3 solveInteract, AtomicInert,
4 InertSet, emptyInert, updInertSet, extractUnsolved, solveOne
7 #include "HsVersions.h"
30 import Control.Monad ( when )
39 import qualified Data.Map as Map
42 import Control.Monad( zipWithM, unless )
43 import FastString ( sLit )
47 Note [InertSet invariants]
48 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
50 An InertSet is a bag of canonical constraints, with the following invariants:
52 1 No two constraints react with each other.
54 A tricky case is when there exists a given (solved) dictionary
55 constraint and a wanted identical constraint in the inert set, but do
56 not react because reaction would create loopy dictionary evidence for
57 the wanted. See note [Recursive dictionaries]
59 2 Given equalities form an idempotent substitution [none of the
60 given LHS's occur in any of the given RHS's or reactant parts]
62 3 Wanted equalities also form an idempotent substitution
63 4 The entire set of equalities is acyclic.
65 5 Wanted dictionaries are inert with the top-level axiom set
67 6 Equalities of the form tv1 ~ tv2 always have a touchable variable
68 on the left (if possible).
69 7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints
70 will be marked as solved right before being pushed into the inert set.
71 See note [Touchables and givens].
73 Note that 6 and 7 are /not/ enforced by canonicalization but rather by
74 insertion in the inert list, ie by TcInteract.
76 During the process of solving, the inert set will contain some
77 previously given constraints, some wanted constraints, and some given
78 constraints which have arisen from solving wanted constraints. For
79 now we do not distinguish between given and solved constraints.
81 Note that we must switch wanted inert items to given when going under an
82 implication constraint (when in top-level inference mode).
84 Note [InertSet FlattenSkolemEqClass]
85 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
86 The inert_fsks field of the inert set contains an "inverse map" of all the
87 flatten skolem equalities in the inert set. For instance, if inert_cts looks
94 Then, the inert_fsks fields holds the following map:
95 fsk2 |-> { fsk1, fsk3 }
97 Along with the necessary coercions to convert fsk1 and fsk3 back to fsk2
98 and fsk4 back to fsk5. Hence, the invariants of the inert_fsks field are:
100 (a) All TcTyVars in the domain and range of inert_fsks are flatten skolems
101 (b) All TcTyVars in the domain of inert_fsk occur naked as rhs in some
102 equalities of inert_cts
103 (c) For every mapping fsk1 |-> { (fsk2,co), ... } it must be:
106 The role of the inert_fsks is to make it easy to maintain the equivalence
107 class of each flatten skolem, which is much needed to correctly do spontaneous
108 solving. See Note [Loopy Spontaneous Solving]
111 -- See Note [InertSet invariants]
113 = IS { inert_eqs :: Bag.Bag CanonicalCt -- Equalities only (CTyEqCan,CFunEqCan)
114 , inert_cts :: Bag.Bag CanonicalCt -- Other constraints
115 , inert_fds :: FDImprovements -- List of pairwise improvements that have kicked in already
116 -- and reside either in the worklist or in the inerts
117 , inert_fsks :: Map.Map TcTyVar [(TcTyVar,Coercion)] }
118 -- See Note [InertSet FlattenSkolemEqClass]
120 type FDImprovement = (PredType,PredType)
121 type FDImprovements = [(PredType,PredType)]
123 instance Outputable InertSet where
124 ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_eqs is))
125 , vcat (map ppr (Bag.bagToList $ inert_cts is))
126 , vcat (map (\(v,rest) -> ppr v <+> text "|->" <+> hsep (map (ppr.fst) rest))
127 (Map.toList $ inert_fsks is)
131 emptyInert :: InertSet
132 emptyInert = IS { inert_eqs = Bag.emptyBag
133 , inert_cts = Bag.emptyBag, inert_fsks = Map.empty, inert_fds = [] }
135 updInertSet :: InertSet -> AtomicInert -> InertSet
136 -- Introduces an element in the inert set for the first time
137 updInertSet (IS { inert_eqs = eqs, inert_cts = cts, inert_fsks = fsks, inert_fds = fdis })
138 item@(CTyEqCan { cc_id = cv
141 | Just tv2 <- tcGetTyVar_maybe xi,
142 FlatSkol {} <- tcTyVarDetails tv1,
143 FlatSkol {} <- tcTyVarDetails tv2
144 = let eqs' = eqs `Bag.snocBag` item
145 fsks' = Map.insertWith (++) tv2 [(tv1, mkCoVarCoercion cv)] fsks
146 -- See Note [InertSet FlattenSkolemEqClass]
147 in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks', inert_fds = fdis }
148 updInertSet (IS { inert_eqs = eqs, inert_cts = cts
149 , inert_fsks = fsks, inert_fds = fdis }) item
151 = let eqs' = eqs `Bag.snocBag` item
152 in IS { inert_eqs = eqs', inert_cts = cts, inert_fsks = fsks, inert_fds = fdis }
154 = let cts' = cts `Bag.snocBag` item
155 in IS { inert_eqs = eqs, inert_cts = cts', inert_fsks = fsks, inert_fds = fdis }
157 updInertSetFDImprs :: InertSet -> Maybe FDImprovement -> InertSet
158 updInertSetFDImprs is (Just fdi) = is { inert_fds = fdi : inert_fds is }
159 updInertSetFDImprs is Nothing = is
161 foldlInertSetM :: (Monad m) => (a -> AtomicInert -> m a) -> a -> InertSet -> m a
162 -- Prioritize over the equalities see Note [Prioritizing Equalities]
163 foldlInertSetM k z (IS { inert_eqs = eqs, inert_cts = cts })
164 = do { z' <- Bag.foldlBagM k z eqs
165 ; Bag.foldlBagM k z' cts }
167 extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
168 extractUnsolved is@(IS {inert_eqs = eqs, inert_cts = cts, inert_fds = fdis })
169 = let is_init = is { inert_eqs = emptyCCan
170 , inert_cts = solved_cts, inert_fsks = Map.empty, inert_fds = fdis }
171 is_final = Bag.foldlBag updInertSet is_init solved_eqs -- Add equalities carefully
172 in (is_final, unsolved)
173 where (unsolved_cts, solved_cts) = Bag.partitionBag isWantedCt cts
174 (unsolved_eqs, solved_eqs) = Bag.partitionBag isWantedCt eqs
175 unsolved = unsolved_cts `unionBags` unsolved_eqs
178 getFskEqClass :: InertSet -> TcTyVar -> [(TcTyVar,Coercion)]
179 -- Precondition: tv is a FlatSkol. See Note [InertSet FlattenSkolemEqClass]
180 getFskEqClass (IS { inert_cts = cts, inert_fsks = fsks }) tv
181 = case lkpTyEqCanByLhs of
182 Nothing -> fromMaybe [] (Map.lookup tv fsks)
184 case tcGetTyVar_maybe (cc_rhs ceq) of
185 Just tv_rhs | FlatSkol {} <- tcTyVarDetails tv_rhs
186 -> let ceq_co = mkSymCoercion $ mkCoVarCoercion (cc_id ceq)
187 mk_co (v,c) = (v, mkTransCoercion c ceq_co)
188 in (tv_rhs, ceq_co): map mk_co (fromMaybe [] $ Map.lookup tv fsks)
190 where lkpTyEqCanByLhs = Bag.foldlBag lkp Nothing cts
191 lkp :: Maybe CanonicalCt -> CanonicalCt -> Maybe CanonicalCt
192 lkp Nothing ct@(CTyEqCan {cc_tyvar = tv'}) | tv' == tv = Just ct
193 lkp other _ct = other
195 haveBeenImproved :: FDImprovements -> PredType -> PredType -> Bool
196 haveBeenImproved [] _ _ = False
197 haveBeenImproved ((pty1,pty2):fdimprs) pty1' pty2'
198 | tcEqPred pty1 pty1' && tcEqPred pty2 pty2'
200 | tcEqPred pty1 pty2' && tcEqPred pty2 pty1'
203 = haveBeenImproved fdimprs pty1' pty2'
205 getFDImprovements :: InertSet -> FDImprovements
206 -- Return a list of the improvements that have kicked in so far
207 getFDImprovements = inert_fds
210 isWantedCt :: CanonicalCt -> Bool
211 isWantedCt ct = isWanted (cc_flavor ct)
214 data Inert = IS { class_inerts :: FiniteMap Class Atomics
215 ip_inerts :: FiniteMap Class Atomics
216 tyfun_inerts :: FiniteMap TyCon Atomics
217 tyvar_inerts :: FiniteMap TyVar Atomics
220 Later should we also separate out givens and wanteds?
225 Note [Touchables and givens]
226 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
227 Touchable variables will never show up in givens which are inputs to
228 the solver. However, touchables may show up in givens generated by the flattener.
243 which can be put in the inert set. Suppose we also have a wanted
247 We cannot rewrite the given G alpha ~g b using the wanted alpha ~w
248 Int. Instead, after reacting alpha ~w Int with the whole inert set,
249 we observe that we can solve it by unifying alpha with Int, so we mark
250 it as solved and put it back in the *work list*. [We also immediately unify
251 alpha := Int, without telling anyone, see trySpontaneousSolve function, to
252 avoid doing this in the end.]
