not using the givens.
1933 We are choosing option 2 below but we might consider having a flag as well.
1936 Note [New Wanted Superclass Work]
1937 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1938 Even in the case of wanted constraints, we may add some superclasses
1939 as new given work. The reason is:
1941 To allow FD-like improvement for type families. Assume that
1943 class C a b | a -> b
1944 and we have to solve the implication constraint:
1946 Then, FD improvement can help us to produce a new wanted (beta ~ b)
1948 We want to have the same effect with the type family encoding of
1949 functional dependencies. Namely, consider:
1950 class (F a ~ b) => C a b
1951 Now suppose that we have:
1954 By interacting the given we will get given (F a ~ b) which is not
1955 enough by itself to make us discharge (C a beta). However, we
1956 may create a new derived equality from the super-class of the
1957 wanted constraint (C a beta), namely derived (F a ~ beta).
1958 Now we may interact this with given (F a ~ b) to get:
1960 But 'beta' is a touchable unification variable, and hence OK to
1961 unify it with 'b', replacing the derived evidence with the identity.
1963 This requires trySpontaneousSolve to solve *derived*
1964 equalities that have a touchable in their RHS, *in addition*
1965 to solving wanted equalities.
1967 We also need to somehow use the superclasses to quantify over a minimal,
1968 constraint see note [Minimize by Superclasses] in TcSimplify.
1971 Finally, here is another example where this is useful.
1975 class (F a ~ b) => C a b
1976 And we are given the wanteds:
1980 We surely do *not* want to quantify over (b ~ c), since if someone provides
1981 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
1982 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
1984 Step 1: We will get new *given* superclass work,
1985 provisionally to our solving of w1 and w2
1987 g1: F a ~ b, g2 : F a ~ c,
1988 w1 : C a b, w2 : C a c, w3 : b ~ c
1990 The evidence for g1 and g2 is a superclass evidence term:
1992 g1 := sc w1, g2 := sc w2
1994 Step 2: The givens will solve the wanted w3, so that
1995 w3 := sym (sc w1) ; sc w2
1997 Step 3: Now, one may naively assume that then w2 can be solve from w1
1998 after rewriting with the (now solved equality) (b ~ c).
2000 But this rewriting is ruled out by the isGoodRectDict!
2002 Conclusion, we will (correctly) end up with the unsolved goals
2005 NB: The desugarer needs be more clever to deal with equalities
2006 that participate in recursive dictionary bindings.
2009 data LookupInstResult
2011 | GenInst [WantedEvVar] EvTerm
2013 matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
2014 matchClassInst clas tys loc
2015 = do { let pred = mkClassPred clas tys
2016 ; mb_result <- matchClass clas tys
2018 MatchInstNo -> return NoInstance
2019 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
2020 -- we learn more about the reagent
2021 MatchInstSingle (dfun_id, mb_inst_tys) ->
2022 do { checkWellStagedDFun pred dfun_id loc
2024 -- It's possible that not all the tyvars are in
2025 -- the substitution, tenv. For example:
2026 -- instance C X a => D X where ...
2027 -- (presumably there's a functional dependency in class C)
2028 -- Hence mb_inst_tys :: Either TyVar TcType
2030 ; tys <- instDFunTypes mb_inst_tys
2031 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
2032 ; if null theta then
2033 return (GenInst [] (EvDFunApp dfun_id tys []))
2035 { ev_vars <- instDFunConstraints theta
2036 ; let wevs = [EvVarX w loc | w <- ev_vars]
2037 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }