3 solveInteract, AtomicInert,
4 InertSet, emptyInert, updInertSet, extractUnsolved, solveOne, foldISEqCts
7 #include "HsVersions.h"
28 import Control.Monad ( when )
37 import qualified Data.Map as Map
39 import Control.Monad( zipWithM, unless )
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_givder :: Map.Map a CanonicalCts
88 -- Invariant: all Given or Derived
89 , cts_wanted :: Map.Map a CanonicalCts }
90 -- Invariant: all Wanted
91 cCanMapToBag :: Ord a => CCanMap a -> CanonicalCts
92 cCanMapToBag cmap = Map.fold unionBags rest_cts (cts_givder cmap)
93 where rest_cts = Map.fold unionBags emptyCCan (cts_wanted cmap)
95 emptyCCanMap :: CCanMap a
96 emptyCCanMap = CCanMap { cts_givder = Map.empty, cts_wanted = Map.empty }
98 updCCanMap:: Ord a => (a,CanonicalCt) -> CCanMap a -> CCanMap a
99 updCCanMap (a,ct) cmap
100 = case cc_flavor ct of
102 -> cmap { cts_wanted = Map.insertWith unionBags a this_ct (cts_wanted cmap) }
104 -> cmap { cts_givder = Map.insertWith unionBags a this_ct (cts_givder cmap) }
105 where this_ct = singleCCan ct
107 getRelevantCts :: Ord a => a -> CCanMap a -> (CanonicalCts, CCanMap a)
108 -- Gets the relevant constraints and returns the rest of the CCanMap
109 getRelevantCts a cmap
110 = let relevant = unionBags (Map.findWithDefault emptyCCan a (cts_wanted cmap))
111 (Map.findWithDefault emptyCCan a (cts_givder cmap))
112 residual_map = cmap { cts_wanted = Map.delete a (cts_wanted cmap)
113 , cts_givder = Map.delete a (cts_givder cmap) }
114 in (relevant, residual_map)
116 extractUnsolvedCMap :: Ord a => CCanMap a -> (CanonicalCts, CCanMap a)
117 -- Gets the wanted constraints and returns a residual CCanMap
118 extractUnsolvedCMap cmap =
119 let unsolved = Map.fold unionBags emptyCCan (cts_wanted cmap)
120 in (unsolved, cmap { cts_wanted = Map.empty})
122 -- See Note [InertSet invariants]
124 = IS { inert_eqs :: CanonicalCts -- Equalities only (CTyEqCan)
126 , inert_dicts :: CCanMap Class -- Dictionaries only
127 , inert_ips :: CCanMap (IPName Name) -- Implicit parameters
128 , inert_funeqs :: CCanMap TyCon -- Type family equalities only
129 -- This representation allows us to quickly get to the relevant
130 -- inert constraints when interacting a work item with the inert set.
133 , inert_fds :: FDImprovements -- List of pairwise improvements that have kicked in already
134 -- and reside either in the worklist or in the inerts
137 type FDImprovement = (PredType,PredType)
138 type FDImprovements = [(PredType,PredType)]
140 instance Outputable InertSet where
141 ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
142 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_dicts is)))
143 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_ips is)))
144 , vcat (map ppr (Bag.bagToList $ cCanMapToBag (inert_funeqs is)))
147 emptyInert :: InertSet
148 emptyInert = IS { inert_eqs = Bag.emptyBag
149 , inert_dicts = emptyCCanMap
150 , inert_ips = emptyCCanMap
151 , inert_funeqs = emptyCCanMap
154 updInertSet :: InertSet -> AtomicInert -> InertSet
156 | isCTyEqCan item -- Other equality
157 = let eqs' = inert_eqs is `Bag.snocBag` item
158 in is { inert_eqs = eqs' }
159 | Just cls <- isCDictCan_Maybe item -- Dictionary
160 = is { inert_dicts = updCCanMap (cls,item) (inert_dicts is) }
161 | Just x <- isCIPCan_Maybe item -- IP
162 = is { inert_ips = updCCanMap (x,item) (inert_ips is) }
163 | Just tc <- isCFunEqCan_Maybe item -- Function equality
164 = is { inert_funeqs = updCCanMap (tc,item) (inert_funeqs is) }
166 = pprPanic "Unknown form of constraint!" (ppr item)
168 updInertSetFDImprs :: InertSet -> Maybe FDImprovement -> InertSet
169 updInertSetFDImprs is (Just fdi) = is { inert_fds = fdi : inert_fds is }
170 updInertSetFDImprs is Nothing = is
172 foldISEqCtsM :: Monad m => (a -> AtomicInert -> m a) -> a -> InertSet -> m a
173 -- Fold over the equalities of the inerts
174 foldISEqCtsM k z IS { inert_eqs = eqs }
175 = Bag.foldlBagM k z eqs
177 foldISEqCts :: (a -> AtomicInert -> a) -> a -> InertSet -> a
178 foldISEqCts k z IS { inert_eqs = eqs }
179 = Bag.foldlBag k z eqs
181 extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
182 extractUnsolved is@(IS {inert_eqs = eqs})
183 = let is_solved = is { inert_eqs = solved_eqs
184 , inert_dicts = solved_dicts
185 , inert_ips = solved_ips
186 , inert_funeqs = solved_funeqs }
187 in (is_solved, unsolved)
189 where (unsolved_eqs, solved_eqs) = Bag.partitionBag isWantedCt eqs
190 (unsolved_ips, solved_ips) = extractUnsolvedCMap (inert_ips is)
191 (unsolved_dicts, solved_dicts) = extractUnsolvedCMap (inert_dicts is)
192 (unsolved_funeqs, solved_funeqs) = extractUnsolvedCMap (inert_funeqs is)
194 unsolved = unsolved_eqs `unionBags`
195 unsolved_ips `unionBags` unsolved_dicts `unionBags` unsolved_funeqs
197 haveBeenImproved :: FDImprovements -> PredType -> PredType -> Bool
198 haveBeenImproved [] _ _ = False
199 haveBeenImproved ((pty1,pty2):fdimprs) pty1' pty2'
200 | tcEqPred pty1 pty1' && tcEqPred pty2 pty2'
202 | tcEqPred pty1 pty2' && tcEqPred pty2 pty1'
205 = haveBeenImproved fdimprs pty1' pty2'
207 getFDImprovements :: InertSet -> FDImprovements
208 -- Return a list of the improvements that have kicked in so far
209 getFDImprovements = inert_fds
213 {-- DV: This note will go away!
215 Note [Touchables and givens]
216 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
217 Touchable variables will never show up in givens which are inputs to
218 the solver. However, touchables may show up in givens generated by the flattener.
233 which can be put in the inert set. Suppose we also have a wanted
237 We cannot rewrite the given G alpha ~g b using the wanted alpha ~w
238 Int. Instead, after reacting alpha ~w Int with the whole inert set,
239 we observe that we can solve it by unifying alpha with Int, so we mark
240 it as solved and put it back in the *work list*. [We also immediately unify
241 alpha := Int, without telling anyone, see trySpontaneousSolve function, to
242 avoid doing this in the end.]
244 Later, because it is solved (given, in effect), we can use it to rewrite
245 G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually,
246 we will dispatch the remaining wanted constraints using the top-level axioms.
248 Finally, note that after reacting a wanted equality with the entire inert set
249 we may end up with something like
253 which we should flip around to generate the solved constraint alpha ~s b.
259 %*********************************************************************
261 * Main Interaction Solver *
263 **********************************************************************
267 1. Canonicalise (unary)
268 2. Pairwise interaction (binary)
269 * Take one from work list
270 * Try all pair-wise interactions with each constraint in inert
272 As an optimisation, we prioritize the equalities both in the
273 worklist and in the inerts.
275 3. Try to solve spontaneously for equalities involving touchables
276 4. Top-level interaction (binary wrt top-level)
277 Superclass decomposition belongs in (4), see note [Superclasses]
280 type AtomicInert = CanonicalCt -- constraint pulled from InertSet
281 type WorkItem = CanonicalCt -- constraint pulled from WorkList
283 -- A mixture of Given, Wanted, and Derived constraints.
284 -- We split between equalities and the rest to process equalities first.
285 type WorkList = CanonicalCts
287 unionWorkLists :: WorkList -> WorkList -> WorkList
288 unionWorkLists = andCCan
290 isEmptyWorkList :: WorkList -> Bool
291 isEmptyWorkList = isEmptyCCan
293 emptyWorkList :: WorkList
294 emptyWorkList = emptyCCan
296 workListFromCCan :: CanonicalCt -> WorkList
297 workListFromCCan = singleCCan
299 ------------------------
301 = Stop -- Work item is consumed
302 | ContinueWith WorkItem -- Not consumed
304 instance Outputable StopOrContinue where
305 ppr Stop = ptext (sLit "Stop")
306 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
308 -- Results after interacting a WorkItem as far as possible with an InertSet
310 = SR { sr_inerts :: InertSet
311 -- The new InertSet to use (REPLACES the old InertSet)
312 , sr_new_work :: WorkList
313 -- Any new work items generated (should be ADDED to the old WorkList)
315 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
316 -- workitem is inert wrt to sr_inerts
317 , sr_stop :: StopOrContinue
320 instance Outputable StageResult where
321 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
322 = ptext (sLit "SR") <+>
323 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
324 , ptext (sLit "new work =") <+> ppr work <> comma
325 , ptext (sLit "stop =") <+> ppr stop])
327 type SimplifierStage = WorkItem -> InertSet -> TcS StageResult
329 -- Combine a sequence of simplifier 'stages' to create a pipeline
330 runSolverPipeline :: [(String, SimplifierStage)]
331 -> InertSet -> WorkItem
332 -> TcS (InertSet, WorkList)
333 -- Precondition: non-empty list of stages
334 runSolverPipeline pipeline inerts workItem
335 = do { traceTcS "Start solver pipeline" $
336 vcat [ ptext (sLit "work item =") <+> ppr workItem
337 , ptext (sLit "inerts =") <+> ppr inerts]
339 ; let itr_in = SR { sr_inerts = inerts
340 , sr_new_work = emptyWorkList
341 , sr_stop = ContinueWith workItem }
342 ; itr_out <- run_pipeline pipeline itr_in
344 = case sr_stop itr_out of
345 Stop -> sr_inerts itr_out
346 ContinueWith item -> sr_inerts itr_out `updInertSet` item
347 ; return (new_inert, sr_new_work itr_out) }
349 run_pipeline :: [(String, SimplifierStage)]
350 -> StageResult -> TcS StageResult
351 run_pipeline [] itr = return itr
352 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
354 run_pipeline ((name,stage):stages)
355 (SR { sr_new_work = accum_work
357 , sr_stop = ContinueWith work_item })
358 = do { itr <- stage work_item inerts
359 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
360 ; let itr' = itr { sr_new_work = accum_work `unionWorkLists` sr_new_work itr }
361 ; run_pipeline stages itr' }
365 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
366 Reagent: a ~ [b] (given)
368 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
369 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
370 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
373 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
376 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
377 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
381 Inert: {a ~ Int, F Int ~ b} (given)
382 Reagent: F a ~ b (wanted)
384 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
385 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
388 -- Main interaction solver: we fully solve the worklist 'in one go',
389 -- returning an extended inert set.
391 -- See Note [Touchables and givens].
392 solveInteract :: InertSet -> CanonicalCts -> TcS InertSet
393 solveInteract inert ws
394 = do { dyn_flags <- getDynFlags
395 ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert ws
397 solveOne :: InertSet -> WorkItem -> TcS InertSet
398 solveOne inerts workItem
399 = do { dyn_flags <- getDynFlags
400 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
404 solveInteractWithDepth :: (Int, Int, [WorkItem])
405 -> InertSet -> WorkList -> TcS InertSet
406 solveInteractWithDepth ctxt@(max_depth,n,stack) inert ws
411 = solverDepthErrorTcS n stack
414 = do { traceTcS "solveInteractWithDepth" $
415 vcat [ text "Current depth =" <+> ppr n
416 , text "Max depth =" <+> ppr max_depth ]
418 -- Solve equalities first
419 ; let (eqs, non_eqs) = Bag.partitionBag isCTyEqCan ws
420 ; is_from_eqs <- Bag.foldlBagM (solveOneWithDepth ctxt) inert eqs
421 ; Bag.foldlBagM (solveOneWithDepth ctxt) is_from_eqs non_eqs }
424 -- Fully interact the given work item with an inert set, and return a
425 -- new inert set which has assimilated the new information.
426 solveOneWithDepth :: (Int, Int, [WorkItem])
427 -> InertSet -> WorkItem -> TcS InertSet
428 solveOneWithDepth (max_depth, n, stack) inert work
429 = do { traceTcS0 (indent ++ "Solving {") (ppr work)
430 ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work
432 ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work)
434 -- Recursively solve the new work generated
435 -- from workItem, with a greater depth
436 ; res_inert <- solveInteractWithDepth (max_depth, n+1, work:stack)
439 ; traceTcS0 (indent ++ "Done }") (ppr work)
442 indent = replicate (2*n) ' '
444 thePipeline :: [(String,SimplifierStage)]
445 thePipeline = [ ("interact with inert eqs", interactWithInertEqsStage)
446 , ("interact with inerts", interactWithInertsStage)
447 , ("spontaneous solve", spontaneousSolveStage)
448 , ("top-level reactions", topReactionsStage) ]
451 *********************************************************************************
453 The spontaneous-solve Stage
455 *********************************************************************************
457 Note [Efficient Orientation]
458 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
460 There are two cases where we have to be careful about
461 orienting equalities to get better efficiency.
463 Case 1: In Rewriting Equalities (function rewriteEqLHS)
465 When rewriting two equalities with the same LHS:
468 We have a choice of producing work (xi1 ~ xi2) (up-to the
469 canonicalization invariants) However, to prevent the inert items
470 from getting kicked out of the inerts first, we prefer to
471 canonicalize (xi1 ~ xi2) if (b) comes from the inert set, or (xi2
472 ~ xi1) if (a) comes from the inert set.
474 This choice is implemented using the WhichComesFromInert flag.
476 Case 2: Functional Dependencies
477 Again, we should prefer, if possible, the inert variables on the RHS
479 Case 3: IP improvement work
480 We must always rewrite so that the inert type is on the right.
483 spontaneousSolveStage :: SimplifierStage
484 spontaneousSolveStage workItem inerts
485 = do { mSolve <- trySpontaneousSolve workItem
488 SPCantSolve -> -- No spontaneous solution for him, keep going
489 return $ SR { sr_new_work = emptyWorkList
491 , sr_stop = ContinueWith workItem }
494 | not (isGivenCt workItem)
495 -- Original was wanted or derived but we have now made him
496 -- given so we have to interact him with the inerts due to
497 -- its status change. This in turn may produce more work.
498 -- We do this *right now* (rather than just putting workItem'
499 -- back into the work-list) because we've solved
500 -> do { (new_inert, new_work) <- runSolverPipeline
501 [ ("recursive interact with inert eqs", interactWithInertEqsStage)
502 , ("recursive interact with inerts", interactWithInertsStage)
504 ; return $ SR { sr_new_work = new_work
505 , sr_inerts = new_inert -- will include workItem'
509 -> -- Original was given; he must then be inert all right, and
510 -- workList' are all givens from flattening
511 return $ SR { sr_new_work = emptyWorkList
512 , sr_inerts = inerts `updInertSet` workItem'
514 SPError -> -- Return with no new work
515 return $ SR { sr_new_work = emptyWorkList
520 data SPSolveResult = SPCantSolve | SPSolved WorkItem | SPError
521 -- SPCantSolve means that we can't do the unification because e.g. the variable is untouchable
522 -- SPSolved workItem' gives us a new *given* to go on
523 -- SPError means that it's completely impossible to solve this equality, eg due to a kind error
526 -- @trySpontaneousSolve wi@ solves equalities where one side is a
527 -- touchable unification variable.
528 -- See Note [Touchables and givens]
529 trySpontaneousSolve :: WorkItem -> TcS SPSolveResult
530 trySpontaneousSolve workItem@(CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi })
533 | Just tv2 <- tcGetTyVar_maybe xi
534 = do { tch1 <- isTouchableMetaTyVar tv1
535 ; tch2 <- isTouchableMetaTyVar tv2
536 ; case (tch1, tch2) of
537 (True, True) -> trySpontaneousEqTwoWay cv gw tv1 tv2
538 (True, False) -> trySpontaneousEqOneWay cv gw tv1 xi
539 (False, True) -> trySpontaneousEqOneWay cv gw tv2 (mkTyVarTy tv1)
540 _ -> return SPCantSolve }
542 = do { tch1 <- isTouchableMetaTyVar tv1
543 ; if tch1 then trySpontaneousEqOneWay cv gw tv1 xi
544 else do { traceTcS "Untouchable LHS, can't spontaneously solve workitem:" (ppr workItem)
545 ; return SPCantSolve }
549 -- trySpontaneousSolve (CFunEqCan ...) = ...
550 -- See Note [No touchables as FunEq RHS] in TcSMonad
551 trySpontaneousSolve _ = return SPCantSolve
554 trySpontaneousEqOneWay :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
555 -- tv is a MetaTyVar, not untouchable
556 trySpontaneousEqOneWay cv gw tv xi
557 | not (isSigTyVar tv) || isTyVarTy xi
558 = do { let kxi = typeKind xi -- NB: 'xi' is fully rewritten according to the inerts
559 -- so we have its more specific kind in our hands
560 ; if kxi `isSubKind` tyVarKind tv then
561 solveWithIdentity cv gw tv xi
562 else if tyVarKind tv `isSubKind` kxi then
563 return SPCantSolve -- kinds are compatible but we can't solveWithIdentity this way
564 -- This case covers the a_touchable :: * ~ b_untouchable :: ??
565 -- which has to be deferred or floated out for someone else to solve
566 -- it in a scope where 'b' is no longer untouchable.
567 else do { addErrorTcS KindError gw (mkTyVarTy tv) xi -- See Note [Kind errors]
570 | otherwise -- Still can't solve, sig tyvar and non-variable rhs
574 trySpontaneousEqTwoWay :: CoVar -> CtFlavor -> TcTyVar -> TcTyVar -> TcS SPSolveResult
575 -- Both tyvars are *touchable* MetaTyvars so there is only a chance for kind error here
576 trySpontaneousEqTwoWay cv gw tv1 tv2
578 , nicer_to_update_tv2 = solveWithIdentity cv gw tv2 (mkTyVarTy tv1)
580 = solveWithIdentity cv gw tv1 (mkTyVarTy tv2)
581 | otherwise -- None is a subkind of the other, but they are both touchable!
582 = do { addErrorTcS KindError gw (mkTyVarTy tv1) (mkTyVarTy tv2)
587 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
591 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
592 Consider the wanted problem:
593 alpha ~ (# Int, Int #)
594 where alpha :: ?? and (# Int, Int #) :: (#). We can't spontaneously solve this constraint,
595 but we should rather reject the program that give rise to it. If 'trySpontaneousEqTwoWay'
596 simply returns @CantSolve@ then that wanted constraint is going to propagate all the way and
597 get quantified over in inference mode. That's bad because we do know at this point that the
598 constraint is insoluble. Instead, we call 'recKindErrorTcS' here, which will fail later on.
600 The same applies in canonicalization code in case of kind errors in the givens.
602 However, when we canonicalize givens we only check for compatibility (@compatKind@).
603 If there were a kind error in the givens, this means some form of inconsistency or dead code.
605 You may think that when we spontaneously solve wanteds we may have to look through the
606 bindings to determine the right kind of the RHS type. E.g one may be worried that xi is
607 @alpha@ where alpha :: ? and a previous spontaneous solving has set (alpha := f) with (f :: *).
608 But we orient our constraints so that spontaneously solved ones can rewrite all other constraint
609 so this situation can't happen.
611 Note [Spontaneous solving and kind compatibility]
612 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
614 Note that our canonical constraints insist that only *given* equalities (tv ~ xi)
615 or (F xis ~ rhs) require the LHS and the RHS to have exactly the same kinds.
617 - We have to require this because:
618 Given equalities can be freely used to rewrite inside
619 other types or constraints.
620 - We do not have to do the same for wanteds because:
621 First, wanted equations (tv ~ xi) where tv is a touchable
622 unification variable may have kinds that do not agree (the
623 kind of xi must be a sub kind of the kind of tv). Second, any
624 potential kind mismatch will result in the constraint not
625 being soluble, which will be reported anyway. This is the
626 reason that @trySpontaneousOneWay@ and @trySpontaneousTwoWay@
627 will perform a kind compatibility check, and only then will
628 they proceed to @solveWithIdentity@.
631 - Givens from higher-rank, such as:
632 type family T b :: * -> * -> *
633 type instance T Bool = (->)
635 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
637 Whereas we would be able to apply the type instance, we would not be able to
638 use the given (T Bool ~ (->)) in the body of 'flop'
641 Note [Avoid double unifications]
642 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
643 The spontaneous solver has to return a given which mentions the unified unification
644 variable *on the left* of the equality. Here is what happens if not:
645 Original wanted: (a ~ alpha), (alpha ~ Int)
646 We spontaneously solve the first wanted, without changing the order!
647 given : a ~ alpha [having unified alpha := a]
648 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
649 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
651 We avoid this problem by orienting the resulting given so that the unification
652 variable is on the left. [Note that alternatively we could attempt to
653 enforce this at canonicalization]
655 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
656 double unifications is the main reason we disallow touchable
657 unification variables as RHS of type family equations: F xis ~ alpha.
662 solveWithIdentity :: CoVar -> CtFlavor -> TcTyVar -> Xi -> TcS SPSolveResult
663 -- Solve with the identity coercion
664 -- Precondition: kind(xi) is a sub-kind of kind(tv)
665 -- Precondition: CtFlavor is Wanted or Derived
666 -- See [New Wanted Superclass Work] to see why solveWithIdentity
667 -- must work for Derived as well as Wanted
668 -- Returns: workItem where
669 -- workItem = the new Given constraint
670 solveWithIdentity cv wd tv xi
671 = do { traceTcS "Sneaky unification:" $
672 vcat [text "Coercion variable: " <+> ppr wd,
673 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
674 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
675 text "Right Kind is : " <+> ppr (typeKind xi)
678 ; setWantedTyBind tv xi -- Set tv := xi_unflat
679 ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi xi
681 ; case wd of Wanted {} -> setWantedCoBind cv xi
682 Derived {} -> setDerivedCoBind cv xi
683 _ -> pprPanic "Can't spontaneously solve given!" empty
685 ; return $ SPSolved (CTyEqCan { cc_id = cv_given
686 , cc_flavor = mkGivenFlavor wd UnkSkol
687 , cc_tyvar = tv, cc_rhs = xi })
695 *********************************************************************************
697 The interact-with-inert Stage
699 *********************************************************************************
702 -- Interaction result of WorkItem <~> AtomicInert
704 = IR { ir_stop :: StopOrContinue
706 -- => Reagent (work item) consumed.
707 -- ContinueWith new_reagent
708 -- => Reagent transformed but keep gathering interactions.
709 -- The transformed item remains inert with respect
710 -- to any previously encountered inerts.
712 , ir_inert_action :: InertAction
713 -- Whether the inert item should remain in the InertSet.
715 , ir_new_work :: WorkList
716 -- new work items to add to the WorkList
718 , ir_improvement :: Maybe FDImprovement -- In case improvement kicked in
721 -- What to do with the inert reactant.
722 data InertAction = KeepInert
724 | KeepTransformedInert CanonicalCt -- Keep a slightly transformed inert
726 mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
727 mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork Nothing
729 mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
730 mkIRStop keep newWork = return $ IR Stop keep newWork Nothing
732 mkIRStop_RecordImprovement :: Monad m => InertAction -> WorkList -> FDImprovement -> m InteractResult
733 mkIRStop_RecordImprovement keep newWork fdimpr = return $ IR Stop keep newWork (Just fdimpr)
735 dischargeWorkItem :: Monad m => m InteractResult
736 dischargeWorkItem = mkIRStop KeepInert emptyWorkList
738 noInteraction :: Monad m => WorkItem -> m InteractResult
739 noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList
741 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
742 -- See Note [Efficient Orientation]
745 ---------------------------------------------------
746 -- Interact a single WorkItem with the equalities of an inert set as far as possible, i.e. until we
747 -- get a Stop result from an individual reaction (i.e. when the WorkItem is consumed), or until we've
748 -- interact the WorkItem with the entire equalities of the InertSet
750 interactWithInertEqsStage :: SimplifierStage
751 interactWithInertEqsStage workItem inert
752 = foldISEqCtsM interactNext initITR inert
753 where initITR = SR { sr_inerts = IS { inert_eqs = emptyCCan -- Will fold over equalities
754 , inert_dicts = inert_dicts inert
755 , inert_ips = inert_ips inert
756 , inert_funeqs = inert_funeqs inert
757 , inert_fds = inert_fds inert
759 , sr_new_work = emptyWorkList
760 , sr_stop = ContinueWith workItem }
763 ---------------------------------------------------
764 -- Interact a single WorkItem with *non-equality* constraints in the inert set.
765 -- Precondition: equality interactions must have already happened, hence we have
766 -- to pick up some information from the incoming inert, before folding over the
767 -- "Other" constraints it contains!