254 Later, because it is solved (given, in effect), we can use it to rewrite
255 G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually,
256 we will dispatch the remaining wanted constraints using the top-level axioms.
258 Finally, note that after reacting a wanted equality with the entire inert set
259 we may end up with something like
263 which we should flip around to generate the solved constraint alpha ~s b.
265 %*********************************************************************
267 * Main Interaction Solver *
269 **********************************************************************
273 1. Canonicalise (unary)
274 2. Pairwise interaction (binary)
275 * Take one from work list
276 * Try all pair-wise interactions with each constraint in inert
277 3. Try to solve spontaneously for equalities involving touchables
278 4. Top-level interaction (binary wrt top-level)
279 Superclass decomposition belongs in (4), see note [Superclasses]
283 type AtomicInert = CanonicalCt -- constraint pulled from InertSet
284 type WorkItem = CanonicalCt -- constraint pulled from WorkList
286 -- A mixture of Given, Wanted, and Derived constraints.
287 -- We split between equalities and the rest to process equalities first.
288 data WorkList = WL { wl_eqs :: CanonicalCts -- Equalities (CTyEqCan, CFunEqCan)
289 , wl_other :: CanonicalCts -- Other
291 type SWorkList = WorkList -- A worklist of solved
293 unionWorkLists :: WorkList -> WorkList -> WorkList
294 unionWorkLists wl1 wl2
295 = WL { wl_eqs = andCCan (wl_eqs wl1) (wl_eqs wl2)
296 , wl_other = andCCan (wl_other wl1) (wl_other wl2) }
298 foldlWorkListM :: (Monad m) => (a -> WorkItem -> m a) -> a -> WorkList -> m a
299 -- This fold prioritizes equalities
300 foldlWorkListM f r wl
301 = do { r' <- Bag.foldlBagM f r (wl_eqs wl)
302 ; Bag.foldlBagM f r' (wl_other wl) }
304 isEmptyWorkList :: WorkList -> Bool
305 isEmptyWorkList wl = isEmptyCCan (wl_eqs wl) && isEmptyCCan (wl_other wl)
307 emptyWorkList :: WorkList
308 emptyWorkList = WL { wl_eqs = emptyCCan, wl_other = emptyCCan }
310 mkEqWorkList :: CanonicalCts -> WorkList
311 -- Precondition: *ALL* equalities
312 mkEqWorkList eqs = WL { wl_eqs = eqs, wl_other = emptyCCan }
314 mkNonEqWorkList :: CanonicalCts -> WorkList
315 -- Precondition: *NO* equalities
316 mkNonEqWorkList cts = WL { wl_eqs = emptyCCan, wl_other = cts }
318 workListFromCCans :: CanonicalCts -> WorkList
319 -- Generic, no precondition
320 workListFromCCans cts = WL eqs others
321 where (eqs, others) = Bag.partitionBag isEqCCan cts
324 singleEqWL :: CanonicalCt -> WorkList
325 singleNonEqWL :: CanonicalCt -> WorkList
326 singleEqWL = mkEqWorkList . singleCCan
327 singleNonEqWL = mkNonEqWorkList . singleCCan
331 = Stop -- Work item is consumed
332 | ContinueWith WorkItem -- Not consumed
334 instance Outputable StopOrContinue where
335 ppr Stop = ptext (sLit "Stop")
336 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
338 -- Results after interacting a WorkItem as far as possible with an InertSet
340 = SR { sr_inerts :: InertSet
341 -- The new InertSet to use (REPLACES the old InertSet)
342 , sr_new_work :: WorkList
343 -- Any new work items generated (should be ADDED to the old WorkList)
345 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
346 -- workitem is inert wrt to sr_inerts
347 , sr_stop :: StopOrContinue
350 instance Outputable StageResult where
351 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
352 = ptext (sLit "SR") <+>
353 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
354 , ptext (sLit "new work =") <+> ppr work <> comma
355 , ptext (sLit "stop =") <+> ppr stop])
357 instance Outputable WorkList where
358 ppr (WL eqcts othercts) = vcat [ppr eqcts, ppr othercts]
360 type SimplifierStage = WorkItem -> InertSet -> TcS StageResult
362 -- Combine a sequence of simplifier 'stages' to create a pipeline
363 runSolverPipeline :: [(String, SimplifierStage)]
364 -> InertSet -> WorkItem
365 -> TcS (InertSet, WorkList)
366 -- Precondition: non-empty list of stages
367 runSolverPipeline pipeline inerts workItem
368 = do { traceTcS "Start solver pipeline" $
369 vcat [ ptext (sLit "work item =") <+> ppr workItem
370 , ptext (sLit "inerts =") <+> ppr inerts]
372 ; let itr_in = SR { sr_inerts = inerts
373 , sr_new_work = emptyWorkList
374 , sr_stop = ContinueWith workItem }
375 ; itr_out <- run_pipeline pipeline itr_in
377 = case sr_stop itr_out of
378 Stop -> sr_inerts itr_out
379 ContinueWith item -> sr_inerts itr_out `updInertSet` item
380 ; return (new_inert, sr_new_work itr_out) }
382 run_pipeline :: [(String, SimplifierStage)]
383 -> StageResult -> TcS StageResult
384 run_pipeline [] itr = return itr
385 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
387 run_pipeline ((name,stage):stages)
388 (SR { sr_new_work = accum_work
390 , sr_stop = ContinueWith work_item })
391 = do { itr <- stage work_item inerts
392 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
393 ; let itr' = itr { sr_new_work = accum_work `unionWorkLists` sr_new_work itr }
394 ; run_pipeline stages itr' }
398 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
399 Reagent: a ~ [b] (given)
401 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
402 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
403 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
406 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
409 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
410 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
414 Inert: {a ~ Int, F Int ~ b} (given)
415 Reagent: F a ~ b (wanted)
417 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
418 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
421 -- Main interaction solver: we fully solve the worklist 'in one go',
422 -- returning an extended inert set.
424 -- See Note [Touchables and givens].
425 solveInteract :: InertSet -> CanonicalCts -> TcS InertSet
426 solveInteract inert ws
427 = do { dyn_flags <- getDynFlags
428 ; let worklist = workListFromCCans ws
429 ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert worklist
431 solveOne :: InertSet -> WorkItem -> TcS InertSet
432 solveOne inerts workItem
433 = do { dyn_flags <- getDynFlags
434 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
438 solveInteractWithDepth :: (Int, Int, [WorkItem])
439 -> InertSet -> WorkList -> TcS InertSet
440 solveInteractWithDepth ctxt@(max_depth,n,stack) inert ws
445 = solverDepthErrorTcS n stack
448 = do { traceTcS "solveInteractWithDepth" $
449 vcat [ text "Current depth =" <+> ppr n
450 , text "Max depth =" <+> ppr max_depth
452 ; foldlWorkListM (solveOneWithDepth ctxt) inert ws }
455 -- Fully interact the given work item with an inert set, and return a
456 -- new inert set which has assimilated the new information.
457 solveOneWithDepth :: (Int, Int, [WorkItem])
458 -> InertSet -> WorkItem -> TcS InertSet
459 solveOneWithDepth (max_depth, n, stack) inert work
460 = do { traceTcS0 (indent ++ "Solving {") (ppr work)
461 ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work
463 ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work)
465 -- Recursively solve the new work generated
466 -- from workItem, with a greater depth
467 ; res_inert <- solveInteractWithDepth (max_depth, n+1, work:stack)
470 ; traceTcS0 (indent ++ "Done }") (ppr work)
473 indent = replicate (2*n) ' '
475 thePipeline :: [(String,SimplifierStage)]
476 thePipeline = [ ("interact with inerts", interactWithInertsStage)
477 , ("spontaneous solve", spontaneousSolveStage)
478 , ("top-level reactions", topReactionsStage) ]
481 *********************************************************************************
483 The spontaneous-solve Stage
485 *********************************************************************************
488 spontaneousSolveStage :: SimplifierStage
489 spontaneousSolveStage workItem inerts
490 = do { mSolve <- trySpontaneousSolve workItem inerts
492 Nothing -> -- no spontaneous solution for him, keep going
493 return $ SR { sr_new_work = emptyWorkList
495 , sr_stop = ContinueWith workItem }
497 Just workList' -> -- He has been solved; workList' are all givens
498 return $ SR { sr_new_work = workList'
503 {-- This is all old code, but does not quite work now. The problem is that due to
504 Note [Loopy Spontaneous Solving] we may have unflattened a type, to be able to
505 perform a sneaky unification. This unflattening means that we may have to recanonicalize
506 a given (solved) equality, this is why the result of trySpontaneousSolve is now a list
507 of constraints (instead of an atomic solved constraint). We would have to react all of
508 them once again with the worklist but that is very tiresome. Instead we throw them back
511 | isWantedCt workItem
512 -- Original was wanted we have now made him given so
513 -- we have to ineract him with the inerts again because
514 -- of the change in his status. This may produce some work.
515 -> do { traceTcS "recursive interact with inerts {" $ vcat
516 [ text "work = " <+> ppr workItem'
517 , text "inerts = " <+> ppr inerts ]
518 ; itr_again <- interactWithInertsStage workItem' inerts
519 ; case sr_stop itr_again of
520 Stop -> pprPanic "BUG: Impossible to happen" $
521 vcat [ text "Original workitem:" <+> ppr workItem
522 , text "Spontaneously solved:" <+> ppr workItem'
523 , text "Solved was consumed, when reacting with inerts:"
524 , nest 2 (ppr inerts) ]
525 ContinueWith workItem'' -- Now *this* guy is inert wrt to inerts
526 -> do { traceTcS "end recursive interact }" $ ppr workItem''
527 ; return $ SR { sr_new_work = sr_new_work itr_again
528 , sr_inerts = sr_inerts itr_again
529 `extendInertSet` workItem''
533 -> return $ SR { sr_new_work = emptyWorkList
534 , sr_inerts = inerts `extendInertSet` workItem'
538 -- @trySpontaneousSolve wi@ solves equalities where one side is a
539 -- touchable unification variable. Returns:
540 -- * Nothing if we were not able to solve it
541 -- * Just wi' if we solved it, wi' (now a "given") should be put in the work list.
542 -- See Note [Touchables and givens]
543 -- NB: just passing the inerts through for the skolem equivalence classes
544 trySpontaneousSolve :: WorkItem -> InertSet -> TcS (Maybe SWorkList)
545 trySpontaneousSolve (CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi }) inerts
548 | Just tv2 <- tcGetTyVar_maybe xi
549 = do { tch1 <- isTouchableMetaTyVar tv1
550 ; tch2 <- isTouchableMetaTyVar tv2
551 ; case (tch1, tch2) of
552 (True, True) -> trySpontaneousEqTwoWay inerts cv gw tv1 tv2
553 (True, False) -> trySpontaneousEqOneWay inerts cv gw tv1 xi
554 (False, True) -> trySpontaneousEqOneWay inerts cv gw tv2 (mkTyVarTy tv1)
555 _ -> return Nothing }
557 = do { tch1 <- isTouchableMetaTyVar tv1
558 ; if tch1 then trySpontaneousEqOneWay inerts cv gw tv1 xi
559 else return Nothing }
562 -- trySpontaneousSolve (CFunEqCan ...) = ...
563 -- See Note [No touchables as FunEq RHS] in TcSMonad
564 trySpontaneousSolve _ _ = return Nothing
567 trySpontaneousEqOneWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> Xi
568 -> TcS (Maybe SWorkList)
569 -- tv is a MetaTyVar, not untouchable
570 trySpontaneousEqOneWay inerts cv gw tv xi
571 | not (isSigTyVar tv) || isTyVarTy xi,
572 typeKind xi `isSubKind` tyVarKind tv
573 = solveWithIdentity inerts cv gw tv xi
578 trySpontaneousEqTwoWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> TcTyVar
579 -> TcS (Maybe SWorkList)
580 -- Both tyvars are *touchable* MetaTyvars
581 -- By the CTyEqCan invariant, k2 `isSubKind` k1
582 trySpontaneousEqTwoWay inerts cv gw tv1 tv2
584 , nicer_to_update_tv2 = solveWithIdentity inerts cv gw tv2 (mkTyVarTy tv1)
586 = solveWithIdentity inerts cv gw tv1 (mkTyVarTy tv2)
587 | otherwise = return Nothing
591 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
595 Note [Spontaneous solving and kind compatibility]
596 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
598 Note that our canonical constraints insist that only *given* equalities (tv ~ xi)
599 or (F xis ~ rhs) require the LHS and the RHS to have exactly the same kinds.
601 - We have to require this because:
602 Given equalities can be freely used to rewrite inside
603 other types or constraints.
604 - We do not have to do the same for wanteds because:
605 First, wanted equations (tv ~ xi) where tv is a touchable unification variable
606 may have kinds that do not agree (the kind of xi must be a sub kind of the kind of tv).
607 Second, any potential kind mismatch will result in the constraint not being soluble,
608 which will be reported anyway. This is the reason that @trySpontaneousOneWay@ and
609 @trySpontaneousTwoWay@ will perform a kind compatibility check, and only then will
610 they proceed to @solveWithIdentity@.
613 - Givens from higher-rank, such as:
614 type family T b :: * -> * -> *
615 type instance T Bool = (->)
617 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
619 Whereas we would be able to apply the type instance, we would not be able to
620 use the given (T Bool ~ (->)) in the body of 'flop'
622 Note [Loopy spontaneous solving]
623 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
624 Consider the original wanted:
625 wanted : Maybe (E alpha) ~ alpha
626 where E is a type family, such that E (T x) = x. After canonicalization,
627 as a result of flattening, we will get:
628 given : E alpha ~ fsk
629 wanted : alpha ~ Maybe fsk
630 where (fsk := E alpha, on the side). Now, if we spontaneously *solve*
631 (alpha := Maybe fsk) we are in trouble! Instead, we should refrain from solving
632 it and keep it as wanted. In inference mode we'll end up quantifying over
633 (alpha ~ Maybe (E alpha))
634 Hence, 'solveWithIdentity' performs a small occurs check before
635 actually solving. But this occurs check *must look through* flatten skolems.
637 However, it may be the case that the flatten skolem in hand is equal to some other
638 flatten skolem whith *does not* mention our unification variable. Here's a typical example:
643 After canonicalization:
648 After some reactions:
653 At this point, we will try to spontaneously solve (alpha ~ f2) which remains as yet unsolved.
654 We will look inside f2, which immediately mentions (F alpha), so it's not good to unify! However
655 by looking at the equivalence class of the flatten skolems, we can see that it is fine to
656 unify (alpha ~ f1) which solves our goals!
658 A similar problem happens because of other spontaneous solving. Suppose we have the
659 following wanteds, arriving in this exact order:
660 (first) w: beta ~ alpha
661 (second) w: alpha ~ fsk
662 (third) g: F beta ~ fsk
663 Then, we first spontaneously solve the first constraint, making (beta := alpha), and having
664 (beta ~ alpha) as given. *Then* we encounter the second wanted (alpha ~ fsk). "fsk" does not
665 obviously mention alpha, so naively we can also spontaneously solve (alpha := fsk). But
666 that is wrong since fsk mentions beta, which has already secretly been unified to alpha!
668 To avoid this problem, the same occurs check must unveil rewritings that can happen because
669 of spontaneously having solved other constraints.
672 Note [Avoid double unifications]
673 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
674 The spontaneous solver has to return a given which mentions the unified unification
675 variable *on the left* of the equality. Here is what happens if not:
676 Original wanted: (a ~ alpha), (alpha ~ Int)
677 We spontaneously solve the first wanted, without changing the order!
678 given : a ~ alpha [having unified alpha := a]
679 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
680 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
682 We avoid this problem by orienting the given so that the unification
683 variable is on the left. [Note that alternatively we could attempt to
684 enforce this at canonicalization]
686 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
687 double unifications is the main reason we disallow touchable
688 unification variables as RHS of type family equations: F xis ~ alpha.
692 solveWithIdentity :: InertSet
693 -> CoVar -> CtFlavor -> TcTyVar -> Xi
694 -> TcS (Maybe SWorkList)
695 -- Solve with the identity coercion
696 -- Precondition: kind(xi) is a sub-kind of kind(tv)
697 -- Precondition: CtFlavor is Wanted or Derived
698 -- See [New Wanted Superclass Work] to see why solveWithIdentity
699 -- must work for Derived as well as Wanted
700 solveWithIdentity inerts cv gw tv xi
701 = do { tybnds <- getTcSTyBindsMap
702 ; case occurCheck tybnds inerts tv xi of
703 Nothing -> return Nothing
704 Just (xi_unflat,coi) -> solve_with xi_unflat coi }
706 solve_with xi_unflat coi -- coi : xi_unflat ~ xi
707 = do { traceTcS "Sneaky unification:" $
708 vcat [text "Coercion variable: " <+> ppr gw,
709 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
710 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
711 text "Right Kind is : " <+> ppr (typeKind xi)
713 ; setWantedTyBind tv xi_unflat -- Set tv := xi_unflat
714 ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi_unflat xi_unflat
715 ; let flav = mkGivenFlavor gw UnkSkol
716 ; (cts, co) <- case coi of
717 ACo co -> do { can_eqs <- canEq flav cv_given (mkTyVarTy tv) xi_unflat
718 ; return (can_eqs, co) }
720 (singleCCan (CTyEqCan { cc_id = cv_given
721 , cc_flavor = mkGivenFlavor gw UnkSkol
722 , cc_tyvar = tv, cc_rhs = xi }
723 -- xi, *not* xi_unflat because
724 -- xi_unflat may require flattening!
727 Wanted {} -> setWantedCoBind cv co
728 Derived {} -> setDerivedCoBind cv co
729 _ -> pprPanic "Can't spontaneously solve *given*" empty
730 -- See Note [Avoid double unifications]
731 ; return $ Just (mkEqWorkList cts) }
733 occurCheck :: VarEnv (TcTyVar, TcType) -> InertSet
734 -> TcTyVar -> TcType -> Maybe (TcType,CoercionI)
735 -- Traverse @ty@ to make sure that @tv@ does not appear under some flatten skolem.
