3 solveInteract, AtomicInert,
4 InertSet, emptyInert, updInertSet, extractUnsolved, solveOne,
8 #include "HsVersions.h"
31 import Control.Monad ( when )
40 import qualified Data.Map as Map
43 import Control.Monad( zipWithM, unless )
44 import FastString ( sLit )
48 Note [InertSet invariants]
49 ~~~~~~~~~~~~~~~~~~~~~~~~~~~
51 An InertSet is a bag of canonical constraints, with the following invariants:
53 1 No two constraints react with each other.
55 A tricky case is when there exists a given (solved) dictionary
56 constraint and a wanted identical constraint in the inert set, but do
57 not react because reaction would create loopy dictionary evidence for
58 the wanted. See note [Recursive dictionaries]
60 2 Given equalities form an idempotent substitution [none of the
61 given LHS's occur in any of the given RHS's or reactant parts]
63 3 Wanted equalities also form an idempotent substitution
64 4 The entire set of equalities is acyclic.
66 5 Wanted dictionaries are inert with the top-level axiom set
68 6 Equalities of the form tv1 ~ tv2 always have a touchable variable
69 on the left (if possible).
70 7 No wanted constraints tv1 ~ tv2 with tv1 touchable. Such constraints
71 will be marked as solved right before being pushed into the inert set.
72 See note [Touchables and givens].
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).
85 Note [InertSet FlattenSkolemEqClass]
86 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
87 The inert_fsks field of the inert set contains an "inverse map" of all the
88 flatten skolem equalities in the inert set. For instance, if inert_cts looks
95 Then, the inert_fsks fields holds the following map:
96 fsk2 |-> { fsk1, fsk3 }
98 Along with the necessary coercions to convert fsk1 and fsk3 back to fsk2
99 and fsk4 back to fsk5. Hence, the invariants of the inert_fsks field are:
101 (a) All TcTyVars in the domain and range of inert_fsks are flatten skolems
102 (b) All TcTyVars in the domain of inert_fsk occur naked as rhs in some
103 equalities of inert_cts
104 (c) For every mapping fsk1 |-> { (fsk2,co), ... } it must be:
107 The role of the inert_fsks is to make it easy to maintain the equivalence
108 class of each flatten skolem, which is much needed to correctly do spontaneous
109 solving. See Note [Loopy Spontaneous Solving]
112 -- See Note [InertSet invariants]
114 = IS { inert_cts :: Bag.Bag CanonicalCt
115 , inert_fsks :: Map.Map TcTyVar [(TcTyVar,Coercion)] }
116 -- See Note [InertSet FlattenSkolemEqClass]
118 instance Outputable InertSet where
119 ppr is = vcat [ vcat (map ppr (Bag.bagToList $ inert_cts is))
120 , vcat (map (\(v,rest) -> ppr v <+> text "|->" <+> hsep (map (ppr.fst) rest))
121 (Map.toList $ inert_fsks is)
125 emptyInert :: InertSet
126 emptyInert = IS { inert_cts = Bag.emptyBag, inert_fsks = Map.empty }
128 updInertSet :: InertSet -> AtomicInert -> InertSet
129 -- Introduces an element in the inert set for the first time
130 updInertSet (IS { inert_cts = cts, inert_fsks = fsks })
131 item@(CTyEqCan { cc_id = cv
134 | Just tv2 <- tcGetTyVar_maybe xi,
135 FlatSkol {} <- tcTyVarDetails tv1,
136 FlatSkol {} <- tcTyVarDetails tv2
137 = let cts' = cts `Bag.snocBag` item
138 fsks' = Map.insertWith (++) tv2 [(tv1, mkCoVarCoercion cv)] fsks
139 -- See Note [InertSet FlattenSkolemEqClass]
140 in IS { inert_cts = cts', inert_fsks = fsks' }
141 updInertSet (IS { inert_cts = cts
142 , inert_fsks = fsks }) item
143 = let cts' = cts `Bag.snocBag` item
144 in IS { inert_cts = cts', inert_fsks = fsks }
146 foldlInertSetM :: (Monad m) => (a -> AtomicInert -> m a) -> a -> InertSet -> m a
147 foldlInertSetM k z (IS { inert_cts = cts })
148 = Bag.foldlBagM k z cts
150 extractUnsolved :: InertSet -> (InertSet, CanonicalCts)
151 extractUnsolved is@(IS {inert_cts = cts})
152 = (is { inert_cts = cts'}, unsolved)
153 where (unsolved, cts') = Bag.partitionBag isWantedCt cts
156 getFskEqClass :: InertSet -> TcTyVar -> [(TcTyVar,Coercion)]
157 -- Precondition: tv is a FlatSkol. See Note [InertSet FlattenSkolemEqClass]
158 getFskEqClass (IS { inert_cts = cts, inert_fsks = fsks }) tv
159 = case lkpTyEqCanByLhs of
160 Nothing -> fromMaybe [] (Map.lookup tv fsks)
162 case tcGetTyVar_maybe (cc_rhs ceq) of
163 Just tv_rhs | FlatSkol {} <- tcTyVarDetails tv_rhs
164 -> let ceq_co = mkSymCoercion $ mkCoVarCoercion (cc_id ceq)
165 mk_co (v,c) = (v, mkTransCoercion c ceq_co)
166 in (tv_rhs, ceq_co): map mk_co (fromMaybe [] $ Map.lookup tv fsks)
168 where lkpTyEqCanByLhs = Bag.foldlBag lkp Nothing cts
169 lkp :: Maybe CanonicalCt -> CanonicalCt -> Maybe CanonicalCt
170 lkp Nothing ct@(CTyEqCan {cc_tyvar = tv'}) | tv' == tv = Just ct
171 lkp other _ct = other
174 isWantedCt :: CanonicalCt -> Bool
175 isWantedCt ct = isWanted (cc_flavor ct)
178 data Inert = IS { class_inerts :: FiniteMap Class Atomics
179 ip_inerts :: FiniteMap Class Atomics
180 tyfun_inerts :: FiniteMap TyCon Atomics
181 tyvar_inerts :: FiniteMap TyVar Atomics
184 Later should we also separate out givens and wanteds?
189 Note [Touchables and givens]
190 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~
191 Touchable variables will never show up in givens which are inputs to
192 the solver. However, touchables may show up in givens generated by the flattener.
207 which can be put in the inert set. Suppose we also have a wanted
211 We cannot rewrite the given G alpha ~g b using the wanted alpha ~w
212 Int. Instead, after reacting alpha ~w Int with the whole inert set,
213 we observe that we can solve it by unifying alpha with Int, so we mark
214 it as solved and put it back in the *work list*. [We also immediately unify
215 alpha := Int, without telling anyone, see trySpontaneousSolve function, to
216 avoid doing this in the end.]
218 Later, because it is solved (given, in effect), we can use it to rewrite
219 G alpha ~g b to G Int ~g b, which gets put back in the work list. Eventually,
220 we will dispatch the remaining wanted constraints using the top-level axioms.
222 Finally, note that after reacting a wanted equality with the entire inert set
223 we may end up with something like
227 which we should flip around to generate the solved constraint alpha ~s b.
229 %*********************************************************************
231 * Main Interaction Solver *
233 **********************************************************************
237 1. Canonicalise (unary)
238 2. Pairwise interaction (binary)
239 * Take one from work list
240 * Try all pair-wise interactions with each constraint in inert
241 3. Try to solve spontaneously for equalities involving touchables
242 4. Top-level interaction (binary wrt top-level)
243 Superclass decomposition belongs in (4), see note [Superclasses]
247 type AtomicInert = CanonicalCt -- constraint pulled from InertSet
248 type WorkItem = CanonicalCt -- constraint pulled from WorkList
250 type WorkList = CanonicalCts -- A mixture of Given, Wanted, and Solved
251 type SWorkList = WorkList -- A worklist of solved
254 listToWorkList :: [WorkItem] -> WorkList
255 listToWorkList = Bag.listToBag
257 unionWorkLists :: WorkList -> WorkList -> WorkList
258 unionWorkLists = Bag.unionBags
260 foldlWorkListM :: (Monad m) => (a -> WorkItem -> m a) -> a -> WorkList -> m a
261 foldlWorkListM = Bag.foldlBagM
263 isEmptyWorkList :: WorkList -> Bool
264 isEmptyWorkList = Bag.isEmptyBag
266 emptyWorkList :: WorkList
267 emptyWorkList = Bag.emptyBag
269 singletonWorkList :: CanonicalCt -> WorkList
270 singletonWorkList ct = singleCCan ct
273 = Stop -- Work item is consumed
274 | ContinueWith WorkItem -- Not consumed
276 instance Outputable StopOrContinue where
277 ppr Stop = ptext (sLit "Stop")
278 ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w
280 -- Results after interacting a WorkItem as far as possible with an InertSet
282 = SR { sr_inerts :: InertSet
283 -- The new InertSet to use (REPLACES the old InertSet)
284 , sr_new_work :: WorkList
285 -- Any new work items generated (should be ADDED to the old WorkList)
287 -- sr_stop = Just workitem => workitem is *not* in sr_inerts and
288 -- workitem is inert wrt to sr_inerts
289 , sr_stop :: StopOrContinue
292 instance Outputable StageResult where
293 ppr (SR { sr_inerts = inerts, sr_new_work = work, sr_stop = stop })
294 = ptext (sLit "SR") <+>
295 braces (sep [ ptext (sLit "inerts =") <+> ppr inerts <> comma
296 , ptext (sLit "new work =") <+> ppr work <> comma
297 , ptext (sLit "stop =") <+> ppr stop])
299 type SimplifierStage = WorkItem -> InertSet -> TcS StageResult
301 -- Combine a sequence of simplifier 'stages' to create a pipeline
302 runSolverPipeline :: [(String, SimplifierStage)]
303 -> InertSet -> WorkItem
304 -> TcS (InertSet, WorkList)
305 -- Precondition: non-empty list of stages
306 runSolverPipeline pipeline inerts workItem
307 = do { traceTcS "Start solver pipeline" $
308 vcat [ ptext (sLit "work item =") <+> ppr workItem
309 , ptext (sLit "inerts =") <+> ppr inerts]
311 ; let itr_in = SR { sr_inerts = inerts
312 , sr_new_work = emptyWorkList
313 , sr_stop = ContinueWith workItem }
314 ; itr_out <- run_pipeline pipeline itr_in
316 = case sr_stop itr_out of
317 Stop -> sr_inerts itr_out
318 ContinueWith item -> sr_inerts itr_out `updInertSet` item
319 ; return (new_inert, sr_new_work itr_out) }
321 run_pipeline :: [(String, SimplifierStage)]
322 -> StageResult -> TcS StageResult
323 run_pipeline [] itr = return itr
324 run_pipeline _ itr@(SR { sr_stop = Stop }) = return itr
326 run_pipeline ((name,stage):stages)
327 (SR { sr_new_work = accum_work
329 , sr_stop = ContinueWith work_item })
330 = do { itr <- stage work_item inerts
331 ; traceTcS ("Stage result (" ++ name ++ ")") (ppr itr)
332 ; let itr' = itr { sr_new_work = sr_new_work itr
333 `unionWorkLists` accum_work }
334 ; run_pipeline stages itr' }
338 Inert: {c ~ d, F a ~ t, b ~ Int, a ~ ty} (all given)
339 Reagent: a ~ [b] (given)
341 React with (c~d) ==> IR (ContinueWith (a~[b])) True []
342 React with (F a ~ t) ==> IR (ContinueWith (a~[b])) False [F [b] ~ t]
343 React with (b ~ Int) ==> IR (ContinueWith (a~[Int]) True []
346 Inert: {c ~w d, F a ~g t, b ~w Int, a ~w ty}
349 React with (c ~w d) ==> IR (ContinueWith (a~[b])) True []
350 React with (F a ~g t) ==> IR (ContinueWith (a~[b])) True [] (can't rewrite given with wanted!)
354 Inert: {a ~ Int, F Int ~ b} (given)
355 Reagent: F a ~ b (wanted)
357 React with (a ~ Int) ==> IR (ContinueWith (F Int ~ b)) True []
358 React with (F Int ~ b) ==> IR Stop True [] -- after substituting we re-canonicalize and get nothing
361 -- Main interaction solver: we fully solve the worklist 'in one go',
362 -- returning an extended inert set.
364 -- See Note [Touchables and givens].
365 solveInteract :: InertSet -> WorkList -> TcS InertSet
366 solveInteract inert ws
367 = do { dyn_flags <- getDynFlags
368 ; solveInteractWithDepth (ctxtStkDepth dyn_flags,0,[]) inert ws
370 solveOne :: InertSet -> WorkItem -> TcS InertSet
371 solveOne inerts workItem
372 = do { dyn_flags <- getDynFlags
373 ; solveOneWithDepth (ctxtStkDepth dyn_flags,0,[]) inerts workItem
377 solveInteractWithDepth :: (Int, Int, [WorkItem])
378 -> InertSet -> WorkList -> TcS InertSet
379 solveInteractWithDepth ctxt@(max_depth,n,stack) inert ws
384 = solverDepthErrorTcS n stack
387 = do { traceTcS "solveInteractWithDepth" $
388 vcat [ text "Current depth =" <+> ppr n
389 , text "Max depth =" <+> ppr max_depth
391 ; foldlWorkListM (solveOneWithDepth ctxt) inert ws }
394 -- Fully interact the given work item with an inert set, and return a
395 -- new inert set which has assimilated the new information.
396 solveOneWithDepth :: (Int, Int, [WorkItem])
397 -> InertSet -> WorkItem -> TcS InertSet
398 solveOneWithDepth (max_depth, n, stack) inert work
399 = do { traceTcS0 (indent ++ "Solving {") (ppr work)
400 ; (new_inert, new_work) <- runSolverPipeline thePipeline inert work
402 ; traceTcS0 (indent ++ "Subgoals:") (ppr new_work)
404 -- Recursively solve the new work generated
405 -- from workItem, with a greater depth
406 ; res_inert <- solveInteractWithDepth (max_depth, n+1, work:stack)
409 ; traceTcS0 (indent ++ "Done }") (ppr work)
412 indent = replicate (2*n) ' '
414 thePipeline :: [(String,SimplifierStage)]
415 thePipeline = [ ("interact with inerts", interactWithInertsStage)
416 , ("spontaneous solve", spontaneousSolveStage)
417 , ("top-level reactions", topReactionsStage) ]
420 *********************************************************************************
422 The spontaneous-solve Stage
424 *********************************************************************************
427 spontaneousSolveStage :: SimplifierStage
428 spontaneousSolveStage workItem inerts
429 = do { mSolve <- trySpontaneousSolve workItem inerts
431 Nothing -> -- no spontaneous solution for him, keep going
432 return $ SR { sr_new_work = emptyWorkList
434 , sr_stop = ContinueWith workItem }
436 Just workList' -> -- He has been solved; workList' are all givens
437 return $ SR { sr_new_work = workList'
442 {-- This is all old code, but does not quite work now. The problem is that due to
443 Note [Loopy Spontaneous Solving] we may have unflattened a type, to be able to
444 perform a sneaky unification. This unflattening means that we may have to recanonicalize
445 a given (solved) equality, this is why the result of trySpontaneousSolve is now a list
446 of constraints (instead of an atomic solved constraint). We would have to react all of
447 them once again with the worklist but that is very tiresome. Instead we throw them back
450 | isWantedCt workItem
451 -- Original was wanted we have now made him given so
452 -- we have to ineract him with the inerts again because
453 -- of the change in his status. This may produce some work.
454 -> do { traceTcS "recursive interact with inerts {" $ vcat
455 [ text "work = " <+> ppr workItem'
456 , text "inerts = " <+> ppr inerts ]
457 ; itr_again <- interactWithInertsStage workItem' inerts
458 ; case sr_stop itr_again of
459 Stop -> pprPanic "BUG: Impossible to happen" $
460 vcat [ text "Original workitem:" <+> ppr workItem
461 , text "Spontaneously solved:" <+> ppr workItem'
462 , text "Solved was consumed, when reacting with inerts:"
463 , nest 2 (ppr inerts) ]
464 ContinueWith workItem'' -- Now *this* guy is inert wrt to inerts
465 -> do { traceTcS "end recursive interact }" $ ppr workItem''
466 ; return $ SR { sr_new_work = sr_new_work itr_again
467 , sr_inerts = sr_inerts itr_again
468 `extendInertSet` workItem''
472 -> return $ SR { sr_new_work = emptyWorkList
473 , sr_inerts = inerts `extendInertSet` workItem'
477 -- @trySpontaneousSolve wi@ solves equalities where one side is a
478 -- touchable unification variable. Returns:
479 -- * Nothing if we were not able to solve it
480 -- * Just wi' if we solved it, wi' (now a "given") should be put in the work list.
481 -- See Note [Touchables and givens]
482 -- NB: just passing the inerts through for the skolem equivalence classes
483 trySpontaneousSolve :: WorkItem -> InertSet -> TcS (Maybe SWorkList)
484 trySpontaneousSolve (CTyEqCan { cc_id = cv, cc_flavor = gw, cc_tyvar = tv1, cc_rhs = xi }) inerts
487 | Just tv2 <- tcGetTyVar_maybe xi
488 = do { tch1 <- isTouchableMetaTyVar tv1
489 ; tch2 <- isTouchableMetaTyVar tv2
490 ; case (tch1, tch2) of
491 (True, True) -> trySpontaneousEqTwoWay inerts cv gw tv1 tv2
492 (True, False) -> trySpontaneousEqOneWay inerts cv gw tv1 xi
493 (False, True) -> trySpontaneousEqOneWay inerts cv gw tv2 (mkTyVarTy tv1)
494 _ -> return Nothing }
496 = do { tch1 <- isTouchableMetaTyVar tv1
497 ; if tch1 then trySpontaneousEqOneWay inerts cv gw tv1 xi
498 else return Nothing }
501 -- trySpontaneousSolve (CFunEqCan ...) = ...
502 -- See Note [No touchables as FunEq RHS] in TcSMonad
503 trySpontaneousSolve _ _ = return Nothing
506 trySpontaneousEqOneWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> Xi
507 -> TcS (Maybe SWorkList)
508 -- tv is a MetaTyVar, not untouchable
509 trySpontaneousEqOneWay inerts cv gw tv xi
510 | not (isSigTyVar tv) || isTyVarTy xi,
511 typeKind xi `isSubKind` tyVarKind tv
512 = solveWithIdentity inerts cv gw tv xi
517 trySpontaneousEqTwoWay :: InertSet -> CoVar -> CtFlavor -> TcTyVar -> TcTyVar
518 -> TcS (Maybe SWorkList)
519 -- Both tyvars are *touchable* MetaTyvars
520 -- By the CTyEqCan invariant, k2 `isSubKind` k1
521 trySpontaneousEqTwoWay inerts cv gw tv1 tv2
523 , nicer_to_update_tv2 = solveWithIdentity inerts cv gw tv2 (mkTyVarTy tv1)
525 = solveWithIdentity inerts cv gw tv1 (mkTyVarTy tv2)
526 | otherwise = return Nothing
530 nicer_to_update_tv2 = isSigTyVar tv1 || isSystemName (Var.varName tv2)
534 Note [Spontaneous solving and kind compatibility]
535 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
537 Note that our canonical constraints insist that only *given* equalities (tv ~ xi)
538 or (F xis ~ rhs) require the LHS and the RHS to have exactly the same kinds.
540 - We have to require this because:
541 Given equalities can be freely used to rewrite inside
542 other types or constraints.
543 - We do not have to do the same for wanteds because:
544 First, wanted equations (tv ~ xi) where tv is a touchable unification variable
545 may have kinds that do not agree (the kind of xi must be a sub kind of the kind of tv).
546 Second, any potential kind mismatch will result in the constraint not being soluble,
547 which will be reported anyway. This is the reason that @trySpontaneousOneWay@ and
548 @trySpontaneousTwoWay@ will perform a kind compatibility check, and only then will
549 they proceed to @solveWithIdentity@.
552 - Givens from higher-rank, such as:
553 type family T b :: * -> * -> *
554 type instance T Bool = (->)
556 f :: forall a. ((T a ~ (->)) => ...) -> a -> ...
558 Whereas we would be able to apply the type instance, we would not be able to
559 use the given (T Bool ~ (->)) in the body of 'flop'
561 Note [Loopy spontaneous solving]
562 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
563 Consider the original wanted:
564 wanted : Maybe (E alpha) ~ alpha
565 where E is a type family, such that E (T x) = x. After canonicalization,
566 as a result of flattening, we will get:
567 given : E alpha ~ fsk
568 wanted : alpha ~ Maybe fsk
569 where (fsk := E alpha, on the side). Now, if we spontaneously *solve*
570 (alpha := Maybe fsk) we are in trouble! Instead, we should refrain from solving
571 it and keep it as wanted. In inference mode we'll end up quantifying over
572 (alpha ~ Maybe (E alpha))
573 Hence, 'solveWithIdentity' performs a small occurs check before
574 actually solving. But this occurs check *must look through* flatten skolems.
576 However, it may be the case that the flatten skolem in hand is equal to some other
577 flatten skolem whith *does not* mention our unification variable. Here's a typical example:
582 After canonicalization:
587 After some reactions:
592 At this point, we will try to spontaneously solve (alpha ~ f2) which remains as yet unsolved.
593 We will look inside f2, which immediately mentions (F alpha), so it's not good to unify! However
594 by looking at the equivalence class of the flatten skolems, we can see that it is fine to
595 unify (alpha ~ f1) which solves our goals!
597 A similar problem happens because of other spontaneous solving. Suppose we have the
598 following wanteds, arriving in this exact order:
599 (first) w: beta ~ alpha
600 (second) w: alpha ~ fsk
601 (third) g: F beta ~ fsk
602 Then, we first spontaneously solve the first constraint, making (beta := alpha), and having
603 (beta ~ alpha) as given. *Then* we encounter the second wanted (alpha ~ fsk). "fsk" does not
604 obviously mention alpha, so naively we can also spontaneously solve (alpha := fsk). But
605 that is wrong since fsk mentions beta, which has already secretly been unified to alpha!
607 To avoid this problem, the same occurs check must unveil rewritings that can happen because
608 of spontaneously having solved other constraints.
611 Note [Avoid double unifications]
612 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
613 The spontaneous solver has to return a given which mentions the unified unification
614 variable *on the left* of the equality. Here is what happens if not:
615 Original wanted: (a ~ alpha), (alpha ~ Int)
616 We spontaneously solve the first wanted, without changing the order!
617 given : a ~ alpha [having unified alpha := a]
618 Now the second wanted comes along, but he cannot rewrite the given, so we simply continue.
619 At the end we spontaneously solve that guy, *reunifying* [alpha := Int]
621 We avoid this problem by orienting the given so that the unification
622 variable is on the left. [Note that alternatively we could attempt to
623 enforce this at canonicalization]
625 See also Note [No touchables as FunEq RHS] in TcSMonad; avoiding
626 double unifications is the main reason we disallow touchable
627 unification variables as RHS of type family equations: F xis ~ alpha.
631 solveWithIdentity :: InertSet
632 -> CoVar -> CtFlavor -> TcTyVar -> Xi
633 -> TcS (Maybe SWorkList)
634 -- Solve with the identity coercion
635 -- Precondition: kind(xi) is a sub-kind of kind(tv)
636 -- Precondition: CtFlavor is Wanted or Derived
637 -- See [New Wanted Superclass Work] to see why solveWithIdentity
638 -- must work for Derived as well as Wanted
639 solveWithIdentity inerts cv gw tv xi
640 = do { tybnds <- getTcSTyBindsMap
641 ; case occurCheck tybnds inerts tv xi of
642 Nothing -> return Nothing
643 Just (xi_unflat,coi) -> solve_with xi_unflat coi }
645 solve_with xi_unflat coi -- coi : xi_unflat ~ xi
646 = do { traceTcS "Sneaky unification:" $
647 vcat [text "Coercion variable: " <+> ppr gw,
648 text "Coercion: " <+> pprEq (mkTyVarTy tv) xi,
649 text "Left Kind is : " <+> ppr (typeKind (mkTyVarTy tv)),
650 text "Right Kind is : " <+> ppr (typeKind xi)
652 ; setWantedTyBind tv xi_unflat -- Set tv := xi_unflat
653 ; cv_given <- newGivOrDerCoVar (mkTyVarTy tv) xi_unflat xi_unflat
654 ; let flav = mkGivenFlavor gw UnkSkol
655 ; (cts, co) <- case coi of
656 ACo co -> do { can_eqs <- canEq flav cv_given (mkTyVarTy tv) xi_unflat
657 ; return (can_eqs, co) }
659 (singleCCan (CTyEqCan { cc_id = cv_given
660 , cc_flavor = mkGivenFlavor gw UnkSkol
661 , cc_tyvar = tv, cc_rhs = xi }
662 -- xi, *not* xi_unflat because
663 -- xi_unflat may require flattening!
666 Wanted {} -> setWantedCoBind cv co
667 Derived {} -> setDerivedCoBind cv co
668 _ -> pprPanic "Can't spontaneously solve *given*" empty
669 -- See Note [Avoid double unifications]
670 ; return (Just cts) }
672 occurCheck :: VarEnv (TcTyVar, TcType) -> InertSet
673 -> TcTyVar -> TcType -> Maybe (TcType,CoercionI)
674 -- Traverse @ty@ to make sure that @tv@ does not appear under some flatten skolem.
675 -- If it appears under some flatten skolem look in that flatten skolem equivalence class
676 -- (see Note [InertSet FlattenSkolemEqClass], [Loopy Spontaneous Solving]) to see if you
677 -- can find a different flatten skolem to use, that is, one that does not mention @tv@.
679 -- Postcondition: Just (ty', coi) = occurCheck binds inerts tv ty
681 -- NB: The returned type ty' may not be flat!
683 occurCheck ty_binds inerts the_tv the_ty
684 = ok emptyVarSet the_ty
686 -- If (fsk `elem` bad) then tv occurs in any rendering
687 -- of the type under the expansion of fsk
688 ok bad this_ty@(TyConApp tc tys)
689 | Just tys_cois <- allMaybes (map (ok bad) tys)
690 , (tys',cois') <- unzip tys_cois
691 = Just (TyConApp tc tys', mkTyConAppCoI tc cois')
692 | isSynTyCon tc, Just ty_expanded <- tcView this_ty
693 = ok bad ty_expanded -- See Note [Type synonyms and the occur check] in TcUnify
695 | Just (sty',coi) <- ok_pred bad sty
696 = Just (PredTy sty', coi)
697 ok bad (FunTy arg res)
698 | Just (arg', coiarg) <- ok bad arg, Just (res', coires) <- ok bad res
699 = Just (FunTy arg' res', mkFunTyCoI coiarg coires)
700 ok bad (AppTy fun arg)
701 | Just (fun', coifun) <- ok bad fun, Just (arg', coiarg) <- ok bad arg
702 = Just (AppTy fun' arg', mkAppTyCoI coifun coiarg)
703 ok bad (ForAllTy tv1 ty1)
704 -- WARNING: What if it is a (t1 ~ t2) => t3? It's not handled properly at the moment.
705 | Just (ty1', coi) <- ok bad ty1
706 = Just (ForAllTy tv1 ty1', mkForAllTyCoI tv1 coi)
709 ok bad this_ty@(TyVarTy tv)
710 | tv == the_tv = Nothing -- Occurs check error
711 | not (isTcTyVar tv) = Just (this_ty, IdCo this_ty) -- Bound var
712 | FlatSkol zty <- tcTyVarDetails tv = ok_fsk bad tv zty
713 | Just (_,ty) <- lookupVarEnv ty_binds tv = ok bad ty
714 | otherwise = Just (this_ty, IdCo this_ty)
716 -- Check if there exists a ty bind already, as a result of sneaky unification.
718 ok _bad _ty = Nothing
721 ok_pred bad (ClassP cn tys)
722 | Just tys_cois <- allMaybes $ map (ok bad) tys
723 = let (tys', cois') = unzip tys_cois
724 in Just (ClassP cn tys', mkClassPPredCoI cn cois')
725 ok_pred bad (IParam nm ty)
726 | Just (ty',co') <- ok bad ty
727 = Just (IParam nm ty', mkIParamPredCoI nm co')
728 ok_pred bad (EqPred ty1 ty2)
729 | Just (ty1',coi1) <- ok bad ty1, Just (ty2',coi2) <- ok bad ty2
730 = Just (EqPred ty1' ty2', mkEqPredCoI coi1 coi2)
731 ok_pred _ _ = Nothing
735 | fsk `elemVarSet` bad
736 -- We are already trying to find a rendering of fsk,
737 -- and to do that it seems we need a rendering, so fail
740 = firstJusts (ok new_bad zty : map (go_under_fsk new_bad) fsk_equivs)
742 fsk_equivs = getFskEqClass inerts fsk
743 new_bad = bad `extendVarSetList` (fsk : map fst fsk_equivs)
746 go_under_fsk bad_tvs (fsk,co)
747 | FlatSkol zty <- tcTyVarDetails fsk
748 = case ok bad_tvs zty of
750 Just (ty,coi') -> Just (ty, mkTransCoI coi' (ACo co))
751 | otherwise = pprPanic "go_down_equiv" (ppr fsk)
755 *********************************************************************************
757 The interact-with-inert Stage
759 *********************************************************************************
762 -- Interaction result of WorkItem <~> AtomicInert
764 = IR { ir_stop :: StopOrContinue
766 -- => Reagent (work item) consumed.
767 -- ContinueWith new_reagent
768 -- => Reagent transformed but keep gathering interactions.
769 -- The transformed item remains inert with respect
770 -- to any previously encountered inerts.
772 , ir_inert_action :: InertAction
773 -- Whether the inert item should remain in the InertSet.
775 , ir_new_work :: WorkList
776 -- new work items to add to the WorkList
779 -- What to do with the inert reactant.
780 data InertAction = KeepInert | DropInert
783 mkIRContinue :: Monad m => WorkItem -> InertAction -> WorkList -> m InteractResult
784 mkIRContinue wi keep newWork = return $ IR (ContinueWith wi) keep newWork
786 mkIRStop :: Monad m => InertAction -> WorkList -> m InteractResult
787 mkIRStop keep newWork = return $ IR Stop keep newWork
789 dischargeWorkItem :: Monad m => m InteractResult
790 dischargeWorkItem = mkIRStop KeepInert emptyCCan
792 noInteraction :: Monad m => WorkItem -> m InteractResult
793 noInteraction workItem = mkIRContinue workItem KeepInert emptyCCan
795 data WhichComesFromInert = LeftComesFromInert | RightComesFromInert
797 ---------------------------------------------------
798 -- Interact a single WorkItem with an InertSet as far as possible, i.e. until we get a Stop
799 -- result from an individual interaction (i.e. when the WorkItem is consumed), or until we've
800 -- interacted the WorkItem with the entire InertSet.
802 -- Postcondition: the new InertSet in the resulting StageResult is subset
803 -- of the input InertSet.
805 interactWithInertsStage :: SimplifierStage
806 interactWithInertsStage workItem inert
807 = foldlInertSetM interactNext initITR inert
809 initITR = SR { sr_inerts = emptyInert
810 , sr_new_work = emptyCCan
811 , sr_stop = ContinueWith workItem }
814 interactNext :: StageResult -> AtomicInert -> TcS StageResult
815 interactNext it inert
816 | ContinueWith workItem <- sr_stop it
817 = do { ir <- interactWithInert inert workItem
818 ; let inerts = sr_inerts it
819 ; return $ SR { sr_inerts = if ir_inert_action ir == KeepInert
820 then inerts `updInertSet` inert
822 , sr_new_work = sr_new_work it `unionWorkLists` ir_new_work ir
823 , sr_stop = ir_stop ir } }
824 | otherwise = return $ itrAddInert inert it
827 itrAddInert :: AtomicInert -> StageResult -> StageResult
828 itrAddInert inert itr = itr { sr_inerts = (sr_inerts itr) `updInertSet` inert }
830 -- Do a single interaction of two constraints.
831 interactWithInert :: AtomicInert -> WorkItem -> TcS InteractResult
832 interactWithInert inert workitem
833 = do { ctxt <- getTcSContext
834 ; let is_allowed = allowedInteraction (simplEqsOnly ctxt) inert workitem
835 inert_ev = cc_id inert
836 work_ev = cc_id workitem
838 -- Never interact a wanted and a derived where the derived's evidence
839 -- mentions the wanted evidence in an unguarded way.
840 -- See Note [Superclasses and recursive dictionaries]
841 -- and Note [New Wanted Superclass Work]
842 -- We don't have to do this for givens, as we fully know the evidence for them.
844 case (cc_flavor inert, cc_flavor workitem) of
845 (Wanted loc, Derived _) -> isGoodRecEv work_ev (WantedEvVar inert_ev loc)
846 (Derived _, Wanted loc) -> isGoodRecEv inert_ev (WantedEvVar work_ev loc)
849 ; if is_allowed && rec_ev_ok then
850 doInteractWithInert inert workitem
852 noInteraction workitem
855 allowedInteraction :: Bool -> AtomicInert -> WorkItem -> Bool
856 -- Allowed interactions
857 allowedInteraction eqs_only (CDictCan {}) (CDictCan {}) = not eqs_only
858 allowedInteraction eqs_only (CIPCan {}) (CIPCan {}) = not eqs_only
859 allowedInteraction _ _ _ = True
861 --------------------------------------------
862 doInteractWithInert :: CanonicalCt -> CanonicalCt -> TcS InteractResult
863 -- Identical class constraints.
866 (CDictCan { cc_id = d1, cc_flavor = fl1, cc_class = cls1, cc_tyargs = tys1 })
867 workItem@(CDictCan { cc_id = d2, cc_flavor = fl2, cc_class = cls2, cc_tyargs = tys2 })
868 | cls1 == cls2 && (and $ zipWith tcEqType tys1 tys2)
869 = solveOneFromTheOther (d1,fl1) workItem
871 | cls1 == cls2 && (not (isGiven fl1 && isGiven fl2))
872 = -- See Note [When improvement happens]
873 do { let work_item_pred_loc = (ClassP cls2 tys2, ppr d2)
874 inert_pred_loc = (ClassP cls1 tys1, ppr d1)
875 loc = combineCtLoc fl1 fl2
876 eqn_pred_locs = improveFromAnother work_item_pred_loc inert_pred_loc
877 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
878 -- See Note [Generating extra equalities]
879 ; workList <- canWanteds wevvars
880 ; mkIRContinue workItem KeepInert workList -- Keep the inert there so we avoid
881 -- re-introducing the fundep equalities
882 -- See Note [FunDep Reactions]
885 -- Class constraint and given equality: use the equality to rewrite
886 -- the class constraint.
887 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
888 (CDictCan { cc_id = dv, cc_flavor = wfl, cc_class = cl, cc_tyargs = xis })
889 | ifl `canRewrite` wfl
890 , tv `elemVarSet` tyVarsOfTypes xis
891 -- substitute for tv in xis. Note that the resulting class
892 -- constraint is still canonical, since substituting xi-types in
893 -- xi-types generates xi-types. However, it may no longer be
894 -- inert with respect to the inert set items we've already seen.
895 -- For example, consider the inert set
900 -- and the work item D a (w). D a does not interact with D Int.
901 -- Next, it does interact with a ~g Int, getting rewritten to D
902 -- Int (w). But now we must go back through the rest of the inert
903 -- set again, to find that it can now be discharged by the given D
905 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,wfl,cl,xis)
906 ; mkIRStop KeepInert (singleCCan rewritten_dict) }
908 doInteractWithInert (CDictCan { cc_id = dv, cc_flavor = ifl, cc_class = cl, cc_tyargs = xis })
909 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
910 | wfl `canRewrite` ifl
911 , tv `elemVarSet` tyVarsOfTypes xis
912 = do { rewritten_dict <- rewriteDict (cv,tv,xi) (dv,ifl,cl,xis)
913 ; mkIRContinue workItem DropInert (singleCCan rewritten_dict) }
915 -- Class constraint and given equality: use the equality to rewrite
916 -- the class constraint.
917 doInteractWithInert (CTyEqCan { cc_id = cv, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi })
918 (CIPCan { cc_id = ipid, cc_flavor = wfl, cc_ip_nm = nm, cc_ip_ty = ty })
919 | ifl `canRewrite` wfl
920 , tv `elemVarSet` tyVarsOfType ty
921 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,wfl,nm,ty)
922 ; mkIRStop KeepInert (singleCCan rewritten_ip) }
924 doInteractWithInert (CIPCan { cc_id = ipid, cc_flavor = ifl, cc_ip_nm = nm, cc_ip_ty = ty })
925 workItem@(CTyEqCan { cc_id = cv, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi })
926 | wfl `canRewrite` ifl
927 , tv `elemVarSet` tyVarsOfType ty
928 = do { rewritten_ip <- rewriteIP (cv,tv,xi) (ipid,ifl,nm,ty)
929 ; mkIRContinue workItem DropInert (singleCCan rewritten_ip) }
931 -- Two implicit parameter constraints. If the names are the same,
932 -- but their types are not, we generate a wanted type equality
933 -- that equates the type (this is "improvement").
934 -- However, we don't actually need the coercion evidence,
935 -- so we just generate a fresh coercion variable that isn't used anywhere.
936 doInteractWithInert (CIPCan { cc_id = id1, cc_flavor = ifl, cc_ip_nm = nm1, cc_ip_ty = ty1 })
937 workItem@(CIPCan { cc_flavor = wfl, cc_ip_nm = nm2, cc_ip_ty = ty2 })
938 | nm1 == nm2 && isGiven wfl && isGiven ifl
939 = -- See Note [Overriding implicit parameters]
940 -- Dump the inert item, override totally with the new one
941 -- Do not require type equality
942 mkIRContinue workItem DropInert emptyCCan
944 | nm1 == nm2 && ty1 `tcEqType` ty2
945 = solveOneFromTheOther (id1,ifl) workItem
948 = -- See Note [When improvement happens]
949 do { co_var <- newWantedCoVar ty1 ty2
950 ; let flav = Wanted (combineCtLoc ifl wfl)
951 ; mkCanonical flav co_var >>= mkIRContinue workItem KeepInert }
954 -- Inert: equality, work item: function equality
956 -- Never rewrite a given with a wanted equality, and a type function
957 -- equality can never rewrite an equality. Note also that if we have
958 -- F x1 ~ x2 and a ~ x3, and a occurs in x2, we don't rewrite it. We
959 -- can wait until F x1 ~ x2 matches another F x1 ~ x4, and only then
960 -- we will ``expose'' x2 and x4 to rewriting.
962 -- Otherwise, we can try rewriting the type function equality with the equality.
963 doInteractWithInert (CTyEqCan { cc_id = cv1, cc_flavor = ifl, cc_tyvar = tv, cc_rhs = xi1 })
964 (CFunEqCan { cc_id = cv2, cc_flavor = wfl, cc_fun = tc
965 , cc_tyargs = args, cc_rhs = xi2 })
966 | ifl `canRewrite` wfl
967 , tv `elemVarSet` tyVarsOfTypes args
968 = do { rewritten_funeq <- rewriteFunEq (cv1,tv,xi1) (cv2,wfl,tc,args,xi2)
969 ; mkIRStop KeepInert (singleCCan rewritten_funeq) }
971 -- Inert: function equality, work item: equality
973 doInteractWithInert (CFunEqCan {cc_id = cv1, cc_flavor = ifl, cc_fun = tc
974 , cc_tyargs = args, cc_rhs = xi1 })
975 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = wfl, cc_tyvar = tv, cc_rhs = xi2 })
976 | wfl `canRewrite` ifl
977 , tv `elemVarSet` tyVarsOfTypes args
978 = do { rewritten_funeq <- rewriteFunEq (cv2,tv,xi2) (cv1,ifl,tc,args,xi1)
979 ; mkIRContinue workItem DropInert (singleCCan rewritten_funeq) }
981 doInteractWithInert (CFunEqCan { cc_id = cv1, cc_flavor = fl1, cc_fun = tc1
982 , cc_tyargs = args1, cc_rhs = xi1 })
983 workItem@(CFunEqCan { cc_id = cv2, cc_flavor = fl2, cc_fun = tc2
984 , cc_tyargs = args2, cc_rhs = xi2 })
985 | fl1 `canSolve` fl2 && lhss_match
986 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
987 ; mkIRStop KeepInert cans }
988 | fl2 `canSolve` fl1 && lhss_match
989 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
990 ; mkIRContinue workItem DropInert cans }
992 lhss_match = tc1 == tc2 && and (zipWith tcEqType args1 args2)
995 inert@(CTyEqCan { cc_id = cv1, cc_flavor = fl1, cc_tyvar = tv1, cc_rhs = xi1 })
996 workItem@(CTyEqCan { cc_id = cv2, cc_flavor = fl2, cc_tyvar = tv2, cc_rhs = xi2 })
997 -- Check for matching LHS
998 | fl1 `canSolve` fl2 && tv1 == tv2
999 = do { cans <- rewriteEqLHS LeftComesFromInert (mkCoVarCoercion cv1,xi1) (cv2,fl2,xi2)
1000 ; mkIRStop KeepInert cans }
1002 | fl2 `canSolve` fl1 && tv1 == tv2
1003 = do { cans <- rewriteEqLHS RightComesFromInert (mkCoVarCoercion cv2,xi2) (cv1,fl1,xi1)
1004 ; mkIRContinue workItem DropInert cans }
1006 -- Check for rewriting RHS
1007 | fl1 `canRewrite` fl2 && tv1 `elemVarSet` tyVarsOfType xi2
1008 = do { rewritten_eq <- rewriteEqRHS (cv1,tv1,xi1) (cv2,fl2,tv2,xi2)
1009 ; mkIRStop KeepInert rewritten_eq }
1010 | fl2 `canRewrite` fl1 && tv2 `elemVarSet` tyVarsOfType xi1
1011 = do { rewritten_eq <- rewriteEqRHS (cv2,tv2,xi2) (cv1,fl1,tv1,xi1)
1012 ; mkIRContinue workItem DropInert rewritten_eq }
1014 -- Finally, if workitem is a Flatten Equivalence Class constraint and the
1015 -- inert is a wanted constraint, even when the workitem cannot rewrite the
1016 -- inert, drop the inert out because you may have to reconsider solving the
1017 -- inert *using* the equivalence class you created. See note [Loopy Spontaneous Solving]
1018 -- and [InertSet FlattenSkolemEqClass]
1020 | not $ isGiven fl1, -- The inert is wanted or derived
1021 isMetaTyVar tv1, -- and has a unification variable lhs
1022 FlatSkol {} <- tcTyVarDetails tv2, -- And workitem is a flatten skolem equality
1023 Just tv2' <- tcGetTyVar_maybe xi2, FlatSkol {} <- tcTyVarDetails tv2'
1024 = mkIRContinue workItem DropInert (singletonWorkList inert)
1027 -- Fall-through case for all other situations
1028 doInteractWithInert _ workItem = noInteraction workItem
1030 -------------------------
1031 -- Equational Rewriting
1032 rewriteDict :: (CoVar, TcTyVar, Xi) -> (DictId, CtFlavor, Class, [Xi]) -> TcS CanonicalCt
1033 rewriteDict (cv,tv,xi) (dv,gw,cl,xis)
1034 = do { let cos = substTysWith [tv] [mkCoVarCoercion cv] xis -- xis[tv] ~ xis[xi]
1035 args = substTysWith [tv] [xi] xis
1037 dict_co = mkTyConCoercion con cos
1038 ; dv' <- newDictVar cl args
1040 Wanted {} -> setDictBind dv (EvCast dv' (mkSymCoercion dict_co))
1041 _given_or_derived -> setDictBind dv' (EvCast dv dict_co)
1042 ; return (CDictCan { cc_id = dv'
1045 , cc_tyargs = args }) }
1047 rewriteIP :: (CoVar,TcTyVar,Xi) -> (EvVar,CtFlavor, IPName Name, TcType) -> TcS CanonicalCt
1048 rewriteIP (cv,tv,xi) (ipid,gw,nm,ty)
1049 = do { let ip_co = substTyWith [tv] [mkCoVarCoercion cv] ty -- ty[tv] ~ t[xi]
1050 ty' = substTyWith [tv] [xi] ty
1051 ; ipid' <- newIPVar nm ty'
1053 Wanted {} -> setIPBind ipid (EvCast ipid' (mkSymCoercion ip_co))
1054 _given_or_derived -> setIPBind ipid' (EvCast ipid ip_co)
1055 ; return (CIPCan { cc_id = ipid'
1058 , cc_ip_ty = ty' }) }
1060 rewriteFunEq :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TyCon, [Xi], Xi) -> TcS CanonicalCt
1061 rewriteFunEq (cv1,tv,xi1) (cv2,gw, tc,args,xi2)
1062 = do { let arg_cos = substTysWith [tv] [mkCoVarCoercion cv1] args
1063 args' = substTysWith [tv] [xi1] args
1064 fun_co = mkTyConCoercion tc arg_cos
1065 ; cv2' <- case gw of
1066 Wanted {} -> do { cv2' <- newWantedCoVar (mkTyConApp tc args') xi2
1067 ; setWantedCoBind cv2 $
1068 mkTransCoercion fun_co (mkCoVarCoercion cv2')
1070 _giv_or_der -> newGivOrDerCoVar (mkTyConApp tc args') xi2 $
1071 mkTransCoercion (mkSymCoercion fun_co) (mkCoVarCoercion cv2)
1072 ; return (CFunEqCan { cc_id = cv2'
1079 rewriteEqRHS :: (CoVar,TcTyVar,Xi) -> (CoVar,CtFlavor,TcTyVar,Xi) -> TcS CanonicalCts
1080 -- Use the first equality to rewrite the second, flavors already checked.
1081 -- E.g. c1 : tv1 ~ xi1 c2 : tv2 ~ xi2
1082 -- rewrites c2 to give
1083 -- c2' : tv2 ~ xi2[xi1/tv1]
1084 -- We must do an occurs check to sure the new constraint is canonical
1085 -- So we might return an empty bag
1086 rewriteEqRHS (cv1,tv1,xi1) (cv2,gw,tv2,xi2)
1087 | Just tv2' <- tcGetTyVar_maybe xi2'
1088 , tv2 == tv2' -- In this case xi2[xi1/tv1] = tv2, so we have tv2~tv2
1089 = do { when (isWanted gw) (setWantedCoBind cv2 (mkSymCoercion co2'))
1090 ; return emptyCCan }
1095 -> do { cv2' <- newWantedCoVar (mkTyVarTy tv2) xi2'
1096 ; setWantedCoBind cv2 $
1097 mkCoVarCoercion cv2' `mkTransCoercion` mkSymCoercion co2'
1100 -> newGivOrDerCoVar (mkTyVarTy tv2) xi2' $
1101 mkCoVarCoercion cv2 `mkTransCoercion` co2'
1103 ; xi2'' <- canOccursCheck gw tv2 xi2' -- we know xi2' is *not* tv2
1104 ; return (singleCCan $ CTyEqCan { cc_id = cv2'
1110 xi2' = substTyWith [tv1] [xi1] xi2
1111 co2' = substTyWith [tv1] [mkCoVarCoercion cv1] xi2 -- xi2 ~ xi2[xi1/tv1]
1114 rewriteEqLHS :: WhichComesFromInert -> (Coercion,Xi) -> (CoVar,CtFlavor,Xi) -> TcS CanonicalCts
1115 -- Used to ineratct two equalities of the following form:
1116 -- First Equality: co1: (XXX ~ xi1)
1117 -- Second Equality: cv2: (XXX ~ xi2)
1118 -- Where the cv1 `canSolve` cv2 equality
1119 -- We have an option of creating new work (xi1 ~ xi2) OR (xi2 ~ xi1). This
1120 -- depends on whether the left or the right equality comes from the inert set.
1122 -- prefer to create (xi2 ~ xi1) if the first comes from the inert
1123 -- prefer to create (xi1 ~ xi2) if the second comes from the inert
1124 rewriteEqLHS which (co1,xi1) (cv2,gw,xi2)
1125 = do { cv2' <- case (isWanted gw, which) of
1126 (True,LeftComesFromInert) ->
1127 do { cv2' <- newWantedCoVar xi2 xi1
1128 ; setWantedCoBind cv2 $
1129 co1 `mkTransCoercion` mkSymCoercion (mkCoVarCoercion cv2')
1131 (True,RightComesFromInert) ->
1132 do { cv2' <- newWantedCoVar xi1 xi2
1133 ; setWantedCoBind cv2 $
1134 co1 `mkTransCoercion` mkCoVarCoercion cv2'
1136 (False,LeftComesFromInert) ->
1137 newGivOrDerCoVar xi2 xi1 $
1138 mkSymCoercion (mkCoVarCoercion cv2) `mkTransCoercion` co1
1139 (False,RightComesFromInert) ->
1140 newGivOrDerCoVar xi1 xi2 $
1141 mkSymCoercion co1 `mkTransCoercion` mkCoVarCoercion cv2
1142 ; mkCanonical gw cv2' }
1146 solveOneFromTheOther :: (EvVar, CtFlavor) -> CanonicalCt -> TcS InteractResult
1147 -- First argument inert, second argument workitem. They both represent
1148 -- wanted/given/derived evidence for the *same* predicate so we try here to
1149 -- discharge one directly from the other.
1151 -- Precondition: value evidence only (implicit parameters, classes)
1153 solveOneFromTheOther (iid,ifl) workItem
1154 -- Both derived needs a special case. You might think that we do not need
1155 -- two evidence terms for the same claim. But, since the evidence is partial,
1156 -- either evidence may do in some cases; see TcSMonad.isGoodRecEv.
1157 -- See also Example 3 in Note [Superclasses and recursive dictionaries]
1158 | isDerived ifl && isDerived wfl
1159 = noInteraction workItem
1161 | ifl `canSolve` wfl
1162 = do { unless (isGiven wfl) $ setEvBind wid (EvId iid)
1163 -- Overwrite the binding, if one exists
1164 -- For Givens, which are lambda-bound, nothing to overwrite,
1165 ; dischargeWorkItem }
1167 | otherwise -- wfl `canSolve` ifl
1168 = do { unless (isGiven ifl) $ setEvBind iid (EvId wid)
1169 ; mkIRContinue workItem DropInert emptyCCan }
1172 wfl = cc_flavor workItem
1173 wid = cc_id workItem
1176 Note [Superclasses and recursive dictionaries]
1177 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1178 Overlaps with Note [SUPERCLASS-LOOP 1]
1179 Note [SUPERCLASS-LOOP 2]
1180 Note [Recursive instances and superclases]
1181 ToDo: check overlap and delete redundant stuff
1183 Right before adding a given into the inert set, we must
1184 produce some more work, that will bring the superclasses
1185 of the given into scope. The superclass constraints go into
1188 When we simplify a wanted constraint, if we first see a matching
1189 instance, we may produce new wanted work. To (1) avoid doing this work
1190 twice in the future and (2) to handle recursive dictionaries we may ``cache''
1191 this item as solved (in effect, given) into our inert set and with that add
1192 its superclass constraints (as given) in our worklist.
1194 But now we have added partially solved constraints to the worklist which may
1195 interact with other wanteds. Consider the example:
1199 class Eq b => Foo a b --- 0-th selector
1200 instance Eq a => Foo [a] a --- fooDFun
1202 and wanted (Foo [t] t). We are first going to see that the instance matches
1203 and create an inert set that includes the solved (Foo [t] t) and its
1205 d1 :_g Foo [t] t d1 := EvDFunApp fooDFun d3
1206 d2 :_g Eq t d2 := EvSuperClass d1 0
1207 Our work list is going to contain a new *wanted* goal
1209 It is wrong to react the wanted (Eq t) with the given (Eq t) because that would
1210 construct loopy evidence. Hence the check isGoodRecEv in doInteractWithInert.
1212 OK, so we have ruled out bad behaviour, but how do we ge recursive dictionaries,
1217 data D r = ZeroD | SuccD (r (D r));
1219 instance (Eq (r (D r))) => Eq (D r) where
1220 ZeroD == ZeroD = True
1221 (SuccD a) == (SuccD b) = a == b
1224 equalDC :: D [] -> D [] -> Bool;
1227 We need to prove (Eq (D [])). Here's how we go:
1231 by instance decl, holds if
1235 *BUT* we have an inert set which gives us (no superclasses):
1237 By the instance declaration of Eq we can show the 'd2' goal if
1239 where d2 = dfEqList d3
1241 Now, however this wanted can interact with our inert d1 to set:
1243 and solve the goal. Why was this interaction OK? Because, if we chase the
1244 evidence of d1 ~~> dfEqD d2 ~~-> dfEqList d3, so by setting d3 := d1 we
1246 d3 := dfEqD2 (dfEqList d3)
1247 which is FINE because the use of d3 is protected by the instance function
1250 So, our strategy is to try to put solved wanted dictionaries into the
1251 inert set along with their superclasses (when this is meaningful,
1252 i.e. when new wanted goals are generated) but solve a wanted dictionary
1253 from a given only in the case where the evidence variable of the
1254 wanted is mentioned in the evidence of the given (recursively through
1255 the evidence binds) in a protected way: more instance function applications
1256 than superclass selectors.
1258 Here are some more examples from GHC's previous type checker
1262 This code arises in the context of "Scrap Your Boilerplate with Class"
1266 instance Sat (ctx Char) => Data ctx Char -- dfunData1
1267 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a] -- dfunData2
1269 class Data Maybe a => Foo a
1271 instance Foo t => Sat (Maybe t) -- dfunSat
1273 instance Data Maybe a => Foo a -- dfunFoo1
1274 instance Foo a => Foo [a] -- dfunFoo2
1275 instance Foo [Char] -- dfunFoo3
1277 Consider generating the superclasses of the instance declaration
1278 instance Foo a => Foo [a]
1280 So our problem is this
1282 d1 :_w Data Maybe [t]
1284 We may add the given in the inert set, along with its superclasses
1285 [assuming we don't fail because there is a matching instance, see
1286 tryTopReact, given case ]
1290 d01 :_g Data Maybe t -- d2 := EvDictSuperClass d0 0
1291 d1 :_w Data Maybe [t]
1292 Then d2 can readily enter the inert, and we also do solving of the wanted
1295 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1297 d2 :_w Sat (Maybe [t])
1299 d01 :_g Data Maybe t
1300 Now, we may simplify d2 more:
1303 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1304 d1 :_g Data Maybe [t]
1305 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1309 d01 :_g Data Maybe t
1311 Now, we can just solve d3.
1314 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1315 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1318 d01 :_g Data Maybe t
1319 And now we can simplify d4 again, but since it has superclasses we *add* them to the worklist:
1322 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1323 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1324 d4 :_g Foo [t] d4 := dfunFoo2 d5
1327 d6 :_g Data Maybe [t] d6 := EvDictSuperClass d4 0
1328 d01 :_g Data Maybe t
1329 Now, d5 can be solved! (and its superclass enter scope)
1332 d1 :_s Data Maybe [t] d1 := dfunData2 d2 d3
1333 d2 :_g Sat (Maybe [t]) d2 := dfunSat d4
1334 d4 :_g Foo [t] d4 := dfunFoo2 d5
1335 d5 :_g Foo t d5 := dfunFoo1 d7
1338 d6 :_g Data Maybe [t]
1339 d8 :_g Data Maybe t d8 := EvDictSuperClass d5 0
1340 d01 :_g Data Maybe t
1343 [1] Suppose we pick d8 and we react him with d01. Which of the two givens should
1344 we keep? Well, we *MUST NOT* drop d01 because d8 contains recursive evidence
1345 that must not be used (look at case interactInert where both inert and workitem
1346 are givens). So we have several options:
1347 - Drop the workitem always (this will drop d8)
1348 This feels very unsafe -- what if the work item was the "good" one
1349 that should be used later to solve another wanted?
1350 - Don't drop anyone: the inert set may contain multiple givens!
1351 [This is currently implemented]
1353 The "don't drop anyone" seems the most safe thing to do, so now we come to problem 2:
1354 [2] We have added both d6 and d01 in the inert set, and we are interacting our wanted
1355 d7. Now the [isRecDictEv] function in the ineration solver
1356 [case inert-given workitem-wanted] will prevent us from interacting d7 := d8
1357 precisely because chasing the evidence of d8 leads us to an unguarded use of d7.
1359 So, no interaction happens there. Then we meet d01 and there is no recursion
1360 problem there [isRectDictEv] gives us the OK to interact and we do solve d7 := d01!
1362 Note [SUPERCLASS-LOOP 1]
1363 ~~~~~~~~~~~~~~~~~~~~~~~~
1364 We have to be very, very careful when generating superclasses, lest we
1365 accidentally build a loop. Here's an example:
1369 class S a => C a where { opc :: a -> a }
1370 class S b => D b where { opd :: b -> b }
1372 instance C Int where
1375 instance D Int where
1378 From (instance C Int) we get the constraint set {ds1:S Int, dd:D Int}
1379 Simplifying, we may well get:
1380 $dfCInt = :C ds1 (opd dd)
1383 Notice that we spot that we can extract ds1 from dd.
1385 Alas! Alack! We can do the same for (instance D Int):
1387 $dfDInt = :D ds2 (opc dc)
1391 And now we've defined the superclass in terms of itself.
1392 Two more nasty cases are in
1397 - Satisfy the superclass context *all by itself*
1398 (tcSimplifySuperClasses)
1399 - And do so completely; i.e. no left-over constraints
1400 to mix with the constraints arising from method declarations
1403 Note [SUPERCLASS-LOOP 2]
1404 ~~~~~~~~~~~~~~~~~~~~~~~~
1405 We need to be careful when adding "the constaint we are trying to prove".
1406 Suppose we are *given* d1:Ord a, and want to deduce (d2:C [a]) where
1408 class Ord a => C a where
1409 instance Ord [a] => C [a] where ...
1411 Then we'll use the instance decl to deduce C [a] from Ord [a], and then add the
1412 superclasses of C [a] to avails. But we must not overwrite the binding
1413 for Ord [a] (which is obtained from Ord a) with a superclass selection or we'll just
1416 Here's another variant, immortalised in tcrun020
1417 class Monad m => C1 m
1418 class C1 m => C2 m x
1419 instance C2 Maybe Bool
1420 For the instance decl we need to build (C1 Maybe), and it's no good if
1421 we run around and add (C2 Maybe Bool) and its superclasses to the avails
1422 before we search for C1 Maybe.
1424 Here's another example
1425 class Eq b => Foo a b
1426 instance Eq a => Foo [a] a
1430 we'll first deduce that it holds (via the instance decl). We must not
1431 then overwrite the Eq t constraint with a superclass selection!
1433 At first I had a gross hack, whereby I simply did not add superclass constraints
1434 in addWanted, though I did for addGiven and addIrred. This was sub-optimal,
1435 becuase it lost legitimate superclass sharing, and it still didn't do the job:
1436 I found a very obscure program (now tcrun021) in which improvement meant the
1437 simplifier got two bites a the cherry... so something seemed to be an Stop
1438 first time, but reducible next time.
1440 Now we implement the Right Solution, which is to check for loops directly
1441 when adding superclasses. It's a bit like the occurs check in unification.
1443 Note [Recursive instances and superclases]
1444 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1445 Consider this code, which arises in the context of "Scrap Your
1446 Boilerplate with Class".
1450 instance Sat (ctx Char) => Data ctx Char
1451 instance (Sat (ctx [a]), Data ctx a) => Data ctx [a]
1453 class Data Maybe a => Foo a
1455 instance Foo t => Sat (Maybe t)
1457 instance Data Maybe a => Foo a
1458 instance Foo a => Foo [a]
1461 In the instance for Foo [a], when generating evidence for the superclasses
1462 (ie in tcSimplifySuperClasses) we need a superclass (Data Maybe [a]).
1463 Using the instance for Data, we therefore need
1464 (Sat (Maybe [a], Data Maybe a)
1465 But we are given (Foo a), and hence its superclass (Data Maybe a).
1466 So that leaves (Sat (Maybe [a])). Using the instance for Sat means
1467 we need (Foo [a]). And that is the very dictionary we are bulding
1468 an instance for! So we must put that in the "givens". So in this
1470 Given: Foo a, Foo [a]
1471 Wanted: Data Maybe [a]
1473 BUT we must *not not not* put the *superclasses* of (Foo [a]) in
1474 the givens, which is what 'addGiven' would normally do. Why? Because
1475 (Data Maybe [a]) is the superclass, so we'd "satisfy" the wanted
1476 by selecting a superclass from Foo [a], which simply makes a loop.
1478 On the other hand we *must* put the superclasses of (Foo a) in
1479 the givens, as you can see from the derivation described above.
1481 Conclusion: in the very special case of tcSimplifySuperClasses
1482 we have one 'given' (namely the "this" dictionary) whose superclasses
1483 must not be added to 'givens' by addGiven.
1485 There is a complication though. Suppose there are equalities
1486 instance (Eq a, a~b) => Num (a,b)
1487 Then we normalise the 'givens' wrt the equalities, so the original
1488 given "this" dictionary is cast to one of a different type. So it's a
1489 bit trickier than before to identify the "special" dictionary whose
1490 superclasses must not be added. See test
1491 indexed-types/should_run/EqInInstance
1493 We need a persistent property of the dictionary to record this
1494 special-ness. Current I'm using the InstLocOrigin (a bit of a hack,
1495 but cool), which is maintained by dictionary normalisation.
1496 Specifically, the InstLocOrigin is
1498 then the no-superclass thing kicks in. WATCH OUT if you fiddle
1501 Note [MATCHING-SYNONYMS]
1502 ~~~~~~~~~~~~~~~~~~~~~~~~
1503 When trying to match a dictionary (D tau) to a top-level instance, or a
1504 type family equation (F taus_1 ~ tau_2) to a top-level family instance,
1505 we do *not* need to expand type synonyms because the matcher will do that for us.
1508 Note [RHS-FAMILY-SYNONYMS]
1509 ~~~~~~~~~~~~~~~~~~~~~~~~~~
1510 The RHS of a family instance is represented as yet another constructor which is
1511 like a type synonym for the real RHS the programmer declared. Eg:
1512 type instance F (a,a) = [a]
1514 :R32 a = [a] -- internal type synonym introduced
1515 F (a,a) ~ :R32 a -- instance
1517 When we react a family instance with a type family equation in the work list
1518 we keep the synonym-using RHS without expansion.
1521 *********************************************************************************
1523 The top-reaction Stage
1525 *********************************************************************************
1528 -- If a work item has any form of interaction with top-level we get this
1529 data TopInteractResult
1530 = NoTopInt -- No top-level interaction
1532 { tir_new_work :: WorkList -- Sub-goals or new work (could be given,
1533 -- for superclasses)
1534 , tir_new_inert :: StopOrContinue -- The input work item, ready to become *inert* now:
1535 } -- NB: in ``given'' (solved) form if the
1536 -- original was wanted or given and instance match
1537 -- was found, but may also be in wanted form if we
1538 -- only reacted with functional dependencies
1539 -- arising from top-level instances.
1541 topReactionsStage :: SimplifierStage
1542 topReactionsStage workItem inerts
1543 = do { tir <- tryTopReact workItem
1546 return $ SR { sr_inerts = inerts
1547 , sr_new_work = emptyWorkList
1548 , sr_stop = ContinueWith workItem }
1549 SomeTopInt tir_new_work tir_new_inert ->
1550 return $ SR { sr_inerts = inerts
1551 , sr_new_work = tir_new_work
1552 , sr_stop = tir_new_inert
1556 tryTopReact :: WorkItem -> TcS TopInteractResult
1557 tryTopReact workitem
1558 = do { -- A flag controls the amount of interaction allowed
1559 -- See Note [Simplifying RULE lhs constraints]
1560 ctxt <- getTcSContext
1561 ; if allowedTopReaction (simplEqsOnly ctxt) workitem
1562 then do { traceTcS "tryTopReact / calling doTopReact" (ppr workitem)
1563 ; doTopReact workitem }
1564 else return NoTopInt
1567 allowedTopReaction :: Bool -> WorkItem -> Bool
1568 allowedTopReaction eqs_only (CDictCan {}) = not eqs_only
1569 allowedTopReaction _ _ = True
1572 doTopReact :: WorkItem -> TcS TopInteractResult
1573 -- The work item does not react with the inert set,
1574 -- so try interaction with top-level instances
1575 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = Wanted loc
1576 , cc_class = cls, cc_tyargs = xis })
1577 = do { -- See Note [MATCHING-SYNONYMS]
1578 ; lkp_inst_res <- matchClassInst cls xis loc
1579 ; case lkp_inst_res of
1580 NoInstance -> do { traceTcS "doTopReact/ no class instance for" (ppr dv)
1582 GenInst wtvs ev_term -> -- Solved
1583 -- No need to do fundeps stuff here; the instance
1584 -- matches already so we won't get any more info
1585 -- from functional dependencies
1586 do { traceTcS "doTopReact/ found class instance for" (ppr dv)
1587 ; setDictBind dv ev_term
1588 ; workList <- canWanteds wtvs
1590 -- Solved in one step and no new wanted work produced.
1591 -- i.e we directly matched a top-level instance
1592 -- No point in caching this in 'inert', nor in adding superclasses
1593 then return $ SomeTopInt { tir_new_work = emptyCCan
1594 , tir_new_inert = Stop }
1596 -- Solved and new wanted work produced, you may cache the
1597 -- (tentatively solved) dictionary as Derived and its superclasses
1598 else do { let solved = makeSolved workItem
1599 ; sc_work <- newSCWorkFromFlavored dv (Derived loc) cls xis
1600 ; return $ SomeTopInt
1601 { tir_new_work = workList `unionWorkLists` sc_work
1602 , tir_new_inert = ContinueWith solved } }
1606 -- Try for a fundep reaction beween the wanted item
1607 -- and a top-level instance declaration
1609 = do { instEnvs <- getInstEnvs
1610 ; let eqn_pred_locs = improveFromInstEnv (classInstances instEnvs)
1611 (ClassP cls xis, ppr dv)
1612 ; wevvars <- mkWantedFunDepEqns loc eqn_pred_locs
1613 -- NB: fundeps generate some wanted equalities, but
1614 -- we don't use their evidence for anything
1615 ; fd_work <- canWanteds wevvars
1616 ; sc_work <- newSCWorkFromFlavored dv (Derived loc) cls xis
1617 ; return $ SomeTopInt { tir_new_work = fd_work `unionWorkLists` sc_work
1618 , tir_new_inert = ContinueWith workItem }
1619 -- NB: workItem is inert, but it isn't solved
1620 -- keep it as inert, although it's not solved because we
1621 -- have now reacted all its top-level fundep-induced equalities!
1623 -- See Note [FunDep Reactions]
1626 -- Otherwise, we have a given or derived
1627 doTopReact workItem@(CDictCan { cc_id = dv, cc_flavor = fl
1628 , cc_class = cls, cc_tyargs = xis })
1629 = do { sc_work <- newSCWorkFromFlavored dv fl cls xis
1630 ; return $ SomeTopInt sc_work (ContinueWith workItem) }
1631 -- See Note [Given constraint that matches an instance declaration]
1634 doTopReact (CFunEqCan { cc_id = cv, cc_flavor = fl
1635 , cc_fun = tc, cc_tyargs = args, cc_rhs = xi })
1636 = ASSERT (isSynFamilyTyCon tc) -- No associated data families have reached that far
1637 do { match_res <- matchFam tc args -- See Note [MATCHING-SYNONYMS]
1641 MatchInstSingle (rep_tc, rep_tys)
1642 -> do { let Just coe_tc = tyConFamilyCoercion_maybe rep_tc
1643 Just rhs_ty = tcView (mkTyConApp rep_tc rep_tys)
1644 -- Eagerly expand away the type synonym on the
1645 -- RHS of a type function, so that it never
1646 -- appears in an error message
1647 -- See Note [Type synonym families] in TyCon
1648 coe = mkTyConApp coe_tc rep_tys
1650 Wanted {} -> do { cv' <- newWantedCoVar rhs_ty xi
1651 ; setWantedCoBind cv $
1652 coe `mkTransCoercion`
1655 _ -> newGivOrDerCoVar xi rhs_ty $
1656 mkSymCoercion (mkCoVarCoercion cv) `mkTransCoercion` coe
1658 ; workList <- mkCanonical fl cv'
1659 ; return $ SomeTopInt workList Stop }
1661 -> panicTcS $ text "TcSMonad.matchFam returned multiple instances!"
1665 -- Any other work item does not react with any top-level equations
1666 doTopReact _workItem = return NoTopInt
1669 Note [FunDep and implicit parameter reactions]
1670 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1671 Currently, our story of interacting two dictionaries (or a dictionary
1672 and top-level instances) for functional dependencies, and implicit
1673 paramters, is that we simply produce new wanted equalities. So for example
1675 class D a b | a -> b where ...
1681 We generate the extra work item
1683 where 'cv' is currently unused. However, this new item reacts with d2,
1684 discharging it in favour of a new constraint d2' thus:
1686 d2 := d2' |> D Int cv
1687 Now d2' can be discharged from d1
1689 We could be more aggressive and try to *immediately* solve the dictionary
1690 using those extra equalities. With the same inert set and work item we
1691 might dischard d2 directly:
1694 d2 := d1 |> D Int cv
1696 But in general it's a bit painful to figure out the necessary coercion,
1697 so we just take the first approach.
1699 It's exactly the same with implicit parameters, except that the
1700 "aggressive" approach would be much easier to implement.
1702 Note [When improvement happens]
1703 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1704 We fire an improvement rule when
1706 * Two constraints match (modulo the fundep)
1707 e.g. C t1 t2, C t1 t3 where C a b | a->b
1708 The two match because the first arg is identical
1710 * At least one is not Given. If they are both given, we don't fire
1711 the reaction because we have no way of constructing evidence for a
1712 new equality nor does it seem right to create a new wanted goal
1713 (because the goal will most likely contain untouchables, which
1714 can't be solved anyway)!
1716 Note that we *do* fire the improvement if one is Given and one is Derived.
1717 The latter can be a superclass of a wanted goal. Example (tcfail138)
1718 class L a b | a -> b
1719 class (G a, L a b) => C a b
1721 instance C a b' => G (Maybe a)
1722 instance C a b => C (Maybe a) a
1723 instance L (Maybe a) a
1725 When solving the superclasses of the (C (Maybe a) a) instance, we get
1726 Given: C a b ... and hance by superclasses, (G a, L a b)
1728 Use the instance decl to get
1730 The (C a b') is inert, so we generate its Derived superclasses (L a b'),
1731 and now we need improvement between that derived superclass an the Given (L a b)
1733 Note [Overriding implicit parameters]
1734 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1736 f :: (?x::a) -> Bool -> a
1738 g v = let ?x::Int = 3
1739 in (f v, let ?x::Bool = True in f v)
1741 This should probably be well typed, with
1742 g :: Bool -> (Int, Bool)
1744 So the inner binding for ?x::Bool *overrides* the outer one.
1745 Hence a work-item Given overrides an inert-item Given.
1747 Note [Given constraint that matches an instance declaration]
1748 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1749 What should we do when we discover that one (or more) top-level
1750 instances match a given (or solved) class constraint? We have
1753 1. Reject the program. The reason is that there may not be a unique
1754 best strategy for the solver. Example, from the OutsideIn(X) paper:
1755 instance P x => Q [x]
1756 instance (x ~ y) => R [x] y
1758 wob :: forall a b. (Q [b], R b a) => a -> Int
1760 g :: forall a. Q [a] => [a] -> Int
1763 will generate the impliation constraint:
1764 Q [a] => (Q [beta], R beta [a])
1765 If we react (Q [beta]) with its top-level axiom, we end up with a
1766 (P beta), which we have no way of discharging. On the other hand,
1767 if we react R beta [a] with the top-level we get (beta ~ a), which
1768 is solvable and can help us rewrite (Q [beta]) to (Q [a]) which is
1769 now solvable by the given Q [a].
1771 However, this option is restrictive, for instance [Example 3] from
1772 Note [Recursive dictionaries] will fail to work.
1774 2. Ignore the problem, hoping that the situations where there exist indeed
1775 such multiple strategies are rare: Indeed the cause of the previous
1776 problem is that (R [x] y) yields the new work (x ~ y) which can be
1777 *spontaneously* solved, not using the givens.
1779 We are choosing option 2 below but we might consider having a flag as well.
1782 Note [New Wanted Superclass Work]
1783 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1784 Even in the case of wanted constraints, we add all of its superclasses as
1785 new given work. There are several reasons for this:
1786 a) to minimise error messages;
1787 eg suppose we have wanted (Eq a, Ord a)
1788 then we report only (Ord a) unsoluble
1790 b) to make the smallest number of constraints when *inferring* a type
1791 (same Eq/Ord example)
1793 c) for recursive dictionaries we *must* add the superclasses
1794 so that we can use them when solving a sub-problem
1796 d) To allow FD-like improvement for type families. Assume that
1798 class C a b | a -> b
1799 and we have to solve the implication constraint:
1801 Then, FD improvement can help us to produce a new wanted (beta ~ b)
1803 We want to have the same effect with the type family encoding of
1804 functional dependencies. Namely, consider:
1805 class (F a ~ b) => C a b
1806 Now suppose that we have:
1809 By interacting the given we will get given (F a ~ b) which is not
1810 enough by itself to make us discharge (C a beta). However, we
1811 may create a new derived equality from the super-class of the
1812 wanted constraint (C a beta), namely derived (F a ~ beta).
1813 Now we may interact this with given (F a ~ b) to get:
1815 But 'beta' is a touchable unification variable, and hence OK to
1816 unify it with 'b', replacing the derived evidence with the identity.
1818 This requires trySpontaneousSolve to solve *derived*
1819 equalities that have a touchable in their RHS, *in addition*
1820 to solving wanted equalities.
1822 Here is another example where this is useful.
1826 class (F a ~ b) => C a b
1827 And we are given the wanteds:
1831 We surely do *not* want to quantify over (b ~ c), since if someone provides
1832 dictionaries for (C a b) and (C a c), these dictionaries can provide a proof
1833 of (b ~ c), hence no extra evidence is necessary. Here is what will happen:
1835 Step 1: We will get new *given* superclass work,
1836 provisionally to our solving of w1 and w2
1838 g1: F a ~ b, g2 : F a ~ c,
1839 w1 : C a b, w2 : C a c, w3 : b ~ c
1841 The evidence for g1 and g2 is a superclass evidence term:
1843 g1 := sc w1, g2 := sc w2
1845 Step 2: The givens will solve the wanted w3, so that
1846 w3 := sym (sc w1) ; sc w2
1848 Step 3: Now, one may naively assume that then w2 can be solve from w1
1849 after rewriting with the (now solved equality) (b ~ c).
1851 But this rewriting is ruled out by the isGoodRectDict!
1853 Conclusion, we will (correctly) end up with the unsolved goals
1856 NB: The desugarer needs be more clever to deal with equalities
1857 that participate in recursive dictionary bindings.
1860 newSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi]
1862 newSCWorkFromFlavored ev flavor cls xis
1863 | Given loc <- flavor -- The NoScSkol says "don't add superclasses"
1864 , NoScSkol <- ctLocOrigin loc -- Very important!
1865 = return emptyWorkList
1868 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
1869 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
1870 -- Add *all* its superclasses (equalities or not) as new given work
1871 -- See Note [New Wanted Superclass Work]
1872 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
1873 ; mkCanonicals flavor sc_vars }
1875 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
1877 data LookupInstResult
1879 | GenInst [WantedEvVar] EvTerm
1881 matchClassInst :: Class -> [Type] -> WantedLoc -> TcS LookupInstResult
1882 matchClassInst clas tys loc
1883 = do { let pred = mkClassPred clas tys
1884 ; mb_result <- matchClass clas tys
1886 MatchInstNo -> return NoInstance
1887 MatchInstMany -> return NoInstance -- defer any reactions of a multitude until
1888 -- we learn more about the reagent
1889 MatchInstSingle (dfun_id, mb_inst_tys) ->
1890 do { checkWellStagedDFun pred dfun_id loc
1892 -- It's possible that not all the tyvars are in
1893 -- the substitution, tenv. For example:
1894 -- instance C X a => D X where ...
1895 -- (presumably there's a functional dependency in class C)
1896 -- Hence mb_inst_tys :: Either TyVar TcType
1898 ; tys <- instDFunTypes mb_inst_tys
1899 ; let (theta, _) = tcSplitPhiTy (applyTys (idType dfun_id) tys)
1900 ; if null theta then
1901 return (GenInst [] (EvDFunApp dfun_id tys []))
1903 { ev_vars <- instDFunConstraints theta
1904 ; let wevs = [WantedEvVar w loc | w <- ev_vars]
1905 ; return $ GenInst wevs (EvDFunApp dfun_id tys ev_vars) }