769 interactWithInertsStage :: SimplifierStage
770 interactWithInertsStage workItem inert
771 = let (relevant, inert_residual) = getISRelevant workItem inert
772 initITR = SR { sr_inerts = inert_residual
773 , sr_new_work = emptyWorkList
774 , sr_stop = ContinueWith workItem }
775 in Bag.foldlBagM interactNext initITR relevant
777 getISRelevant :: CanonicalCt -> InertSet -> (CanonicalCts, InertSet)
778 getISRelevant (CDictCan { cc_class = cls } ) is
779 = let (relevant, residual_map) = getRelevantCts cls (inert_dicts is)
780 in (relevant, is { inert_dicts = residual_map })
781 getISRelevant (CFunEqCan { cc_fun = tc } ) is
782 = let (relevant, residual_map) = getRelevantCts tc (inert_funeqs is)
783 in (relevant, is { inert_funeqs = residual_map })
784 getISRelevant (CIPCan { cc_ip_nm = nm }) is
785 = let (relevant, residual_map) = getRelevantCts nm (inert_ips is)
786 in (relevant, is { inert_ips = residual_map })
787 -- An equality, finally, may kick everything except equalities out
788 -- because we have already interacted the equalities in interactWithInertEqsStage
789 getISRelevant _eq_ct is -- Equality, everything is relevant for this one
790 -- TODO: if we were caching variables, we'd know that only
791 -- some are relevant. Experiment with this for now.
792 = let cts = cCanMapToBag (inert_ips is) `unionBags`
793 cCanMapToBag (inert_dicts is) `unionBags` cCanMapToBag (inert_funeqs is)
794 in (cts, is { inert_dicts = emptyCCanMap
795 , inert_ips = emptyCCanMap
796 , inert_funeqs = emptyCCanMap })
798 interactNext :: StageResult -> AtomicInert -> TcS StageResult
799 interactNext it inert
800 | ContinueWith workItem <- sr_stop it
801 = do { let inerts = sr_inerts it
802 fdimprs_old = getFDImprovements inerts
804 ; ir <- interactWithInert fdimprs_old inert workItem
806 -- New inerts depend on whether we KeepInert or not and must
807 -- be updated with FD improvement information from the interaction result (ir)
808 ; let inerts_new = updInertSetFDImprs upd_inert (ir_improvement ir)
809 upd_inert = case ir_inert_action ir of
810 KeepInert -> inerts `updInertSet` inert
812 KeepTransformedInert inert' -> inerts `updInertSet` inert'
814 ; return $ SR { sr_inerts = inerts_new
815 , sr_new_work = sr_new_work it `unionWorkLists` ir_new_work ir
816 , sr_stop = ir_stop ir } }
818 = return $ it { sr_inerts = (sr_inerts it) `updInertSet` inert }
820 -- Do a single interaction of two constraints.
821 interactWithInert :: FDImprovements -> AtomicInert -> WorkItem -> TcS InteractResult
822 interactWithInert fdimprs inert workitem
823 = do { ctxt <- getTcSContext
824 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workitem
825 inert_ev = cc_id inert
826 work_ev = cc_id workitem
828 -- Never interact a wanted and a derived where the derived's evidence
829 -- mentions the wanted evidence in an unguarded way.
830 -- See Note [Superclasses and recursive dictionaries]
831 -- and Note [New Wanted Superclass Work]
832 -- We don't have to do this for givens, as we fully know the evidence for them.
834 case (cc_flavor inert, cc_flavor workitem) of
835 (Wanted loc, Derived {}) -> isGoodRecEv work_ev (WantedEvVar inert_ev loc)
836 (Derived {}, Wanted loc) -> isGoodRecEv inert_ev (WantedEvVar work_ev loc)
839 ; if is_allowed && rec_ev_ok then
840 doInteractWithInert fdimprs inert workitem
842 noInteraction workitem
845 allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
846 -- Allowed interactions
847 allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
848 allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
849 allowedInteraction _ _ _ = True
851 --------------------------------------------
852 doInteractWithInert :: FDImprovements -> CanonicalCt -> CanonicalCt -> TcS InteractResult
853 -- Identical class constraints.
855 doInteractWithInert fdimprs
856 (CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
857 workItem@(CDictCan { cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
858 | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
859 = solveOneFromTheOther (d1,fl1) workItem
861 | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
862 = -- See Note [When improvement happens]
863 do { let pty1 = ClassP cls1 tys1
864 pty2 = ClassP cls2 tys2
865 work_item_pred_loc = (pty2, pprFlavorArising fl2)
866 inert_pred_loc = (pty1, pprFlavorArising fl1)
867 loc = combineCtLoc fl1 fl2
868 eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc
869 -- See Note [Efficient Orientation]
871 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
872 ; fd_work <- canWanteds wevvars
873 -- See Note [Generating extra equalities]
874 ; traceTcS "Checking if improvements existed." (ppr fdimprs)
875 ; if isEmptyWorkList fd_work || haveBeenImproved fdimprs pty1 pty2 then
877 mkIRContinue workItem KeepInert fd_work
878 else do { traceTcS "Recording improvement and throwing item back in worklist." (ppr (pty1,pty2))
879 ; mkIRStop_RecordImprovement KeepInert
880 (fd_work `unionWorkLists` workListFromCCan workItem) (pty1,pty2)
882 -- See Note [FunDep Reactions]
885 -- Class constraint and given equality: use the equality to rewrite
886 -- the class constraint.
887 doInteractWithInert _fdimprs
888 (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
889 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
890 | ifl `canRewrite` wfl
891 , tv `elemVarSet` tyVarsOfTypes xis
892 = if isDerivedSC wfl then
893 mkIRStop KeepInert $ emptyWorkList -- See Note [Adding Derived Superclasses]
894 else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
895 -- Continue with rewritten Dictionary because we can only be in the
896 -- interactWithEqsStage, so the dictionary is inert.
897 ; mkIRContinue rewritten_dict KeepInert emptyWorkList }
899 doInteractWithInert _fdimprs
900 (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
901 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
902 | wfl `canRewrite` ifl
903 , tv `elemVarSet` tyVarsOfTypes xis
904 = if isDerivedSC ifl then
905 mkIRContinue workItem DropInert emptyWorkList -- No need to do any rewriting,
906 -- see Note [Adding Derived Superclasses]
907 else do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
908 ; mkIRContinue workItem DropInert (workListFromCCan rewritten_dict) }
910 -- Class constraint and given equality: use the equality to rewrite
911 -- the class constraint.
912 doInteractWithInert _fdimprs
913 (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
914 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
915 | ifl `canRewrite` wfl
916 , tv `elemVarSet` tyVarsOfType ty
917 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
918 ; mkIRContinue rewritten_ip KeepInert emptyWorkList }
920 doInteractWithInert _fdimprs
921 (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
922 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
923 | wfl `canRewrite` ifl
924 , tv `elemVarSet` tyVarsOfType ty
925 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
926 ; mkIRContinue workItem DropInert (workListFromCCan rewritten_ip) }
928 -- Two implicit parameter constraints. If the names are the same,
929 -- but their types are not, we generate a wanted type equality
930 -- that equates the type (this is "improvement").
931 -- However, we don't actually need the coercion evidence,
932 -- so we just generate a fresh coercion variable that isn't used anywhere.
933 doInteractWithInert _fdimprs
934 (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
935 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
936 | nm1 == nm2 && isGiven wfl && isGiven ifl
937 = -- See Note [Overriding implicit parameters]
938 -- Dump the inert item, override totally with the new one
939 -- Do not require type equality
940 mkIRContinue workItem DropInert emptyWorkList
942 | nm1 == nm2 && ty1 `tcEqType` ty2
943 = solveOneFromTheOther (id1,ifl) workItem
946 = -- See Note [When improvement happens]
947 do { co_var <- newWantedCoVar ty2 ty1 -- See Note [Efficient Orientation]
948 ; let flav = Wanted (combineCtLoc ifl wfl)
949 ; cans <- mkCanonical flav co_var
950 ; mkIRContinue workItem KeepInert cans }
954 -- Never rewrite a given with a wanted equality, and a type function
955 -- equality can never rewrite an equality. We rewrite LHS *and* RHS
956 -- of function equalities so that our inert set exposes everything that
957 -- we know about equalities.
959 -- Inert: equality, work item: function equality
960 doInteractWithInert _fdimprs
961 (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
962 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
963 , cc_tyargs = args, cc_rhs = xi2 })
964 | ifl `canRewrite` wfl
965 , tv `elemVarSet` tyVarsOfTypes (xi2:args) -- Rewrite RHS as well
966 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
967 ; mkIRStop KeepInert (workListFromCCan rewritten_funeq) }
968 -- Must Stop here, because we may no longer be inert after the rewritting.
970 -- Inert: function equality, work item: equality
971 doInteractWithInert _fdimprs
972 (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
973 , cc_tyargs = args, cc_rhs = xi1 })
974 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
975 | wfl `canRewrite` ifl
976 , tv `elemVarSet` tyVarsOfTypes (xi1:args) -- Rewrite RHS as well
977 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
978 ; mkIRContinue workItem DropInert (workListFromCCan rewritten_funeq) }
979 -- One may think that we could (KeepTransformedInert rewritten_funeq)
980 -- but that is wrong, because it may end up not being inert with respect
981 -- to future inerts. Example:
982 -- Original inert = { F xis ~ [a], b ~ Maybe Int }
983 -- Work item comes along = a ~ [b]
984 -- If we keep { F xis ~ [b] } in the inert set we will end up with:
985 -- { F xis ~ [b], b ~ Maybe Int, a ~ [Maybe Int] }
986 -- At the end, which is *not* inert. So we should unfortunately DropInert here.
988 doInteractWithInert _fdimprs
989 (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
990 , cc_tyargs = args1, cc_rhs = xi1 })
991 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
992 , cc_tyargs = args2, cc_rhs = xi2 })
993 | fl1 `canSolve` fl2 && lhss_match
994 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
995 ; mkIRStop KeepInert cans }
996 | fl2 `canSolve` fl1 && lhss_match
997 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
998 ; mkIRContinue workItem DropInert cans }
1000 lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
1002 doInteractWithInert _fdimprs
1003 (CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1004 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
1005 -- Check for matching LHS
1006 | fl1 `canSolve` fl2 && tv1 == tv2
1007 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1008 ; mkIRStop KeepInert cans }
1010 | fl2 `canSolve` fl1 && tv1 == tv2
1011 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1012 ; mkIRContinue workItem DropInert cans }
1013 -- Check for rewriting RHS
1014 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1015 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1016 ; mkIRStop KeepInert rewritten_eq }
1017 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1018 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1019 ; mkIRContinue workItem DropInert rewritten_eq }
1021 -- Fall-through case for all other situations
1022 doInteractWithInert _fdimprs _ workItem = noInteraction workItem
1024 -------------------------
1025 -- Equational Rewriting
1026 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1027 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1028 = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
1029 args = substTysWith [tv] [xi] xis
1031 dict_co = mkTyConCoercion con cos
1032 ; dv' <- newDictVar cl args
1034 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
1035 _given_or_derived -> setDictBind dv' (EvCast dv dict_co)
1036 ; return (CDictCan { cc_id = dv'
1039 , cc_tyargs = args }) }
1041 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1042 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1043 = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi]
1044 ty' = substTyWith [tv] [xi] ty
1045 ; ipid' <- newIPVar nm ty'
1047 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co))
1048 _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co)
1049 ; return (CIPCan { cc_id = ipid'
1052 , cc_ip_ty = ty' }) }
1054 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1055 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2) -- cv2 :: F args ~ xi2
1056 = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
1057 args' = substTysWith [tv] [xi1] args
1058 fun_co = mkTyConCoercion tc arg_cos -- fun_co :: F args ~ F args'
1060 xi2' = substTyWith [tv] [xi1] xi2
1061 xi2_co = substTyWith [tv] [mkCoVarCoercion cv1] xi2 -- xi2_co :: xi2 ~ xi2'
1062 ; cv2' <- case gw of
1063 Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2'
1064 ; setWantedCoBind cv2 $
1065 fun_co `mkTransCoercion`
1066 mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion xi2_co
1068 _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2' $
1069 mkSymCoercion fun_co `mkTransCoercion`
1070 mkCoVarCoercion cv2 `mkTransCoercion` xi2_co
1071 ; return (CFunEqCan { cc_id = cv2'
1075 , cc_rhs = xi2' }) }
1078 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS WorkList
1079 -- Use the first equality to rewrite the second, flavors already checked.
1080 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1081 -- rewrites c2 to give
1082 -- c2' : tv2 ~ xi2[xi1/tv1]
1083 -- We must do an occurs check to sure the new constraint is canonical
1084 -- So we might return an empty bag
1085 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1086 | Just tv2' <- tcGetTyVar_maybe xi2'
1087 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1088 = do { when (isWanted gw) (setWantedCoBind cv2 (mkSymCoercion co2'))
1089 ; return emptyCCan }
1094 -> do { cv2' <- newWantedCoVar (mkTyVarTy tv2) xi2'
1095 ; setWantedCoBind cv2 $
1096 mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion co2'
1099 -> newGivOrDerCoVar (mkTyVarTy tv2) xi2' $
1100 mkCoVarCoercion cv2 `mkTransCoercion` co2'
1102 ; canEq gw cv2' (mkTyVarTy tv2) xi2'
1105 xi2' = substTyWith [tv1] [xi1] xi2
1106 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1109 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS WorkList
1110 -- Used to ineract two equalities of the following form:
1111 -- First Equality: co1: (XXX ~ xi1)
1112 -- Second Equality: cv2: (XXX ~ xi2)
1113 -- Where the cv1 `canSolve` cv2 equality
1114 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1),
1115 -- See Note [Efficient Orientation] for that
1116 rewriteEqLHS which (co1,xi1) (cv2,gw,xi2)
1117 = do { cv2' <- case (isWanted gw, which) of
1118 (True,LeftComesFromInert) ->
1119 do { cv2' <- newWantedCoVar xi2 xi1
1120 ; setWantedCoBind cv2 $
1121 co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
1123 (True,RightComesFromInert) ->
1124 do { cv2' <- newWantedCoVar xi1 xi2
1125 ; setWantedCoBind cv2 $
1126 co1 `mkTransCoercion` mkCoVarCoercion cv2'
1128 (False,LeftComesFromInert) ->
1129 newGivOrDerCoVar xi2 xi1 $
1130 mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
1131 (False,RightComesFromInert) ->
1132 newGivOrDerCoVar xi1 xi2 $
1133 mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
1134 ; mkCanonical gw cv2'
1137 solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult
1138 -- First argument inert, second argument workitem. They both represent
1139 -- wanted/given/derived evidence for the *same* predicate so we try here to
1140 -- discharge one directly from the other.
1142 -- Precondition: value evidence only (implicit parameters, classes)
1144 solveOneFromTheOther (iid,ifl) workItem
1145 -- Both derived needs a special case. You might think that we do not need
1146 -- two evidence terms for the same claim. But, since the evidence is partial,
1147 -- either evidence may do in some cases; see TcSMonad.isGoodRecEv.
1148 -- See also Example 3 in Note [Superclasses and recursive dictionaries]
1149 | isDerived ifl && isDerived wfl
1150 = noInteraction workItem
1152 | ifl `canSolve` wfl
1153 = do { unless (isGiven wfl) $ setEvBind wid (EvId iid)
1154 -- Overwrite the binding, if one exists
1155 -- For Givens, which are lambda-bound, nothing to overwrite,
1156 ; dischargeWorkItem }
1158 | otherwise -- wfl `canSolve` ifl
1159 = do { unless (isGiven ifl) $ setEvBind iid (EvId wid)
1160 ; mkIRContinue workItem DropInert emptyWorkList }
1163 wfl = cc_flavor workItem
1164 wid = cc_id workItem
1167 Note [Superclasses and recursive dictionaries]
1168 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1169 Overlaps with Note [SUPERCLASS-LOOP 1]
1170 Note [SUPERCLASS-LOOP 2]
1171 Note [Recursive instances and superclases]
1172 ToDo: check overlap and delete redundant stuff
1174 Right before adding a given into the inert set, we must
1175 produce some more work, that will bring the superclasses
1176 of the given into scope. The superclass constraints go into
1179 When we simplify a wanted constraint, if we first see a matching
1180 instance, we may produce new wanted work. To (1) avoid doing this work
1181 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1182 this item as solved (in effect, given) into our inert set and with that add
1183 its superclass constraints (as given) in our worklist.
1185 But now we have added partially solved constraints to the worklist which may
1186 interact with other wanteds. Consider the example:
1190 class Eq b => Foo a b --- 0-th selector
1191 instance Eq a => Foo [a] a --- fooDFun
1193 and wanted (Foo [t] t). We are first going to see that the instance matches
1194 and create an inert set that includes the solved (Foo [t] t) and its
1196 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1197 d2 :_g Eq t d2 := EvSuperClass d1 0
1198 Our work list is going to contain a new *wanted* goal
1200 It is wrong to react the wanted (Eq t) with the given (Eq t) because that would
1201 construct loopy evidence. Hence the check isGoodRecEv in doInteractWithInert.