736 -- If it appears under some flatten skolem look in that flatten skolem equivalence class
737 -- (see Note [InertSet FlattenSkolemEqClass], [Loopy Spontaneous Solving]) to see if you
738 -- can find a different flatten skolem to use, that is, one that does not mention @tv@.
740 -- Postcondition: Just (ty', coi) = occurCheck binds inerts tv ty
742 -- NB: The returned type ty' may not be flat!
744 occurCheck ty_binds inerts the_tv the_ty
745 = ok emptyVarSet the_ty
747 -- If (fsk `elem` bad) then tv occurs in any rendering
748 -- of the type under the expansion of fsk
749 ok bad this_ty@(TyConApp tc tys)
750 | Just tys_cois <- allMaybes (map (ok bad) tys)
751 , (tys',cois') <- unzip tys_cois
752 = Just (TyConApp tc tys', mkTyConAppCoI tc cois')
753 | isSynTyCon tc, Just ty_expanded <- tcView this_ty
754 = ok bad ty_expanded -- See Note [Type synonyms and the occur check] in TcUnify
756 | Just (sty',coi) <- ok_pred bad sty
757 = Just (PredTy sty', coi)
758 ok bad (FunTy arg res)
759 | Just (arg', coiarg) <- ok bad arg, Just (res', coires) <- ok bad res
760 = Just (FunTy arg' res', mkFunTyCoI coiarg coires)
761 ok bad (AppTy fun arg)
762 | Just (fun', coifun) <- ok bad fun, Just (arg', coiarg) <- ok bad arg
763 = Just (AppTy fun' arg', mkAppTyCoI coifun coiarg)
764 ok bad (ForAllTy tv1 ty1)
765 -- WARNING: What if it is a (t1 ~ t2) => t3? It's not handled properly at the moment.
766 | Just (ty1', coi) <- ok bad ty1
767 = Just (ForAllTy tv1 ty1', mkForAllTyCoI tv1 coi)
770 ok bad this_ty@(TyVarTy tv)
771 | tv == the_tv = Nothing -- Occurs check error
772 | not (isTcTyVar tv) = Just (this_ty, IdCo this_ty) -- Bound var
773 | FlatSkol zty <- tcTyVarDetails tv = ok_fsk bad tv zty
774 | Just (_,ty) <- lookupVarEnv ty_binds tv = ok bad ty
775 | otherwise = Just (this_ty, IdCo this_ty)
777 -- Check if there exists a ty bind already, as a result of sneaky unification.
779 ok _bad _ty = Nothing
782 ok_pred bad (ClassP cn tys)
783 | Just tys_cois <- allMaybes $ map (ok bad) tys
784 = let (tys', cois') = unzip tys_cois
785 in Just (ClassP cn tys', mkClassPPredCoI cn cois')
786 ok_pred bad (IParam nm ty)
787 | Just (ty',co') <- ok bad ty
788 = Just (IParam nm ty', mkIParamPredCoI nm co')
789 ok_pred bad (EqPred ty1 ty2)
790 | Just (ty1',coi1) <- ok bad ty1, Just (ty2',coi2) <- ok bad ty2
791 = Just (EqPred ty1' ty2', mkEqPredCoI coi1 coi2)
792 ok_pred _ _ = Nothing
796 | fsk `elemVarSet` bad
797 -- We are already trying to find a rendering of fsk,
798 -- and to do that it seems we need a rendering, so fail
801 = firstJusts (ok new_bad zty : map (go_under_fsk new_bad) fsk_equivs)
803 fsk_equivs = getFskEqClass inerts fsk
804 new_bad = bad `extendVarSetList` (fsk : map fst fsk_equivs)
807 go_under_fsk bad_tvs (fsk,co)
808 | FlatSkol zty <- tcTyVarDetails fsk
809 = case ok bad_tvs zty of
811 Just (ty,coi') -> Just (ty, mkTransCoI coi' (ACo co))
812 | otherwise = pprPanic "go_down_equiv" (ppr fsk)
816 *********************************************************************************
818 The interact-with-inert Stage
820 *********************************************************************************
823 -- Interaction result of WorkItem <~> AtomicInert
825 = IR { ir_stop :: StopOrContinue
827 -- => Reagent (work item) consumed.
828 -- ContinueWith new_reagent
829 -- => Reagent transformed but keep gathering interactions.
830 -- The transformed item remains inert with respect
831 -- to any previously encountered inerts.
833 , ir_inert_action :: InertAction
834 -- Whether the inert item should remain in the InertSet.
836 , ir_new_work :: WorkList
837 -- new work items to add to the WorkList
839 , ir_improvement :: Maybe FDImprovement -- In case improvement kicked in
842 -- What to do with the inert reactant.
843 data InertAction = KeepInert | DropInert
846 mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
847 mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork Nothing
849 mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
850 mkIRStop keep newWork = return $ IR Stop keep newWork Nothing
852 mkIRStop_RecordImprovement :: Monad m => InertAction -> WorkList -> FDImprovement -> m InteractResult
853 mkIRStop_RecordImprovement keep newWork fdimpr = return $ IR Stop keep newWork (Just fdimpr)
856 dischargeWorkItem :: Monad m => m InteractResult
857 dischargeWorkItem = mkIRStop KeepInert emptyWorkList
859 noInteraction :: Monad m => WorkItem -> m InteractResult
860 noInteraction workItem = mkIRContinue workItem KeepInert emptyWorkList
862 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
864 ---------------------------------------------------
865 -- Interact a single WorkItem with an InertSet as far as possible, i.e. until we get a Stop
866 -- result from an individual interaction (i.e. when the WorkItem is consumed), or until we've
867 -- interacted the WorkItem with the entire InertSet.
869 -- Postcondition: the new InertSet in the resulting StageResult is subset
870 -- of the input InertSet.
872 interactWithInertsStage :: SimplifierStage
873 interactWithInertsStage workItem inert
874 = foldlInertSetM interactNext initITR inert
876 initITR = SR { sr_inerts = emptyInert { inert_fds = inert_fds inert } -- Pick up the improvements!
877 , sr_new_work = emptyWorkList
878 , sr_stop = ContinueWith workItem }
881 interactNext :: StageResult -> AtomicInert -> TcS StageResult
882 interactNext it inert
883 | ContinueWith workItem <- sr_stop it
884 = do { let inerts = sr_inerts it
885 fdimprs_old = getFDImprovements inerts
887 ; ir <- interactWithInert fdimprs_old inert workItem
889 -- New inerts depend on whether we KeepInert or not and must
890 -- be updated with FD improvement information from the interaction result (ir)
891 ; let inerts_new = updInertSetFDImprs upd_inert (ir_improvement ir)
892 upd_inert = if ir_inert_action ir == KeepInert
893 then inerts `updInertSet` inert else inerts
895 ; return $ SR { sr_inerts = inerts_new
896 , sr_new_work = sr_new_work it `unionWorkLists` ir_new_work ir
897 , sr_stop = ir_stop ir } }
898 | otherwise = return $ itrAddInert inert it
901 itrAddInert :: AtomicInert -> StageResult -> StageResult
902 itrAddInert inert itr = itr { sr_inerts = (sr_inerts itr) `updInertSet` inert }
904 -- Do a single interaction of two constraints.
905 interactWithInert :: FDImprovements -> AtomicInert -> WorkItem -> TcS InteractResult
906 interactWithInert fdimprs inert workitem
907 = do { ctxt <- getTcSContext
908 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workitem
909 inert_ev = cc_id inert
910 work_ev = cc_id workitem
912 -- Never interact a wanted and a derived where the derived's evidence
913 -- mentions the wanted evidence in an unguarded way.
914 -- See Note [Superclasses and recursive dictionaries]
915 -- and Note [New Wanted Superclass Work]
916 -- We don't have to do this for givens, as we fully know the evidence for them.
918 case (cc_flavor inert, cc_flavor workitem) of
919 (Wanted loc, Derived _) -> isGoodRecEv work_ev (WantedEvVar inert_ev loc)
920 (Derived _, Wanted loc) -> isGoodRecEv inert_ev (WantedEvVar work_ev loc)
923 ; if is_allowed && rec_ev_ok then
924 doInteractWithInert fdimprs 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 :: FDImprovements -> CanonicalCt -> CanonicalCt -> TcS InteractResult
937 -- Identical class constraints.
939 doInteractWithInert fdimprs
940 (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 (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 work_item_pred_loc = (pty2, ppr d2)
950 inert_pred_loc = (pty1, ppr d1)
951 loc = combineCtLoc fl1 fl2
952 eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc
954 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
955 ; fd_cts <- canWanteds wevvars
956 ; let fd_work = mkEqWorkList fd_cts
957 -- See Note [Generating extra equalities]
958 ; traceTcS "Checking if improvements existed." (ppr fdimprs)
959 -- ; if isEmptyCCan fd_cts || not (isWanted fl2) || haveBeenImproved fdimprs pty1 pty2 then
960 ; if isEmptyCCan fd_cts || haveBeenImproved fdimprs pty1 pty2 then
962 mkIRContinue workItem KeepInert fd_work
963 else do { traceTcS "Recording improvement and throwing item back in worklist." (ppr (pty1,pty2))
964 ; mkIRStop_RecordImprovement KeepInert
965 (fd_work `unionWorkLists` singleNonEqWL workItem) (pty1,pty2)
967 -- See Note [FunDep Reactions]
970 -- Class constraint and given equality: use the equality to rewrite
971 -- the class constraint.
972 doInteractWithInert _fdimprs
973 (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
974 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
975 | ifl `canRewrite` wfl
976 , tv `elemVarSet` tyVarsOfTypes xis
977 -- substitute for tv in xis. Note that the resulting class
978 -- constraint is still canonical, since substituting xi-types in
979 -- xi-types generates xi-types. However, it may no longer be
980 -- inert with respect to the inert set items we've already seen.
981 -- For example, consider the inert set
986 -- and the work item D a (w). D a does not interact with D Int.
987 -- Next, it does interact with a ~g Int, getting rewritten to D
988 -- Int (w). But now we must go back through the rest of the inert
989 -- set again, to find that it can now be discharged by the given D
992 -- DV: Update to the comment above:
993 -- This situation can no longer happen, see Note [Prioritizing equalities]
994 -- so we are good to simply keep going with the rewritten dictionary to rewrite
995 -- it as much as possible before reaching any other dictionary constraints!
996 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
997 ; mkIRContinue rewritten_dict KeepInert emptyWorkList }
998 -- ; mkIRStop KeepInert $ singleNonEqWL rewritten_dict }
1000 doInteractWithInert _fdimprs
1001 (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
1002 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1003 | wfl `canRewrite` ifl
1004 , tv `elemVarSet` tyVarsOfTypes xis
1005 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
1006 ; mkIRContinue workItem DropInert (singleNonEqWL rewritten_dict) }
1008 -- Class constraint and given equality: use the equality to rewrite
1009 -- the class constraint.
1010 doInteractWithInert _fdimprs
1011 (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
1012 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
1013 | ifl `canRewrite` wfl
1014 , tv `elemVarSet` tyVarsOfType ty
1015 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
1016 ; mkIRContinue rewritten_ip KeepInert emptyWorkList }
1017 -- ; mkIRStop KeepInert (singleNonEqWL rewritten_ip) }
1019 doInteractWithInert _fdimprs
1020 (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
1021 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
1022 | wfl `canRewrite` ifl
1023 , tv `elemVarSet` tyVarsOfType ty
1024 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
1025 ; mkIRContinue workItem DropInert (singleNonEqWL rewritten_ip) }
1027 -- Two implicit parameter constraints. If the names are the same,
1028 -- but their types are not, we generate a wanted type equality
1029 -- that equates the type (this is "improvement").
1030 -- However, we don't actually need the coercion evidence,
1031 -- so we just generate a fresh coercion variable that isn't used anywhere.
1032 doInteractWithInert _fdimprs
1033 (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
1034 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
1035 | nm1 == nm2 && isGiven wfl && isGiven ifl
1036 = -- See Note [Overriding implicit parameters]
1037 -- Dump the inert item, override totally with the new one
1038 -- Do not require type equality
1039 mkIRContinue workItem DropInert emptyWorkList
1041 | nm1 == nm2 && ty1 `tcEqType` ty2
1042 = solveOneFromTheOther (id1,ifl) workItem
1045 = -- See Note [When improvement happens]
1046 do { co_var <- newWantedCoVar ty1 ty2
1047 ; let flav = Wanted (combineCtLoc ifl wfl)
1048 ; cans <- mkCanonical flav co_var
1049 ; mkIRContinue workItem KeepInert (mkEqWorkList cans) }
1052 -- Inert: equality, work item: function equality
1054 -- Never rewrite a given with a wanted equality, and a type function
1055 -- equality can never rewrite an equality. Note also that if we have
1056 -- F x1 ~ x2 and a ~ x3, and a occurs in x2, we don't rewrite it. We
1057 -- can wait until F x1 ~ x2 matches another F x1 ~ x4, and only then
1058 -- we will ``expose'' x2 and x4 to rewriting.
1060 -- Otherwise, we can try rewriting the type function equality with the equality.
1061 doInteractWithInert _fdimprs
1062 (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
1063 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
1064 , cc_tyargs = args, cc_rhs = xi2 })
1065 | ifl `canRewrite` wfl
1066 , tv `elemVarSet` tyVarsOfTypes args
1067 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
1068 ; mkIRStop KeepInert (singleEqWL rewritten_funeq) } -- DV: must stop here, because we may no longer be inert after the rewritting.
1070 -- Inert: function equality, work item: equality
1072 doInteractWithInert _fdimprs
1073 (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
1074 , cc_tyargs = args, cc_rhs = xi1 })
1075 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
1076 | wfl `canRewrite` ifl
1077 , tv `elemVarSet` tyVarsOfTypes args
1078 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
1079 ; mkIRContinue workItem DropInert (singleEqWL rewritten_funeq) }
1081 doInteractWithInert _fdimprs
1082 (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
1083 , cc_tyargs = args1, cc_rhs = xi1 })
1084 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
1085 , cc_tyargs = args2, cc_rhs = xi2 })
1086 | fl1 `canSolve` fl2 && lhss_match
1087 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1088 ; mkIRStop KeepInert (mkEqWorkList cans) }
1089 | fl2 `canSolve` fl1 && lhss_match
1090 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1091 ; mkIRContinue workItem DropInert (mkEqWorkList cans) }
1093 lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
1095 doInteractWithInert _fdimprs
1096 inert@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
1097 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
1098 -- Check for matching LHS
1099 | fl1 `canSolve` fl2 && tv1 == tv2
1100 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1101 ; mkIRStop KeepInert (mkEqWorkList cans) }
1103 | fl2 `canSolve` fl1 && tv1 == tv2
1104 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1105 ; mkIRContinue workItem DropInert (mkEqWorkList cans) }
1107 -- Check for rewriting RHS
1108 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1109 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1110 ; mkIRStop KeepInert (mkEqWorkList rewritten_eq) }
1111 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1112 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1113 ; mkIRContinue workItem DropInert (mkEqWorkList rewritten_eq) }
1115 -- Finally, if workitem is a Flatten Equivalence Class constraint and the
1116 -- inert is a wanted constraint, even when the workitem cannot rewrite the
1117 -- inert, drop the inert out because you may have to reconsider solving the
1118 -- inert *using* the equivalence class you created. See note [Loopy Spontaneous Solving]
1119 -- and [InertSet FlattenSkolemEqClass]
1121 | not $ isGiven fl1, -- The inert is wanted or derived
1122 isMetaTyVar tv1, -- and has a unification variable lhs
1123 FlatSkol {} <- tcTyVarDetails tv2, -- And workitem is a flatten skolem equality
1124 Just tv2' <- tcGetTyVar_maybe xi2, FlatSkol {} <- tcTyVarDetails tv2'
1125 = mkIRContinue workItem DropInert (singleEqWL inert)
1128 -- Fall-through case for all other situations
1129 doInteractWithInert _fdimprs _ workItem = noInteraction workItem
1131 -------------------------
1132 -- Equational Rewriting
1133 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1134 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1135 = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
1136 args = substTysWith [tv] [xi] xis
1138 dict_co = mkTyConCoercion con cos
1139 ; dv' <- newDictVar cl args
1141 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
1142 _given_or_derived -> setDictBind dv' (EvCast dv dict_co)
1143 ; return (CDictCan { cc_id = dv'
1146 , cc_tyargs = args }) }
1148 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1149 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1150 = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi]
1151 ty' = substTyWith [tv] [xi] ty
1152 ; ipid' <- newIPVar nm ty'
1154 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co))
1155 _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co)
1156 ; return (CIPCan { cc_id = ipid'
1159 , cc_ip_ty = ty' }) }
1161 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1162 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2)
1163 = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
1164 args' = substTysWith [tv] [xi1] args
1165 fun_co = mkTyConCoercion tc arg_cos
1166 ; cv2' <- case gw of
1167 Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2
1168 ; setWantedCoBind cv2 $
1169 mkTransCoercion fun_co (mkCoVarCoercion cv2')
1171 _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2 $
1172 mkTransCoercion (mkSymCoercion fun_co) (mkCoVarCoercion cv2)
1173 ; return (CFunEqCan { cc_id = cv2'
1180 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS CanonicalCts
1181 -- Use the first equality to rewrite the second, flavors already checked.
1182 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1183 -- rewrites c2 to give
1184 -- c2' : tv2 ~ xi2[xi1/tv1]
1185 -- We must do an occurs check to sure the new constraint is canonical
1186 -- So we might return an empty bag
1187 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1188 | Just tv2' <- tcGetTyVar_maybe xi2'
1189 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1190 = do { when (isWanted gw) (setWantedCoBind cv2 (mkSymCoercion co2'))
1191 ; return emptyCCan }
1196 -> do { cv2' <- newWantedCoVar (mkTyVarTy tv2) xi2'
1197 ; setWantedCoBind cv2 $
1198 mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion co2'
1201 -> newGivOrDerCoVar (mkTyVarTy tv2) xi2' $
1202 mkCoVarCoercion cv2 `mkTransCoercion` co2'
1204 ; xi2'' <- canOccursCheck gw tv2 xi2' -- we know xi2' is *not* tv2
1205 ; return (singleCCan $ CTyEqCan { cc_id = cv2'
1211 xi2' = substTyWith [tv1] [xi1] xi2
1212 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1215 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS CanonicalCts
1216 -- Used to ineratct two equalities of the following form:
1217 -- First Equality: co1: (XXX ~ xi1)
1218 -- Second Equality: cv2: (XXX ~ xi2)
1219 -- Where the cv1 `canSolve` cv2 equality
1220 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1). This
1221 -- depends on whether the left or the right equality comes from the inert set.
1223 -- prefer to create (xi2 ~ xi1) if the first comes from the inert
1224 -- prefer to create (xi1 ~ xi2) if the second comes from the inert
1225 rewriteEqLHS which (co1,xi1) (cv2,gw,xi2)
1226 = do { cv2' <- case (isWanted gw, which) of
1227 (True,LeftComesFromInert) ->
1228 do { cv2' <- newWantedCoVar xi2 xi1
1229 ; setWantedCoBind cv2 $
1230 co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
1232 (True,RightComesFromInert) ->
1233 do { cv2' <- newWantedCoVar xi1 xi2
1234 ; setWantedCoBind cv2 $
1235 co1 `mkTransCoercion` mkCoVarCoercion cv2'
1237 (False,LeftComesFromInert) ->
1238 newGivOrDerCoVar xi2 xi1 $
1239 mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
1240 (False,RightComesFromInert) ->
1241 newGivOrDerCoVar xi1 xi2 $
1242 mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
1243 ; mkCanonical gw cv2'
1246 solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult
1247 -- First argument inert, second argument workitem. They both represent
1248 -- wanted/given/derived evidence for the *same* predicate so we try here to
1249 -- discharge one directly from the other.
1251 -- Precondition: value evidence only (implicit parameters, classes)
1253 solveOneFromTheOther (iid,ifl) workItem
1254 -- Both derived needs a special case. You might think that we do not need
1255 -- two evidence terms for the same claim. But, since the evidence is partial,
1256 -- either evidence may do in some cases; see TcSMonad.isGoodRecEv.
1257 -- See also Example 3 in Note [Superclasses and recursive dictionaries]
1258 | isDerived ifl && isDerived wfl
1259 = noInteraction workItem
1261 | ifl `canSolve` wfl
1262 = do { unless (isGiven wfl) $ setEvBind wid (EvId iid)
1263 -- Overwrite the binding, if one exists
1264 -- For Givens, which are lambda-bound, nothing to overwrite,
1265 ; dischargeWorkItem }
1267 | otherwise -- wfl `canSolve` ifl
1268 = do { unless (isGiven ifl) $ setEvBind iid (EvId wid)
1269 ; mkIRContinue workItem DropInert emptyWorkList }
1272 wfl = cc_flavor workItem
1273 wid = cc_id workItem
1276 Note [Superclasses and recursive dictionaries]
1277 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1278 Overlaps with Note [SUPERCLASS-LOOP 1]
1279 Note [SUPERCLASS-LOOP 2]
1280 Note [Recursive instances and superclases]
1281 ToDo: check overlap and delete redundant stuff
1283 Right before adding a given into the inert set, we must
1284 produce some more work, that will bring the superclasses
1285 of the given into scope. The superclass constraints go into
1288 When we simplify a wanted constraint, if we first see a matching
1289 instance, we may produce new wanted work. To (1) avoid doing this work
1290 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1291 this item as solved (in effect, given) into our inert set and with that add
1292 its superclass constraints (as given) in our worklist.
1294 But now we have added partially solved constraints to the worklist which may
1295 interact with other wanteds. Consider the example:
1299 class Eq b => Foo a b --- 0-th selector
1300 instance Eq a => Foo [a] a --- fooDFun
1302 and wanted (Foo [t] t). We are first going to see that the instance matches
1303 and create an inert set that includes the solved (Foo [t] t) and its
1305 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1306 d2 :_g Eq t d2 := EvSuperClass d1 0
1307 Our work list is going to contain a new *wanted* goal
1309 It is wrong to react the wanted (Eq t) with the given (Eq t) because that would
1310 construct loopy evidence. Hence the check isGoodRecEv in doInteractWithInert.
1312 OK, so we have ruled out bad behaviour, but how do we ge recursive dictionaries,
1317 data D r = ZeroD | SuccD (r (D r));
1319 instance (Eq (r (D r))) => Eq (D r) where
1320 ZeroD == ZeroD = True
1321 (SuccD a) == (SuccD b) = a == b
1324 equalDC :: D [] -> D [] -> Bool;
1327 We need to prove (Eq (D [])). Here's how we go:
1331 by instance decl, holds if
1335 *BUT* we have an inert set which gives us (no superclasses):
1337 By the instance declaration of Eq we can show the 'd2' goal if
1339 where d2 = dfEqList d3
1341 Now, however this wanted can interact with our inert d1 to set:
1343 and solve the goal. Why was this interaction OK? Because, if we chase the
1344 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1346 d3 := dfEqD2 (dfEqList d3)
1347 which is FINE because the use of d3 is protected by the instance function
1350 So, our strategy is to try to put solved wanted dictionaries into the
1351 inert set along with their superclasses (when this is meaningful,
1352 i.e. when new wanted goals are generated) but solve a wanted dictionary
1353 from a given only in the case where the evidence variable of the
1354 wanted is mentioned in the evidence of the given (recursively through
1355 the evidence binds) in a protected way: more instance function applications
1356 than superclass selectors.
1358 Here are some more examples from GHC's previous type checker
1362 This code arises in the context of "Scrap Your Boilerplate with Class"
1366 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1367 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1369 class Data Maybe a => Foo a
1371 instance Foo t => Sat (Maybe t) -- dfunSat
1373 instance Data Maybe a => Foo a -- dfunFoo1
1374 instance Foo a => Foo [a] -- dfunFoo2
1375 instance Foo [Char] -- dfunFoo3
1377 Consider generating the superclasses of the instance declaration
1378 instance Foo a => Foo [a]
1380 So our problem is this
1382 d1 :_w Data Maybe [t]
1384 We may add the given in the inert set, along with its superclasses
1385 [assuming we don't fail because there is a matching instance, see
1386 tryTopReact, given case ]
1390 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1391 d1 :_w Data Maybe [t]
1392 Then d2 can readily enter the inert, and we also do solving of the wanted
1395 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1397 d2 :_w Sat (Maybe [t])
1399 d01 :_g Data Maybe t
1400 Now, we may simplify d2 more:
1403 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1404 d1 :_g Data Maybe [t]
1405 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1409 d01 :_g Data Maybe t
1411 Now, we can just solve d3.
1414 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1415 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1418 d01 :_g Data Maybe t
1419 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1422 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1423 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1424 d4 :_g Foo [t] d4 := dfunFoo2 d5
1427 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1428 d01 :_g Data Maybe t
1429 Now, d5 can be solved! (and its superclass enter scope)
1432 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1433 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1434 d4 :_g Foo [t] d4 := dfunFoo2 d5
1435 d5 :_g Foo t d5 := dfunFoo1 d7
1438 d6 :_g Data Maybe [t]
1439 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1440 d01 :_g Data Maybe t
1443 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1444 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1445 that must not be used (look at case interactInert where both inert and workitem
1446 are givens). So we have several options:
1447 - Drop the workitem always (this will drop d8)
1448 This feels very unsafe -- what if the work item was the "good" one
1449 that should be used later to solve another wanted?
1450 - Don't drop anyone: the inert set may contain multiple givens!
1451 [This is currently implemented]
1453 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1454 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1455 d7. Now the [isRecDictEv] function in the ineration solver
1456 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1457 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1459 So, no interaction happens there. Then we meet d01 and there is no recursion
1460 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1462 Note [SUPERCLASS-LOOP 1]
1463 ~~~~~~~~~~~~~~~~~~~~~~~~
1464 We have to be very, very careful when generating superclasses, lest we
1465 accidentally build a loop. Here's an example:
1469 class S a => C a where { opc :: a -> a }
1470 class S b => D b where { opd :: b -> b }
1472 instance C Int where
1475 instance D Int where
1478 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1479 Simplifying, we may well get:
1480 $dfCInt = :C ds1 (opd dd)
1483 Notice that we spot that we can extract ds1 from dd.
1485 Alas! Alack! We can do the same for (instance D Int):
1487 $dfDInt = :D ds2 (opc dc)
1491 And now we've defined the superclass in terms of itself.
1492 Two more nasty cases are in
1497 - Satisfy the superclass context *all by itself*
1498 (tcSimplifySuperClasses)
1499 - And do so completely; i.e. no left-over constraints
1500 to mix with the constraints arising from method declarations
1503 Note [SUPERCLASS-LOOP 2]
1504 ~~~~~~~~~~~~~~~~~~~~~~~~
1505 We need to be careful when adding "the constaint we are trying to prove".
1506 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1508 class Ord a => C a where
1509 instance Ord [a] => C [a] where ...
1511 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1512 superclasses of C [a] to avails. But we must not overwrite the binding
1513 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1516 Here's another variant, immortalised in tcrun020
1517 class Monad m => C1 m
1518 class C1 m => C2 m x
1519 instance C2 Maybe Bool
1520 For the instance decl we need to build (C1 Maybe), and it's no good if
1521 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1522 before we search for C1 Maybe.
1524 Here's another example
1525 class Eq b => Foo a b
1526 instance Eq a => Foo [a] a
1530 we'll first deduce that it holds (via the instance decl). We must not
1531 then overwrite the Eq t constraint with a superclass selection!
1533 At first I had a gross hack, whereby I simply did not add superclass constraints
1534 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1535 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1536 I found a very obscure program (now tcrun021) in which improvement meant the
1537 simplifier got two bites a the cherry... so something seemed to be an Stop
1538 first time, but reducible next time.
1540 Now we implement the Right Solution, which is to check for loops directly
1541 when adding superclasses. It's a bit like the occurs check in unification.
1543 Note [Recursive instances and superclases]
1544 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1545 Consider this code, which arises in the context of "Scrap Your
1546 Boilerplate with Class".
1550 instance Sat (ctx Char) => Data ctx Char
1551 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1553 class Data Maybe a => Foo a
1555 instance Foo t => Sat (Maybe t)
1557 instance Data Maybe a => Foo a
1558 instance Foo a => Foo [a]
1561 In the instance for Foo [a], when generating evidence for the superclasses
1562 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1563 Using the instance for Data, we therefore need
1564 (Sat (Maybe [a], Data Maybe a)
1565 But we are given (Foo a), and hence its superclass (Data Maybe a).
1566 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1567 we need (Foo [a]). And that is the very dictionary we are bulding
1568 an instance for! So we must put that in the "givens". So in this
1570 Given: Foo a, Foo [a]
1571 Wanted: Data Maybe [a]
1573 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1574 the givens, which is what 'addGiven' would normally do. Why? Because
1575 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1576 by selecting a superclass from Foo [a], which simply makes a loop.
1578 On the other hand we *must* put the superclasses of (Foo a) in
1579 the givens, as you can see from the derivation described above.
1581 Conclusion: in the very special case of tcSimplifySuperClasses
1582 we have one 'given' (namely the "this" dictionary) whose superclasses
1583 must not be added to 'givens' by addGiven.
1585 There is a complication though. Suppose there are equalities
1586 instance (Eq a, a~b) => Num (a,b)
1587 Then we normalise the 'givens' wrt the equalities, so the original
1588 given "this" dictionary is cast to one of a different type. So it's a
1589 bit trickier than before to identify the "special" dictionary whose
1590 superclasses must not be added. See test
1591 indexed-types/should_run/EqInInstance
1593 We need a persistent property of the dictionary to record this
1594 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1595 but cool), which is maintained by dictionary normalisation.
1596 Specifically, the InstLocOrigin is
1598 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1601 Note [MATCHING-SYNONYMS]
1602 ~~~~~~~~~~~~~~~~~~~~~~~~
1603 When trying to match a dictionary (D tau) to a top-level instance, or a
1604 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1605 we do *not* need to expand type synonyms because the matcher will do that for us.
1608 Note [RHS-FAMILY-SYNONYMS]
1609 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1610 The RHS of a family instance is represented as yet another constructor which is
1611 like a type synonym for the real RHS the programmer declared. Eg:
1612 type instance F (a,a) = [a]
1614 :R32 a = [a] -- internal type synonym introduced
1615 F (a,a) ~ :R32 a -- instance
1617 When we react a family instance with a type family equation in the work list
1618 we keep the synonym-using RHS without expansion.
1621 *********************************************************************************
1623 The top-reaction Stage
1625 *********************************************************************************
1628 -- If a work item has any form of interaction with top-level we get this
1629 data TopInteractResult
1630 = NoTopInt -- No top-level interaction
1632 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1633 -- for superclasses)
1634 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1635 } -- NB: in ``given'' (solved) form if the
1636 -- original was wanted or given and instance match
1637 -- was found, but may also be in wanted form if we
1638 -- only reacted with functional dependencies
1639 -- arising from top-level instances.
1641 topReactionsStage :: SimplifierStage
1642 topReactionsStage workItem inerts
1643 = do { tir <- tryTopReact workItem
1646 return $ SR { sr_inerts = inerts
1647 , sr_new_work = emptyWorkList
1648 , sr_stop = ContinueWith workItem }
1649 SomeTopInt tir_new_work tir_new_inert ->
1650 return $ SR { sr_inerts = inerts
1651 , sr_new_work = tir_new_work
1652 , sr_stop = tir_new_inert
1656 tryTopReact :: WorkItem -> TcS TopInteractResult
1657 tryTopReact workitem
1658 = do { -- A flag controls the amount of interaction allowed
1659 -- See Note [Simplifying RULE lhs constraints]
1660 ctxt <- getTcSContext
1661 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1662 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1663 ; doTopReact workitem }
1664 else return NoTopInt
1667 allowedTopReaction :: Bool -> WorkItem -> Bool
1668 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1669 allowedTopReaction _ _ = True
1672 doTopReact :: WorkItem -> TcS TopInteractResult
1673 -- The work item does not react with the inert set,
1674 -- so try interaction with top-level instances
1675 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Wanted loc
1676 , cc_class = cls, cc_tyargs = xis })
1677 = do { -- See Note [MATCHING-SYNONYMS]
1678 ; lkp_inst_res <- matchClassInst cls xis loc
1679 ; case lkp_inst_res of
1680 NoInstance -> do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1682 GenInst wtvs ev_term -> -- Solved
1683 -- No need to do fundeps stuff here; the instance
1684 -- matches already so we won't get any more info
1685 -- from functional dependencies
1686 do { traceTcS "doTopReact/ found class instance for" (ppr dv)
1687 ; setDictBind dv ev_term
1688 ; workList <- canWanteds wtvs
1690 -- Solved in one step and no new wanted work produced.
1691 -- i.e we directly matched a top-level instance
1692 -- No point in caching this in 'inert', nor in adding superclasses
1693 then return $ SomeTopInt { tir_new_work = emptyWorkList
1694 , tir_new_inert = Stop }
1696 -- Solved and new wanted work produced, you may cache the
1697 -- (tentatively solved) dictionary as Derived and its superclasses
1698 else do { let solved = makeSolved workItem
1699 ; sc_work <- newSCWorkFromFlavored dv (Derived loc) cls xis
1700 ; let inst_work = workListFromCCans workList
1701 ; return $ SomeTopInt
1702 { tir_new_work = inst_work `unionWorkLists` sc_work
1703 , tir_new_inert = ContinueWith solved } }
1707 -- Try for a fundep reaction beween the wanted item
1708 -- and a top-level instance declaration
1710 = do { instEnvs <- getInstEnvs
1711 ; let eqn_pred_locs = improveFromInstEnv (classInstances instEnvs)
1712 (ClassP cls xis, ppr dv)
1713 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
1714 -- NB: fundeps generate some wanted equalities, but
1715 -- we don't use their evidence for anything
1716 ; fd_cts <- canWanteds wevvars
1717 ; let fd_work = mkEqWorkList fd_cts
1719 ; if isEmptyCCan fd_cts then
1720 do { sc_work <- newSCWorkFromFlavored dv (Derived loc) cls xis
1721 ; return $ SomeTopInt { tir_new_work = fd_work `unionWorkLists` sc_work
1722 , tir_new_inert = ContinueWith workItem }
1724 else -- More fundep work produced, don't do any superlcass stuff, just
1725 -- thow him back in the worklist prioritizing the solution of fd equalities
1727 SomeTopInt { tir_new_work = fd_work `unionWorkLists` singleNonEqWL workItem
1728 , tir_new_inert = Stop }
1730 -- NB: workItem is inert, but it isn't solved
1731 -- keep it as inert, although it's not solved because we
1732 -- have now reacted all its top-level fundep-induced equalities!
1734 -- See Note [FunDep Reactions]
1737 -- DV: Derived, we will not add any further derived superclasses
1738 -- [no deep recursive dictionaries!]
1739 doTopReact (CDictCan { cc_flavor = fl })
1743 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = fl
1744 , cc_class = cls, cc_tyargs = xis })
1745 = do { sc_work <- newSCWorkFromFlavored dv fl cls xis
1746 ; return $ SomeTopInt sc_work (ContinueWith workItem) }
1747 -- See Note [Given constraint that matches an instance declaration]
1750 doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
1751 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1752 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1753 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1757 MatchInstSingle (rep_tc, rep_tys)
1758 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1759 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1760 -- Eagerly expand away the type synonym on the
1761 -- RHS of a type function, so that it never
1762 -- appears in an error message
1763 -- See Note [Type synonym families] in TyCon
1764 coe = mkTyConApp coe_tc rep_tys
1766 Wanted {} -> do { cv' <- newWantedCoVar rhs_ty xi
1767 ; setWantedCoBind cv $
1768 coe `mkTransCoercion`
1771 _ -> newGivOrDerCoVar xi rhs_ty $
1772 mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
1774 ; can_cts <- mkCanonical fl cv'
1775 ; let workList = mkEqWorkList can_cts
1776 ; return $ SomeTopInt workList Stop }
1778 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1782 -- Any other work item does not react with any top-level equations
1783 doTopReact _workItem = return NoTopInt
1786 Note [FunDep and implicit parameter reactions]
1787 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1788 Currently, our story of interacting two dictionaries (or a dictionary
1789 and top-level instances) for functional dependencies, and implicit
1790 paramters, is that we simply produce new wanted equalities. So for example
1792 class D a b | a -> b where ...
1798 We generate the extra work item
1800 where 'cv' is currently unused. However, this new item reacts with d2,
1801 discharging it in favour of a new constraint d2' thus:
1803 d2 := d2' |> D Int cv
1804 Now d2' can be discharged from d1
1806 We could be more aggressive and try to *immediately* solve the dictionary
1807 using those extra equalities. With the same inert set and work item we
1808 might dischard d2 directly:
1811 d2 := d1 |> D Int cv
1813 But in general it's a bit painful to figure out the necessary coercion,
1814 so we just take the first approach. Here is a better example. Consider:
1815 class C a b c | a -> b
1817 [Given] d1 : C T Int Char
1818 [Wanted] d2 : C T beta Int
1819 In this case, it's *not even possible* to solve the wanted immediately.
1820 So we should simply output the functional dependency and add this guy
1821 [but NOT its superclasses] back in the worklist. Even worse:
1822 [Given] d1 : C T Int beta
1823 [Wanted] d2: C T beta Int
1824 Then it is solvable, but its very hard to detect this on the spot.
1826 It's exactly the same with implicit parameters, except that the
1827 "aggressive" approach would be much easier to implement.
1829 Note [When improvement happens]
1830 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1831 We fire an improvement rule when
1833 * Two constraints match (modulo the fundep)
1834 e.g. C t1 t2, C t1 t3 where C a b | a->b
1835 The two match because the first arg is identical
1837 * At least one is not Given. If they are both given, we don't fire
1838 the reaction because we have no way of constructing evidence for a
1839 new equality nor does it seem right to create a new wanted goal
1840 (because the goal will most likely contain untouchables, which
1841 can't be solved anyway)!
1843 Note that we *do* fire the improvement if one is Given and one is Derived.
1844 The latter can be a superclass of a wanted goal. Example (tcfail138)
1845 class L a b | a -> b
1846 class (G a, L a b) => C a b
1848 instance C a b' => G (Maybe a)
1849 instance C a b => C (Maybe a) a
1850 instance L (Maybe a) a
1852 When solving the superclasses of the (C (Maybe a) a) instance, we get
1853 Given: C a b ... and hance by superclasses, (G a, L a b)
1855 Use the instance decl to get
1857 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
1858 and now we need improvement between that derived superclass an the Given (L a b)
1860 Note [Overriding implicit parameters]
1861 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1863 f :: (?x::a) -> Bool -> a
1865 g v = let ?x::Int = 3
1866 in (f v, let ?x::Bool = True in f v)
1868 This should probably be well typed, with
1869 g :: Bool -> (Int, Bool)
1871 So the inner binding for ?x::Bool *overrides* the outer one.
1872 Hence a work-item Given overrides an inert-item Given.
1874 Note [Given constraint that matches an instance declaration]
1875 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1876 What should we do when we discover that one (or more) top-level
1877 instances match a given (or solved) class constraint? We have
1880 1. Reject the program. The reason is that there may not be a unique
1881 best strategy for the solver. Example, from the OutsideIn(X) paper:
1882 instance P x => Q [x]
1883 instance (x ~ y) => R [x] y
1885 wob :: forall a b. (Q [b], R b a) => a -> Int
1887 g :: forall a. Q [a] => [a] -> Int
1890 will generate the impliation constraint:
1891 Q [a] => (Q [beta], R beta [a])
1892 If we react (Q [beta]) with its top-level axiom, we end up with a
1893 (P beta), which we have no way of discharging. On the other hand,
1894 if we react R beta [a] with the top-level we get (beta ~ a), which
1895 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
1896 now solvable by the given Q [a].
1898 However, this option is restrictive, for instance [Example 3] from
1899 Note [Recursive dictionaries] will fail to work.
1901 2. Ignore the problem, hoping that the situations where there exist indeed
1902 such multiple strategies are rare: Indeed the cause of the previous
1903 problem is that (R [x] y) yields the new work (x ~ y) which can be
1904 *spontaneously* solved, not using the givens.
1906 We are choosing option 2 below but we might consider having a flag as well.
1909 Note [New Wanted Superclass Work]
1910 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1911 Even in the case of wanted constraints, we add all of its superclasses as
1912 new given work. There are several reasons for this:
1913 a) to minimise error messages;
1914 eg suppose we have wanted (Eq a, Ord a)
1915 then we report only (Ord a) unsoluble
1917 b) to make the smallest number of constraints when *inferring* a type
1918 (same Eq/Ord example)
1920 c) for recursive dictionaries we *must* add the superclasses
1921 so that we can use them when solving a sub-problem
1923 d) To allow FD-like improvement for type families. Assume that
1925 class C a b | a -> b
1926 and we have to solve the implication constraint:
1928 Then, FD improvement can help us to produce a new wanted (beta ~ b)
1930 We want to have the same effect with the type family encoding of
1931 functional dependencies. Namely, consider:
1932 class (F a ~ b) => C a b
1933 Now suppose that we have:
1936 By interacting the given we will get given (F a ~ b) which is not
1937 enough by itself to make us discharge (C a beta). However, we
1938 may create a new derived equality from the super-class of the
1939 wanted constraint (C a beta), namely derived (F a ~ beta).
1940 Now we may interact this with given (F a ~ b) to get:
1942 But 'beta' is a touchable unification variable, and hence OK to
1943 unify it with 'b', replacing the derived evidence with the identity.
1945 This requires trySpontaneousSolve to solve *derived*
1946 equalities that have a touchable in their RHS, *in addition*
1947 to solving wanted equalities.
1949 Here is another example where this is useful.
1953 class (F a ~ b) => C a b
1954 And we are given the wanteds:
1958 We surely do *not* want to quantify over (b ~ c), since if someone provides
1959 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
1960 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
1962 Step 1: We will get new *given* superclass work,
1963 provisionally to our solving of w1 and w2
1965 g1: F a ~ b, g2 : F a ~ c,
1966 w1 : C a b, w2 : C a c, w3 : b ~ c
1968 The evidence for g1 and g2 is a superclass evidence term:
1970 g1 := sc w1, g2 := sc w2
1972 Step 2: The givens will solve the wanted w3, so that
1973 w3 := sym (sc w1) ; sc w2
1975 Step 3: Now, one may naively assume that then w2 can be solve from w1
1976 after rewriting with the (now solved equality) (b ~ c).
1978 But this rewriting is ruled out by the isGoodRectDict!
1980 Conclusion, we will (correctly) end up with the unsolved goals
1983 NB: The desugarer needs be more clever to deal with equalities
1984 that participate in recursive dictionary bindings.
1987 newSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi]
1989 newSCWorkFromFlavored ev flavor cls xis
1990 | Given loc <- flavor -- The NoScSkol says "don't add superclasses"
1991 , NoScSkol <- ctLocOrigin loc -- Very important!
1992 = return emptyWorkList
1995 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
1996 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
1997 -- Add *all* its superclasses (equalities or not) as new given work
1998 -- See Note [New Wanted Superclass Work]
1999 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
2000 ; can_cts <- mkCanonicals flavor sc_vars
2001 ; return $ workListFromCCans can_cts
2004 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
2006 data LookupInstResult
2008 | GenInst [WantedEvVar] EvTerm
2010 matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
2011 matchClassInst clas tys loc
2012 = do { let pred = mkClassPred clas tys
2013 ; mb_result <- matchClass clas tys
2015 MatchInstNo -> return NoInstance
2016 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
2017 -- we learn more about the reagent
2018 MatchInstSingle (dfun_id, mb_inst_tys) ->
2019 do { checkWellStagedDFun pred dfun_id loc
2021 -- It's possible that not all the tyvars are in
2022 -- the substitution, tenv. For example:
2023 -- instance C X a => D X where ...
2024 -- (presumably there's a functional dependency in class C)
2025 -- Hence mb_inst_tys :: Either TyVar TcType
2027 ; tys <- instDFunTypes mb_inst_tys
2028 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
2029 ; if null theta then
2030 return (GenInst [] (EvDFunApp dfun_id tys []))
2032 { ev_vars <- instDFunConstraints theta
2033 ; let wevs = [WantedEvVar w loc | w <- ev_vars]
2034 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }