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 -- A mixture of Given, Wanted, and Derived constraints.
229 -- We split between equalities and the rest to process equalities first.
230 type WorkList = CanonicalCts
232 unionWorkLists :: WorkList -> WorkList -> WorkList
233 unionWorkLists = andCCan
235 isEmptyWorkList :: WorkList -> Bool
236 isEmptyWorkList = isEmptyCCan
238 emptyWorkList :: WorkList
239 emptyWorkList = emptyCCan
241 workListFromCCan :: CanonicalCt -> WorkList
242 workListFromCCan = singleCCan
244 ------------------------
246 = Stop -- Work item is consumed
247 | ContinueWith WorkItem -- Not consumed
249 instance Outputable StopOrContinue where
250 ppr Stop = ptext (sLit "Stop")
251 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
253 -- Results after interacting a WorkItem as far as possible with an InertSet
255 = SR { sr_inerts :: InertSet
256 -- The new InertSet to use (REPLACES the old InertSet)
257 , sr_new_work :: WorkList
258 -- Any new work items generated (should be ADDED to the old WorkList)
260 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
261 -- workitem is inert wrt to sr_inerts
262 , sr_stop :: StopOrContinue
265 instance Outputable StageResult where
266 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
267 = ptext (sLit "SR") <+>
268 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
269 , ptext (sLit "new work =") <+> ppr work <> comma
270 , ptext (sLit "stop =") <+> ppr stop])
272 type SubGoalDepth = Int -- Starts at zero; used to limit infinite
273 -- recursion of sub-goals
274 type SimplifierStage = SubGoalDepth -> WorkItem -> InertSet -> TcS StageResult
276 -- Combine a sequence of simplifier 'stages' to create a pipeline
277 runSolverPipeline :: SubGoalDepth
278 -> [(String, SimplifierStage)]
279 -> InertSet -> WorkItem
280 -> TcS (InertSet, WorkList)
281 -- Precondition: non-empty list of stages
282 runSolverPipeline depth pipeline inerts workItem
283 = do { traceTcS "Start solver pipeline" $
284 vcat [ ptext (sLit "work item =") <+> ppr workItem
285 , ptext (sLit "inerts =") <+> ppr inerts]
287 ; let itr_in = SR { sr_inerts = inerts
288 , sr_new_work = emptyWorkList
289 , sr_stop = ContinueWith workItem }
290 ; itr_out <- run_pipeline pipeline itr_in
292 = case sr_stop itr_out of
293 Stop -> sr_inerts itr_out
294 ContinueWith item -> sr_inerts itr_out `updInertSet` item
295 ; return (new_inert, sr_new_work itr_out) }
297 run_pipeline :: [(String, SimplifierStage)]
298 -> StageResult -> TcS StageResult
299 run_pipeline [] itr = return itr
300 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
302 run_pipeline ((name,stage):stages)
303 (SR { sr_new_work = accum_work
305 , sr_stop = ContinueWith work_item })
306 = do { itr <- stage depth work_item inerts
307 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
308 ; let itr' = itr { sr_new_work = accum_work `unionWorkLists` sr_new_work itr }
309 ; run_pipeline stages itr' }
313 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
314 Reagent: a ~ [b] (given)
316 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
317 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
318 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
321 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
324 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
325 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
329 Inert: {a ~ Int, F Int ~ b} (given)
330 Reagent: F a ~ b (wanted)
332 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
333 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
336 -- Main interaction solver: we fully solve the worklist 'in one go',
337 -- returning an extended inert set.
339 -- See Note [Touchables and givens].
340 solveInteractGiven :: InertSet -> GivenLoc -> [EvVar] -> TcS InertSet
341 solveInteractGiven inert gloc evs
342 = do { (_, inert_ret) <- solveInteract inert $ listToBag $
347 mk_given ev = mkEvVarX ev flav
349 solveInteractWanted :: InertSet -> [WantedEvVar] -> TcS InertSet
350 solveInteractWanted inert wvs
351 = do { (_,inert_ret) <- solveInteract inert $ listToBag $
352 map wantedToFlavored wvs
355 solveInteract :: InertSet -> Bag FlavoredEvVar -> TcS (Bool, InertSet)
356 -- Post: (True, inert_set) means we managed to discharge all constraints
357 -- without actually doing any interactions!
358 -- (False, inert_set) means some interactions occurred
359 solveInteract inert ws
360 = do { dyn_flags <- getDynFlags
361 ; sctx <- getTcSContext
363 ; traceTcS "solveInteract, before clever canonicalization:" $
364 vcat [ text "ws = " <+> ppr (mapBag (\(EvVarX ev ct)
365 -> (ct,evVarPred ev)) ws)
366 , text "inert = " <+> ppr inert ]
368 ; (flag, inert_ret) <- foldrBagM (tryPreSolveAndInteract sctx dyn_flags) (True,inert) ws
369 -- use foldr to preserve the order
371 ; traceTcS "solveInteract, after clever canonicalization (and interaction):" $
372 vcat [ text "No interaction happened = " <+> ppr flag
373 , text "inert_ret = " <+> ppr inert_ret ]
375 ; return (flag, inert_ret) }
378 tryPreSolveAndInteract :: SimplContext
382 -> TcS (Bool, InertSet)
383 -- Returns: True if it was able to discharge this constraint AND all previous ones
384 tryPreSolveAndInteract sctx dyn_flags flavev@(EvVarX ev_var fl) (all_previous_discharged, inert)
385 = do { let inert_cts = get_inert_cts (evVarPred ev_var)
387 ; this_one_discharged <- dischargeFromCCans inert_cts flavev
389 ; if this_one_discharged
390 then return (all_previous_discharged, inert)
393 { extra_cts <- mkCanonical fl ev_var
394 ; inert_ret <- solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) extra_cts inert
395 ; return (False, inert_ret) } }
398 get_inert_cts (ClassP clas _)
399 | simplEqsOnly sctx = emptyCCan
400 | otherwise = fst (getRelevantCts clas (inert_dicts inert))
401 get_inert_cts (IParam {})
402 = emptyCCan -- We must not do the same thing for IParams, because (contrary
403 -- to dictionaries), work items /must/ override inert items.
404 -- See Note [Overriding implicit parameters] in TcInteract.
405 get_inert_cts (EqPred {})
406 = inert_eqs inert `unionBags` cCanMapToBag (inert_funeqs inert)
408 dischargeFromCCans :: CanonicalCts -> FlavoredEvVar -> TcS Bool
409 -- See if this (pre-canonicalised) work-item is identical to a
410 -- one already in the inert set. Reasons:
411 -- a) Avoid creating superclass constraints for millions of incoming (Num a) constraints
412 -- b) Termination for improve_eqs in TcSimplify.simpl_loop
413 dischargeFromCCans cans (EvVarX ev fl)
414 = Bag.foldrBag discharge_ct (return False) cans
416 the_pred = evVarPred ev
418 discharge_ct :: CanonicalCt -> TcS Bool -> TcS Bool
419 discharge_ct ct _rest
420 | evVarPred (cc_id ct) `tcEqPred` the_pred
421 , cc_flavor ct `canSolve` fl
422 = do { when (isWanted fl) $ set_ev_bind ev (cc_id ct)
423 -- Deriveds need no evidence
424 -- For Givens, we already have evidence, and we don't need it twice
428 | EqPred {} <- evVarPred y = setEvBind x (EvCoercion (mkCoVarCoercion y))
429 | otherwise = setEvBind x (EvId y)
431 discharge_ct _ct rest = rest
434 Note [Avoiding the superclass explosion]
435 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
436 This note now is not as significant as it used to be because we no
437 longer add the superclasses of Wanted as Derived, except only if they
438 have equality superclasses or superclasses with functional
439 dependencies. The fear was that hundreds of identical wanteds would
440 give rise each to the same superclass or equality Derived's which
441 would lead to a blo-up in the number of interactions.