1203 OK, so we have ruled out bad behaviour, but how do we ge recursive dictionaries,
1208 data D r = ZeroD | SuccD (r (D r));
1210 instance (Eq (r (D r))) => Eq (D r) where
1211 ZeroD == ZeroD = True
1212 (SuccD a) == (SuccD b) = a == b
1215 equalDC :: D [] -> D [] -> Bool;
1218 We need to prove (Eq (D [])). Here's how we go:
1222 by instance decl, holds if
1226 *BUT* we have an inert set which gives us (no superclasses):
1228 By the instance declaration of Eq we can show the 'd2' goal if
1230 where d2 = dfEqList d3
1232 Now, however this wanted can interact with our inert d1 to set:
1234 and solve the goal. Why was this interaction OK? Because, if we chase the
1235 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1237 d3 := dfEqD2 (dfEqList d3)
1238 which is FINE because the use of d3 is protected by the instance function
1241 So, our strategy is to try to put solved wanted dictionaries into the
1242 inert set along with their superclasses (when this is meaningful,
1243 i.e. when new wanted goals are generated) but solve a wanted dictionary
1244 from a given only in the case where the evidence variable of the
1245 wanted is mentioned in the evidence of the given (recursively through
1246 the evidence binds) in a protected way: more instance function applications
1247 than superclass selectors.
1249 Here are some more examples from GHC's previous type checker
1253 This code arises in the context of "Scrap Your Boilerplate with Class"
1257 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1258 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1260 class Data Maybe a => Foo a
1262 instance Foo t => Sat (Maybe t) -- dfunSat
1264 instance Data Maybe a => Foo a -- dfunFoo1
1265 instance Foo a => Foo [a] -- dfunFoo2
1266 instance Foo [Char] -- dfunFoo3
1268 Consider generating the superclasses of the instance declaration
1269 instance Foo a => Foo [a]
1271 So our problem is this
1273 d1 :_w Data Maybe [t]
1275 We may add the given in the inert set, along with its superclasses
1276 [assuming we don't fail because there is a matching instance, see
1277 tryTopReact, given case ]
1281 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1282 d1 :_w Data Maybe [t]
1283 Then d2 can readily enter the inert, and we also do solving of the wanted
1286 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1288 d2 :_w Sat (Maybe [t])
1290 d01 :_g Data Maybe t
1291 Now, we may simplify d2 more:
1294 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1295 d1 :_g Data Maybe [t]
1296 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1300 d01 :_g Data Maybe t
1302 Now, we can just solve d3.
1305 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1306 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1309 d01 :_g Data Maybe t
1310 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1313 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1314 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1315 d4 :_g Foo [t] d4 := dfunFoo2 d5
1318 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1319 d01 :_g Data Maybe t
1320 Now, d5 can be solved! (and its superclass enter scope)
1323 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1324 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1325 d4 :_g Foo [t] d4 := dfunFoo2 d5
1326 d5 :_g Foo t d5 := dfunFoo1 d7
1329 d6 :_g Data Maybe [t]
1330 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1331 d01 :_g Data Maybe t
1334 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1335 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1336 that must not be used (look at case interactInert where both inert and workitem
1337 are givens). So we have several options:
1338 - Drop the workitem always (this will drop d8)
1339 This feels very unsafe -- what if the work item was the "good" one
1340 that should be used later to solve another wanted?
1341 - Don't drop anyone: the inert set may contain multiple givens!
1342 [This is currently implemented]
1344 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1345 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1346 d7. Now the [isRecDictEv] function in the ineration solver
1347 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1348 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1350 So, no interaction happens there. Then we meet d01 and there is no recursion
1351 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1353 Note [SUPERCLASS-LOOP 1]
1354 ~~~~~~~~~~~~~~~~~~~~~~~~
1355 We have to be very, very careful when generating superclasses, lest we
1356 accidentally build a loop. Here's an example:
1360 class S a => C a where { opc :: a -> a }
1361 class S b => D b where { opd :: b -> b }
1363 instance C Int where
1366 instance D Int where
1369 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1370 Simplifying, we may well get:
1371 $dfCInt = :C ds1 (opd dd)
1374 Notice that we spot that we can extract ds1 from dd.
1376 Alas! Alack! We can do the same for (instance D Int):
1378 $dfDInt = :D ds2 (opc dc)
1382 And now we've defined the superclass in terms of itself.
1383 Two more nasty cases are in
1388 - Satisfy the superclass context *all by itself*
1389 (tcSimplifySuperClasses)
1390 - And do so completely; i.e. no left-over constraints
1391 to mix with the constraints arising from method declarations
1394 Note [SUPERCLASS-LOOP 2]
1395 ~~~~~~~~~~~~~~~~~~~~~~~~
1396 We need to be careful when adding "the constaint we are trying to prove".
1397 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1399 class Ord a => C a where
1400 instance Ord [a] => C [a] where ...
1402 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1403 superclasses of C [a] to avails. But we must not overwrite the binding
1404 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1407 Here's another variant, immortalised in tcrun020
1408 class Monad m => C1 m
1409 class C1 m => C2 m x
1410 instance C2 Maybe Bool
1411 For the instance decl we need to build (C1 Maybe), and it's no good if
1412 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1413 before we search for C1 Maybe.
1415 Here's another example
1416 class Eq b => Foo a b
1417 instance Eq a => Foo [a] a
1421 we'll first deduce that it holds (via the instance decl). We must not
1422 then overwrite the Eq t constraint with a superclass selection!
1424 At first I had a gross hack, whereby I simply did not add superclass constraints
1425 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1426 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1427 I found a very obscure program (now tcrun021) in which improvement meant the
1428 simplifier got two bites a the cherry... so something seemed to be an Stop
1429 first time, but reducible next time.
1431 Now we implement the Right Solution, which is to check for loops directly
1432 when adding superclasses. It's a bit like the occurs check in unification.
1434 Note [Recursive instances and superclases]
1435 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1436 Consider this code, which arises in the context of "Scrap Your
1437 Boilerplate with Class".
1441 instance Sat (ctx Char) => Data ctx Char
1442 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1444 class Data Maybe a => Foo a
1446 instance Foo t => Sat (Maybe t)
1448 instance Data Maybe a => Foo a
1449 instance Foo a => Foo [a]
1452 In the instance for Foo [a], when generating evidence for the superclasses
1453 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1454 Using the instance for Data, we therefore need
1455 (Sat (Maybe [a], Data Maybe a)
1456 But we are given (Foo a), and hence its superclass (Data Maybe a).
1457 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1458 we need (Foo [a]). And that is the very dictionary we are bulding
1459 an instance for! So we must put that in the "givens". So in this
1461 Given: Foo a, Foo [a]
1462 Wanted: Data Maybe [a]
1464 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1465 the givens, which is what 'addGiven' would normally do. Why? Because
1466 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1467 by selecting a superclass from Foo [a], which simply makes a loop.
1469 On the other hand we *must* put the superclasses of (Foo a) in
1470 the givens, as you can see from the derivation described above.
1472 Conclusion: in the very special case of tcSimplifySuperClasses
1473 we have one 'given' (namely the "this" dictionary) whose superclasses
1474 must not be added to 'givens' by addGiven.
1476 There is a complication though. Suppose there are equalities
1477 instance (Eq a, a~b) => Num (a,b)
1478 Then we normalise the 'givens' wrt the equalities, so the original
1479 given "this" dictionary is cast to one of a different type. So it's a
1480 bit trickier than before to identify the "special" dictionary whose
1481 superclasses must not be added. See test
1482 indexed-types/should_run/EqInInstance
1484 We need a persistent property of the dictionary to record this
1485 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1486 but cool), which is maintained by dictionary normalisation.
1487 Specifically, the InstLocOrigin is
1489 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1492 Note [MATCHING-SYNONYMS]
1493 ~~~~~~~~~~~~~~~~~~~~~~~~
1494 When trying to match a dictionary (D tau) to a top-level instance, or a
1495 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1496 we do *not* need to expand type synonyms because the matcher will do that for us.
1499 Note [RHS-FAMILY-SYNONYMS]
1500 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1501 The RHS of a family instance is represented as yet another constructor which is
1502 like a type synonym for the real RHS the programmer declared. Eg:
1503 type instance F (a,a) = [a]
1505 :R32 a = [a] -- internal type synonym introduced
1506 F (a,a) ~ :R32 a -- instance
1508 When we react a family instance with a type family equation in the work list
1509 we keep the synonym-using RHS without expansion.
1512 *********************************************************************************
1514 The top-reaction Stage
1516 *********************************************************************************
1519 -- If a work item has any form of interaction with top-level we get this
1520 data TopInteractResult
1521 = NoTopInt -- No top-level interaction
1523 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1524 -- for superclasses)
1525 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1526 } -- NB: in ``given'' (solved) form if the
1527 -- original was wanted or given and instance match
1528 -- was found, but may also be in wanted form if we
1529 -- only reacted with functional dependencies
1530 -- arising from top-level instances.
1532 topReactionsStage :: SimplifierStage
1533 topReactionsStage workItem inerts
1534 = do { tir <- tryTopReact workItem
1537 return $ SR { sr_inerts = inerts
1538 , sr_new_work = emptyWorkList
1539 , sr_stop = ContinueWith workItem }
1540 SomeTopInt tir_new_work tir_new_inert ->
1541 return $ SR { sr_inerts = inerts
1542 , sr_new_work = tir_new_work
1543 , sr_stop = tir_new_inert
1547 tryTopReact :: WorkItem -> TcS TopInteractResult
1548 tryTopReact workitem
1549 = do { -- A flag controls the amount of interaction allowed
1550 -- See Note [Simplifying RULE lhs constraints]
1551 ctxt <- getTcSContext
1552 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1553 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1554 ; doTopReact workitem }
1555 else return NoTopInt
1558 allowedTopReaction :: Bool -> WorkItem -> Bool
1559 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1560 allowedTopReaction _ _ = True
1563 doTopReact :: WorkItem -> TcS TopInteractResult
1564 -- The work item does not react with the inert set,
1565 -- so try interaction with top-level instances
1567 -- Given dictionary; just add superclasses
1568 -- See Note [Given constraint that matches an instance declaration]
1569 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Given loc
1570 , cc_class = cls, cc_tyargs = xis })
1571 = do { sc_work <- newGivenSCWork dv loc cls xis
1572 ; return $ SomeTopInt sc_work (ContinueWith workItem) }
1574 -- Derived dictionary
1575 -- Do not add any further derived superclasses; their
1576 -- full transitive closure has already been added.
1577 -- But do look for functional dependencies
1578 doTopReact workItem@(CDictCan { cc_flavor = Derived loc _
1579 , cc_class = cls, cc_tyargs = xis })
1580 = do { fd_work <- findClassFunDeps cls xis loc
1581 ; if isEmptyWorkList fd_work then
1583 else return $ SomeTopInt { tir_new_work = fd_work
1584 , tir_new_inert = ContinueWith workItem } }
1586 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Wanted loc
1587 , cc_class = cls, cc_tyargs = xis })
1588 = do { -- See Note [MATCHING-SYNONYMS]
1589 ; lkp_inst_res <- matchClassInst cls xis loc
1590 ; case lkp_inst_res of
1592 do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1593 ; fd_work <- findClassFunDeps cls xis loc
1594 ; if isEmptyWorkList fd_work then
1595 do { sc_work <- newDerivedSCWork dv loc cls xis
1596 -- See Note [Adding Derived Superclasses]
1597 -- NB: workItem is inert, but it isn't solved
1598 -- keep it as inert, although it's not solved
1599 -- because we have now reacted all its
1600 -- top-level fundep-induced equalities!
1601 ; return $ SomeTopInt
1602 { tir_new_work = fd_work `unionWorkLists` sc_work
1603 , tir_new_inert = ContinueWith workItem } }
1605 else -- More fundep work produced, don't do any superclass stuff,
1606 -- just thow him back in the worklist, which will prioritize
1607 -- the solution of fd equalities
1609 { tir_new_work = fd_work `unionWorkLists`
1610 workListFromCCan workItem
1611 , tir_new_inert = Stop } }
1613 GenInst wtvs ev_term -> -- Solved
1614 -- No need to do fundeps stuff here; the instance
1615 -- matches already so we won't get any more info
1616 -- from functional dependencies
1617 do { traceTcS "doTopReact/ found class instance for" (ppr dv)
1618 ; setDictBind dv ev_term
1619 ; inst_work <- canWanteds wtvs
1621 -- Solved in one step and no new wanted work produced.
1622 -- i.e we directly matched a top-level instance
1623 -- No point in caching this in 'inert', nor in adding superclasses
1624 then return $ SomeTopInt { tir_new_work = emptyWorkList
1625 , tir_new_inert = Stop }
1627 -- Solved and new wanted work produced, you may cache the
1628 -- (tentatively solved) dictionary as Derived and its superclasses
1629 else do { let solved = makeSolvedByInst workItem
1630 ; sc_work <- newDerivedSCWork dv loc cls xis
1631 -- See Note [Adding Derived Superclasses]
1632 ; return $ SomeTopInt
1633 { tir_new_work = inst_work `unionWorkLists` sc_work
1634 , tir_new_inert = ContinueWith solved } }
1638 doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
1639 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1640 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1641 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1645 MatchInstSingle (rep_tc, rep_tys)
1646 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1647 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1648 -- Eagerly expand away the type synonym on the
1649 -- RHS of a type function, so that it never
1650 -- appears in an error message
1651 -- See Note [Type synonym families] in TyCon
1652 coe = mkTyConApp coe_tc rep_tys
1654 Wanted {} -> do { cv' <- newWantedCoVar rhs_ty xi
1655 ; setWantedCoBind cv $
1656 coe `mkTransCoercion`
1659 _ -> newGivOrDerCoVar xi rhs_ty $
1660 mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
1662 ; can_cts <- mkCanonical fl cv'
1663 ; return $ SomeTopInt can_cts Stop }
1665 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1669 -- Any other work item does not react with any top-level equations
1670 doTopReact _workItem = return NoTopInt
1672 ----------------------
1673 findClassFunDeps :: Class -> [Xi] -> WantedLoc -> TcS WorkList
1674 -- Look for a fundep reaction beween the wanted item
1675 -- and a top-level instance declaration
1676 findClassFunDeps cls xis loc
1677 = do { instEnvs <- getInstEnvs
1678 ; let eqn_pred_locs = improveFromInstEnv (classInstances instEnvs)
1679 (ClassP cls xis, pprArisingAt loc)
1680 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
1681 -- NB: fundeps generate some wanted equalities, but
1682 -- we don't use their evidence for anything
1683 ; canWanteds wevvars }
1686 Note [Adding Derived Superclasses]
1687 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1688 Generally speaking, we want to be able to add derived superclasses of
1689 unsolved wanteds, and wanteds that have been partially being solved
1690 via an instance. This is important to be able to simplify the inferred
1691 constraints more (and to allow for recursive dictionaries, less
1692 importantly). Example:
1694 Inferred wanted constraint is (Eq a, Ord a), but we'd only like to
1695 quantify over Ord a, hence we would like to be able to add the
1696 superclass of Ord a as Derived and use it to solve the wanted Eq a.
1698 Hence we will add Derived superclasses in the following two cases:
1699 (1) When we meet an unsolved wanted in top-level reactions
1700 (2) When we partially solve a wanted in top-level reactions using an instance decl.
1702 At that point, we have two options:
1703 (1) Add transitively add *ALL* of the superclasses of the Derived
1704 (2) Add only the immediate ones, but whenever we meet a Derived in
1705 the future, add its own superclasses as Derived.
1707 Option (2) is terrible, because deriveds may be rewritten or kicked
1708 out of the inert set, which will result in slightly rewritten
1709 superclasses being reintroduced in the worklist and the inert set. Eg:
1712 instance Foo a => B [a]
1714 Original constraints:
1716 [Given] co : a ~ Int
1718 We apply the instance to the wanted and put it and its superclasses as
1719 as Deriveds in the inerts:
1722 [Derived] (sel d) : C [a]
1725 [Given] co : a ~ Int
1728 Now, suppose that we interact the Derived with the Given equality, and
1729 kick him out of the inert, the next time around a superclass C [Int]
1730 will be produced -- but we already *have* C [a] in the inerts which
1731 will anyway get rewritten to C [Int].
1733 So we choose (1), and *never* introduce any more superclass work from
1734 Deriveds. This enables yet another optimisation: If we ever meet an
1735 equality that can rewrite a Derived, if that Derived is a superclass
1736 derived (like C [a] above), i.e. not a partially solved one (like B
1737 [a]) above, we may simply completely *discard* that Derived. The
1738 reason is because somewhere in the inert lies the original wanted, or
1739 partially solved constraint that gave rise to that superclass, and
1740 that constraint *will* be kicked out, and *will* result in the
1741 rewritten superclass to be added in the inerts later on, anyway.
1745 Note [FunDep and implicit parameter reactions]
1746 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1747 Currently, our story of interacting two dictionaries (or a dictionary
1748 and top-level instances) for functional dependencies, and implicit
1749 paramters, is that we simply produce new wanted equalities. So for example
1751 class D a b | a -> b where ...
1757 We generate the extra work item
1759 where 'cv' is currently unused. However, this new item reacts with d2,
1760 discharging it in favour of a new constraint d2' thus:
1762 d2 := d2' |> D Int cv
1763 Now d2' can be discharged from d1
1765 We could be more aggressive and try to *immediately* solve the dictionary
1766 using those extra equalities. With the same inert set and work item we
1767 might dischard d2 directly:
1770 d2 := d1 |> D Int cv
1772 But in general it's a bit painful to figure out the necessary coercion,
1773 so we just take the first approach. Here is a better example. Consider:
1774 class C a b c | a -> b
1776 [Given] d1 : C T Int Char
1777 [Wanted] d2 : C T beta Int
1778 In this case, it's *not even possible* to solve the wanted immediately.
1779 So we should simply output the functional dependency and add this guy
1780 [but NOT its superclasses] back in the worklist. Even worse:
1781 [Given] d1 : C T Int beta
1782 [Wanted] d2: C T beta Int
1783 Then it is solvable, but its very hard to detect this on the spot.
1785 It's exactly the same with implicit parameters, except that the
1786 "aggressive" approach would be much easier to implement.
1788 Note [When improvement happens]
1789 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1790 We fire an improvement rule when
1792 * Two constraints match (modulo the fundep)
1793 e.g. C t1 t2, C t1 t3 where C a b | a->b
1794 The two match because the first arg is identical
1796 * At least one is not Given. If they are both given, we don't fire
1797 the reaction because we have no way of constructing evidence for a
1798 new equality nor does it seem right to create a new wanted goal
1799 (because the goal will most likely contain untouchables, which
1800 can't be solved anyway)!
1802 Note that we *do* fire the improvement if one is Given and one is Derived.
1803 The latter can be a superclass of a wanted goal. Example (tcfail138)
1804 class L a b | a -> b
1805 class (G a, L a b) => C a b
1807 instance C a b' => G (Maybe a)
1808 instance C a b => C (Maybe a) a
1809 instance L (Maybe a) a
1811 When solving the superclasses of the (C (Maybe a) a) instance, we get
1812 Given: C a b ... and hance by superclasses, (G a, L a b)
1814 Use the instance decl to get
1816 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
1817 and now we need improvement between that derived superclass an the Given (L a b)
1819 Note [Overriding implicit parameters]
1820 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1822 f :: (?x::a) -> Bool -> a
1824 g v = let ?x::Int = 3
1825 in (f v, let ?x::Bool = True in f v)
1827 This should probably be well typed, with
1828 g :: Bool -> (Int, Bool)
1830 So the inner binding for ?x::Bool *overrides* the outer one.
1831 Hence a work-item Given overrides an inert-item Given.
1833 Note [Given constraint that matches an instance declaration]
1834 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1835 What should we do when we discover that one (or more) top-level
1836 instances match a given (or solved) class constraint? We have
1839 1. Reject the program. The reason is that there may not be a unique
1840 best strategy for the solver. Example, from the OutsideIn(X) paper:
1841 instance P x => Q [x]
1842 instance (x ~ y) => R [x] y
1844 wob :: forall a b. (Q [b], R b a) => a -> Int
1846 g :: forall a. Q [a] => [a] -> Int
1849 will generate the impliation constraint:
1850 Q [a] => (Q [beta], R beta [a])
1851 If we react (Q [beta]) with its top-level axiom, we end up with a
1852 (P beta), which we have no way of discharging. On the other hand,
1853 if we react R beta [a] with the top-level we get (beta ~ a), which
1854 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
1855 now solvable by the given Q [a].
1857 However, this option is restrictive, for instance [Example 3] from
1858 Note [Recursive dictionaries] will fail to work.
1860 2. Ignore the problem, hoping that the situations where there exist indeed
1861 such multiple strategies are rare: Indeed the cause of the previous
1862 problem is that (R [x] y) yields the new work (x ~ y) which can be
1863 *spontaneously* solved, not using the givens.
1865 We are choosing option 2 below but we might consider having a flag as well.
1868 Note [New Wanted Superclass Work]
1869 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1870 Even in the case of wanted constraints, we add all of its superclasses as
1871 new given work. There are several reasons for this:
1872 a) to minimise error messages;
1873 eg suppose we have wanted (Eq a, Ord a)
1874 then we report only (Ord a) unsoluble
1876 b) to make the smallest number of constraints when *inferring* a type
1877 (same Eq/Ord example)
1879 c) for recursive dictionaries we *must* add the superclasses
1880 so that we can use them when solving a sub-problem
1882 d) To allow FD-like improvement for type families. Assume that
1884 class C a b | a -> b
1885 and we have to solve the implication constraint:
1887 Then, FD improvement can help us to produce a new wanted (beta ~ b)
1889 We want to have the same effect with the type family encoding of
1890 functional dependencies. Namely, consider:
1891 class (F a ~ b) => C a b
1892 Now suppose that we have:
1895 By interacting the given we will get given (F a ~ b) which is not
1896 enough by itself to make us discharge (C a beta). However, we
1897 may create a new derived equality from the super-class of the
1898 wanted constraint (C a beta), namely derived (F a ~ beta).
1899 Now we may interact this with given (F a ~ b) to get:
1901 But 'beta' is a touchable unification variable, and hence OK to
1902 unify it with 'b', replacing the derived evidence with the identity.
1904 This requires trySpontaneousSolve to solve *derived*
1905 equalities that have a touchable in their RHS, *in addition*
1906 to solving wanted equalities.
1908 Here is another example where this is useful.
1912 class (F a ~ b) => C a b
1913 And we are given the wanteds:
1917 We surely do *not* want to quantify over (b ~ c), since if someone provides
1918 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
1919 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
1921 Step 1: We will get new *given* superclass work,
1922 provisionally to our solving of w1 and w2
1924 g1: F a ~ b, g2 : F a ~ c,
1925 w1 : C a b, w2 : C a c, w3 : b ~ c
1927 The evidence for g1 and g2 is a superclass evidence term:
1929 g1 := sc w1, g2 := sc w2
1931 Step 2: The givens will solve the wanted w3, so that
1932 w3 := sym (sc w1) ; sc w2
1934 Step 3: Now, one may naively assume that then w2 can be solve from w1
1935 after rewriting with the (now solved equality) (b ~ c).
1937 But this rewriting is ruled out by the isGoodRectDict!
1939 Conclusion, we will (correctly) end up with the unsolved goals
1942 NB: The desugarer needs be more clever to deal with equalities
1943 that participate in recursive dictionary bindings.
1947 newGivenSCWork :: EvVar -> GivenLoc -> Class -> [Xi] -> TcS WorkList
1948 newGivenSCWork ev loc cls xis
1949 | NoScSkol <- ctLocOrigin loc -- Very important!
1950 = return emptyWorkList
1952 = newImmSCWorkFromFlavored ev (Given loc) cls xis >>= return
1954 newDerivedSCWork :: EvVar -> WantedLoc -> Class -> [Xi] -> TcS WorkList
1955 newDerivedSCWork ev loc cls xis
1956 = do { ims <- newImmSCWorkFromFlavored ev flavor cls xis
1959 rec_sc_work :: CanonicalCts -> TcS CanonicalCts
1961 = do { bg <- mapBagM (\c -> do { ims <- imm_sc_work c
1962 ; recs_ims <- rec_sc_work ims
1963 ; return $ consBag c recs_ims }) cts
1964 ; return $ concatBag bg }
1965 imm_sc_work (CDictCan { cc_id = dv, cc_flavor = fl, cc_class = cls, cc_tyargs = xis })
1966 = newImmSCWorkFromFlavored dv fl cls xis
1967 imm_sc_work _ct = return emptyCCan
1969 flavor = Derived loc DerSC
1971 newImmSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS WorkList
1972 -- Returns immediate superclasses
1973 newImmSCWorkFromFlavored ev flavor cls xis
1974 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
1975 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
1976 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
1977 ; mkCanonicals flavor sc_vars }
1979 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
1982 data LookupInstResult
1984 | GenInst [WantedEvVar] EvTerm
1986 matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
1987 matchClassInst clas tys loc
1988 = do { let pred = mkClassPred clas tys
1989 ; mb_result <- matchClass clas tys
1991 MatchInstNo -> return NoInstance
1992 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
1993 -- we learn more about the reagent
1994 MatchInstSingle (dfun_id, mb_inst_tys) ->
1995 do { checkWellStagedDFun pred dfun_id loc
1997 -- It's possible that not all the tyvars are in
1998 -- the substitution, tenv. For example:
1999 -- instance C X a => D X where ...
2000 -- (presumably there's a functional dependency in class C)
2001 -- Hence mb_inst_tys :: Either TyVar TcType
2003 ; tys <- instDFunTypes mb_inst_tys
2004 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
2005 ; if null theta then
2006 return (GenInst [] (EvDFunApp dfun_id tys []))
2008 { ev_vars <- instDFunConstraints theta
2009 ; let wevs = [WantedEvVar w loc | w <- ev_vars]
2010 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }