3 solveInteract, solveInteractGiven, solveInteractWanted,
4 AtomicInert, tyVarsOfInert,
5 InertSet, emptyInert, updInertSet, extractUnsolved, solveOne,
8 #include "HsVersions.h"
23 import Inst( tyVarsOfEvVar )
34 import TcMType ( isSilentEvVar )
38 import qualified Data.Map as Map
40 import Control.Monad( when )
42 import FastString ( sLit )
46 Note [InertSet invariants]
47 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
48 An InertSet is a bag of canonical constraints, with the following invariants:
50 1 No two constraints react with each other.
52 A tricky case is when there exists a given (solved) dictionary
53 constraint and a wanted identical constraint in the inert set, but do
54 not react because reaction would create loopy dictionary evidence for
55 the wanted. See note [Recursive dictionaries]
57 2 Given equalities form an idempotent substitution [none of the
58 given LHS's occur in any of the given RHS's or reactant parts]
60 3 Wanted equalities also form an idempotent substitution
62 4 The entire set of equalities is acyclic.
64 5 Wanted dictionaries are inert with the top-level axiom set
66 6 Equalities of the form tv1 ~ tv2 always have a touchable variable
67 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 8 No Given constraint mentions a touchable unification variable, but
74 Given/Solved may do so.
76 9 Given constraints will also have their superclasses in the inert set,
77 but Given/Solved will not.
79 Note that 6 and 7 are /not/ enforced by canonicalization but rather by
80 insertion in the inert list, ie by TcInteract.
82 During the process of solving, the inert set will contain some
83 previously given constraints, some wanted constraints, and some given
84 constraints which have arisen from solving wanted constraints. For
85 now we do not distinguish between given and solved constraints.
87 Note that we must switch wanted inert items to given when going under an
88 implication constraint (when in top-level inference mode).
92 data CCanMap a = CCanMap { cts_given :: Map.Map a CanonicalCts
93 -- Invariant: all Given
94 , cts_derived :: Map.Map a CanonicalCts
95 -- Invariant: all Derived
96 , cts_wanted :: Map.Map a CanonicalCts }
97 -- Invariant: all Wanted
99 cCanMapToBag :: Ord a => CCanMap a -> CanonicalCts
100 cCanMapToBag cmap = Map.fold unionBags rest_wder (cts_given cmap)
101 where rest_wder = Map.fold unionBags rest_der (cts_wanted cmap)
102 rest_der = Map.fold unionBags emptyCCan (cts_derived cmap)
104 emptyCCanMap :: CCanMap a
105 emptyCCanMap = CCanMap { cts_given = Map.empty
106 , cts_derived = Map.empty, cts_wanted = Map.empty }
108 updCCanMap:: Ord a => (a,CanonicalCt) -> CCanMap a -> CCanMap a
109 updCCanMap (a,ct) cmap
110 = case cc_flavor ct of
112 -> cmap { cts_wanted = Map.insertWith unionBags a this_ct (cts_wanted cmap) }
114 -> cmap { cts_given = Map.insertWith unionBags a this_ct (cts_given cmap) }
116 -> cmap { cts_derived = Map.insertWith unionBags a this_ct (cts_derived cmap) }
117 where this_ct = singleCCan ct
119 getRelevantCts :: Ord a => a -> CCanMap a -> (CanonicalCts, CCanMap a)
120 -- Gets the relevant constraints and returns the rest of the CCanMap
121 getRelevantCts a cmap
122 = let relevant = unionManyBags [ Map.findWithDefault emptyCCan a (cts_wanted cmap)
123 , Map.findWithDefault emptyCCan a (cts_given cmap)
124 , Map.findWithDefault emptyCCan a (cts_derived cmap) ]
125 residual_map = cmap { cts_wanted = Map.delete a (cts_wanted cmap)
126 , cts_given = Map.delete a (cts_given cmap)
127 , cts_derived = Map.delete a (cts_derived cmap) }
128 in (relevant, residual_map)
130 extractUnsolvedCMap :: Ord a => CCanMap a -> (CanonicalCts, CCanMap a)
131 -- Gets the wanted or derived constraints and returns a residual
132 -- CCanMap with only givens.
133 extractUnsolvedCMap cmap =
134 let wntd = Map.fold unionBags emptyCCan (cts_wanted cmap)
135 derd = Map.fold unionBags emptyCCan (cts_derived cmap)
136 in (wntd `unionBags` derd,
137 cmap { cts_wanted = Map.empty, cts_derived = Map.empty })
140 -- See Note [InertSet invariants]
142 = IS { inert_eqs :: CanonicalCts -- Equalities only (CTyEqCan)
143 , inert_dicts :: CCanMap Class -- Dictionaries only
144 , inert_ips :: CCanMap (IPName Name) -- Implicit parameters
145 , inert_frozen :: CanonicalCts
146 , inert_funeqs :: CCanMap TyCon -- Type family equalities only
147 -- This representation allows us to quickly get to the relevant
148 -- inert constraints when interacting a work item with the inert set.
151 tyVarsOfInert :: InertSet -> TcTyVarSet
152 tyVarsOfInert (IS { inert_eqs = eqs
153 , inert_dicts = dictmap
155 , inert_frozen = frozen
156 , inert_funeqs = funeqmap }) = tyVarsOfCanonicals cts
158 cts = eqs `andCCan` frozen `andCCan` cCanMapToBag dictmap
159 `andCCan` cCanMapToBag ipmap `andCCan` cCanMapToBag funeqmap
161 instance Outputable InertSet where
162 ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
163 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_dicts is)))
164 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_ips is)))
165 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_funeqs is)))
166 , vcat (map ppr (Bag.bagToList $ inert_frozen is))
169 emptyInert :: InertSet
170 emptyInert = IS { inert_eqs = Bag.emptyBag
171 , inert_frozen = Bag.emptyBag
172 , inert_dicts = emptyCCanMap
173 , inert_ips = emptyCCanMap
174 , inert_funeqs = emptyCCanMap }
176 updInertSet :: InertSet -> AtomicInert -> InertSet
178 | isCTyEqCan item -- Other equality
179 = let eqs' = inert_eqs is `Bag.snocBag` item
180 in is { inert_eqs = eqs' }
181 | Just cls <- isCDictCan_Maybe item -- Dictionary
182 = is { inert_dicts = updCCanMap (cls,item) (inert_dicts is) }
183 | Just x <- isCIPCan_Maybe item -- IP
184 = is { inert_ips = updCCanMap (x,item) (inert_ips is) }
185 | Just tc <- isCFunEqCan_Maybe item -- Function equality
186 = is { inert_funeqs = updCCanMap (tc,item) (inert_funeqs is) }
188 = is { inert_frozen = inert_frozen is `Bag.snocBag` item }
190 extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
191 -- Postcondition: the returned canonical cts are either Derived, or Wanted.
192 extractUnsolved is@(IS {inert_eqs = eqs})
193 = let is_solved = is { inert_eqs = solved_eqs
194 , inert_dicts = solved_dicts
195 , inert_ips = solved_ips
196 , inert_frozen = emptyCCan
197 , inert_funeqs = solved_funeqs }
198 in (is_solved, unsolved)
200 where (unsolved_eqs, solved_eqs) = Bag.partitionBag (not.isGivenOrSolvedCt) eqs
201 (unsolved_ips, solved_ips) = extractUnsolvedCMap (inert_ips is)
202 (unsolved_dicts, solved_dicts) = extractUnsolvedCMap (inert_dicts is)
203 (unsolved_funeqs, solved_funeqs) = extractUnsolvedCMap (inert_funeqs is)
205 unsolved = unsolved_eqs `unionBags` inert_frozen is `unionBags`
206 unsolved_ips `unionBags` unsolved_dicts `unionBags` unsolved_funeqs
209 %*********************************************************************
211 * Main Interaction Solver *
213 **********************************************************************
217 1. Canonicalise (unary)
218 2. Pairwise interaction (binary)
219 * Take one from work list
220 * Try all pair-wise interactions with each constraint in inert
222 As an optimisation, we prioritize the equalities both in the
223 worklist and in the inerts.
225 3. Try to solve spontaneously for equalities involving touchables
226 4. Top-level interaction (binary wrt top-level)
227 Superclass decomposition belongs in (4), see note [Superclasses]
230 type AtomicInert = CanonicalCt -- constraint pulled from InertSet
231 type WorkItem = CanonicalCt -- constraint pulled from WorkList
233 ------------------------
235 = Stop -- Work item is consumed
236 | ContinueWith WorkItem -- Not consumed
238 instance Outputable StopOrContinue where
239 ppr Stop = ptext (sLit "Stop")
240 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
242 -- Results after interacting a WorkItem as far as possible with an InertSet
244 = SR { sr_inerts :: InertSet
245 -- The new InertSet to use (REPLACES the old InertSet)
246 , sr_new_work :: WorkList
247 -- Any new work items generated (should be ADDED to the old WorkList)
249 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
250 -- workitem is inert wrt to sr_inerts
251 , sr_stop :: StopOrContinue
254 instance Outputable StageResult where
255 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
256 = ptext (sLit "SR") <+>
257 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
258 , ptext (sLit "new work =") <+> ppr work <> comma
259 , ptext (sLit "stop =") <+> ppr stop])
261 type SubGoalDepth = Int -- Starts at zero; used to limit infinite
262 -- recursion of sub-goals
263 type SimplifierStage = SubGoalDepth -> WorkItem -> InertSet -> TcS StageResult
265 -- Combine a sequence of simplifier 'stages' to create a pipeline
266 runSolverPipeline :: SubGoalDepth
267 -> [(String, SimplifierStage)]
268 -> InertSet -> WorkItem
269 -> TcS (InertSet, WorkList)
270 -- Precondition: non-empty list of stages
271 runSolverPipeline depth pipeline inerts workItem
272 = do { traceTcS "Start solver pipeline" $
273 vcat [ ptext (sLit "work item =") <+> ppr workItem
274 , ptext (sLit "inerts =") <+> ppr inerts]
276 ; let itr_in = SR { sr_inerts = inerts
277 , sr_new_work = emptyWorkList
278 , sr_stop = ContinueWith workItem }
279 ; itr_out <- run_pipeline pipeline itr_in
281 = case sr_stop itr_out of
282 Stop -> sr_inerts itr_out
283 ContinueWith item -> sr_inerts itr_out `updInertSet` item
284 ; return (new_inert, sr_new_work itr_out) }
286 run_pipeline :: [(String, SimplifierStage)]
287 -> StageResult -> TcS StageResult
288 run_pipeline [] itr = return itr
289 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
291 run_pipeline ((name,stage):stages)
292 (SR { sr_new_work = accum_work
294 , sr_stop = ContinueWith work_item })
295 = do { itr <- stage depth work_item inerts
296 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
297 ; let itr' = itr { sr_new_work = accum_work `unionWorkList` sr_new_work itr }
298 ; run_pipeline stages itr' }
302 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
303 Reagent: a ~ [b] (given)
305 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
306 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
307 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
310 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
313 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
314 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
318 Inert: {a ~ Int, F Int ~ b} (given)
319 Reagent: F a ~ b (wanted)
321 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
322 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
325 -- Main interaction solver: we fully solve the worklist 'in one go',
326 -- returning an extended inert set.
328 -- See Note [Touchables and givens].
329 solveInteractGiven :: InertSet -> GivenLoc -> [EvVar] -> TcS InertSet
330 solveInteractGiven inert gloc evs
331 = do { (_, inert_ret) <- solveInteract inert $ listToBag $
335 flav = Given gloc GivenOrig
336 mk_given ev = mkEvVarX ev flav
338 solveInteractWanted :: InertSet -> [WantedEvVar] -> TcS InertSet
339 solveInteractWanted inert wvs
340 = do { (_,inert_ret) <- solveInteract inert $ listToBag $
341 map wantedToFlavored wvs
344 solveInteract :: InertSet -> Bag FlavoredEvVar -> TcS (Bool, InertSet)
345 -- Post: (True, inert_set) means we managed to discharge all constraints
346 -- without actually doing any interactions!
347 -- (False, inert_set) means some interactions occurred
348 solveInteract inert ws
349 = do { dyn_flags <- getDynFlags
350 ; sctx <- getTcSContext
352 ; traceTcS "solveInteract, before clever canonicalization:" $
353 vcat [ text "ws = " <+> ppr (mapBag (\(EvVarX ev ct)
354 -> (ct,evVarPred ev)) ws)
355 , text "inert = " <+> ppr inert ]
357 ; can_ws <- mkCanonicalFEVs ws
360 <- foldrWorkListM (tryPreSolveAndInteract sctx dyn_flags) (True,inert) can_ws
362 ; traceTcS "solveInteract, after clever canonicalization (and interaction):" $
363 vcat [ text "No interaction happened = " <+> ppr flag
364 , text "inert_ret = " <+> ppr inert_ret ]
366 ; return (flag, inert_ret) }
368 tryPreSolveAndInteract :: SimplContext
372 -> TcS (Bool, InertSet)
373 -- Returns: True if it was able to discharge this constraint AND all previous ones
374 tryPreSolveAndInteract sctx dyn_flags ct (all_previous_discharged, inert)
375 = do { let inert_cts = get_inert_cts (evVarPred ev_var)
377 ; this_one_discharged <-
378 if isCFrozenErr ct then
381 dischargeFromCCans inert_cts ev_var fl
383 ; if this_one_discharged
384 then return (all_previous_discharged, inert)
387 { inert_ret <- solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) ct inert
388 ; return (False, inert_ret) } }
394 get_inert_cts (ClassP clas _)
395 | simplEqsOnly sctx = emptyCCan
396 | otherwise = fst (getRelevantCts clas (inert_dicts inert))
397 get_inert_cts (IParam {})
398 = emptyCCan -- We must not do the same thing for IParams, because (contrary
399 -- to dictionaries), work items /must/ override inert items.
400 -- See Note [Overriding implicit parameters] in TcInteract.
401 get_inert_cts (EqPred {})
402 = inert_eqs inert `unionBags` cCanMapToBag (inert_funeqs inert)
404 dischargeFromCCans :: CanonicalCts -> EvVar -> CtFlavor -> TcS Bool
405 -- See if this (pre-canonicalised) work-item is identical to a
406 -- one already in the inert set. Reasons:
407 -- a) Avoid creating superclass constraints for millions of incoming (Num a) constraints
408 -- b) Termination for improve_eqs in TcSimplify.simpl_loop
409 dischargeFromCCans cans ev fl
410 = Bag.foldrBag discharge_ct (return False) cans
412 the_pred = evVarPred ev
414 discharge_ct :: CanonicalCt -> TcS Bool -> TcS Bool
415 discharge_ct ct _rest
416 | evVarPred (cc_id ct) `tcEqPred` the_pred
417 , cc_flavor ct `canSolve` fl
418 -- DV: No special care should be taken for Given/Solveds, we will
419 -- never encounter a Given entering the constraint bag after a Given/Solved
420 = do { when (isWanted fl) $ set_ev_bind ev (cc_id ct)
421 -- Deriveds need no evidence
422 -- For Givens, we already have evidence, and we don't need it twice
426 | EqPred {} <- evVarPred y = setEvBind x (EvCoercion (mkCoVarCoercion y))
427 | otherwise = setEvBind x (EvId y)
429 discharge_ct _ct rest = rest
432 Note [Avoiding the superclass explosion]
433 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
434 This note now is not as significant as it used to be because we no
435 longer add the superclasses of Wanted as Derived, except only if they
436 have equality superclasses or superclasses with functional
437 dependencies. The fear was that hundreds of identical wanteds would
438 give rise each to the same superclass or equality Derived's which
439 would lead to a blo-up in the number of interactions.
441 Instead, what we do with tryPreSolveAndCanon, is when we encounter a
442 new constraint, we very quickly see if it can be immediately
443 discharged by a class constraint in our inert set or the previous
444 canonicals. If so, we add nothing to the returned canonical
448 solveOne :: WorkItem -> InertSet -> TcS InertSet
449 solveOne workItem inerts
450 = do { dyn_flags <- getDynFlags
451 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) workItem inerts
455 solveInteractWithDepth :: (Int, Int, [WorkItem])
456 -> WorkList -> InertSet -> TcS InertSet
457 solveInteractWithDepth ctxt@(max_depth,n,stack) ws inert
462 = solverDepthErrorTcS n stack
465 = do { traceTcS "solveInteractWithDepth" $
466 vcat [ text "Current depth =" <+> ppr n
467 , text "Max depth =" <+> ppr max_depth
468 , text "ws =" <+> ppr ws ]
471 ; foldrWorkListM (solveOneWithDepth ctxt) inert ws }
472 -- use foldr to preserve the order
475 -- Fully interact the given work item with an inert set, and return a
476 -- new inert set which has assimilated the new information.
477 solveOneWithDepth :: (Int, Int, [WorkItem])
478 -> WorkItem -> InertSet -> TcS InertSet
479 solveOneWithDepth (max_depth, depth, stack) work inert
480 = do { traceFireTcS depth (text "Solving {" <+> ppr work)
481 ; (new_inert, new_work) <- runSolverPipeline depth thePipeline inert work
483 -- Recursively solve the new work generated
484 -- from workItem, with a greater depth
485 ; res_inert <- solveInteractWithDepth (max_depth, depth+1, work:stack) new_work new_inert
487 ; traceFireTcS depth (text "Done }" <+> ppr work)
491 thePipeline :: [(String,SimplifierStage)]
492 thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
493 , ("interact with inerts", interactWithInertsStage)
494 , ("spontaneous solve", spontaneousSolveStage)
495 , ("top-level reactions", topReactionsStage) ]
498 *********************************************************************************
500 The spontaneous-solve Stage
502 *********************************************************************************
504 Note [Efficient Orientation]
505 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
507 There are two cases where we have to be careful about
508 orienting equalities to get better efficiency.
510 Case 1: In Rewriting Equalities (function rewriteEqLHS)
512 When rewriting two equalities with the same LHS:
515 We have a choice of producing work (xi1 ~ xi2) (up-to the
516 canonicalization invariants) However, to prevent the inert items
517 from getting kicked out of the inerts first, we prefer to
518 canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
519 ~ xi1) if (a) comes from the inert set.
521 This choice is implemented using the WhichComesFromInert flag.
523 Case 2: Functional Dependencies
524 Again, we should prefer, if possible, the inert variables on the RHS
526 Case 3: IP improvement work
527 We must always rewrite so that the inert type is on the right.
530 spontaneousSolveStage :: SimplifierStage
531 spontaneousSolveStage depth workItem inerts
532 = do { mSolve <- trySpontaneousSolve workItem
535 SPCantSolve -> -- No spontaneous solution for him, keep going
536 return $ SR { sr_new_work = emptyWorkList
538 , sr_stop = ContinueWith workItem }
541 | not (isGivenOrSolvedCt workItem)
542 -- Original was wanted or derived but we have now made him
543 -- given so we have to interact him with the inerts due to
544 -- its status change. This in turn may produce more work.
545 -- We do this *right now* (rather than just putting workItem'
546 -- back into the work-list) because we've solved
547 -> do { bumpStepCountTcS
548 ; traceFireTcS depth (ptext (sLit "Spontaneous (w/d)") <+> ppr workItem)
549 ; (new_inert, new_work) <- runSolverPipeline depth
550 [ ("recursive interact with inert eqs", interactWithInertEqsStage)
551 , ("recursive interact with inerts", interactWithInertsStage)
553 ; return $ SR { sr_new_work = new_work
554 , sr_inerts = new_inert -- will include workItem'
558 -> -- Original was given; he must then be inert all right, and
559 -- workList' are all givens from flattening
560 do { bumpStepCountTcS
561 ; traceFireTcS depth (ptext (sLit "Spontaneous (g)") <+> ppr workItem)
562 ; return $ SR { sr_new_work = emptyWorkList
563 , sr_inerts = inerts `updInertSet` workItem'
565 SPError -> -- Return with no new work
566 return $ SR { sr_new_work = emptyWorkList
571 data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
572 -- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
573 -- SPSolved workItem' gives us a new *given* to go on
574 -- SPError means that it's completely impossible to solve this equality, eg due to a kind error
577 -- @trySpontaneousSolve wi@ solves equalities where one side is a
578 -- touchable unification variable.
579 -- See Note [Touchables and givens]
580 trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
581 trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
584 | Just tv2 <- tcGetTyVar_maybe xi
585 = do { tch1 <- isTouchableMetaTyVar tv1
586 ; tch2 <- isTouchableMetaTyVar tv2
587 ; case (tch1, tch2) of
588 (True, True) -> trySpontaneousEqTwoWay cv gw tv1 tv2
589 (True, False) -> trySpontaneousEqOneWay cv gw tv1 xi
590 (False, True) -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
591 _ -> return SPCantSolve }
593 = do { tch1 <- isTouchableMetaTyVar tv1
594 ; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
595 else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:"
597 ; return SPCantSolve }
601 -- trySpontaneousSolve (CFunEqCan ...) = ...
602 -- See Note [No touchables as FunEq RHS] in TcSMonad
603 trySpontaneousSolve _ = return SPCantSolve
606 trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
607 -- tv is a MetaTyVar, not untouchable
608 trySpontaneousEqOneWay cv gw tv xi
609 | not (isSigTyVar tv) || isTyVarTy xi
610 = do { let kxi = typeKind xi -- NB: 'xi' is fully rewritten according to the inerts
611 -- so we have its more specific kind in our hands
612 ; if kxi `isSubKind` tyVarKind tv then
613 solveWithIdentity cv gw tv xi
614 else return SPCantSolve
616 else if tyVarKind tv `isSubKind` kxi then
617 return SPCantSolve -- kinds are compatible but we can't solveWithIdentity this way
618 -- This case covers the a_touchable :: * ~ b_untouchable :: ??
619 -- which has to be deferred or floated out for someone else to solve
620 -- it in a scope where 'b' is no longer untouchable.
621 else do { addErrorTcS KindError gw (mkTyVarTy tv) xi -- See Note [Kind errors]
625 | otherwise -- Still can't solve, sig tyvar and non-variable rhs
629 trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
630 -- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
631 trySpontaneousEqTwoWay cv gw tv1 tv2
633 , nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
635 = solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
636 | otherwise -- None is a subkind of the other, but they are both touchable!
638 -- do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
639 -- ; return SPError }
643 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
647 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
648 Consider the wanted problem:
649 alpha ~ (# Int, Int #)
650 where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
651 but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
652 simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and
653 get quantified over in inference mode. That's bad because we do know at this point that the
654 constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
656 The same applies in canonicalization code in case of kind errors in the givens.
658 However, when we canonicalize givens we only check for compatibility (@compatKind@).
659 If there were a kind error in the givens, this means some form of inconsistency or dead code.
661 You may think that when we spontaneously solve wanteds we may have to look through the
662 bindings to determine the right kind of the RHS type. E.g one may be worried that xi is
663 @alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
664 But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
665 so this situation can't happen.
667 Note [Spontaneous solving and kind compatibility]
668 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
669 Note that our canonical constraints insist that *all* equalities (tv ~
670 xi) or (F xis ~ rhs) require the LHS and the RHS to have *compatible*
671 the same kinds. ("compatible" means one is a subKind of the other.)
673 - It can't be *equal* kinds, because
674 b) wanted constraints don't necessarily have identical kinds
676 b) a solved wanted constraint becomes a given
678 - SPJ thinks that *given* constraints (tv ~ tau) always have that
679 tau has a sub-kind of tv; and when solving wanted constraints
680 in trySpontaneousEqTwoWay we re-orient to achieve this.
682 - Note that the kind invariant is maintained by rewriting.
683 Eg wanted1 rewrites wanted2; if both were compatible kinds before,
684 wanted2 will be afterwards. Similarly givens.
687 - Givens from higher-rank, such as:
688 type family T b :: * -> * -> *
689 type instance T Bool = (->)
691 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
693 Whereas we would be able to apply the type instance, we would not be able to
694 use the given (T Bool ~ (->)) in the body of 'flop'
697 Note [Avoid double unifications]
698 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
699 The spontaneous solver has to return a given which mentions the unified unification
700 variable *on the left* of the equality. Here is what happens if not:
701 Original wanted: (a ~ alpha), (alpha ~ Int)
702 We spontaneously solve the first wanted, without changing the order!
703 given : a ~ alpha [having unified alpha := a]
704 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
705 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
707 We avoid this problem by orienting the resulting given so that the unification
708 variable is on the left. [Note that alternatively we could attempt to
709 enforce this at canonicalization]
711 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
712 double unifications is the main reason we disallow touchable
713 unification variables as RHS of type family equations: F xis ~ alpha.
718 solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
719 -- Solve with the identity coercion
720 -- Precondition: kind(xi) is a sub-kind of kind(tv)
721 -- Precondition: CtFlavor is Wanted or Derived
722 -- See [New Wanted Superclass Work] to see why solveWithIdentity
723 -- must work for Derived as well as Wanted
724 -- Returns: workItem where
725 -- workItem = the new Given constraint
726 solveWithIdentity cv wd tv xi
727 = do { traceTcS "Sneaky unification:" $
728 vcat [text "Coercion variable: " <+> ppr wd,
729 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
730 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
731 text "Right Kind is : " <+> ppr (typeKind xi)
734 ; setWantedTyBind tv xi
735 ; cv_given <- newGivenCoVar (mkTyVarTy tv) xi xi
737 ; when (isWanted wd) (setCoBind cv xi)
738 -- We don't want to do this for Derived, that's why we use 'when (isWanted wd)'
739 ; return $ SPSolved (CTyEqCan { cc_id = cv_given
740 , cc_flavor = mkSolvedFlavor wd UnkSkol
741 , cc_tyvar = tv, cc_rhs = xi }) }
745 *********************************************************************************
747 The interact-with-inert Stage
749 *********************************************************************************
751 Note [The Solver Invariant]
752 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
753 We always add Givens first. So you might think that the solver has
756 If the work-item is Given,
757 then the inert item must Given
759 But this isn't quite true. Suppose we have,
760 c1: [W] beta ~ [alpha], c2 : [W] blah, c3 :[W] alpha ~ Int
761 After processing the first two, we get
762 c1: [G] beta ~ [alpha], c2 : [W] blah
763 Now, c3 does not interact with the the given c1, so when we spontaneously
764 solve c3, we must re-react it with the inert set. So we can attempt a
765 reaction between inert c2 [W] and work-item c3 [G].
767 It *is* true that [Solver Invariant]
768 If the work-item is Given,
769 AND there is a reaction
770 then the inert item must Given
772 If the work-item is Given,
773 and the inert item is Wanted/Derived
774 then there is no reaction
777 -- Interaction result of WorkItem <~> AtomicInert
779 = IR { ir_stop :: StopOrContinue
781 -- => Reagent (work item) consumed.
782 -- ContinueWith new_reagent
783 -- => Reagent transformed but keep gathering interactions.
784 -- The transformed item remains inert with respect
785 -- to any previously encountered inerts.
787 , ir_inert_action :: InertAction
788 -- Whether the inert item should remain in the InertSet.
790 , ir_new_work :: WorkList
791 -- new work items to add to the WorkList
793 , ir_fire :: Maybe String -- Tells whether a rule fired, and if so what
796 -- What to do with the inert reactant.
797 data InertAction = KeepInert | DropInert
799 mkIRContinue :: String -> WorkItem -> InertAction -> WorkList -> TcS InteractResult
800 mkIRContinue rule wi keep newWork
801 = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = keep
802 , ir_new_work = newWork, ir_fire = Just rule }
804 mkIRStopK :: String -> WorkList -> TcS InteractResult
805 mkIRStopK rule newWork
806 = return $ IR { ir_stop = Stop, ir_inert_action = KeepInert
807 , ir_new_work = newWork, ir_fire = Just rule }
809 mkIRStopD :: String -> WorkList -> TcS InteractResult
810 mkIRStopD rule newWork
811 = return $ IR { ir_stop = Stop, ir_inert_action = DropInert
812 , ir_new_work = newWork, ir_fire = Just rule }
814 noInteraction :: Monad m => WorkItem -> m InteractResult
816 = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = KeepInert
817 , ir_new_work = emptyWorkList, ir_fire = Nothing }
819 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
820 -- See Note [Efficient Orientation]
823 ---------------------------------------------------
824 -- Interact a single WorkItem with the equalities of an inert set as
825 -- far as possible, i.e. until we get a Stop result from an individual
826 -- reaction (i.e. when the WorkItem is consumed), or until we've
827 -- interact the WorkItem with the entire equalities of the InertSet
829 interactWithInertEqsStage :: SimplifierStage
830 interactWithInertEqsStage depth workItem inert
831 = Bag.foldrBagM (interactNext depth) initITR (inert_eqs inert)
832 -- use foldr to preserve the order
834 initITR = SR { sr_inerts = inert { inert_eqs = emptyCCan }
835 , sr_new_work = emptyWorkList
836 , sr_stop = ContinueWith workItem }
838 ---------------------------------------------------
839 -- Interact a single WorkItem with *non-equality* constraints in the inert set.
840 -- Precondition: equality interactions must have already happened, hence we have
841 -- to pick up some information from the incoming inert, before folding over the
842 -- "Other" constraints it contains!
844 interactWithInertsStage :: SimplifierStage
845 interactWithInertsStage depth workItem inert
846 = let (relevant, inert_residual) = getISRelevant workItem inert
847 initITR = SR { sr_inerts = inert_residual
848 , sr_new_work = emptyWorkList
849 , sr_stop = ContinueWith workItem }
850 in Bag.foldrBagM (interactNext depth) initITR relevant
851 -- use foldr to preserve the order
853 getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet)
854 getISRelevant (CFrozenErr {}) is = (emptyCCan, is)
855 -- Nothing s relevant; we have alread interacted
856 -- it with the equalities in the inert set
858 getISRelevant (CDictCan { cc_class = cls } ) is
859 = let (relevant, residual_map) = getRelevantCts cls (inert_dicts is)
860 in (relevant, is { inert_dicts = residual_map })
861 getISRelevant (CFunEqCan { cc_fun = tc } ) is
862 = let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is)
863 in (relevant, is { inert_funeqs = residual_map })
864 getISRelevant (CIPCan { cc_ip_nm = nm }) is
865 = let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
866 in (relevant, is { inert_ips = residual_map })
867 -- An equality, finally, may kick everything except equalities out
868 -- because we have already interacted the equalities in interactWithInertEqsStage
869 getISRelevant _eq_ct is -- Equality, everything is relevant for this one
870 -- TODO: if we were caching variables, we'd know that only
871 -- some are relevant. Experiment with this for now.
872 = let cts = cCanMapToBag (inert_ips is) `unionBags`
873 cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
874 in (cts, is { inert_dicts = emptyCCanMap
875 , inert_ips = emptyCCanMap
876 , inert_funeqs = emptyCCanMap })
878 interactNext :: SubGoalDepth -> AtomicInert -> StageResult -> TcS StageResult
879 interactNext depth inert it
880 | ContinueWith work_item <- sr_stop it
881 = do { let inerts = sr_inerts it
883 ; IR { ir_new_work = new_work, ir_inert_action = inert_action
884 , ir_fire = fire_info, ir_stop = stop }
885 <- interactWithInert inert work_item
888 = text rule <+> keep_doc
889 <+> vcat [ ptext (sLit "Inert =") <+> ppr inert
890 , ptext (sLit "Work =") <+> ppr work_item
891 , ppUnless (isEmptyWorkList new_work) $
892 ptext (sLit "New =") <+> ppr new_work ]
893 keep_doc = case inert_action of
894 KeepInert -> ptext (sLit "[keep]")
895 DropInert -> ptext (sLit "[drop]")
897 Just rule -> do { bumpStepCountTcS
898 ; traceFireTcS depth (mk_msg rule) }
901 -- New inerts depend on whether we KeepInert or not
902 ; let inerts_new = case inert_action of
903 KeepInert -> inerts `updInertSet` inert
906 ; return $ SR { sr_inerts = inerts_new
907 , sr_new_work = sr_new_work it `unionWorkList` new_work
910 = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
912 -- Do a single interaction of two constraints.
913 interactWithInert :: AtomicInert -> WorkItem -> TcS InteractResult
914 interactWithInert inert workItem
915 = do { ctxt <- getTcSContext
916 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workItem
919 doInteractWithInert inert workItem
921 noInteraction workItem
924 allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
925 -- Allowed interactions
926 allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
927 allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
928 allowedInteraction _ _ _ = True
930 --------------------------------------------
931 doInteractWithInert :: CanonicalCt -> CanonicalCt -> TcS InteractResult
932 -- Identical class constraints.
935 inertItem@(CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
936 workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
937 | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
938 = solveOneFromTheOther "Cls/Cls" (EvId d1,fl1) workItem
940 | cls1 == cls2 && (not (isGivenOrSolved fl1 && isGivenOrSolved fl2))
941 = -- See Note [When improvement happens]
942 do { let pty1 = ClassP cls1 tys1
943 pty2 = ClassP cls2 tys2
944 inert_pred_loc = (pty1, pprFlavorArising fl1)
945 work_item_pred_loc = (pty2, pprFlavorArising fl2)
946 fd_eqns = improveFromAnother
947 inert_pred_loc -- the template
948 work_item_pred_loc -- the one we aim to rewrite
949 -- See Note [Efficient Orientation]
951 ; m <- rewriteWithFunDeps fd_eqns tys2 fl2
953 Nothing -> noInteraction workItem
954 Just (rewritten_tys2, cos2, fd_work)
955 | tcEqTypes tys1 rewritten_tys2
956 -> -- Solve him on the spot in this case
958 Given {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
959 Derived {} -> mkIRStopK "Cls/Cls fundep (solved)" fd_work
962 -> do { setDictBind d2 (EvCast d1 dict_co)
963 ; let inert_w = inertItem { cc_flavor = fl2 }
964 -- A bit naughty: we take the inert Derived,
965 -- turn it into a Wanted, use it to solve the work-item
966 -- and put it back into the work-list
967 -- Maybe rather than starting again, we could *replace* the
968 -- inert item, but its safe and simple to restart
969 ; mkIRStopD "Cls/Cls fundep (solved)" $
970 workListFromNonEq inert_w `unionWorkList` fd_work }
972 -> do { setDictBind d2 (EvCast d1 dict_co)
973 ; mkIRStopK "Cls/Cls fundep (solved)" fd_work }
976 -> -- We could not quite solve him, but we still rewrite him
977 -- Example: class C a b c | a -> b
978 -- Given: C Int Bool x, Wanted: C Int beta y
979 -- Then rewrite the wanted to C Int Bool y
980 -- but note that is still not identical to the given
981 -- The important thing is that the rewritten constraint is
982 -- inert wrt the given.
983 -- However it is not necessarily inert wrt previous inert-set items.
984 -- class C a b c d | a -> b, b c -> d
985 -- Inert: c1: C b Q R S, c2: C P Q a b
986 -- Work: C P alpha R beta
987 -- Does not react with c1; reacts with c2, with alpha:=Q
988 -- NOW it reacts with c1!
989 -- So we must stop, and put the rewritten constraint back in the work list
990 do { d2' <- newDictVar cls1 rewritten_tys2
992 Given {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
993 Wanted {} -> setDictBind d2 (EvCast d2' dict_co)
994 Derived {} -> return ()
995 ; let workItem' = workItem { cc_id = d2', cc_tyargs = rewritten_tys2 }
996 ; mkIRStopK "Cls/Cls fundep (partial)" $
997 workListFromNonEq workItem' `unionWorkList` fd_work }
1000 dict_co = mkTyConCoercion (classTyCon cls1) cos2
1003 -- Class constraint and given equality: use the equality to rewrite
1004 -- the class constraint.
1005 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1006 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
1007 | ifl `canRewrite` wfl
1008 , tv `elemVarSet` tyVarsOfTypes xis
1009 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
1010 -- Continue with rewritten Dictionary because we can only be in the
1011 -- interactWithEqsStage, so the dictionary is inert.
1012 ; mkIRContinue "Eq/Cls" rewritten_dict KeepInert emptyWorkList }
1014 doInteractWithInert (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
1015 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1016 | wfl `canRewrite` ifl
1017 , tv `elemVarSet` tyVarsOfTypes xis
1018 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
1019 ; mkIRContinue "Cls/Eq" workItem DropInert (workListFromNonEq rewritten_dict) }
1021 -- Class constraint and given equality: use the equality to rewrite
1022 -- the class constraint.
1023 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1024 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
1025 | ifl `canRewrite` wfl
1026 , tv `elemVarSet` tyVarsOfType ty
1027 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
1028 ; mkIRContinue "Eq/IP" rewritten_ip KeepInert emptyWorkList }
1030 doInteractWithInert (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
1031 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1032 | wfl `canRewrite` ifl
1033 , tv `elemVarSet` tyVarsOfType ty
1034 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
1035 ; mkIRContinue "IP/Eq" workItem DropInert (workListFromNonEq rewritten_ip) }
1037 -- Two implicit parameter constraints. If the names are the same,
1038 -- but their types are not, we generate a wanted type equality
1039 -- that equates the type (this is "improvement").
1040 -- However, we don't actually need the coercion evidence,
1041 -- so we just generate a fresh coercion variable that isn't used anywhere.
1042 doInteractWithInert (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
1043 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
1044 | nm1 == nm2 && isGivenOrSolved wfl && isGivenOrSolved ifl
1045 = -- See Note [Overriding implicit parameters]
1046 -- Dump the inert item, override totally with the new one
1047 -- Do not require type equality
1048 -- For example, given let ?x::Int = 3 in let ?x::Bool = True in ...
1049 -- we must *override* the outer one with the inner one
1050 mkIRContinue "IP/IP override" workItem DropInert emptyWorkList
1052 | nm1 == nm2 && ty1 `tcEqType` ty2
1053 = solveOneFromTheOther "IP/IP" (EvId id1,ifl) workItem
1056 = -- See Note [When improvement happens]
1057 do { co_var <- newCoVar ty2 ty1 -- See Note [Efficient Orientation]
1058 ; let flav = Wanted (combineCtLoc ifl wfl)
1059 ; cans <- mkCanonical flav co_var
1061 Given {} -> pprPanic "Unexpected given IP" (ppr workItem)
1062 Derived {} -> pprPanic "Unexpected derived IP" (ppr workItem)
1064 do { setIPBind (cc_id workItem) $
1065 EvCast id1 (mkSymCoercion (mkCoVarCoercion co_var))
1066 ; mkIRStopK "IP/IP interaction (solved)" cans }
1069 -- Never rewrite a given with a wanted equality, and a type function
1070 -- equality can never rewrite an equality. We rewrite LHS *and* RHS
1071 -- of function equalities so that our inert set exposes everything that
1072 -- we know about equalities.
1074 -- Inert: equality, work item: function equality
1075 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
1076 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
1077 , cc_tyargs = args, cc_rhs = xi2 })
1078 | ifl `canRewrite` wfl
1079 , tv `elemVarSet` tyVarsOfTypes (xi2:args) -- Rewrite RHS as well
1080 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
1081 ; mkIRStopK "Eq/FunEq" (workListFromEq rewritten_funeq) }
1082 -- Must Stop here, because we may no longer be inert after the rewritting.
1084 -- Inert: function equality, work item: equality
1085 doInteractWithInert (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
1086 , cc_tyargs = args, cc_rhs = xi1 })
1087 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
1088 | wfl `canRewrite` ifl
1089 , tv `elemVarSet` tyVarsOfTypes (xi1:args) -- Rewrite RHS as well
1090 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
1091 ; mkIRContinue "FunEq/Eq" workItem DropInert (workListFromEq rewritten_funeq) }
1092 -- One may think that we could (KeepTransformedInert rewritten_funeq)
1093 -- but that is wrong, because it may end up not being inert with respect
1094 -- to future inerts. Example:
1095 -- Original inert = { F xis ~ [a], b ~ Maybe Int }
1096 -- Work item comes along = a ~ [b]
1097 -- If we keep { F xis ~ [b] } in the inert set we will end up with:
1098 -- { F xis ~ [b], b ~ Maybe Int, a ~ [Maybe Int] }
1099 -- At the end, which is *not* inert. So we should unfortunately DropInert here.
1101 doInteractWithInert (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
1102 , cc_tyargs = args1, cc_rhs = xi1 })
1103 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
1104 , cc_tyargs = args2, cc_rhs = xi2 })
1105 | tc1 == tc2 && and (zipWith tcEqType args1 args2)
1106 , Just GivenSolved <- isGiven_maybe fl1
1107 = mkIRContinue "Funeq/Funeq" workItem DropInert emptyWorkList
1108 | tc1 == tc2 && and (zipWith tcEqType args1 args2)
1109 , Just GivenSolved <- isGiven_maybe fl2
1110 = mkIRStopK "Funeq/Funeq" emptyWorkList
1112 | fl1 `canSolve` fl2 && lhss_match
1113 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1114 ; mkIRStopK "FunEq/FunEq" cans }
1115 | fl2 `canSolve` fl1 && lhss_match
1116 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1117 ; mkIRContinue "FunEq/FunEq" workItem DropInert cans }
1119 lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
1121 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1122 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
1123 -- Check for matching LHS
1124 | fl1 `canSolve` fl2 && tv1 == tv2
1125 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1126 ; mkIRStopK "Eq/Eq lhs" cans }
1128 | fl2 `canSolve` fl1 && tv1 == tv2
1129 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1130 ; mkIRContinue "Eq/Eq lhs" workItem DropInert cans }
1132 -- Check for rewriting RHS
1133 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1134 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1135 ; mkIRStopK "Eq/Eq rhs" rewritten_eq }
1137 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1138 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1139 ; mkIRContinue "Eq/Eq rhs" workItem DropInert rewritten_eq }
1141 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1142 (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
1143 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
1144 = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1145 ; mkIRStopK "Frozen/Eq" rewritten_frozen }
1147 doInteractWithInert (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
1148 workItem@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1149 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
1150 = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1151 ; mkIRContinue "Frozen/Eq" workItem DropInert rewritten_frozen }
1153 -- Fall-through case for all other situations
1154 doInteractWithInert _ workItem = noInteraction workItem
1156 -------------------------
1157 -- Equational Rewriting
1158 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1159 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1160 = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
1161 args = substTysWith [tv] [xi] xis
1163 dict_co = mkTyConCoercion con cos
1164 ; dv' <- newDictVar cl args
1166 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
1167 Given {} -> setDictBind dv' (EvCast dv dict_co)
1168 Derived {} -> return () -- Derived dicts we don't set any evidence
1170 ; return (CDictCan { cc_id = dv'
1173 , cc_tyargs = args }) }
1175 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1176 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1177 = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi]
1178 ty' = substTyWith [tv] [xi] ty
1179 ; ipid' <- newIPVar nm ty'
1181 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co))
1182 Given {} -> setIPBind ipid' (EvCast ipid ip_co)
1183 Derived {} -> return () -- Derived ips: we don't set any evidence
1185 ; return (CIPCan { cc_id = ipid'
1188 , cc_ip_ty = ty' }) }
1190 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1191 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2) -- cv2 :: F args ~ xi2
1192 = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
1193 args' = substTysWith [tv] [xi1] args
1194 fun_co = mkTyConCoercion tc arg_cos -- fun_co :: F args ~ F args'
1196 xi2' = substTyWith [tv] [xi1] xi2
1197 xi2_co = substTyWith [tv] [mkCoVarCoercion cv1] xi2 -- xi2_co :: xi2 ~ xi2'
1199 ; cv2' <- newCoVar (mkTyConApp tc args') xi2'
1201 Wanted {} -> setCoBind cv2 (fun_co `mkTransCoercion`
1202 mkCoVarCoercion cv2' `mkTransCoercion`
1203 mkSymCoercion xi2_co)
1204 Given {} -> setCoBind cv2' (mkSymCoercion fun_co `mkTransCoercion`
1205 mkCoVarCoercion cv2 `mkTransCoercion`
1207 Derived {} -> return ()
1209 ; return (CFunEqCan { cc_id = cv2'
1213 , cc_rhs = xi2' }) }
1216 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
1217 -- Use the first equality to rewrite the second, flavors already checked.
1218 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1219 -- rewrites c2 to give
1220 -- c2' : tv2 ~ xi2[xi1/tv1]
1221 -- We must do an occurs check to sure the new constraint is canonical
1222 -- So we might return an empty bag
1223 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1224 | Just tv2' <- tcGetTyVar_maybe xi2'
1225 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1226 = do { when (isWanted gw) (setCoBind cv2 (mkSymCoercion co2'))
1227 ; return emptyWorkList }
1229 = do { cv2' <- newCoVar (mkTyVarTy tv2) xi2'
1231 Wanted {} -> setCoBind cv2 $ mkCoVarCoercion cv2' `mkTransCoercion`
1233 Given {} -> setCoBind cv2' $ mkCoVarCoercion cv2 `mkTransCoercion`
1235 Derived {} -> return ()
1236 ; canEqToWorkList gw cv2' (mkTyVarTy tv2) xi2' }
1238 xi2' = substTyWith [tv1] [xi1] xi2
1239 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1241 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
1242 -- Used to ineract two equalities of the following form:
1243 -- First Equality: co1: (XXX ~ xi1)
1244 -- Second Equality: cv2: (XXX ~ xi2)
1245 -- Where the cv1 `canRewrite` cv2 equality
1246 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1),
1247 -- See Note [Efficient Orientation] for that
1248 rewriteEqLHS LeftComesFromInert (co1,xi1) (cv2,gw,xi2)
1249 = do { cv2' <- newCoVar xi2 xi1
1251 Wanted {} -> setCoBind cv2 $
1252 co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
1253 Given {} -> setCoBind cv2' $
1254 mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
1255 Derived {} -> return ()
1256 ; mkCanonical gw cv2' }
1258 rewriteEqLHS RightComesFromInert (co1,xi1) (cv2,gw,xi2)
1259 = do { cv2' <- newCoVar xi1 xi2
1261 Wanted {} -> setCoBind cv2 $
1262 co1 `mkTransCoercion` mkCoVarCoercion cv2'
1263 Given {} -> setCoBind cv2' $
1264 mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
1265 Derived {} -> return ()
1266 ; mkCanonical gw cv2' }
1268 rewriteFrozen :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor) -> TcS WorkList
1269 rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1270 = do { cv2' <- newCoVar ty2a' ty2b' -- ty2a[xi1/tv1] ~ ty2b[xi1/tv1]
1272 Wanted {} -> setCoBind cv2 $ co2a' `mkTransCoercion`
1273 mkCoVarCoercion cv2' `mkTransCoercion`
1276 Given {} -> setCoBind cv2' $ mkSymCoercion co2a' `mkTransCoercion`
1277 mkCoVarCoercion cv2 `mkTransCoercion`
1280 Derived {} -> return ()
1282 ; return (workListFromNonEq $ CFrozenErr { cc_id = cv2', cc_flavor = fl2 }) }
1284 (ty2a, ty2b) = coVarKind cv2 -- cv2 : ty2a ~ ty2b
1285 ty2a' = substTyWith [tv1] [xi1] ty2a
1286 ty2b' = substTyWith [tv1] [xi1] ty2b
1288 co2a' = substTyWith [tv1] [mkCoVarCoercion cv1] ty2a -- ty2a ~ ty2a[xi1/tv1]
1289 co2b' = substTyWith [tv1] [mkCoVarCoercion cv1] ty2b -- ty2b ~ ty2b[xi1/tv1]
1291 solveOneFromTheOther :: String -> (EvTerm, CtFlavor) -> CanonicalCt -> TcS InteractResult
1292 -- First argument inert, second argument work-item. They both represent
1293 -- wanted/given/derived evidence for the *same* predicate so
1294 -- we can discharge one directly from the other.
1296 -- Precondition: value evidence only (implicit parameters, classes)
1298 solveOneFromTheOther info (ev_term,ifl) workItem
1300 = mkIRStopK ("Solved[DW] " ++ info) emptyWorkList
1302 | isDerived ifl -- The inert item is Derived, we can just throw it away,
1303 -- The workItem is inert wrt earlier inert-set items,
1304 -- so it's safe to continue on from this point
1305 = mkIRContinue ("Solved[DI] " ++ info) workItem DropInert emptyWorkList
1307 | Just GivenSolved <- isGiven_maybe ifl, isGivenOrSolved wfl
1308 -- Same if the inert is a GivenSolved -- just get rid of it
1309 = mkIRContinue ("Solved[SI] " ++ info) workItem DropInert emptyWorkList
1312 = ASSERT( ifl `canSolve` wfl )
1313 -- Because of Note [The Solver Invariant], plus Derived dealt with
1314 do { when (isWanted wfl) $ setEvBind wid ev_term
1315 -- Overwrite the binding, if one exists
1316 -- If both are Given, we already have evidence; no need to duplicate
1317 ; mkIRStopK ("Solved " ++ info) emptyWorkList }
1319 wfl = cc_flavor workItem
1320 wid = cc_id workItem
1323 Note [Superclasses and recursive dictionaries]
1324 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1325 Overlaps with Note [SUPERCLASS-LOOP 1]
1326 Note [SUPERCLASS-LOOP 2]
1327 Note [Recursive instances and superclases]
1328 ToDo: check overlap and delete redundant stuff
1330 Right before adding a given into the inert set, we must
1331 produce some more work, that will bring the superclasses
1332 of the given into scope. The superclass constraints go into
1335 When we simplify a wanted constraint, if we first see a matching
1336 instance, we may produce new wanted work. To (1) avoid doing this work
1337 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1338 this item as given into our inert set WITHOUT adding its superclass constraints,
1339 otherwise we'd be in danger of creating a loop [In fact this was the exact reason
1340 for doing the isGoodRecEv check in an older version of the type checker].
1342 But now we have added partially solved constraints to the worklist which may
1343 interact with other wanteds. Consider the example:
1347 class Eq b => Foo a b --- 0-th selector
1348 instance Eq a => Foo [a] a --- fooDFun
1350 and wanted (Foo [t] t). We are first going to see that the instance matches
1351 and create an inert set that includes the solved (Foo [t] t) but not its superclasses:
1352 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1353 Our work list is going to contain a new *wanted* goal
1356 Ok, so how do we get recursive dictionaries, at all:
1360 data D r = ZeroD | SuccD (r (D r));
1362 instance (Eq (r (D r))) => Eq (D r) where
1363 ZeroD == ZeroD = True
1364 (SuccD a) == (SuccD b) = a == b
1367 equalDC :: D [] -> D [] -> Bool;
1370 We need to prove (Eq (D [])). Here's how we go:
1374 by instance decl, holds if
1378 *BUT* we have an inert set which gives us (no superclasses):
1380 By the instance declaration of Eq we can show the 'd2' goal if
1382 where d2 = dfEqList d3
1384 Now, however this wanted can interact with our inert d1 to set:
1386 and solve the goal. Why was this interaction OK? Because, if we chase the
1387 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1389 d3 := dfEqD2 (dfEqList d3)
1390 which is FINE because the use of d3 is protected by the instance function
1393 So, our strategy is to try to put solved wanted dictionaries into the
1394 inert set along with their superclasses (when this is meaningful,
1395 i.e. when new wanted goals are generated) but solve a wanted dictionary
1396 from a given only in the case where the evidence variable of the
1397 wanted is mentioned in the evidence of the given (recursively through
1398 the evidence binds) in a protected way: more instance function applications
1399 than superclass selectors.
1401 Here are some more examples from GHC's previous type checker
1405 This code arises in the context of "Scrap Your Boilerplate with Class"
1409 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1410 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1412 class Data Maybe a => Foo a
1414 instance Foo t => Sat (Maybe t) -- dfunSat
1416 instance Data Maybe a => Foo a -- dfunFoo1
1417 instance Foo a => Foo [a] -- dfunFoo2
1418 instance Foo [Char] -- dfunFoo3
1420 Consider generating the superclasses of the instance declaration
1421 instance Foo a => Foo [a]
1423 So our problem is this
1425 d1 :_w Data Maybe [t]
1427 We may add the given in the inert set, along with its superclasses
1428 [assuming we don't fail because there is a matching instance, see
1429 tryTopReact, given case ]
1433 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1434 d1 :_w Data Maybe [t]
1435 Then d2 can readily enter the inert, and we also do solving of the wanted
1438 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1440 d2 :_w Sat (Maybe [t])
1442 d01 :_g Data Maybe t
1443 Now, we may simplify d2 more:
1446 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1447 d1 :_g Data Maybe [t]
1448 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1452 d01 :_g Data Maybe t
1454 Now, we can just solve d3.
1457 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1458 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1461 d01 :_g Data Maybe t
1462 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1465 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1466 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1467 d4 :_g Foo [t] d4 := dfunFoo2 d5
1470 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1471 d01 :_g Data Maybe t
1472 Now, d5 can be solved! (and its superclass enter scope)
1475 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1476 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1477 d4 :_g Foo [t] d4 := dfunFoo2 d5
1478 d5 :_g Foo t d5 := dfunFoo1 d7
1481 d6 :_g Data Maybe [t]
1482 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1483 d01 :_g Data Maybe t
1486 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1487 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1488 that must not be used (look at case interactInert where both inert and workitem
1489 are givens). So we have several options:
1490 - Drop the workitem always (this will drop d8)
1491 This feels very unsafe -- what if the work item was the "good" one
1492 that should be used later to solve another wanted?
1493 - Don't drop anyone: the inert set may contain multiple givens!
1494 [This is currently implemented]
1496 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1497 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1498 d7. Now the [isRecDictEv] function in the ineration solver
1499 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1500 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1502 So, no interaction happens there. Then we meet d01 and there is no recursion
1503 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1505 Note [SUPERCLASS-LOOP 1]
1506 ~~~~~~~~~~~~~~~~~~~~~~~~
1507 We have to be very, very careful when generating superclasses, lest we
1508 accidentally build a loop. Here's an example:
1512 class S a => C a where { opc :: a -> a }
1513 class S b => D b where { opd :: b -> b }
1515 instance C Int where
1518 instance D Int where
1521 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1522 Simplifying, we may well get:
1523 $dfCInt = :C ds1 (opd dd)
1526 Notice that we spot that we can extract ds1 from dd.
1528 Alas! Alack! We can do the same for (instance D Int):
1530 $dfDInt = :D ds2 (opc dc)
1534 And now we've defined the superclass in terms of itself.
1535 Two more nasty cases are in
1540 - Satisfy the superclass context *all by itself*
1541 (tcSimplifySuperClasses)
1542 - And do so completely; i.e. no left-over constraints
1543 to mix with the constraints arising from method declarations
1546 Note [SUPERCLASS-LOOP 2]
1547 ~~~~~~~~~~~~~~~~~~~~~~~~
1548 We need to be careful when adding "the constaint we are trying to prove".
1549 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1551 class Ord a => C a where
1552 instance Ord [a] => C [a] where ...
1554 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1555 superclasses of C [a] to avails. But we must not overwrite the binding
1556 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1559 Here's another variant, immortalised in tcrun020
1560 class Monad m => C1 m
1561 class C1 m => C2 m x
1562 instance C2 Maybe Bool
1563 For the instance decl we need to build (C1 Maybe), and it's no good if
1564 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1565 before we search for C1 Maybe.
1567 Here's another example
1568 class Eq b => Foo a b
1569 instance Eq a => Foo [a] a
1573 we'll first deduce that it holds (via the instance decl). We must not
1574 then overwrite the Eq t constraint with a superclass selection!
1576 At first I had a gross hack, whereby I simply did not add superclass constraints
1577 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1578 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1579 I found a very obscure program (now tcrun021) in which improvement meant the
1580 simplifier got two bites a the cherry... so something seemed to be an Stop
1581 first time, but reducible next time.
1583 Now we implement the Right Solution, which is to check for loops directly
1584 when adding superclasses. It's a bit like the occurs check in unification.
1586 Note [Recursive instances and superclases]
1587 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1588 Consider this code, which arises in the context of "Scrap Your
1589 Boilerplate with Class".
1593 instance Sat (ctx Char) => Data ctx Char
1594 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1596 class Data Maybe a => Foo a
1598 instance Foo t => Sat (Maybe t)
1600 instance Data Maybe a => Foo a
1601 instance Foo a => Foo [a]
1604 In the instance for Foo [a], when generating evidence for the superclasses
1605 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1606 Using the instance for Data, we therefore need
1607 (Sat (Maybe [a], Data Maybe a)
1608 But we are given (Foo a), and hence its superclass (Data Maybe a).
1609 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1610 we need (Foo [a]). And that is the very dictionary we are bulding
1611 an instance for! So we must put that in the "givens". So in this
1613 Given: Foo a, Foo [a]
1614 Wanted: Data Maybe [a]
1616 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1617 the givens, which is what 'addGiven' would normally do. Why? Because
1618 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1619 by selecting a superclass from Foo [a], which simply makes a loop.
1621 On the other hand we *must* put the superclasses of (Foo a) in
1622 the givens, as you can see from the derivation described above.
1624 Conclusion: in the very special case of tcSimplifySuperClasses
1625 we have one 'given' (namely the "this" dictionary) whose superclasses
1626 must not be added to 'givens' by addGiven.
1628 There is a complication though. Suppose there are equalities
1629 instance (Eq a, a~b) => Num (a,b)
1630 Then we normalise the 'givens' wrt the equalities, so the original
1631 given "this" dictionary is cast to one of a different type. So it's a
1632 bit trickier than before to identify the "special" dictionary whose
1633 superclasses must not be added. See test
1634 indexed-types/should_run/EqInInstance
1636 We need a persistent property of the dictionary to record this
1637 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1638 but cool), which is maintained by dictionary normalisation.
1639 Specifically, the InstLocOrigin is
1641 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1644 Note [MATCHING-SYNONYMS]
1645 ~~~~~~~~~~~~~~~~~~~~~~~~
1646 When trying to match a dictionary (D tau) to a top-level instance, or a
1647 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1648 we do *not* need to expand type synonyms because the matcher will do that for us.
1651 Note [RHS-FAMILY-SYNONYMS]
1652 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1653 The RHS of a family instance is represented as yet another constructor which is
1654 like a type synonym for the real RHS the programmer declared. Eg:
1655 type instance F (a,a) = [a]
1657 :R32 a = [a] -- internal type synonym introduced
1658 F (a,a) ~ :R32 a -- instance
1660 When we react a family instance with a type family equation in the work list
1661 we keep the synonym-using RHS without expansion.
1664 *********************************************************************************
1666 The top-reaction Stage
1668 *********************************************************************************
1671 -- If a work item has any form of interaction with top-level we get this
1672 data TopInteractResult
1673 = NoTopInt -- No top-level interaction
1674 -- Equivalent to (SomeTopInt emptyWorkList (ContinueWith work_item))
1676 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1677 -- for superclasses)
1678 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1679 } -- NB: in ``given'' (solved) form if the
1680 -- original was wanted or given and instance match
1681 -- was found, but may also be in wanted form if we
1682 -- only reacted with functional dependencies
1683 -- arising from top-level instances.
1685 topReactionsStage :: SimplifierStage
1686 topReactionsStage depth workItem inerts
1687 = do { tir <- tryTopReact inerts workItem
1688 -- NB: we pass the inerts as well. See Note [Instance and Given overlap]
1691 return $ SR { sr_inerts = inerts
1692 , sr_new_work = emptyWorkList
1693 , sr_stop = ContinueWith workItem }
1694 SomeTopInt tir_new_work tir_new_inert ->
1695 do { bumpStepCountTcS
1696 ; traceFireTcS depth (ptext (sLit "Top react")
1697 <+> vcat [ ptext (sLit "Work =") <+> ppr workItem
1698 , ptext (sLit "New =") <+> ppr tir_new_work ])
1699 ; return $ SR { sr_inerts = inerts
1700 , sr_new_work = tir_new_work
1701 , sr_stop = tir_new_inert
1705 tryTopReact :: InertSet -> WorkItem -> TcS TopInteractResult
1706 tryTopReact inerts workitem
1707 = do { -- A flag controls the amount of interaction allowed
1708 -- See Note [Simplifying RULE lhs constraints]
1709 ctxt <- getTcSContext
1710 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1711 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1712 ; doTopReact inerts workitem }
1713 else return NoTopInt
1716 allowedTopReaction :: Bool -> WorkItem -> Bool
1717 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1718 allowedTopReaction _ _ = True
1720 doTopReact :: InertSet -> WorkItem -> TcS TopInteractResult
1721 -- The work item does not react with the inert set, so try interaction with top-level instances
1722 -- NB: The place to add superclasses in *not* in doTopReact stage. Instead superclasses are
1723 -- added in the worklist as part of the canonicalisation process.
1724 -- See Note [Adding superclasses] in TcCanonical.
1727 -- See Note [Given constraint that matches an instance declaration]
1728 doTopReact _inerts (CDictCan { cc_flavor = Given {} })
1729 = return NoTopInt -- NB: Superclasses already added since it's canonical
1731 -- Derived dictionary: just look for functional dependencies
1732 doTopReact _inerts workItem@(CDictCan { cc_flavor = fl@(Derived loc)
1733 , cc_class = cls, cc_tyargs = xis })
1734 = do { instEnvs <- getInstEnvs
1735 ; let fd_eqns = improveFromInstEnv instEnvs
1736 (ClassP cls xis, pprArisingAt loc)
1737 ; m <- rewriteWithFunDeps fd_eqns xis fl
1739 Nothing -> return NoTopInt
1740 Just (xis',_,fd_work) ->
1741 let workItem' = workItem { cc_tyargs = xis' }
1742 -- Deriveds are not supposed to have identity (cc_id is unused!)
1743 in return $ SomeTopInt { tir_new_work = fd_work
1744 , tir_new_inert = ContinueWith workItem' } }
1746 -- Wanted dictionary
1747 doTopReact inerts workItem@(CDictCan { cc_id = dv, cc_flavor = fl@(Wanted loc)
1748 , cc_class = cls, cc_tyargs = xis })
1749 = do { -- See Note [MATCHING-SYNONYMS]
1750 ; lkp_inst_res <- matchClassInst inerts cls xis loc
1751 ; case lkp_inst_res of
1753 do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1755 ; instEnvs <- getInstEnvs
1756 ; let fd_eqns = improveFromInstEnv instEnvs
1757 (ClassP cls xis, pprArisingAt loc)
1758 ; m <- rewriteWithFunDeps fd_eqns xis fl
1760 Nothing -> return NoTopInt
1761 Just (xis',cos,fd_work) ->
1762 do { let dict_co = mkTyConCoercion (classTyCon cls) cos
1763 ; dv'<- newDictVar cls xis'
1764 ; setDictBind dv (EvCast dv' dict_co)
1765 ; let workItem' = CDictCan { cc_id = dv', cc_flavor = fl,
1766 cc_class = cls, cc_tyargs = xis' }
1768 SomeTopInt { tir_new_work = workListFromNonEq workItem' `unionWorkList` fd_work
1769 , tir_new_inert = Stop } } }
1771 GenInst wtvs ev_term -- Solved
1772 -- No need to do fundeps stuff here; the instance
1773 -- matches already so we won't get any more info
1774 -- from functional dependencies
1776 -> do { traceTcS "doTopReact/found nullary class instance for" (ppr dv)
1777 ; setDictBind dv ev_term
1778 -- Solved in one step and no new wanted work produced.
1779 -- i.e we directly matched a top-level instance
1780 -- No point in caching this in 'inert'; hence Stop
1781 ; return $ SomeTopInt { tir_new_work = emptyWorkList
1782 , tir_new_inert = Stop } }
1785 -> do { traceTcS "doTopReact/found non-nullary class instance for" (ppr dv)
1786 ; setDictBind dv ev_term
1787 -- Solved and new wanted work produced, you may cache the
1788 -- (tentatively solved) dictionary as Solved given.
1789 ; let solved = workItem { cc_flavor = solved_fl }
1790 solved_fl = mkSolvedFlavor fl UnkSkol
1791 ; inst_work <- canWanteds wtvs
1792 ; return $ SomeTopInt { tir_new_work = inst_work
1793 , tir_new_inert = ContinueWith solved } }
1797 doTopReact _inerts (CFunEqCan { cc_flavor = fl })
1798 | Just GivenSolved <- isGiven_maybe fl
1799 = return NoTopInt -- If Solved, no more interactions should happen
1801 -- Otherwise, it's a Given, Derived, or Wanted
1802 doTopReact _inerts workItem@(CFunEqCan { cc_id = cv, cc_flavor = fl
1803 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1804 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1805 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1807 MatchInstNo -> return NoTopInt
1808 MatchInstSingle (rep_tc, rep_tys)
1809 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1810 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1811 -- Eagerly expand away the type synonym on the
1812 -- RHS of a type function, so that it never
1813 -- appears in an error message
1814 -- See Note [Type synonym families] in TyCon
1815 coe = mkTyConApp coe_tc rep_tys
1817 Wanted {} -> do { cv' <- newCoVar rhs_ty xi
1819 coe `mkTransCoercion` mkCoVarCoercion cv'
1820 ; can_cts <- mkCanonical fl cv'
1821 ; let solved = workItem { cc_flavor = solved_fl }
1822 solved_fl = mkSolvedFlavor fl UnkSkol
1823 ; if isEmptyWorkList can_cts then
1824 return (SomeTopInt can_cts Stop) -- No point in caching
1826 SomeTopInt { tir_new_work = can_cts
1827 , tir_new_inert = ContinueWith solved }
1829 Given {} -> do { cv' <- newGivenCoVar xi rhs_ty $
1830 mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
1831 ; can_cts <- mkCanonical fl cv'
1833 SomeTopInt { tir_new_work = can_cts
1834 , tir_new_inert = Stop }
1836 Derived {} -> do { cv' <- newDerivedId (EqPred xi rhs_ty)
1837 ; can_cts <- mkCanonical fl cv'
1839 SomeTopInt { tir_new_work = can_cts
1840 , tir_new_inert = Stop }
1844 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1848 -- Any other work item does not react with any top-level equations
1849 doTopReact _inerts _workItem = return NoTopInt
1853 Note [FunDep and implicit parameter reactions]
1854 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1855 Currently, our story of interacting two dictionaries (or a dictionary
1856 and top-level instances) for functional dependencies, and implicit
1857 paramters, is that we simply produce new wanted equalities. So for example
1859 class D a b | a -> b where ...
1865 We generate the extra work item
1867 where 'cv' is currently unused. However, this new item reacts with d2,
1868 discharging it in favour of a new constraint d2' thus:
1870 d2 := d2' |> D Int cv
1871 Now d2' can be discharged from d1
1873 We could be more aggressive and try to *immediately* solve the dictionary
1874 using those extra equalities. With the same inert set and work item we
1875 might dischard d2 directly:
1878 d2 := d1 |> D Int cv
1880 But in general it's a bit painful to figure out the necessary coercion,
1881 so we just take the first approach. Here is a better example. Consider:
1882 class C a b c | a -> b
1884 [Given] d1 : C T Int Char
1885 [Wanted] d2 : C T beta Int
1886 In this case, it's *not even possible* to solve the wanted immediately.
1887 So we should simply output the functional dependency and add this guy
1888 [but NOT its superclasses] back in the worklist. Even worse:
1889 [Given] d1 : C T Int beta
1890 [Wanted] d2: C T beta Int
1891 Then it is solvable, but its very hard to detect this on the spot.
1893 It's exactly the same with implicit parameters, except that the
1894 "aggressive" approach would be much easier to implement.
1896 Note [When improvement happens]
1897 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1898 We fire an improvement rule when
1900 * Two constraints match (modulo the fundep)
1901 e.g. C t1 t2, C t1 t3 where C a b | a->b
1902 The two match because the first arg is identical
1904 * At least one is not Given. If they are both given, we don't fire
1905 the reaction because we have no way of constructing evidence for a
1906 new equality nor does it seem right to create a new wanted goal
1907 (because the goal will most likely contain untouchables, which
1908 can't be solved anyway)!
1910 Note that we *do* fire the improvement if one is Given and one is Derived.
1911 The latter can be a superclass of a wanted goal. Example (tcfail138)
1912 class L a b | a -> b
1913 class (G a, L a b) => C a b
1915 instance C a b' => G (Maybe a)
1916 instance C a b => C (Maybe a) a
1917 instance L (Maybe a) a
1919 When solving the superclasses of the (C (Maybe a) a) instance, we get
1920 Given: C a b ... and hance by superclasses, (G a, L a b)
1922 Use the instance decl to get
1924 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
1925 and now we need improvement between that derived superclass an the Given (L a b)
1927 Note [Overriding implicit parameters]
1928 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1930 f :: (?x::a) -> Bool -> a
1932 g v = let ?x::Int = 3
1933 in (f v, let ?x::Bool = True in f v)
1935 This should probably be well typed, with
1936 g :: Bool -> (Int, Bool)
1938 So the inner binding for ?x::Bool *overrides* the outer one.
1939 Hence a work-item Given overrides an inert-item Given.
1941 Note [Given constraint that matches an instance declaration]
1942 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1943 What should we do when we discover that one (or more) top-level
1944 instances match a given (or solved) class constraint? We have
1947 1. Reject the program. The reason is that there may not be a unique
1948 best strategy for the solver. Example, from the OutsideIn(X) paper:
1949 instance P x => Q [x]
1950 instance (x ~ y) => R [x] y
1952 wob :: forall a b. (Q [b], R b a) => a -> Int
1954 g :: forall a. Q [a] => [a] -> Int
1957 will generate the impliation constraint:
1958 Q [a] => (Q [beta], R beta [a])
1959 If we react (Q [beta]) with its top-level axiom, we end up with a
1960 (P beta), which we have no way of discharging. On the other hand,
1961 if we react R beta [a] with the top-level we get (beta ~ a), which
1962 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
1963 now solvable by the given Q [a].
1965 However, this option is restrictive, for instance [Example 3] from
1966 Note [Recursive dictionaries] will fail to work.
1968 2. Ignore the problem, hoping that the situations where there exist indeed
1969 such multiple strategies are rare: Indeed the cause of the previous
1970 problem is that (R [x] y) yields the new work (x ~ y) which can be
1971 *spontaneously* solved, not using the givens.
1973 We are choosing option 2 below but we might consider having a flag as well.
1976 Note [New Wanted Superclass Work]
1977 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1978 Even in the case of wanted constraints, we may add some superclasses
1979 as new given work. The reason is:
1981 To allow FD-like improvement for type families. Assume that
1983 class C a b | a -> b
1984 and we have to solve the implication constraint:
1986 Then, FD improvement can help us to produce a new wanted (beta ~ b)
1988 We want to have the same effect with the type family encoding of
1989 functional dependencies. Namely, consider:
1990 class (F a ~ b) => C a b
1991 Now suppose that we have:
1994 By interacting the given we will get given (F a ~ b) which is not
1995 enough by itself to make us discharge (C a beta). However, we
1996 may create a new derived equality from the super-class of the
1997 wanted constraint (C a beta), namely derived (F a ~ beta).
1998 Now we may interact this with given (F a ~ b) to get:
2000 But 'beta' is a touchable unification variable, and hence OK to
2001 unify it with 'b', replacing the derived evidence with the identity.
2003 This requires trySpontaneousSolve to solve *derived*
2004 equalities that have a touchable in their RHS, *in addition*
2005 to solving wanted equalities.
2007 We also need to somehow use the superclasses to quantify over a minimal,
2008 constraint see note [Minimize by Superclasses] in TcSimplify.
2011 Finally, here is another example where this is useful.
2015 class (F a ~ b) => C a b
2016 And we are given the wanteds:
2020 We surely do *not* want to quantify over (b ~ c), since if someone provides
2021 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
2022 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
2024 Step 1: We will get new *given* superclass work,
2025 provisionally to our solving of w1 and w2
2027 g1: F a ~ b, g2 : F a ~ c,
2028 w1 : C a b, w2 : C a c, w3 : b ~ c
2030 The evidence for g1 and g2 is a superclass evidence term:
2032 g1 := sc w1, g2 := sc w2
2034 Step 2: The givens will solve the wanted w3, so that
2035 w3 := sym (sc w1) ; sc w2
2037 Step 3: Now, one may naively assume that then w2 can be solve from w1
2038 after rewriting with the (now solved equality) (b ~ c).
2040 But this rewriting is ruled out by the isGoodRectDict!
2042 Conclusion, we will (correctly) end up with the unsolved goals
2045 NB: The desugarer needs be more clever to deal with equalities
2046 that participate in recursive dictionary bindings.
2049 data LookupInstResult
2051 | GenInst [WantedEvVar] EvTerm
2053 matchClassInst :: InertSet -> Class -> [Type] -> WantedLoc -> TcS LookupInstResult
2054 matchClassInst inerts clas tys loc
2055 = do { let pred = mkClassPred clas tys
2056 ; mb_result <- matchClass clas tys
2057 ; untch <- getUntouchables
2059 MatchInstNo -> return NoInstance
2060 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
2061 -- we learn more about the reagent
2062 MatchInstSingle (_,_)
2063 | given_overlap untch ->
2064 do { traceTcS "Delaying instance application" $
2065 vcat [ text "Workitem=" <+> pprPred (ClassP clas tys)
2066 , text "Silents and their superclasses=" <+> ppr silents_and_their_scs
2067 , text "All given dictionaries=" <+> ppr all_given_dicts ]
2068 ; return NoInstance -- see Note [Instance and Given overlap]
2071 MatchInstSingle (dfun_id, mb_inst_tys) ->
2072 do { checkWellStagedDFun pred dfun_id loc
2074 -- It's possible that not all the tyvars are in
2075 -- the substitution, tenv. For example:
2076 -- instance C X a => D X where ...
2077 -- (presumably there's a functional dependency in class C)
2078 -- Hence mb_inst_tys :: Either TyVar TcType
2080 ; tys <- instDFunTypes mb_inst_tys
2081 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
2082 ; if null theta then
2083 return (GenInst [] (EvDFunApp dfun_id tys []))
2085 { ev_vars <- instDFunConstraints theta
2086 ; let wevs = [EvVarX w loc | w <- ev_vars]
2087 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }
2090 where given_overlap :: TcsUntouchables -> Bool
2092 = foldlBag (\r d -> r || matchable untch d) False all_given_dicts
2094 matchable untch (CDictCan { cc_class = clas', cc_tyargs = sys, cc_flavor = fl })
2095 | Just GivenOrig <- isGiven_maybe fl
2097 , does_not_originate_in_a_silent clas' sys
2098 = case tcUnifyTys (\tv -> if isTouchableMetaTyVar_InRange untch tv &&
2099 tv `elemVarSet` tyVarsOfTypes tys
2100 then BindMe else Skolem) tys sys of
2101 -- We can't learn anything more about any variable at this point, so the only
2102 -- cause of overlap can be by an instantiation of a touchable unification
2103 -- variable. Hence we only bind touchable unification variables. In addition,
2104 -- we use tcUnifyTys instead of tcMatchTys to rule out cyclic substitutions.
2107 | otherwise = False -- No overlap with a solved, already been taken care of
2108 -- by the overlap check with the instance environment.
2109 matchable _tys ct = pprPanic "Expecting dictionary!" (ppr ct)
2111 does_not_originate_in_a_silent clas sys
2112 -- UGLY: See Note [Silent parameters overlapping]
2113 = null $ filter (tcEqPred (ClassP clas sys)) silents_and_their_scs
2115 silents_and_their_scs
2116 = foldlBag (\acc rvnt -> case rvnt of
2117 CDictCan { cc_id = d, cc_class = c, cc_tyargs = s }
2118 | isSilentEvVar d -> (ClassP c s) : (transSuperClasses c s) ++ acc
2119 _ -> acc) [] all_given_dicts
2122 -- When silent parameters will go away we should simply select from
2123 -- the given map of the inert set.
2124 all_given_dicts = Map.fold unionBags emptyCCan (cts_given $ inert_dicts inerts)
2128 Note [Silent parameters overlapping]
2129 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2131 The long-term goal is to completely remove silent superclass
2132 parameters when checking instance declarations. But until then we must
2133 make sure that we never prevent the application of an instance
2134 declaration because of a potential match from a silent parameter --
2135 after all we are supposed to have solved that silent parameter from
2136 some instance, anyway! In effect silent parameters behave more like
2137 Solved than like Given.
2139 A concrete example appears in typecheck/SilentParametersOverlapping.hs
2141 Note [Instance and Given overlap]
2142 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2143 Assume that we have an inert set that looks as follows:
2145 And an instance declaration:
2146 instance C a => D [a]
2147 A new wanted comes along of the form:
2150 One possibility is to apply the instance declaration which will leave us
2151 with an unsolvable goal (C alpha). However, later on a new constraint may
2152 arise (for instance due to a functional dependency between two later dictionaries),
2153 that will add the equality (alpha ~ Int), in which case our ([Wanted] D [alpha])
2154 will be transformed to [Wanted] D [Int], which could have been discharged by the given.
2156 The solution is that in matchClassInst and eventually in topReact, we get back with
2157 a matching instance, only when there is no Given in the inerts which is unifiable to
2158 this particular dictionary.
2160 The end effect is that, much as we do for overlapping instances, we delay choosing a
2161 class instance if there is a possibility of another instance OR a given to match our
2162 constraint later on. This fixes bugs #4981 and #5002.
2164 This is arguably not easy to appear in practice due to our aggressive prioritization
2165 of equality solving over other constraints, but it is possible. I've added a test case
2166 in typecheck/should-compile/GivenOverlapping.hs
2168 Moreover notice that our goals here are different than the goals of the top-level
2169 overlapping checks. There we are interested in validating the following principle:
2171 If we inline a function f at a site where the same global instance environment
2172 is available as the instance environment at the definition site of f then we
2173 should get the same behaviour.
2175 But for the Given Overlap check our goal is just related to completeness of