443 Instead, what we do with tryPreSolveAndCanon, is when we encounter a
444 new constraint, we very quickly see if it can be immediately
445 discharged by a class constraint in our inert set or the previous
446 canonicals. If so, we add nothing to the returned canonical
450 solveOne :: WorkItem -> InertSet -> TcS InertSet
451 solveOne workItem inerts
452 = do { dyn_flags <- getDynFlags
453 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) workItem inerts
457 solveInteractWithDepth :: (Int, Int, [WorkItem])
458 -> WorkList -> InertSet -> TcS InertSet
459 solveInteractWithDepth ctxt@(max_depth,n,stack) ws inert
464 = solverDepthErrorTcS n stack
467 = do { traceTcS "solveInteractWithDepth" $
468 vcat [ text "Current depth =" <+> ppr n
469 , text "Max depth =" <+> ppr max_depth
470 , text "ws =" <+> ppr ws ]
472 -- Solve equalities first
473 ; let (eqs, non_eqs) = Bag.partitionBag isCTyEqCan ws
474 ; is_from_eqs <- Bag.foldrBagM (solveOneWithDepth ctxt) inert eqs
475 ; Bag.foldrBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }
476 -- use foldr to preserve the order
479 -- Fully interact the given work item with an inert set, and return a
480 -- new inert set which has assimilated the new information.
481 solveOneWithDepth :: (Int, Int, [WorkItem])
482 -> WorkItem -> InertSet -> TcS InertSet
483 solveOneWithDepth (max_depth, depth, stack) work inert
484 = do { traceFireTcS depth (text "Solving {" <+> ppr work)
485 ; (new_inert, new_work) <- runSolverPipeline depth thePipeline inert work
487 -- Recursively solve the new work generated
488 -- from workItem, with a greater depth
489 ; res_inert <- solveInteractWithDepth (max_depth, depth+1, work:stack) new_work new_inert
491 ; traceFireTcS depth (text "Done }" <+> ppr work)
495 thePipeline :: [(String,SimplifierStage)]
496 thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
497 , ("interact with inerts", interactWithInertsStage)
498 , ("spontaneous solve", spontaneousSolveStage)
499 , ("top-level reactions", topReactionsStage) ]
502 *********************************************************************************
504 The spontaneous-solve Stage
506 *********************************************************************************
508 Note [Efficient Orientation]
509 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
511 There are two cases where we have to be careful about
512 orienting equalities to get better efficiency.
514 Case 1: In Rewriting Equalities (function rewriteEqLHS)
516 When rewriting two equalities with the same LHS:
519 We have a choice of producing work (xi1 ~ xi2) (up-to the
520 canonicalization invariants) However, to prevent the inert items
521 from getting kicked out of the inerts first, we prefer to
522 canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
523 ~ xi1) if (a) comes from the inert set.
525 This choice is implemented using the WhichComesFromInert flag.
527 Case 2: Functional Dependencies
528 Again, we should prefer, if possible, the inert variables on the RHS
530 Case 3: IP improvement work
531 We must always rewrite so that the inert type is on the right.
534 spontaneousSolveStage :: SimplifierStage
535 spontaneousSolveStage depth workItem inerts
536 = do { mSolve <- trySpontaneousSolve workItem
539 SPCantSolve -> -- No spontaneous solution for him, keep going
540 return $ SR { sr_new_work = emptyWorkList
542 , sr_stop = ContinueWith workItem }
545 | not (isGivenCt workItem)
546 -- Original was wanted or derived but we have now made him
547 -- given so we have to interact him with the inerts due to
548 -- its status change. This in turn may produce more work.
549 -- We do this *right now* (rather than just putting workItem'
550 -- back into the work-list) because we've solved
551 -> do { bumpStepCountTcS
552 ; traceFireTcS depth (ptext (sLit "Spontaneous (w/d)") <+> ppr workItem)
553 ; (new_inert, new_work) <- runSolverPipeline depth
554 [ ("recursive interact with inert eqs", interactWithInertEqsStage)
555 , ("recursive interact with inerts", interactWithInertsStage)
557 ; return $ SR { sr_new_work = new_work
558 , sr_inerts = new_inert -- will include workItem'
562 -> -- Original was given; he must then be inert all right, and
563 -- workList' are all givens from flattening
564 do { bumpStepCountTcS
565 ; traceFireTcS depth (ptext (sLit "Spontaneous (g)") <+> ppr workItem)
566 ; return $ SR { sr_new_work = emptyWorkList
567 , sr_inerts = inerts `updInertSet` workItem'
569 SPError -> -- Return with no new work
570 return $ SR { sr_new_work = emptyWorkList
575 data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
576 -- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
577 -- SPSolved workItem' gives us a new *given* to go on
578 -- SPError means that it's completely impossible to solve this equality, eg due to a kind error
581 -- @trySpontaneousSolve wi@ solves equalities where one side is a
582 -- touchable unification variable.
583 -- See Note [Touchables and givens]
584 trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
585 trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
588 | Just tv2 <- tcGetTyVar_maybe xi
589 = do { tch1 <- isTouchableMetaTyVar tv1
590 ; tch2 <- isTouchableMetaTyVar tv2
591 ; case (tch1, tch2) of
592 (True, True) -> trySpontaneousEqTwoWay cv gw tv1 tv2
593 (True, False) -> trySpontaneousEqOneWay cv gw tv1 xi
594 (False, True) -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
595 _ -> return SPCantSolve }
597 = do { tch1 <- isTouchableMetaTyVar tv1
598 ; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
599 else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:"
601 ; return SPCantSolve }
605 -- trySpontaneousSolve (CFunEqCan ...) = ...
606 -- See Note [No touchables as FunEq RHS] in TcSMonad
607 trySpontaneousSolve _ = return SPCantSolve
610 trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
611 -- tv is a MetaTyVar, not untouchable
612 trySpontaneousEqOneWay cv gw tv xi
613 | not (isSigTyVar tv) || isTyVarTy xi
614 = do { let kxi = typeKind xi -- NB: 'xi' is fully rewritten according to the inerts
615 -- so we have its more specific kind in our hands
616 ; if kxi `isSubKind` tyVarKind tv then
617 solveWithIdentity cv gw tv xi
618 else return SPCantSolve
620 else if tyVarKind tv `isSubKind` kxi then
621 return SPCantSolve -- kinds are compatible but we can't solveWithIdentity this way
622 -- This case covers the a_touchable :: * ~ b_untouchable :: ??
623 -- which has to be deferred or floated out for someone else to solve
624 -- it in a scope where 'b' is no longer untouchable.
625 else do { addErrorTcS KindError gw (mkTyVarTy tv) xi -- See Note [Kind errors]
629 | otherwise -- Still can't solve, sig tyvar and non-variable rhs
633 trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
634 -- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
635 trySpontaneousEqTwoWay cv gw tv1 tv2
637 , nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
639 = solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
640 | otherwise -- None is a subkind of the other, but they are both touchable!
642 -- do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
643 -- ; return SPError }
647 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
651 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
652 Consider the wanted problem:
653 alpha ~ (# Int, Int #)
654 where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
655 but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
656 simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and
657 get quantified over in inference mode. That's bad because we do know at this point that the
658 constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
660 The same applies in canonicalization code in case of kind errors in the givens.
662 However, when we canonicalize givens we only check for compatibility (@compatKind@).
663 If there were a kind error in the givens, this means some form of inconsistency or dead code.
665 You may think that when we spontaneously solve wanteds we may have to look through the
666 bindings to determine the right kind of the RHS type. E.g one may be worried that xi is
667 @alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
668 But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
669 so this situation can't happen.
671 Note [Spontaneous solving and kind compatibility]
672 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
673 Note that our canonical constraints insist that *all* equalities (tv ~
674 xi) or (F xis ~ rhs) require the LHS and the RHS to have *compatible*
675 the same kinds. ("compatible" means one is a subKind of the other.)
677 - It can't be *equal* kinds, because
678 b) wanted constraints don't necessarily have identical kinds
680 b) a solved wanted constraint becomes a given
682 - SPJ thinks that *given* constraints (tv ~ tau) always have that
683 tau has a sub-kind of tv; and when solving wanted constraints
684 in trySpontaneousEqTwoWay we re-orient to achieve this.
686 - Note that the kind invariant is maintained by rewriting.
687 Eg wanted1 rewrites wanted2; if both were compatible kinds before,
688 wanted2 will be afterwards. Similarly givens.
691 - Givens from higher-rank, such as:
692 type family T b :: * -> * -> *
693 type instance T Bool = (->)
695 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
697 Whereas we would be able to apply the type instance, we would not be able to
698 use the given (T Bool ~ (->)) in the body of 'flop'
701 Note [Avoid double unifications]
702 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
703 The spontaneous solver has to return a given which mentions the unified unification
704 variable *on the left* of the equality. Here is what happens if not:
705 Original wanted: (a ~ alpha), (alpha ~ Int)
706 We spontaneously solve the first wanted, without changing the order!
707 given : a ~ alpha [having unified alpha := a]
708 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
709 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
711 We avoid this problem by orienting the resulting given so that the unification
712 variable is on the left. [Note that alternatively we could attempt to
713 enforce this at canonicalization]
715 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
716 double unifications is the main reason we disallow touchable
717 unification variables as RHS of type family equations: F xis ~ alpha.
722 solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
723 -- Solve with the identity coercion
724 -- Precondition: kind(xi) is a sub-kind of kind(tv)
725 -- Precondition: CtFlavor is Wanted or Derived
726 -- See [New Wanted Superclass Work] to see why solveWithIdentity
727 -- must work for Derived as well as Wanted
728 -- Returns: workItem where
729 -- workItem = the new Given constraint
730 solveWithIdentity cv wd tv xi
731 = do { traceTcS "Sneaky unification:" $
732 vcat [text "Coercion variable: " <+> ppr wd,
733 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
734 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
735 text "Right Kind is : " <+> ppr (typeKind xi)
738 ; setWantedTyBind tv xi
739 ; cv_given <- newGivenCoVar (mkTyVarTy tv) xi xi
741 ; when (isWanted wd) (setCoBind cv xi)
742 -- We don't want to do this for Derived, that's why we use 'when (isWanted wd)'
744 ; return $ SPSolved (CTyEqCan { cc_id = cv_given
745 , cc_flavor = mkGivenFlavor wd UnkSkol
746 , cc_tyvar = tv, cc_rhs = xi }) }
750 *********************************************************************************
752 The interact-with-inert Stage
754 *********************************************************************************
756 Note [The Solver Invariant]
757 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
758 We always add Givens first. So you might think that the solver has
761 If the work-item is Given,
762 then the inert item must Given
764 But this isn't quite true. Suppose we have,
765 c1: [W] beta ~ [alpha], c2 : [W] blah, c3 :[W] alpha ~ Int
766 After processing the first two, we get
767 c1: [G] beta ~ [alpha], c2 : [W] blah
768 Now, c3 does not interact with the the given c1, so when we spontaneously
769 solve c3, we must re-react it with the inert set. So we can attempt a
770 reaction between inert c2 [W] and work-item c3 [G].
772 It *is* true that [Solver Invariant]
773 If the work-item is Given,
774 AND there is a reaction
775 then the inert item must Given
777 If the work-item is Given,
778 and the inert item is Wanted/Derived
779 then there is no reaction
782 -- Interaction result of WorkItem <~> AtomicInert
784 = IR { ir_stop :: StopOrContinue
786 -- => Reagent (work item) consumed.
787 -- ContinueWith new_reagent
788 -- => Reagent transformed but keep gathering interactions.
789 -- The transformed item remains inert with respect
790 -- to any previously encountered inerts.
792 , ir_inert_action :: InertAction
793 -- Whether the inert item should remain in the InertSet.
795 , ir_new_work :: WorkList
796 -- new work items to add to the WorkList
798 , ir_fire :: Maybe String -- Tells whether a rule fired, and if so what
801 -- What to do with the inert reactant.
802 data InertAction = KeepInert | DropInert
804 mkIRContinue :: String -> WorkItem -> InertAction -> WorkList -> TcS InteractResult
805 mkIRContinue rule wi keep newWork
806 = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = keep
807 , ir_new_work = newWork, ir_fire = Just rule }
809 mkIRStopK :: String -> WorkList -> TcS InteractResult
810 mkIRStopK rule newWork
811 = return $ IR { ir_stop = Stop, ir_inert_action = KeepInert
812 , ir_new_work = newWork, ir_fire = Just rule }
814 mkIRStopD :: String -> WorkList -> TcS InteractResult
815 mkIRStopD rule newWork
816 = return $ IR { ir_stop = Stop, ir_inert_action = DropInert
817 , ir_new_work = newWork, ir_fire = Just rule }
819 noInteraction :: Monad m => WorkItem -> m InteractResult
821 = return $ IR { ir_stop = ContinueWith wi, ir_inert_action = KeepInert
822 , ir_new_work = emptyWorkList, ir_fire = Nothing }
824 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
825 -- See Note [Efficient Orientation]
828 ---------------------------------------------------
829 -- Interact a single WorkItem with the equalities of an inert set as
830 -- far as possible, i.e. until we get a Stop result from an individual
831 -- reaction (i.e. when the WorkItem is consumed), or until we've
832 -- interact the WorkItem with the entire equalities of the InertSet
834 interactWithInertEqsStage :: SimplifierStage
835 interactWithInertEqsStage depth workItem inert
836 = Bag.foldrBagM (interactNext depth) initITR (inert_eqs inert)
837 -- use foldr to preserve the order
839 initITR = SR { sr_inerts = inert { inert_eqs = emptyCCan }
840 , sr_new_work = emptyWorkList
841 , sr_stop = ContinueWith workItem }
843 ---------------------------------------------------
844 -- Interact a single WorkItem with *non-equality* constraints in the inert set.
845 -- Precondition: equality interactions must have already happened, hence we have
846 -- to pick up some information from the incoming inert, before folding over the
847 -- "Other" constraints it contains!
849 interactWithInertsStage :: SimplifierStage
850 interactWithInertsStage depth workItem inert
851 = let (relevant, inert_residual) = getISRelevant workItem inert
852 initITR = SR { sr_inerts = inert_residual
853 , sr_new_work = emptyWorkList
854 , sr_stop = ContinueWith workItem }
855 in Bag.foldrBagM (interactNext depth) initITR relevant
856 -- use foldr to preserve the order
858 getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet)
859 getISRelevant (CFrozenErr {}) is = (emptyCCan, is)
860 -- Nothing s relevant; we have alread interacted
861 -- it with the equalities in the inert set
863 getISRelevant (CDictCan { cc_class = cls } ) is
864 = let (relevant, residual_map) = getRelevantCts cls (inert_dicts is)
865 in (relevant, is { inert_dicts = residual_map })
866 getISRelevant (CFunEqCan { cc_fun = tc } ) is
867 = let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is)
868 in (relevant, is { inert_funeqs = residual_map })
869 getISRelevant (CIPCan { cc_ip_nm = nm }) is
870 = let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
871 in (relevant, is { inert_ips = residual_map })
872 -- An equality, finally, may kick everything except equalities out
873 -- because we have already interacted the equalities in interactWithInertEqsStage
874 getISRelevant _eq_ct is -- Equality, everything is relevant for this one
875 -- TODO: if we were caching variables, we'd know that only
876 -- some are relevant. Experiment with this for now.
877 = let cts = cCanMapToBag (inert_ips is) `unionBags`
878 cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
879 in (cts, is { inert_dicts = emptyCCanMap
880 , inert_ips = emptyCCanMap
881 , inert_funeqs = emptyCCanMap })
883 interactNext :: SubGoalDepth -> AtomicInert -> StageResult -> TcS StageResult
884 interactNext depth inert it
885 | ContinueWith work_item <- sr_stop it
886 = do { let inerts = sr_inerts it
888 ; IR { ir_new_work = new_work, ir_inert_action = inert_action
889 , ir_fire = fire_info, ir_stop = stop }
890 <- interactWithInert inert work_item
893 = text rule <+> keep_doc
894 <+> vcat [ ptext (sLit "Inert =") <+> ppr inert
895 , ptext (sLit "Work =") <+> ppr work_item
896 , ppUnless (isEmptyBag new_work) $
897 ptext (sLit "New =") <+> ppr new_work ]
898 keep_doc = case inert_action of
899 KeepInert -> ptext (sLit "[keep]")
900 DropInert -> ptext (sLit "[drop]")
902 Just rule -> do { bumpStepCountTcS
903 ; traceFireTcS depth (mk_msg rule) }
906 -- New inerts depend on whether we KeepInert or not
907 ; let inerts_new = case inert_action of
908 KeepInert -> inerts `updInertSet` inert
911 ; return $ SR { sr_inerts = inerts_new
912 , sr_new_work = sr_new_work it `unionWorkLists` new_work
915 = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
917 -- Do a single interaction of two constraints.
918 interactWithInert :: AtomicInert -> WorkItem -> TcS InteractResult
919 interactWithInert inert workItem
920 = do { ctxt <- getTcSContext
921 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workItem
924 doInteractWithInert inert workItem
926 noInteraction workItem
929 allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
930 -- Allowed interactions
931 allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
932 allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
933 allowedInteraction _ _ _ = True
935 --------------------------------------------
936 doInteractWithInert :: CanonicalCt -> CanonicalCt -> TcS InteractResult
937 -- Identical class constraints.
940 inertItem@(CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
941 workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
942 | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
943 = solveOneFromTheOther "Cls/Cls" (EvId d1,fl1) workItem
945 | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
946 = -- See Note [When improvement happens]
947 do { let pty1 = ClassP cls1 tys1
948 pty2 = ClassP cls2 tys2
949 inert_pred_loc = (pty1, pprFlavorArising fl1)
950 work_item_pred_loc = (pty2, pprFlavorArising fl2)
951 fd_eqns = improveFromAnother
952 inert_pred_loc -- the template
953 work_item_pred_loc -- the one we aim to rewrite
954 -- See Note [Efficient Orientation]
956 ; m <- rewriteWithFunDeps fd_eqns tys2 fl2
958 Nothing -> noInteraction workItem
959 Just (rewritten_tys2, cos2, fd_work)
960 | tcEqTypes tys1 rewritten_tys2
961 -> -- Solve him on the spot in this case
963 Given {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
964 Derived {} -> mkIRStopK "Cls/Cls fundep (solved)" fd_work
967 -> do { setDictBind d2 (EvCast d1 dict_co)
968 ; let inert_w = inertItem { cc_flavor = fl2 }
969 -- A bit naughty: we take the inert Derived,
970 -- turn it into a Wanted, use it to solve the work-item
971 -- and put it back into the work-list
972 -- Maybe rather than starting again, we could *replace* the
973 -- inert item, but its safe and simple to restart
974 ; mkIRStopD "Cls/Cls fundep (solved)" (inert_w `consBag` fd_work) }
977 -> do { setDictBind d2 (EvCast d1 dict_co)
978 ; mkIRStopK "Cls/Cls fundep (solved)" fd_work }
981 -> -- We could not quite solve him, but we still rewrite him
982 -- Example: class C a b c | a -> b
983 -- Given: C Int Bool x, Wanted: C Int beta y
984 -- Then rewrite the wanted to C Int Bool y
985 -- but note that is still not identical to the given
986 -- The important thing is that the rewritten constraint is
987 -- inert wrt the given.
988 -- However it is not necessarily inert wrt previous inert-set items.
989 -- class C a b c d | a -> b, b c -> d
990 -- Inert: c1: C b Q R S, c2: C P Q a b
991 -- Work: C P alpha R beta
992 -- Does not react with c1; reacts with c2, with alpha:=Q
993 -- NOW it reacts with c1!
994 -- So we must stop, and put the rewritten constraint back in the work list
995 do { d2' <- newDictVar cls1 rewritten_tys2
997 Given {} -> pprPanic "Unexpected given" (ppr inertItem $$ ppr workItem)
998 Wanted {} -> setDictBind d2 (EvCast d2' dict_co)
999 Derived {} -> return ()
1000 ; let workItem' = workItem { cc_id = d2', cc_tyargs = rewritten_tys2 }
1001 ; mkIRStopK "Cls/Cls fundep (partial)" (workItem' `consBag` fd_work) }
1004 dict_co = mkTyConCoercion (classTyCon cls1) cos2
1007 -- Class constraint and given equality: use the equality to rewrite
1008 -- the class constraint.
1009 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1010 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
1011 | ifl `canRewrite` wfl
1012 , tv `elemVarSet` tyVarsOfTypes xis
1013 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
1014 -- Continue with rewritten Dictionary because we can only be in the
1015 -- interactWithEqsStage, so the dictionary is inert.
1016 ; mkIRContinue "Eq/Cls" rewritten_dict KeepInert emptyWorkList }
1018 doInteractWithInert (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
1019 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1020 | wfl `canRewrite` ifl
1021 , tv `elemVarSet` tyVarsOfTypes xis
1022 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
1023 ; mkIRContinue "Cls/Eq" workItem DropInert (workListFromCCan rewritten_dict) }
1025 -- Class constraint and given equality: use the equality to rewrite
1026 -- the class constraint.
1027 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1028 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
1029 | ifl `canRewrite` wfl
1030 , tv `elemVarSet` tyVarsOfType ty
1031 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
1032 ; mkIRContinue "Eq/IP" rewritten_ip KeepInert emptyWorkList }
1034 doInteractWithInert (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
1035 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1036 | wfl `canRewrite` ifl
1037 , tv `elemVarSet` tyVarsOfType ty
1038 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
1039 ; mkIRContinue "IP/Eq" workItem DropInert (workListFromCCan rewritten_ip) }
1041 -- Two implicit parameter constraints. If the names are the same,
1042 -- but their types are not, we generate a wanted type equality
1043 -- that equates the type (this is "improvement").
1044 -- However, we don't actually need the coercion evidence,
1045 -- so we just generate a fresh coercion variable that isn't used anywhere.
1046 doInteractWithInert (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
1047 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
1048 | nm1 == nm2 && isGiven wfl && isGiven ifl
1049 = -- See Note [Overriding implicit parameters]
1050 -- Dump the inert item, override totally with the new one
1051 -- Do not require type equality
1052 -- For example, given let ?x::Int = 3 in let ?x::Bool = True in ...
1053 -- we must *override* the outer one with the inner one
1054 mkIRContinue "IP/IP override" workItem DropInert emptyWorkList
1056 | nm1 == nm2 && ty1 `tcEqType` ty2
1057 = solveOneFromTheOther "IP/IP" (EvId id1,ifl) workItem
1060 = -- See Note [When improvement happens]
1061 do { co_var <- newCoVar ty2 ty1 -- See Note [Efficient Orientation]
1062 ; let flav = Wanted (combineCtLoc ifl wfl)
1063 ; cans <- mkCanonical flav co_var
1064 ; mkIRContinue "IP/IP fundep" workItem KeepInert cans }
1066 -- Never rewrite a given with a wanted equality, and a type function
1067 -- equality can never rewrite an equality. We rewrite LHS *and* RHS
1068 -- of function equalities so that our inert set exposes everything that
1069 -- we know about equalities.
1071 -- Inert: equality, work item: function equality
1072 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
1073 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
1074 , cc_tyargs = args, cc_rhs = xi2 })
1075 | ifl `canRewrite` wfl
1076 , tv `elemVarSet` tyVarsOfTypes (xi2:args) -- Rewrite RHS as well
1077 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
1078 ; mkIRStopK "Eq/FunEq" (workListFromCCan rewritten_funeq) }
1079 -- Must Stop here, because we may no longer be inert after the rewritting.
1081 -- Inert: function equality, work item: equality
1082 doInteractWithInert (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
1083 , cc_tyargs = args, cc_rhs = xi1 })
1084 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
1085 | wfl `canRewrite` ifl
1086 , tv `elemVarSet` tyVarsOfTypes (xi1:args) -- Rewrite RHS as well
1087 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
1088 ; mkIRContinue "FunEq/Eq" workItem DropInert (workListFromCCan rewritten_funeq) }
1089 -- One may think that we could (KeepTransformedInert rewritten_funeq)
1090 -- but that is wrong, because it may end up not being inert with respect
1091 -- to future inerts. Example:
1092 -- Original inert = { F xis ~ [a], b ~ Maybe Int }
1093 -- Work item comes along = a ~ [b]
1094 -- If we keep { F xis ~ [b] } in the inert set we will end up with:
1095 -- { F xis ~ [b], b ~ Maybe Int, a ~ [Maybe Int] }
1096 -- At the end, which is *not* inert. So we should unfortunately DropInert here.
1098 doInteractWithInert (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
1099 , cc_tyargs = args1, cc_rhs = xi1 })
1100 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
1101 , cc_tyargs = args2, cc_rhs = xi2 })
1102 | fl1 `canSolve` fl2 && lhss_match
1103 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1104 ; mkIRStopK "FunEq/FunEq" cans }
1105 | fl2 `canSolve` fl1 && lhss_match
1106 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1107 ; mkIRContinue "FunEq/FunEq" workItem DropInert cans }
1109 lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
1111 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1112 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
1113 -- Check for matching LHS
1114 | fl1 `canSolve` fl2 && tv1 == tv2
1115 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1116 ; mkIRStopK "Eq/Eq lhs" cans }
1118 | fl2 `canSolve` fl1 && tv1 == tv2
1119 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1120 ; mkIRContinue "Eq/Eq lhs" workItem DropInert cans }
1122 -- Check for rewriting RHS
1123 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1124 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1125 ; mkIRStopK "Eq/Eq rhs" rewritten_eq }
1127 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1128 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1129 ; mkIRContinue "Eq/Eq rhs" workItem DropInert rewritten_eq }
1131 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1132 (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
1133 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
1134 = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1135 ; mkIRStopK "Frozen/Eq" rewritten_frozen }
1137 doInteractWithInert (CFrozenErr { cc_id = cv2, cc_flavor = fl2 })
1138 workItem@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1139 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfEvVar cv2
1140 = do { rewritten_frozen <- rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1141 ; mkIRContinue "Frozen/Eq" workItem DropInert rewritten_frozen }
1143 -- Fall-through case for all other situations
1144 doInteractWithInert _ workItem = noInteraction workItem
1146 -------------------------
1147 -- Equational Rewriting
1148 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1149 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1150 = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
1151 args = substTysWith [tv] [xi] xis
1153 dict_co = mkTyConCoercion con cos
1154 ; dv' <- newDictVar cl args
1156 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
1157 Given {} -> setDictBind dv' (EvCast dv dict_co)
1158 Derived {} -> return () -- Derived dicts we don't set any evidence
1160 ; return (CDictCan { cc_id = dv'
1163 , cc_tyargs = args }) }
1165 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1166 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1167 = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi]
1168 ty' = substTyWith [tv] [xi] ty
1169 ; ipid' <- newIPVar nm ty'
1171 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co))
1172 Given {} -> setIPBind ipid' (EvCast ipid ip_co)
1173 Derived {} -> return () -- Derived ips: we don't set any evidence
1175 ; return (CIPCan { cc_id = ipid'
1178 , cc_ip_ty = ty' }) }
1180 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1181 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2) -- cv2 :: F args ~ xi2
1182 = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
1183 args' = substTysWith [tv] [xi1] args
1184 fun_co = mkTyConCoercion tc arg_cos -- fun_co :: F args ~ F args'
1186 xi2' = substTyWith [tv] [xi1] xi2
1187 xi2_co = substTyWith [tv] [mkCoVarCoercion cv1] xi2 -- xi2_co :: xi2 ~ xi2'
1189 ; cv2' <- newCoVar (mkTyConApp tc args') xi2'
1191 Wanted {} -> setCoBind cv2 (fun_co `mkTransCoercion`
1192 mkCoVarCoercion cv2' `mkTransCoercion`
1193 mkSymCoercion xi2_co)
1194 Given {} -> setCoBind cv2' (mkSymCoercion fun_co `mkTransCoercion`
1195 mkCoVarCoercion cv2 `mkTransCoercion`
1197 Derived {} -> return ()
1199 ; return (CFunEqCan { cc_id = cv2'
1203 , cc_rhs = xi2' }) }
1206 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
1207 -- Use the first equality to rewrite the second, flavors already checked.
1208 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1209 -- rewrites c2 to give
1210 -- c2' : tv2 ~ xi2[xi1/tv1]
1211 -- We must do an occurs check to sure the new constraint is canonical
1212 -- So we might return an empty bag
1213 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1214 | Just tv2' <- tcGetTyVar_maybe xi2'
1215 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1216 = do { when (isWanted gw) (setCoBind cv2 (mkSymCoercion co2'))
1217 ; return emptyCCan }
1219 = do { cv2' <- newCoVar (mkTyVarTy tv2) xi2'
1221 Wanted {} -> setCoBind cv2 $ mkCoVarCoercion cv2' `mkTransCoercion`
1223 Given {} -> setCoBind cv2' $ mkCoVarCoercion cv2 `mkTransCoercion`
1225 Derived {} -> return ()
1226 ; canEq gw cv2' (mkTyVarTy tv2) xi2' }
1228 xi2' = substTyWith [tv1] [xi1] xi2
1229 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1231 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
1232 -- Used to ineract two equalities of the following form:
1233 -- First Equality: co1: (XXX ~ xi1)
1234 -- Second Equality: cv2: (XXX ~ xi2)
1235 -- Where the cv1 `canRewrite` cv2 equality
1236 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1),
1237 -- See Note [Efficient Orientation] for that
1238 rewriteEqLHS LeftComesFromInert (co1,xi1) (cv2,gw,xi2)
1239 = do { cv2' <- newCoVar xi2 xi1
1241 Wanted {} -> setCoBind cv2 $
1242 co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
1243 Given {} -> setCoBind cv2' $
1244 mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
1245 Derived {} -> return ()
1246 ; mkCanonical gw cv2' }
1248 rewriteEqLHS RightComesFromInert (co1,xi1) (cv2,gw,xi2)
1249 = do { cv2' <- newCoVar xi1 xi2
1251 Wanted {} -> setCoBind cv2 $
1252 co1 `mkTransCoercion` mkCoVarCoercion cv2'
1253 Given {} -> setCoBind cv2' $
1254 mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
1255 Derived {} -> return ()
1256 ; mkCanonical gw cv2' }
1258 rewriteFrozen :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor) -> TcS WorkList
1259 rewriteFrozen (cv1, tv1, xi1) (cv2, fl2)
1260 = do { cv2' <- newCoVar ty2a' ty2b' -- ty2a[xi1/tv1] ~ ty2b[xi1/tv1]
1262 Wanted {} -> setCoBind cv2 $ co2a' `mkTransCoercion`
1263 mkCoVarCoercion cv2' `mkTransCoercion`
1266 Given {} -> setCoBind cv2' $ mkSymCoercion co2a' `mkTransCoercion`
1267 mkCoVarCoercion cv2 `mkTransCoercion`
1270 Derived {} -> return ()
1272 ; return (singleCCan $ CFrozenErr { cc_id = cv2', cc_flavor = fl2 }) }
1274 (ty2a, ty2b) = coVarKind cv2 -- cv2 : ty2a ~ ty2b
1275 ty2a' = substTyWith [tv1] [xi1] ty2a
1276 ty2b' = substTyWith [tv1] [xi1] ty2b
1278 co2a' = substTyWith [tv1] [mkCoVarCoercion cv1] ty2a -- ty2a ~ ty2a[xi1/tv1]
1279 co2b' = substTyWith [tv1] [mkCoVarCoercion cv1] ty2b -- ty2b ~ ty2b[xi1/tv1]
1281 solveOneFromTheOther :: String -> (EvTerm, CtFlavor) -> CanonicalCt -> TcS InteractResult
1282 -- First argument inert, second argument work-item. They both represent
1283 -- wanted/given/derived evidence for the *same* predicate so
1284 -- we can discharge one directly from the other.
1286 -- Precondition: value evidence only (implicit parameters, classes)
1288 solveOneFromTheOther info (ev_term,ifl) workItem
1290 = mkIRStopK ("Solved[DW] " ++ info) emptyWorkList
1292 | isDerived ifl -- The inert item is Derived, we can just throw it away,
1293 -- The workItem is inert wrt earlier inert-set items,
1294 -- so it's safe to continue on from this point
1295 = mkIRContinue ("Solved[DI] " ++ info) workItem DropInert emptyWorkList
1298 = ASSERT( ifl `canSolve` wfl )
1299 -- Because of Note [The Solver Invariant], plus Derived dealt with
1300 do { when (isWanted wfl) $ setEvBind wid ev_term
1301 -- Overwrite the binding, if one exists
1302 -- If both are Given, we already have evidence; no need to duplicate
1303 ; mkIRStopK ("Solved " ++ info) emptyWorkList }
1305 wfl = cc_flavor workItem
1306 wid = cc_id workItem
1309 Note [Superclasses and recursive dictionaries]
1310 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1311 Overlaps with Note [SUPERCLASS-LOOP 1]
1312 Note [SUPERCLASS-LOOP 2]
1313 Note [Recursive instances and superclases]
1314 ToDo: check overlap and delete redundant stuff
1316 Right before adding a given into the inert set, we must
1317 produce some more work, that will bring the superclasses
1318 of the given into scope. The superclass constraints go into
1321 When we simplify a wanted constraint, if we first see a matching
1322 instance, we may produce new wanted work. To (1) avoid doing this work
1323 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1324 this item as given into our inert set WITHOUT adding its superclass constraints,
1325 otherwise we'd be in danger of creating a loop [In fact this was the exact reason
1326 for doing the isGoodRecEv check in an older version of the type checker].
1328 But now we have added partially solved constraints to the worklist which may
1329 interact with other wanteds. Consider the example:
1333 class Eq b => Foo a b --- 0-th selector
1334 instance Eq a => Foo [a] a --- fooDFun
1336 and wanted (Foo [t] t). We are first going to see that the instance matches
1337 and create an inert set that includes the solved (Foo [t] t) but not its superclasses:
1338 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1339 Our work list is going to contain a new *wanted* goal
1342 Ok, so how do we get recursive dictionaries, at all:
1346 data D r = ZeroD | SuccD (r (D r));
1348 instance (Eq (r (D r))) => Eq (D r) where
1349 ZeroD == ZeroD = True
1350 (SuccD a) == (SuccD b) = a == b
1353 equalDC :: D [] -> D [] -> Bool;
1356 We need to prove (Eq (D [])). Here's how we go:
1360 by instance decl, holds if
1364 *BUT* we have an inert set which gives us (no superclasses):
1366 By the instance declaration of Eq we can show the 'd2' goal if
1368 where d2 = dfEqList d3
1370 Now, however this wanted can interact with our inert d1 to set:
1372 and solve the goal. Why was this interaction OK? Because, if we chase the
1373 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1375 d3 := dfEqD2 (dfEqList d3)
1376 which is FINE because the use of d3 is protected by the instance function
1379 So, our strategy is to try to put solved wanted dictionaries into the
1380 inert set along with their superclasses (when this is meaningful,
1381 i.e. when new wanted goals are generated) but solve a wanted dictionary
1382 from a given only in the case where the evidence variable of the
1383 wanted is mentioned in the evidence of the given (recursively through
1384 the evidence binds) in a protected way: more instance function applications
1385 than superclass selectors.
1387 Here are some more examples from GHC's previous type checker
1391 This code arises in the context of "Scrap Your Boilerplate with Class"
1395 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1396 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1398 class Data Maybe a => Foo a
1400 instance Foo t => Sat (Maybe t) -- dfunSat
1402 instance Data Maybe a => Foo a -- dfunFoo1
1403 instance Foo a => Foo [a] -- dfunFoo2
1404 instance Foo [Char] -- dfunFoo3
1406 Consider generating the superclasses of the instance declaration
1407 instance Foo a => Foo [a]
1409 So our problem is this
1411 d1 :_w Data Maybe [t]
1413 We may add the given in the inert set, along with its superclasses
1414 [assuming we don't fail because there is a matching instance, see
1415 tryTopReact, given case ]
1419 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1420 d1 :_w Data Maybe [t]
1421 Then d2 can readily enter the inert, and we also do solving of the wanted
1424 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1426 d2 :_w Sat (Maybe [t])
1428 d01 :_g Data Maybe t
1429 Now, we may simplify d2 more:
1432 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1433 d1 :_g Data Maybe [t]
1434 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1438 d01 :_g Data Maybe t
1440 Now, we can just solve d3.
1443 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1444 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1447 d01 :_g Data Maybe t
1448 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1451 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1452 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1453 d4 :_g Foo [t] d4 := dfunFoo2 d5
1456 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1457 d01 :_g Data Maybe t
1458 Now, d5 can be solved! (and its superclass enter scope)
1461 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1462 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1463 d4 :_g Foo [t] d4 := dfunFoo2 d5
1464 d5 :_g Foo t d5 := dfunFoo1 d7
1467 d6 :_g Data Maybe [t]
1468 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1469 d01 :_g Data Maybe t
1472 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1473 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1474 that must not be used (look at case interactInert where both inert and workitem
1475 are givens). So we have several options:
1476 - Drop the workitem always (this will drop d8)
1477 This feels very unsafe -- what if the work item was the "good" one
1478 that should be used later to solve another wanted?
1479 - Don't drop anyone: the inert set may contain multiple givens!
1480 [This is currently implemented]
1482 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1483 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1484 d7. Now the [isRecDictEv] function in the ineration solver
1485 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1486 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1488 So, no interaction happens there. Then we meet d01 and there is no recursion
1489 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1491 Note [SUPERCLASS-LOOP 1]
1492 ~~~~~~~~~~~~~~~~~~~~~~~~
1493 We have to be very, very careful when generating superclasses, lest we
1494 accidentally build a loop. Here's an example:
1498 class S a => C a where { opc :: a -> a }
1499 class S b => D b where { opd :: b -> b }
1501 instance C Int where
1504 instance D Int where
1507 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1508 Simplifying, we may well get:
1509 $dfCInt = :C ds1 (opd dd)
1512 Notice that we spot that we can extract ds1 from dd.
1514 Alas! Alack! We can do the same for (instance D Int):
1516 $dfDInt = :D ds2 (opc dc)
1520 And now we've defined the superclass in terms of itself.
1521 Two more nasty cases are in
1526 - Satisfy the superclass context *all by itself*
1527 (tcSimplifySuperClasses)
1528 - And do so completely; i.e. no left-over constraints
1529 to mix with the constraints arising from method declarations
1532 Note [SUPERCLASS-LOOP 2]
1533 ~~~~~~~~~~~~~~~~~~~~~~~~
1534 We need to be careful when adding "the constaint we are trying to prove".
1535 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1537 class Ord a => C a where
1538 instance Ord [a] => C [a] where ...
1540 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1541 superclasses of C [a] to avails. But we must not overwrite the binding
1542 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1545 Here's another variant, immortalised in tcrun020
1546 class Monad m => C1 m
1547 class C1 m => C2 m x
1548 instance C2 Maybe Bool
1549 For the instance decl we need to build (C1 Maybe), and it's no good if
1550 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1551 before we search for C1 Maybe.
1553 Here's another example
1554 class Eq b => Foo a b
1555 instance Eq a => Foo [a] a
1559 we'll first deduce that it holds (via the instance decl). We must not
1560 then overwrite the Eq t constraint with a superclass selection!
1562 At first I had a gross hack, whereby I simply did not add superclass constraints
1563 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1564 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1565 I found a very obscure program (now tcrun021) in which improvement meant the
1566 simplifier got two bites a the cherry... so something seemed to be an Stop
1567 first time, but reducible next time.
1569 Now we implement the Right Solution, which is to check for loops directly
1570 when adding superclasses. It's a bit like the occurs check in unification.
1572 Note [Recursive instances and superclases]
1573 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1574 Consider this code, which arises in the context of "Scrap Your
1575 Boilerplate with Class".
1579 instance Sat (ctx Char) => Data ctx Char
1580 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1582 class Data Maybe a => Foo a
1584 instance Foo t => Sat (Maybe t)
1586 instance Data Maybe a => Foo a
1587 instance Foo a => Foo [a]
1590 In the instance for Foo [a], when generating evidence for the superclasses
1591 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1592 Using the instance for Data, we therefore need
1593 (Sat (Maybe [a], Data Maybe a)
1594 But we are given (Foo a), and hence its superclass (Data Maybe a).
1595 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1596 we need (Foo [a]). And that is the very dictionary we are bulding
1597 an instance for! So we must put that in the "givens". So in this
1599 Given: Foo a, Foo [a]
1600 Wanted: Data Maybe [a]
1602 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1603 the givens, which is what 'addGiven' would normally do. Why? Because
1604 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1605 by selecting a superclass from Foo [a], which simply makes a loop.
1607 On the other hand we *must* put the superclasses of (Foo a) in
1608 the givens, as you can see from the derivation described above.
1610 Conclusion: in the very special case of tcSimplifySuperClasses
1611 we have one 'given' (namely the "this" dictionary) whose superclasses
1612 must not be added to 'givens' by addGiven.
1614 There is a complication though. Suppose there are equalities
1615 instance (Eq a, a~b) => Num (a,b)
1616 Then we normalise the 'givens' wrt the equalities, so the original
1617 given "this" dictionary is cast to one of a different type. So it's a
1618 bit trickier than before to identify the "special" dictionary whose
1619 superclasses must not be added. See test
1620 indexed-types/should_run/EqInInstance
1622 We need a persistent property of the dictionary to record this
1623 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1624 but cool), which is maintained by dictionary normalisation.
1625 Specifically, the InstLocOrigin is
1627 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1630 Note [MATCHING-SYNONYMS]
1631 ~~~~~~~~~~~~~~~~~~~~~~~~
1632 When trying to match a dictionary (D tau) to a top-level instance, or a
1633 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1634 we do *not* need to expand type synonyms because the matcher will do that for us.
1637 Note [RHS-FAMILY-SYNONYMS]
1638 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1639 The RHS of a family instance is represented as yet another constructor which is
1640 like a type synonym for the real RHS the programmer declared. Eg:
1641 type instance F (a,a) = [a]
1643 :R32 a = [a] -- internal type synonym introduced
1644 F (a,a) ~ :R32 a -- instance
1646 When we react a family instance with a type family equation in the work list
1647 we keep the synonym-using RHS without expansion.
1650 *********************************************************************************
1652 The top-reaction Stage
1654 *********************************************************************************
1657 -- If a work item has any form of interaction with top-level we get this
1658 data TopInteractResult
1659 = NoTopInt -- No top-level interaction
1660 -- Equivalent to (SomeTopInt emptyWorkList (ContinueWith work_item))
1662 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1663 -- for superclasses)
1664 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1665 } -- NB: in ``given'' (solved) form if the
1666 -- original was wanted or given and instance match
1667 -- was found, but may also be in wanted form if we
1668 -- only reacted with functional dependencies
1669 -- arising from top-level instances.
1671 topReactionsStage :: SimplifierStage
1672 topReactionsStage depth workItem inerts
1673 = do { tir <- tryTopReact workItem
1676 return $ SR { sr_inerts = inerts
1677 , sr_new_work = emptyWorkList
1678 , sr_stop = ContinueWith workItem }
1679 SomeTopInt tir_new_work tir_new_inert ->
1680 do { bumpStepCountTcS
1681 ; traceFireTcS depth (ptext (sLit "Top react")
1682 <+> vcat [ ptext (sLit "Work =") <+> ppr workItem
1683 , ptext (sLit "New =") <+> ppr tir_new_work ])
1684 ; return $ SR { sr_inerts = inerts
1685 , sr_new_work = tir_new_work
1686 , sr_stop = tir_new_inert
1690 tryTopReact :: WorkItem -> TcS TopInteractResult
1691 tryTopReact workitem
1692 = do { -- A flag controls the amount of interaction allowed
1693 -- See Note [Simplifying RULE lhs constraints]
1694 ctxt <- getTcSContext
1695 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1696 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1697 ; doTopReact workitem }
1698 else return NoTopInt
1701 allowedTopReaction :: Bool -> WorkItem -> Bool
1702 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1703 allowedTopReaction _ _ = True
1705 doTopReact :: WorkItem -> TcS TopInteractResult
1706 -- The work item does not react with the inert set, so try interaction with top-level instances
1707 -- NB: The place to add superclasses in *not* in doTopReact stage. Instead superclasses are
1708 -- added in the worklist as part of the canonicalisation process.
1709 -- See Note [Adding superclasses] in TcCanonical.
1712 -- See Note [Given constraint that matches an instance declaration]
1713 doTopReact (CDictCan { cc_flavor = Given {} })
1714 = return NoTopInt -- NB: Superclasses already added since it's canonical
1716 -- Derived dictionary: just look for functional dependencies
1717 doTopReact workItem@(CDictCan { cc_flavor = fl@(Derived loc)
1718 , cc_class = cls, cc_tyargs = xis })
1719 = do { instEnvs <- getInstEnvs
1720 ; let fd_eqns = improveFromInstEnv instEnvs
1721 (ClassP cls xis, pprArisingAt loc)
1722 ; m <- rewriteWithFunDeps fd_eqns xis fl
1724 Nothing -> return NoTopInt
1725 Just (xis',_,fd_work) ->
1726 let workItem' = workItem { cc_tyargs = xis' }
1727 -- Deriveds are not supposed to have identity (cc_id is unused!)
1728 in return $ SomeTopInt { tir_new_work = fd_work
1729 , tir_new_inert = ContinueWith workItem' } }
1731 -- Wanted dictionary
1732 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = fl@(Wanted loc)
1733 , cc_class = cls, cc_tyargs = xis })
1734 = do { -- See Note [MATCHING-SYNONYMS]
1735 ; lkp_inst_res <- matchClassInst cls xis loc
1736 ; case lkp_inst_res of
1738 do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1740 ; instEnvs <- getInstEnvs
1741 ; let fd_eqns = improveFromInstEnv instEnvs
1742 (ClassP cls xis, pprArisingAt loc)
1743 ; m <- rewriteWithFunDeps fd_eqns xis fl
1745 Nothing -> return NoTopInt
1746 Just (xis',cos,fd_work) ->
1747 do { let dict_co = mkTyConCoercion (classTyCon cls) cos
1748 ; dv'<- newDictVar cls xis'
1749 ; setDictBind dv (EvCast dv' dict_co)
1750 ; let workItem' = CDictCan { cc_id = dv', cc_flavor = fl,
1751 cc_class = cls, cc_tyargs = xis' }
1753 SomeTopInt { tir_new_work = singleCCan workItem' `andCCan` fd_work
1754 , tir_new_inert = Stop } } }
1756 GenInst wtvs ev_term -- Solved
1757 -- No need to do fundeps stuff here; the instance
1758 -- matches already so we won't get any more info
1759 -- from functional dependencies
1761 -> do { traceTcS "doTopReact/ found nullary class instance for" (ppr dv)
1762 ; setDictBind dv ev_term
1763 -- Solved in one step and no new wanted work produced.
1764 -- i.e we directly matched a top-level instance
1765 -- No point in caching this in 'inert'; hence Stop
1766 ; return $ SomeTopInt { tir_new_work = emptyWorkList
1767 , tir_new_inert = Stop } }
1770 -> do { traceTcS "doTopReact/ found nullary class instance for" (ppr dv)
1771 ; setDictBind dv ev_term
1772 -- Solved and new wanted work produced, you may cache the
1773 -- (tentatively solved) dictionary as Given! (used to be: Derived)
1774 ; let solved = workItem { cc_flavor = given_fl }
1775 given_fl = Given (setCtLocOrigin loc UnkSkol)
1776 ; inst_work <- canWanteds wtvs
1777 ; return $ SomeTopInt { tir_new_work = inst_work
1778 , tir_new_inert = ContinueWith solved } }
1782 doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
1783 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1784 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1785 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1789 MatchInstSingle (rep_tc, rep_tys)
1790 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1791 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1792 -- Eagerly expand away the type synonym on the
1793 -- RHS of a type function, so that it never
1794 -- appears in an error message
1795 -- See Note [Type synonym families] in TyCon
1796 coe = mkTyConApp coe_tc rep_tys
1798 Wanted {} -> do { cv' <- newCoVar rhs_ty xi
1800 coe `mkTransCoercion`
1803 Given {} -> newGivenCoVar xi rhs_ty $
1804 mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
1805 Derived {} -> newDerivedId (EqPred xi rhs_ty)
1806 ; can_cts <- mkCanonical fl cv'
1807 ; return $ SomeTopInt can_cts Stop }
1809 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1813 -- Any other work item does not react with any top-level equations
1814 doTopReact _workItem = return NoTopInt
1818 Note [FunDep and implicit parameter reactions]
1819 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1820 Currently, our story of interacting two dictionaries (or a dictionary
1821 and top-level instances) for functional dependencies, and implicit
1822 paramters, is that we simply produce new wanted equalities. So for example
1824 class D a b | a -> b where ...
1830 We generate the extra work item
1832 where 'cv' is currently unused. However, this new item reacts with d2,
1833 discharging it in favour of a new constraint d2' thus:
1835 d2 := d2' |> D Int cv
1836 Now d2' can be discharged from d1
1838 We could be more aggressive and try to *immediately* solve the dictionary
1839 using those extra equalities. With the same inert set and work item we
1840 might dischard d2 directly:
1843 d2 := d1 |> D Int cv
1845 But in general it's a bit painful to figure out the necessary coercion,
1846 so we just take the first approach. Here is a better example. Consider:
1847 class C a b c | a -> b
1849 [Given] d1 : C T Int Char
1850 [Wanted] d2 : C T beta Int
1851 In this case, it's *not even possible* to solve the wanted immediately.
1852 So we should simply output the functional dependency and add this guy
1853 [but NOT its superclasses] back in the worklist. Even worse:
1854 [Given] d1 : C T Int beta
1855 [Wanted] d2: C T beta Int
1856 Then it is solvable, but its very hard to detect this on the spot.
1858 It's exactly the same with implicit parameters, except that the
1859 "aggressive" approach would be much easier to implement.
1861 Note [When improvement happens]
1862 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1863 We fire an improvement rule when
1865 * Two constraints match (modulo the fundep)
1866 e.g. C t1 t2, C t1 t3 where C a b | a->b
1867 The two match because the first arg is identical
1869 * At least one is not Given. If they are both given, we don't fire
1870 the reaction because we have no way of constructing evidence for a
1871 new equality nor does it seem right to create a new wanted goal
1872 (because the goal will most likely contain untouchables, which
1873 can't be solved anyway)!
1875 Note that we *do* fire the improvement if one is Given and one is Derived.
1876 The latter can be a superclass of a wanted goal. Example (tcfail138)
1877 class L a b | a -> b
1878 class (G a, L a b) => C a b
1880 instance C a b' => G (Maybe a)
1881 instance C a b => C (Maybe a) a
1882 instance L (Maybe a) a
1884 When solving the superclasses of the (C (Maybe a) a) instance, we get
1885 Given: C a b ... and hance by superclasses, (G a, L a b)
1887 Use the instance decl to get
1889 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
1890 and now we need improvement between that derived superclass an the Given (L a b)
1892 Note [Overriding implicit parameters]
1893 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1895 f :: (?x::a) -> Bool -> a
1897 g v = let ?x::Int = 3
1898 in (f v, let ?x::Bool = True in f v)
1900 This should probably be well typed, with
1901 g :: Bool -> (Int, Bool)
1903 So the inner binding for ?x::Bool *overrides* the outer one.
1904 Hence a work-item Given overrides an inert-item Given.
1906 Note [Given constraint that matches an instance declaration]
1907 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1908 What should we do when we discover that one (or more) top-level
1909 instances match a given (or solved) class constraint? We have
1912 1. Reject the program. The reason is that there may not be a unique
1913 best strategy for the solver. Example, from the OutsideIn(X) paper:
1914 instance P x => Q [x]
1915 instance (x ~ y) => R [x] y
1917 wob :: forall a b. (Q [b], R b a) => a -> Int
1919 g :: forall a. Q [a] => [a] -> Int
1922 will generate the impliation constraint:
1923 Q [a] => (Q [beta], R beta [a])
1924 If we react (Q [beta]) with its top-level axiom, we end up with a
1925 (P beta), which we have no way of discharging. On the other hand,
1926 if we react R beta [a] with the top-level we get (beta ~ a), which
1927 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
1928 now solvable by the given Q [a].
1930 However, this option is restrictive, for instance [Example 3] from
1931 Note [Recursive dictionaries] will fail to work.
1933 2. Ignore the problem, hoping that the situations where there exist indeed
1934 such multiple strategies are rare: Indeed the cause of the previous
1935 problem is that (R [x] y) yields the new work (x ~ y) which can be
1936 *spontaneously* solved, not using the givens.
1938 We are choosing option 2 below but we might consider having a flag as well.
1941 Note [New Wanted Superclass Work]
1942 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1943 Even in the case of wanted constraints, we may add some superclasses
1944 as new given work. The reason is:
1946 To allow FD-like improvement for type families. Assume that
1948 class C a b | a -> b
1949 and we have to solve the implication constraint:
1951 Then, FD improvement can help us to produce a new wanted (beta ~ b)
1953 We want to have the same effect with the type family encoding of
1954 functional dependencies. Namely, consider:
1955 class (F a ~ b) => C a b
1956 Now suppose that we have:
1959 By interacting the given we will get given (F a ~ b) which is not
1960 enough by itself to make us discharge (C a beta). However, we
1961 may create a new derived equality from the super-class of the
1962 wanted constraint (C a beta), namely derived (F a ~ beta).
1963 Now we may interact this with given (F a ~ b) to get:
1965 But 'beta' is a touchable unification variable, and hence OK to
1966 unify it with 'b', replacing the derived evidence with the identity.
1968 This requires trySpontaneousSolve to solve *derived*
1969 equalities that have a touchable in their RHS, *in addition*
1970 to solving wanted equalities.
1972 We also need to somehow use the superclasses to quantify over a minimal,
1973 constraint see note [Minimize by Superclasses] in TcSimplify.
1976 Finally, here is another example where this is useful.
1980 class (F a ~ b) => C a b
1981 And we are given the wanteds:
1985 We surely do *not* want to quantify over (b ~ c), since if someone provides
1986 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
1987 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
1989 Step 1: We will get new *given* superclass work,
1990 provisionally to our solving of w1 and w2
1992 g1: F a ~ b, g2 : F a ~ c,
1993 w1 : C a b, w2 : C a c, w3 : b ~ c
1995 The evidence for g1 and g2 is a superclass evidence term:
1997 g1 := sc w1, g2 := sc w2
1999 Step 2: The givens will solve the wanted w3, so that
2000 w3 := sym (sc w1) ; sc w2
2002 Step 3: Now, one may naively assume that then w2 can be solve from w1
2003 after rewriting with the (now solved equality) (b ~ c).
2005 But this rewriting is ruled out by the isGoodRectDict!
2007 Conclusion, we will (correctly) end up with the unsolved goals
2010 NB: The desugarer needs be more clever to deal with equalities
2011 that participate in recursive dictionary bindings.
2014 data LookupInstResult
2016 | GenInst [WantedEvVar] EvTerm
2018 matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
2019 matchClassInst clas tys loc
2020 = do { let pred = mkClassPred clas tys
2021 ; mb_result <- matchClass clas tys
2023 MatchInstNo -> return NoInstance
2024 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
2025 -- we learn more about the reagent
2026 MatchInstSingle (dfun_id, mb_inst_tys) ->
2027 do { checkWellStagedDFun pred dfun_id loc
2029 -- It's possible that not all the tyvars are in
2030 -- the substitution, tenv. For example:
2031 -- instance C X a => D X where ...
2032 -- (presumably there's a functional dependency in class C)
2033 -- Hence mb_inst_tys :: Either TyVar TcType
2035 ; tys <- instDFunTypes mb_inst_tys
2036 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
2037 ; if null theta then
2038 return (GenInst [] (EvDFunApp dfun_id tys []))
2040 { ev_vars <- instDFunConstraints theta
2041 ; let wevs = [EvVarX w loc | w <- ev_vars]
2042 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }