{-# LANGUAGE CPP #-} module TcCanonical( canonicalize, unifyDerived, makeSuperClasses, mkGivensWithSuperClasses, StopOrContinue(..), stopWith, continueWith ) where #include "HsVersions.h" import TcRnTypes import TcType import Type import TcFlatten import TcSMonad import TcEvidence import Class import TyCon import TyCoRep -- cleverly decomposes types, good for completeness checking import Coercion import FamInstEnv ( FamInstEnvs ) import FamInst ( tcTopNormaliseNewTypeTF_maybe ) import Var import Name( isSystemName ) import Outputable import DynFlags( DynFlags ) import VarSet import NameSet import RdrName import Pair import Util import Bag import MonadUtils import Control.Monad import Data.List ( zip4, foldl' ) import BasicTypes #if __GLASGOW_HASKELL__ < 709 bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d bimap f _ (Left x) = Left (f x) bimap _ f (Right x) = Right (f x) #else import Data.Bifunctor ( bimap ) #endif {- ************************************************************************ * * * The Canonicaliser * * * ************************************************************************ Note [Canonicalization] ~~~~~~~~~~~~~~~~~~~~~~~ Canonicalization converts a simple constraint to a canonical form. It is unary (i.e. treats individual constraints one at a time), does not do any zonking, but lives in TcS monad because it needs to create fresh variables (for flattening) and consult the inerts (for efficiency). The execution plan for canonicalization is the following: 1) Decomposition of equalities happens as necessary until we reach a variable or type family in one side. There is no decomposition step for other forms of constraints. 2) If, when we decompose, we discover a variable on the head then we look at inert_eqs from the current inert for a substitution for this variable and contine decomposing. Hence we lazily apply the inert substitution if it is needed. 3) If no more decomposition is possible, we deeply apply the substitution from the inert_eqs and continue with flattening. 4) During flattening, we examine whether we have already flattened some function application by looking at all the CTyFunEqs with the same function in the inert set. The reason for deeply applying the inert substitution at step (3) is to maximise our chances of matching an already flattened family application in the inert. The net result is that a constraint coming out of the canonicalization phase cannot be rewritten any further from the inerts (but maybe /it/ can rewrite an inert or still interact with an inert in a further phase in the simplifier. Note [Caching for canonicals] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Our plan with pre-canonicalization is to be able to solve a constraint really fast from existing bindings in TcEvBinds. So one may think that the condition (isCNonCanonical) is not necessary. However consider the following setup: InertSet = { [W] d1 : Num t } WorkList = { [W] d2 : Num t, [W] c : t ~ Int} Now, we prioritize equalities, but in our concrete example (should_run/mc17.hs) the first (d2) constraint is dealt with first, because (t ~ Int) is an equality that only later appears in the worklist since it is pulled out from a nested implication constraint. So, let's examine what happens: - We encounter work item (d2 : Num t) - Nothing is yet in EvBinds, so we reach the interaction with inerts and set: d2 := d1 and we discard d2 from the worklist. The inert set remains unaffected. - Now the equation ([W] c : t ~ Int) is encountered and kicks-out (d1 : Num t) from the inerts. Then that equation gets spontaneously solved, perhaps. We end up with: InertSet : { [G] c : t ~ Int } WorkList : { [W] d1 : Num t} - Now we examine (d1), we observe that there is a binding for (Num t) in the evidence binds and we set: d1 := d2 and end up in a loop! Now, the constraints that get kicked out from the inert set are always Canonical, so by restricting the use of the pre-canonicalizer to NonCanonical constraints we eliminate this danger. Moreover, for canonical constraints we already have good caching mechanisms (effectively the interaction solver) and we are interested in reducing things like superclasses of the same non-canonical constraint being generated hence I don't expect us to lose a lot by introducing the (isCNonCanonical) restriction. A similar situation can arise in TcSimplify, at the end of the solve_wanteds function, where constraints from the inert set are returned as new work -- our substCt ensures however that if they are not rewritten by subst, they remain canonical and hence we will not attempt to solve them from the EvBinds. If on the other hand they did get rewritten and are now non-canonical they will still not match the EvBinds, so we are again good. -} -- Top-level canonicalization -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ canonicalize :: Ct -> TcS (StopOrContinue Ct) canonicalize ct@(CNonCanonical { cc_ev = ev }) = do { traceTcS "canonicalize (non-canonical)" (ppr ct) ; {-# SCC "canEvVar" #-} canEvNC ev } canonicalize (CDictCan { cc_ev = ev, cc_class = cls , cc_tyargs = xis, cc_pend_sc = pend_sc }) = {-# SCC "canClass" #-} canClass ev cls xis pend_sc canonicalize (CTyEqCan { cc_ev = ev , cc_tyvar = tv , cc_rhs = xi , cc_eq_rel = eq_rel }) = {-# SCC "canEqLeafTyVarEq" #-} canEqNC ev eq_rel (mkTyVarTy tv) xi -- NB: Don't use canEqTyVar because that expects flattened types, -- and tv and xi may not be flat w.r.t. an updated inert set canonicalize (CFunEqCan { cc_ev = ev , cc_fun = fn , cc_tyargs = xis1 , cc_fsk = fsk }) = {-# SCC "canEqLeafFunEq" #-} canCFunEqCan ev fn xis1 fsk canonicalize (CIrredEvCan { cc_ev = ev }) = canIrred ev canonicalize (CHoleCan { cc_ev = ev, cc_hole = hole }) = canHole ev hole canEvNC :: CtEvidence -> TcS (StopOrContinue Ct) -- Called only for non-canonical EvVars canEvNC ev = case classifyPredType (ctEvPred ev) of ClassPred cls tys -> do traceTcS "canEvNC:cls" (ppr cls <+> ppr tys) canClassNC ev cls tys EqPred eq_rel ty1 ty2 -> do traceTcS "canEvNC:eq" (ppr ty1 $$ ppr ty2) canEqNC ev eq_rel ty1 ty2 IrredPred {} -> do traceTcS "canEvNC:irred" (ppr (ctEvPred ev)) canIrred ev {- ************************************************************************ * * * Class Canonicalization * * ************************************************************************ -} canClassNC :: CtEvidence -> Class -> [Type] -> TcS (StopOrContinue Ct) -- Precondition: EvVar is class evidence canClassNC ev cls tys = canClass ev cls tys (has_scs cls) where has_scs cls = not (null (classSCTheta cls)) canClass :: CtEvidence -> Class -> [Type] -> Bool -> TcS (StopOrContinue Ct) -- Precondition: EvVar is class evidence canClass ev cls tys pend_sc = -- all classes do *nominal* matching ASSERT2( ctEvRole ev == Nominal, ppr ev $$ ppr cls $$ ppr tys ) do { (xis, cos) <- flattenManyNom ev tys ; let co = mkTcTyConAppCo Nominal (classTyCon cls) cos xi = mkClassPred cls xis mk_ct new_ev = CDictCan { cc_ev = new_ev , cc_tyargs = xis , cc_class = cls , cc_pend_sc = pend_sc } ; mb <- rewriteEvidence ev xi co ; traceTcS "canClass" (vcat [ ppr ev , ppr xi, ppr mb ]) ; return (fmap mk_ct mb) } {- Note [The superclass story] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We need to add superclass constraints for two reasons: * For givens, they give us a route to to proof. E.g. f :: Ord a => a -> Bool f x = x == x We get a Wanted (Eq a), which can only be solved from the superclass of the Given (Ord a). * For wanteds, they may give useful functional dependencies. E.g. class C a b | a -> b where ... class C a b => D a b where ... Now a Wanted constraint (D Int beta) has (C Int beta) as a superclass and that might tell us about beta, via C's fundeps. We can get this by generateing a Derived (C Int beta) constraint. It's derived because we don't actually have to cough up any evidence for it; it's only there to generate fundep equalities. See Note [Why adding superclasses can help]. For these reasons we want to generate superclass constraints for both Givens and Wanteds. But: * (Minor) they are often not needed, so generating them aggressively is a waste of time. * (Major) if we want recursive superclasses, there would be an infinite number of them. Here is a real-life example (Trac #10318); class (Frac (Frac a) ~ Frac a, Fractional (Frac a), IntegralDomain (Frac a)) => IntegralDomain a where type Frac a :: * Notice that IntegralDomain has an associated type Frac, and one of IntegralDomain's superclasses is another IntegralDomain constraint. So here's the plan: 1. Generate superclasses for given (but not wanted) constraints; see Note [Aggressively expand given superclasses]. However stop if you encounter the same class twice. That is, expand eagerly, but have a conservative termination condition: see Note [Expanding superclasses] in TcType. 2. Solve the wanteds as usual, but do /no/ expansion of superclasses in solveSimpleGivens or solveSimpleWanteds. See Note [Danger of adding superclasses during solving] 3. If we have any remaining unsolved wanteds (see Note [When superclasses help] in TcRnTypes) try harder: take both the Givens and Wanteds, and expand superclasses again. This may succeed in generating (a finite number of) extra Givens, and extra Deriveds. Both may help the proof. This is done in TcSimplify.expandSuperClasses. 4. Go round to (2) again. This loop (2,3,4) is implemented in TcSimplify.simpl_loop. We try to terminate the loop by flagging which class constraints (given or wanted) are potentially un-expanded. This is what the cc_pend_sc flag is for in CDictCan. So in Step 3 we only expand superclasses for constraints with cc_pend_sc set to true (i.e. isPendingScDict holds). When we take a CNonCanonical or CIrredCan, but end up classifying it as a CDictCan, we set the cc_pend_sc flag to False. Note [Aggressively expand given superclasses] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In step (1) of Note [The superclass story], why do we aggressively expand Given superclasses by one layer? Mainly because of some very obscure cases like this: instance Bad a => Eq (T a) f :: (Ord (T a)) => blah f x = ....needs Eq (T a), Ord (T a).... Here if we can't satisfy (Eq (T a)) from the givens we'll use the instance declaration; but then we are stuck with (Bad a). Sigh. This is really a case of non-confluent proofs, but to stop our users complaining we expand one layer in advance. Note [Why adding superclasses can help] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Examples of how adding superclasses can help: --- Example 1 class C a b | a -> b Suppose we want to solve [G] C a b [W] C a beta Then adding [D] beta~b will let us solve it. -- Example 2 (similar but using a type-equality superclass) class (F a ~ b) => C a b And try to sllve: [G] C a b [W] C a beta Follow the superclass rules to add [G] F a ~ b [D] F a ~ beta Now we we get [D] beta ~ b, and can solve that. -- Example (tcfail138) class L a b | a -> b class (G a, L a b) => C a b instance C a b' => G (Maybe a) instance C a b => C (Maybe a) a instance L (Maybe a) a When solving the superclasses of the (C (Maybe a) a) instance, we get [G] C a b, and hance by superclasses, [G] G a, [G] L a b [W] G (Maybe a) Use the instance decl to get [W] C a beta Generate its derived superclass [D] L a beta. Now using fundeps, combine with [G] L a b to get [D] beta ~ b which is what we want. Note [Danger of adding superclasses during solving] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Here's a serious, but now out-dated example, from Trac #4497: class Num (RealOf t) => Normed t type family RealOf x Assume the generated wanted constraint is: [W] RealOf e ~ e [W] Normed e If we were to be adding the superclasses during simplification we'd get: [W] RealOf e ~ e [W] Normed e [D] RealOf e ~ fuv [D] Num fuv ==> e := fuv, Num fuv, Normed fuv, RealOf fuv ~ fuv While looks exactly like our original constraint. If we add the superclass of (Normed fuv) again we'd loop. By adding superclasses definitely only once, during canonicalisation, this situation can't happen. Mind you, now that Wanteds cannot rewrite Derived, I think this particular situation can't happen. -} mkGivensWithSuperClasses :: CtLoc -> [EvId] -> TcS [Ct] -- From a given EvId, make its Ct, plus the Ct's of its superclasses -- See Note [The superclass story] -- The loop-breaking here follows Note [Expanding superclasses] in TcType -- -- Example: class D a => C a -- class C [a] => D a -- makeGivensWithSuperClasses (C x) will return (C x, D x, C[x]) -- i.e. up to and including the first repetition of C mkGivensWithSuperClasses loc ev_ids = concatMapM go ev_ids where go ev_id = mk_superclasses emptyNameSet this_ev where this_ev = CtGiven { ctev_evar = ev_id , ctev_pred = evVarPred ev_id , ctev_loc = loc } makeSuperClasses :: [Ct] -> TcS [Ct] -- Returns strict superclasses, transitively, see Note [The superclasses story] -- See Note [The superclass story] -- The loop-breaking here follows Note [Expanding superclasses] in TcType -- Specifically, for an incoming (C t) constraint, we return all of (C t)'s -- superclasses, up to /and including/ the first repetition of C -- -- Example: class D a => C a -- class C [a] => D a -- makeSuperClasses (C x) will return (D x, C [x]) -- -- NB: the incoming constraints have had their cc_pend_sc flag already -- flipped to False, by isPendingScDict, so we are /obliged/ to at -- least produce the immediate superclasses makeSuperClasses cts = concatMapM go cts where go (CDictCan { cc_ev = ev, cc_class = cls, cc_tyargs = tys }) = mk_strict_superclasses (unitNameSet (className cls)) ev cls tys go ct = pprPanic "makeSuperClasses" (ppr ct) mk_superclasses :: NameSet -> CtEvidence -> TcS [Ct] -- Return this constraint, plus its superclasses, if any mk_superclasses rec_clss ev | ClassPred cls tys <- classifyPredType (ctEvPred ev) = mk_superclasses_of rec_clss ev cls tys | otherwise -- Superclass is not a class predicate = return [mkNonCanonical ev] mk_superclasses_of :: NameSet -> CtEvidence -> Class -> [Type] -> TcS [Ct] -- Always return this class constraint, -- and expand its superclasses mk_superclasses_of rec_clss ev cls tys | loop_found = return [this_ct] -- cc_pend_sc of this_ct = True | otherwise = do { sc_cts <- mk_strict_superclasses rec_clss' ev cls tys ; return (this_ct : sc_cts) } -- cc_pend_sc of this_ct = False where cls_nm = className cls loop_found = cls_nm `elemNameSet` rec_clss rec_clss' | isCTupleClass cls = rec_clss -- Never contribute to recursion | otherwise = rec_clss `extendNameSet` cls_nm this_ct = CDictCan { cc_ev = ev, cc_class = cls, cc_tyargs = tys , cc_pend_sc = loop_found } -- NB: If there is a loop, we cut off, so we have not -- added the superclasses, hence cc_pend_sc = True mk_strict_superclasses :: NameSet -> CtEvidence -> Class -> [Type] -> TcS [Ct] -- Always return the immediate superclasses of (cls tys); -- and expand their superclasses, provided none of them are in rec_clss -- nor are repeated mk_strict_superclasses rec_clss ev cls tys | CtGiven { ctev_evar = evar, ctev_loc = loc } <- ev = do { sc_evs <- newGivenEvVars (mk_given_loc loc) (mkEvScSelectors (EvId evar) cls tys) ; concatMapM (mk_superclasses rec_clss) sc_evs } | isEmptyVarSet (tyCoVarsOfTypes tys) = return [] -- Wanteds with no variables yield no deriveds. -- See Note [Improvement from Ground Wanteds] | otherwise -- Wanted/Derived case, just add those SC that can lead to improvement. = do { let loc = ctEvLoc ev ; sc_evs <- mapM (newDerivedNC loc) (immSuperClasses cls tys) ; concatMapM (mk_superclasses rec_clss) sc_evs } where size = sizeTypes tys mk_given_loc loc | isCTupleClass cls = loc -- For tuple predicates, just take them apart, without -- adding their (large) size into the chain. When we -- get down to a base predicate, we'll include its size. -- Trac #10335 | GivenOrigin skol_info <- ctLocOrigin loc -- See Note [Solving superclass constraints] in TcInstDcls -- for explantation of this transformation for givens = case skol_info of InstSkol -> loc { ctl_origin = GivenOrigin (InstSC size) } InstSC n -> loc { ctl_origin = GivenOrigin (InstSC (n `max` size)) } _ -> loc | otherwise -- Probably doesn't happen, since this function = loc -- is only used for Givens, but does no harm {- ************************************************************************ * * * Irreducibles canonicalization * * ************************************************************************ -} canIrred :: CtEvidence -> TcS (StopOrContinue Ct) -- Precondition: ty not a tuple and no other evidence form canIrred old_ev = do { let old_ty = ctEvPred old_ev ; traceTcS "can_pred" (text "IrredPred = " <+> ppr old_ty) ; (xi,co) <- flatten FM_FlattenAll old_ev old_ty -- co :: xi ~ old_ty ; rewriteEvidence old_ev xi co `andWhenContinue` \ new_ev -> do { -- Re-classify, in case flattening has improved its shape ; case classifyPredType (ctEvPred new_ev) of ClassPred cls tys -> canClassNC new_ev cls tys EqPred eq_rel ty1 ty2 -> canEqNC new_ev eq_rel ty1 ty2 _ -> continueWith $ CIrredEvCan { cc_ev = new_ev } } } canHole :: CtEvidence -> Hole -> TcS (StopOrContinue Ct) canHole ev hole = do { let ty = ctEvPred ev ; (xi,co) <- flatten FM_SubstOnly ev ty -- co :: xi ~ ty ; rewriteEvidence ev xi co `andWhenContinue` \ new_ev -> do { emitInsoluble (CHoleCan { cc_ev = new_ev , cc_hole = hole }) ; stopWith new_ev "Emit insoluble hole" } } {- ************************************************************************ * * * Equalities * * ************************************************************************ Note [Canonicalising equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In order to canonicalise an equality, we look at the structure of the two types at hand, looking for similarities. A difficulty is that the types may look dissimilar before flattening but similar after flattening. However, we don't just want to jump in and flatten right away, because this might be wasted effort. So, after looking for similarities and failing, we flatten and then try again. Of course, we don't want to loop, so we track whether or not we've already flattened. It is conceivable to do a better job at tracking whether or not a type is flattened, but this is left as future work. (Mar '15) -} canEqNC :: CtEvidence -> EqRel -> Type -> Type -> TcS (StopOrContinue Ct) canEqNC ev eq_rel ty1 ty2 = do { result <- zonk_eq_types ty1 ty2 ; case result of Left (Pair ty1' ty2') -> can_eq_nc False ev eq_rel ty1' ty1 ty2' ty2 Right ty -> canEqReflexive ev eq_rel ty } can_eq_nc :: Bool -- True => both types are flat -> CtEvidence -> EqRel -> Type -> Type -- LHS, after and before type-synonym expansion, resp -> Type -> Type -- RHS, after and before type-synonym expansion, resp -> TcS (StopOrContinue Ct) can_eq_nc flat ev eq_rel ty1 ps_ty1 ty2 ps_ty2 = do { traceTcS "can_eq_nc" $ vcat [ ppr ev, ppr eq_rel, ppr ty1, ppr ps_ty1, ppr ty2, ppr ps_ty2 ] ; rdr_env <- getGlobalRdrEnvTcS ; fam_insts <- getFamInstEnvs ; can_eq_nc' flat rdr_env fam_insts ev eq_rel ty1 ps_ty1 ty2 ps_ty2 } can_eq_nc' :: Bool -- True => both input types are flattened -> GlobalRdrEnv -- needed to see which newtypes are in scope -> FamInstEnvs -- needed to unwrap data instances -> CtEvidence -> EqRel -> Type -> Type -- LHS, after and before type-synonym expansion, resp -> Type -> Type -- RHS, after and before type-synonym expansion, resp -> TcS (StopOrContinue Ct) -- Expand synonyms first; see Note [Type synonyms and canonicalization] can_eq_nc' flat _rdr_env _envs ev eq_rel ty1 ps_ty1 ty2 ps_ty2 | Just ty1' <- coreView ty1 = can_eq_nc flat ev eq_rel ty1' ps_ty1 ty2 ps_ty2 | Just ty2' <- coreView ty2 = can_eq_nc flat ev eq_rel ty1 ps_ty1 ty2' ps_ty2 -- need to check for reflexivity in the ReprEq case. -- See Note [Eager reflexivity check] -- Check only when flat because the zonk_eq_types check in canEqNC takes -- care of the non-flat case. can_eq_nc' True _rdr_env _envs ev ReprEq ty1 _ ty2 _ | ty1 `tcEqType` ty2 = canEqReflexive ev ReprEq ty1 -- When working with ReprEq, unwrap newtypes. can_eq_nc' _flat rdr_env envs ev ReprEq ty1 _ ty2 ps_ty2 | Just (co, ty1') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty1 = can_eq_newtype_nc rdr_env ev NotSwapped co ty1 ty1' ty2 ps_ty2 can_eq_nc' _flat rdr_env envs ev ReprEq ty1 ps_ty1 ty2 _ | Just (co, ty2') <- tcTopNormaliseNewTypeTF_maybe envs rdr_env ty2 = can_eq_newtype_nc rdr_env ev IsSwapped co ty2 ty2' ty1 ps_ty1 -- Then, get rid of casts can_eq_nc' flat _rdr_env _envs ev eq_rel (CastTy ty1 co1) _ ty2 ps_ty2 = canEqCast flat ev eq_rel NotSwapped ty1 co1 ty2 ps_ty2 can_eq_nc' flat _rdr_env _envs ev eq_rel ty1 ps_ty1 (CastTy ty2 co2) _ = canEqCast flat ev eq_rel IsSwapped ty2 co2 ty1 ps_ty1 ---------------------- -- Otherwise try to decompose ---------------------- -- Literals can_eq_nc' _flat _rdr_env _envs ev eq_rel ty1@(LitTy l1) _ (LitTy l2) _ | l1 == l2 = do { setEqIfWanted ev (mkReflCo (eqRelRole eq_rel) ty1) ; stopWith ev "Equal LitTy" } -- Try to decompose type constructor applications -- Including FunTy (s -> t) can_eq_nc' _flat _rdr_env _envs ev eq_rel ty1 _ ty2 _ | Just (tc1, tys1) <- tcRepSplitTyConApp_maybe ty1 , Just (tc2, tys2) <- tcRepSplitTyConApp_maybe ty2 , not (isTypeFamilyTyCon tc1) , not (isTypeFamilyTyCon tc2) = canTyConApp ev eq_rel tc1 tys1 tc2 tys2 can_eq_nc' _flat _rdr_env _envs ev eq_rel s1@(ForAllTy (Named {}) _) _ s2@(ForAllTy (Named {}) _) _ | CtWanted { ctev_loc = loc, ctev_dest = orig_dest } <- ev = do { let (bndrs1,body1) = tcSplitNamedPiTys s1 (bndrs2,body2) = tcSplitNamedPiTys s2 ; if not (equalLength bndrs1 bndrs2) || not (map binderVisibility bndrs1 == map binderVisibility bndrs2) then canEqHardFailure ev s1 s2 else do { traceTcS "Creating implication for polytype equality" $ ppr ev ; kind_cos <- zipWithM (unifyWanted loc Nominal) (map binderType bndrs1) (map binderType bndrs2) ; all_co <- deferTcSForAllEq (eqRelRole eq_rel) loc kind_cos (bndrs1,body1) (bndrs2,body2) ; setWantedEq orig_dest all_co ; stopWith ev "Deferred polytype equality" } } | otherwise = do { traceTcS "Omitting decomposition of given polytype equality" $ pprEq s1 s2 -- See Note [Do not decompose given polytype equalities] ; stopWith ev "Discard given polytype equality" } -- See Note [Canonicalising type applications] about why we require flat types can_eq_nc' True _rdr_env _envs ev eq_rel (AppTy t1 s1) _ ty2 _ | Just (t2, s2) <- tcSplitAppTy_maybe ty2 = can_eq_app ev eq_rel t1 s1 t2 s2 can_eq_nc' True _rdr_env _envs ev eq_rel ty1 _ (AppTy t2 s2) _ | Just (t1, s1) <- tcSplitAppTy_maybe ty1 = can_eq_app ev eq_rel t1 s1 t2 s2 -- No similarity in type structure detected. Flatten and try again. can_eq_nc' False rdr_env envs ev eq_rel _ ps_ty1 _ ps_ty2 = do { (xi1, co1) <- flatten FM_FlattenAll ev ps_ty1 ; (xi2, co2) <- flatten FM_FlattenAll ev ps_ty2 ; rewriteEqEvidence ev NotSwapped xi1 xi2 co1 co2 `andWhenContinue` \ new_ev -> can_eq_nc' True rdr_env envs new_ev eq_rel xi1 xi1 xi2 xi2 } -- Type variable on LHS or RHS are last. We want only flat types sent -- to canEqTyVar. -- See also Note [No top-level newtypes on RHS of representational equalities] can_eq_nc' True _rdr_env _envs ev eq_rel (TyVarTy tv1) _ _ ps_ty2 = canEqTyVar ev eq_rel NotSwapped tv1 ps_ty2 can_eq_nc' True _rdr_env _envs ev eq_rel _ ps_ty1 (TyVarTy tv2) _ = canEqTyVar ev eq_rel IsSwapped tv2 ps_ty1 -- We've flattened and the types don't match. Give up. can_eq_nc' True _rdr_env _envs ev _eq_rel _ ps_ty1 _ ps_ty2 = do { traceTcS "can_eq_nc' catch-all case" (ppr ps_ty1 $$ ppr ps_ty2) ; canEqHardFailure ev ps_ty1 ps_ty2 } --------------------------------- -- | Compare types for equality, while zonking as necessary. Gives up -- as soon as it finds that two types are not equal. -- This is quite handy when some unification has made two -- types in an inert wanted to be equal. We can discover the equality without -- flattening, which is sometimes very expensive (in the case of type functions). -- In particular, this function makes a ~20% improvement in test case -- perf/compiler/T5030. -- -- Returns either the (partially zonked) types in the case of -- inequality, or the one type in the case of equality. canEqReflexive is -- a good next step in the 'Right' case. Returning 'Left' is always safe. -- -- NB: This does *not* look through type synonyms. In fact, it treats type -- synonyms as rigid constructors. In the future, it might be convenient -- to look at only those arguments of type synonyms that actually appear -- in the synonym RHS. But we're not there yet. zonk_eq_types :: TcType -> TcType -> TcS (Either (Pair TcType) TcType) zonk_eq_types = go where go (TyVarTy tv1) (TyVarTy tv2) = tyvar_tyvar tv1 tv2 go (TyVarTy tv1) ty2 = tyvar NotSwapped tv1 ty2 go ty1 (TyVarTy tv2) = tyvar IsSwapped tv2 ty1 go ty1 ty2 | Just (tc1, tys1) <- tcRepSplitTyConApp_maybe ty1 , Just (tc2, tys2) <- tcRepSplitTyConApp_maybe ty2 , tc1 == tc2 = tycon tc1 tys1 tys2 go ty1 ty2 | Just (ty1a, ty1b) <- tcRepSplitAppTy_maybe ty1 , Just (ty2a, ty2b) <- tcRepSplitAppTy_maybe ty2 = do { res_a <- go ty1a ty2a ; res_b <- go ty1b ty2b ; return $ combine_rev mkAppTy res_b res_a } go ty1@(LitTy lit1) (LitTy lit2) | lit1 == lit2 = return (Right ty1) go ty1 ty2 = return $ Left (Pair ty1 ty2) -- we don't handle more complex forms here tyvar :: SwapFlag -> TcTyVar -> TcType -> TcS (Either (Pair TcType) TcType) -- try to do as little as possible, as anything we do here is redundant -- with flattening. In particular, no need to zonk kinds. That's why -- we don't use the already-defined zonking functions tyvar swapped tv ty = case tcTyVarDetails tv of MetaTv { mtv_ref = ref } -> do { cts <- readTcRef ref ; case cts of Flexi -> give_up Indirect ty' -> unSwap swapped go ty' ty } _ -> give_up where give_up = return $ Left $ unSwap swapped Pair (mkTyVarTy tv) ty tyvar_tyvar tv1 tv2 | tv1 == tv2 = return (Right (mkTyVarTy tv1)) | otherwise = do { (ty1', progress1) <- quick_zonk tv1 ; (ty2', progress2) <- quick_zonk tv2 ; if progress1 || progress2 then go ty1' ty2' else return $ Left (Pair (TyVarTy tv1) (TyVarTy tv2)) } quick_zonk tv = case tcTyVarDetails tv of MetaTv { mtv_ref = ref } -> do { cts <- readTcRef ref ; case cts of Flexi -> return (TyVarTy tv, False) Indirect ty' -> return (ty', True) } _ -> return (TyVarTy tv, False) -- This happens for type families, too. But recall that failure -- here just means to try harder, so it's OK if the type function -- isn't injective. tycon :: TyCon -> [TcType] -> [TcType] -> TcS (Either (Pair TcType) TcType) tycon tc tys1 tys2 = do { results <- zipWithM go tys1 tys2 ; return $ case combine_results results of Left tys -> Left (mkTyConApp tc <$> tys) Right tys -> Right (mkTyConApp tc tys) } combine_results :: [Either (Pair TcType) TcType] -> Either (Pair [TcType]) [TcType] combine_results = bimap (fmap reverse) reverse . foldl' (combine_rev (:)) (Right []) -- combine (in reverse) a new result onto an already-combined result combine_rev :: (a -> b -> c) -> Either (Pair b) b -> Either (Pair a) a -> Either (Pair c) c combine_rev f (Left list) (Left elt) = Left (f <$> elt <*> list) combine_rev f (Left list) (Right ty) = Left (f <$> pure ty <*> list) combine_rev f (Right tys) (Left elt) = Left (f <$> elt <*> pure tys) combine_rev f (Right tys) (Right ty) = Right (f ty tys) {- Note [Newtypes can blow the stack] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have newtype X = MkX (Int -> X) newtype Y = MkY (Int -> Y) and now wish to prove [W] X ~R Y This Wanted will loop, expanding out the newtypes ever deeper looking for a solid match or a solid discrepancy. Indeed, there is something appropriate to this looping, because X and Y *do* have the same representation, in the limit -- they're both (Fix ((->) Int)). However, no finitely-sized coercion will ever witness it. This loop won't actually cause GHC to hang, though, because we check our depth when unwrapping newtypes. Note [Eager reflexivity check] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have newtype X = MkX (Int -> X) and [W] X ~R X Naively, we would start unwrapping X and end up in a loop. Instead, we do this eager reflexivity check. This is necessary only for representational equality because the flattener technology deals with the similar case (recursive type families) for nominal equality. Note that this check does not catch all cases, but it will catch the cases we're most worried about, types like X above that are actually inhabited. Here's another place where this reflexivity check is key: Consider trying to prove (f a) ~R (f a). The AppTys in there can't be decomposed, because representational equality isn't congruent with respect to AppTy. So, when canonicalising the equality above, we get stuck and would normally produce a CIrredEvCan. However, we really do want to be able to solve (f a) ~R (f a). So, in the representational case only, we do a reflexivity check. (This would be sound in the nominal case, but unnecessary, and I [Richard E.] am worried that it would slow down the common case.) -} ------------------------ -- | We're able to unwrap a newtype. Update the bits accordingly. can_eq_newtype_nc :: GlobalRdrEnv -> CtEvidence -- ^ :: ty1 ~ ty2 -> SwapFlag -> TcCoercion -- ^ :: ty1 ~ ty1' -> TcType -- ^ ty1 -> TcType -- ^ ty1' -> TcType -- ^ ty2 -> TcType -- ^ ty2, with type synonyms -> TcS (StopOrContinue Ct) can_eq_newtype_nc rdr_env ev swapped co ty1 ty1' ty2 ps_ty2 = do { traceTcS "can_eq_newtype_nc" $ vcat [ ppr ev, ppr swapped, ppr co, ppr ty1', ppr ty2 ] -- check for blowing our stack: -- See Note [Newtypes can blow the stack] ; checkReductionDepth (ctEvLoc ev) ty1 ; addUsedDataCons rdr_env (tyConAppTyCon ty1) -- we have actually used the newtype constructor here, so -- make sure we don't warn about importing it! ; rewriteEqEvidence ev swapped ty1' ps_ty2 (mkTcSymCo co) (mkTcReflCo Representational ps_ty2) `andWhenContinue` \ new_ev -> can_eq_nc False new_ev ReprEq ty1' ty1' ty2 ps_ty2 } --------- -- ^ Decompose a type application. -- All input types must be flat. See Note [Canonicalising type applications] can_eq_app :: CtEvidence -- :: s1 t1 ~r s2 t2 -> EqRel -- r -> Xi -> Xi -- s1 t1 -> Xi -> Xi -- s2 t2 -> TcS (StopOrContinue Ct) -- AppTys only decompose for nominal equality, so this case just leads -- to an irreducible constraint; see typecheck/should_compile/T10494 -- See Note [Decomposing equality], note {4} can_eq_app ev ReprEq _ _ _ _ = do { traceTcS "failing to decompose representational AppTy equality" (ppr ev) ; continueWith (CIrredEvCan { cc_ev = ev }) } -- no need to call canEqFailure, because that flattens, and the -- types involved here are already flat can_eq_app ev NomEq s1 t1 s2 t2 | CtDerived { ctev_loc = loc } <- ev = do { unifyDeriveds loc [Nominal, Nominal] [s1, t1] [s2, t2] ; stopWith ev "Decomposed [D] AppTy" } | CtWanted { ctev_dest = dest, ctev_loc = loc } <- ev = do { co_s <- unifyWanted loc Nominal s1 s2 ; co_t <- unifyWanted loc Nominal t1 t2 ; let co = mkAppCo co_s co_t ; setWantedEq dest co ; stopWith ev "Decomposed [W] AppTy" } | CtGiven { ctev_evar = evar, ctev_loc = loc } <- ev = do { let co = mkTcCoVarCo evar co_s = mkTcLRCo CLeft co co_t = mkTcLRCo CRight co ; evar_s <- newGivenEvVar loc ( mkTcEqPredLikeEv ev s1 s2 , EvCoercion co_s ) ; evar_t <- newGivenEvVar loc ( mkTcEqPredLikeEv ev t1 t2 , EvCoercion co_t ) ; emitWorkNC [evar_t] ; canEqNC evar_s NomEq s1 s2 } | otherwise -- Can't happen = error "can_eq_app" ----------------------- -- | Break apart an equality over a casted type canEqCast :: Bool -- are both types flat? -> CtEvidence -> EqRel -> SwapFlag -> TcType -> Coercion -- LHS (res. RHS), the casted type -> TcType -> TcType -- RHS (res. LHS), both normal and pretty -> TcS (StopOrContinue Ct) canEqCast flat ev eq_rel swapped ty1 co1 ty2 ps_ty2 = do { traceTcS "Decomposing cast" (vcat [ ppr ev , ppr ty1 <+> text "|>" <+> ppr co1 , ppr ps_ty2 ]) ; rewriteEqEvidence ev swapped ty1 ps_ty2 (mkTcReflCo role ty1 `mkTcCoherenceRightCo` co1) (mkTcReflCo role ps_ty2) `andWhenContinue` \ new_ev -> can_eq_nc flat new_ev eq_rel ty1 ty1 ty2 ps_ty2 } where role = eqRelRole eq_rel ------------------------ canTyConApp :: CtEvidence -> EqRel -> TyCon -> [TcType] -> TyCon -> [TcType] -> TcS (StopOrContinue Ct) -- See Note [Decomposing TyConApps] canTyConApp ev eq_rel tc1 tys1 tc2 tys2 | tc1 == tc2 , length tys1 == length tys2 = do { inerts <- getTcSInerts ; if can_decompose inerts then do { traceTcS "canTyConApp" (ppr ev $$ ppr eq_rel $$ ppr tc1 $$ ppr tys1 $$ ppr tys2) ; canDecomposableTyConAppOK ev eq_rel tc1 tys1 tys2 ; stopWith ev "Decomposed TyConApp" } else canEqFailure ev eq_rel ty1 ty2 } -- Fail straight away for better error messages -- See Note [Use canEqFailure in canDecomposableTyConApp] | eq_rel == ReprEq && not (isGenerativeTyCon tc1 Representational && isGenerativeTyCon tc2 Representational) = canEqFailure ev eq_rel ty1 ty2 | otherwise = canEqHardFailure ev ty1 ty2 where ty1 = mkTyConApp tc1 tys1 ty2 = mkTyConApp tc2 tys2 loc = ctEvLoc ev pred = ctEvPred ev -- See Note [Decomposing equality] can_decompose inerts = isInjectiveTyCon tc1 (eqRelRole eq_rel) || (ctEvFlavour ev /= Given && isEmptyBag (matchableGivens loc pred inerts)) {- Note [Use canEqFailure in canDecomposableTyConApp] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We must use canEqFailure, not canEqHardFailure here, because there is the possibility of success if working with a representational equality. Here is one case: type family TF a where TF Char = Bool data family DF a newtype instance DF Bool = MkDF Int Suppose we are canonicalising (Int ~R DF (TF a)), where we don't yet know `a`. This is *not* a hard failure, because we might soon learn that `a` is, in fact, Char, and then the equality succeeds. Here is another case: [G] Age ~R Int where Age's constructor is not in scope. We don't want to report an "inaccessible code" error in the context of this Given! For example, see typecheck/should_compile/T10493, repeated here: import Data.Ord (Down) -- no constructor foo :: Coercible (Down Int) Int => Down Int -> Int foo = coerce That should compile, but only because we use canEqFailure and not canEqHardFailure. Note [Decomposing equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ If we have a constraint (of any flavour and role) that looks like T tys1 ~ T tys2, what can we conclude about tys1 and tys2? The answer, of course, is "it depends". This Note spells it all out. In this Note, "decomposition" refers to taking the constraint [fl] (T tys1 ~X T tys2) (for some flavour fl and some role X) and replacing it with [fls'] (tys1 ~Xs' tys2) where that notation indicates a list of new constraints, where the new constraints may have different flavours and different roles. The key property to consider is injectivity. When decomposing a Given the decomposition is sound if and only if T is injective in all of its type arguments. When decomposing a Wanted, the decomposition is sound (assuming the correct roles in the produced equality constraints), but it may be a guess -- that is, an unforced decision by the constraint solver. Decomposing Wanteds over injective TyCons does not entail guessing. But sometimes we want to decompose a Wanted even when the TyCon involved is not injective! (See below.) So, in broad strokes, we want this rule: (*) Decompose a constraint (T tys1 ~X T tys2) if and only if T is injective at role X. Pursuing the details requires exploring three axes: * Flavour: Given vs. Derived vs. Wanted * Role: Nominal vs. Representational * TyCon species: datatype vs. newtype vs. data family vs. type family vs. type variable (So a type variable isn't a TyCon, but it's convenient to put the AppTy case in the same table.) Right away, we can say that Derived behaves just as Wanted for the purposes of decomposition. The difference between Derived and Wanted is the handling of evidence. Since decomposition in these cases isn't a matter of soundness but of guessing, we want the same behavior regardless of evidence. Here is a table (discussion following) detailing where decomposition of (T s1 ... sn) ~r (T t1 .. tn) is allowed. The first four lines (Data types ... type family) refer to TyConApps with various TyCons T; the last line is for AppTy, where there is presumably a type variable at the head, so it's actually (s s1 ... sn) ~r (t t1 .. tn) NOMINAL GIVEN WANTED Datatype YES YES Newtype YES YES Data family YES YES Type family YES, in injective args{1} YES, in injective args{1} Type variable YES YES REPRESENTATIONAL GIVEN WANTED Datatype YES YES Newtype NO{2} MAYBE{2} Data family NO{3} MAYBE{3} Type family NO NO Type variable NO{4} NO{4} {1}: Type families can be injective in some, but not all, of their arguments, so we want to do partial decomposition. This is quite different than the way other decomposition is done, where the decomposed equalities replace the original one. We thus proceed much like we do with superclasses: emitting new Givens when "decomposing" a partially-injective type family Given and new Deriveds when "decomposing" a partially-injective type family Wanted. (As of the time of writing, 13 June 2015, the implementation of injective type families has not been merged, but it should be soon. Please delete this parenthetical if the implementation is indeed merged.) {2}: See Note [Decomposing newtypes at representational role] {3}: Because of the possibility of newtype instances, we must treat data families like newtypes. See also Note [Decomposing newtypes at representational role]. See #10534 and test case typecheck/should_fail/T10534. {4}: Because type variables can stand in for newtypes, we conservatively do not decompose AppTys over representational equality. In the implementation of can_eq_nc and friends, we don't directly pattern match using lines like in the tables above, as those tables don't cover all cases (what about PrimTyCon? tuples?). Instead we just ask about injectivity, boiling the tables above down to rule (*). The exceptions to rule (*) are for injective type families, which are handled separately from other decompositions, and the MAYBE entries above. Note [Decomposing newtypes at representational role] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ This note discusses the 'newtype' line in the REPRESENTATIONAL table in Note [Decomposing equality]. (At nominal role, newtypes are fully decomposable.) Here is a representative example of why representational equality over newtypes is tricky: newtype Nt a = Mk Bool -- NB: a is not used in the RHS, type role Nt representational -- but the user gives it an R role anyway If we have [W] Nt alpha ~R Nt beta, we *don't* want to decompose to [W] alpha ~R beta, because it's possible that alpha and beta aren't representationally equal. Here's another example. newtype Nt a = MkNt (Id a) type family Id a where Id a = a [W] Nt Int ~R Nt Age Because of its use of a type family, Nt's parameter will get inferred to have a nominal role. Thus, decomposing the wanted will yield [W] Int ~N Age, which is unsatisfiable. Unwrapping, though, leads to a solution. Conclusion: * Unwrap newtypes before attempting to decompose them. This is done in can_eq_nc'. It all comes from the fact that newtypes aren't necessarily injective w.r.t. representational equality. Furthermore, as explained in Note [NthCo and newtypes] in TyCoRep, we can't use NthCo on representational coercions over newtypes. NthCo comes into play only when decomposing givens. Conclusion: * Do not decompose [G] N s ~R N t Is it sensible to decompose *Wanted* constraints over newtypes? Yes! It's the only way we could ever prove (IO Int ~R IO Age), recalling that IO is a newtype. However we must be careful. Consider type role Nt representational [G] Nt a ~R Nt b (1) [W] NT alpha ~R Nt b (2) [W] alpha ~ a (3) If we focus on (3) first, we'll substitute in (2), and now it's identical to the given (1), so we succeed. But if we focus on (2) first, and decompose it, we'll get (alpha ~R b), which is not soluble. This is exactly like the question of overlapping Givens for class constraints: see Note [Instance and Given overlap] in TcInteract. Conclusion: * Decompose [W] N s ~R N t iff there no given constraint that could later solve it. -} canDecomposableTyConAppOK :: CtEvidence -> EqRel -> TyCon -> [TcType] -> [TcType] -> TcS () -- Precondition: tys1 and tys2 are the same length, hence "OK" canDecomposableTyConAppOK ev eq_rel tc tys1 tys2 = case ev of CtDerived {} -> unifyDeriveds loc tc_roles tys1 tys2 CtWanted { ctev_dest = dest } -> do { cos <- zipWith4M unifyWanted new_locs tc_roles tys1 tys2 ; setWantedEq dest (mkTyConAppCo role tc cos) } CtGiven { ctev_evar = evar } -> do { let ev_co = mkCoVarCo evar ; given_evs <- newGivenEvVars loc $ [ ( mkPrimEqPredRole r ty1 ty2 , EvCoercion (mkNthCo i ev_co) ) | (r, ty1, ty2, i) <- zip4 tc_roles tys1 tys2 [0..] , r /= Phantom , not (isCoercionTy ty1) && not (isCoercionTy ty2) ] ; emitWorkNC given_evs } where loc = ctEvLoc ev role = eqRelRole eq_rel tc_roles = tyConRolesX role tc -- the following makes a better distinction between "kind" and "type" -- in error messages bndrs = tyConBinders tc kind_loc = toKindLoc loc is_kinds = map isNamedBinder bndrs new_locs | Just KindLevel <- ctLocTypeOrKind_maybe loc = repeat loc | otherwise = map (\is_kind -> if is_kind then kind_loc else loc) is_kinds -- | Call when canonicalizing an equality fails, but if the equality is -- representational, there is some hope for the future. -- Examples in Note [Use canEqFailure in canDecomposableTyConApp] canEqFailure :: CtEvidence -> EqRel -> TcType -> TcType -> TcS (StopOrContinue Ct) canEqFailure ev NomEq ty1 ty2 = canEqHardFailure ev ty1 ty2 canEqFailure ev ReprEq ty1 ty2 = do { (xi1, co1) <- flatten FM_FlattenAll ev ty1 ; (xi2, co2) <- flatten FM_FlattenAll ev ty2 -- We must flatten the types before putting them in the -- inert set, so that we are sure to kick them out when -- new equalities become available ; traceTcS "canEqFailure with ReprEq" $ vcat [ ppr ev, ppr ty1, ppr ty2, ppr xi1, ppr xi2 ] ; rewriteEqEvidence ev NotSwapped xi1 xi2 co1 co2 `andWhenContinue` \ new_ev -> continueWith (CIrredEvCan { cc_ev = new_ev }) } -- | Call when canonicalizing an equality fails with utterly no hope. canEqHardFailure :: CtEvidence -> TcType -> TcType -> TcS (StopOrContinue Ct) -- See Note [Make sure that insolubles are fully rewritten] canEqHardFailure ev ty1 ty2 = do { (s1, co1) <- flatten FM_SubstOnly ev ty1 ; (s2, co2) <- flatten FM_SubstOnly ev ty2 ; rewriteEqEvidence ev NotSwapped s1 s2 co1 co2 `andWhenContinue` \ new_ev -> do { emitInsoluble (mkNonCanonical new_ev) ; stopWith new_ev "Definitely not equal" }} {- Note [Decomposing TyConApps] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If we see (T s1 t1 ~ T s2 t2), then we can just decompose to (s1 ~ s2, t1 ~ t2) and push those back into the work list. But if s1 = K k1 s2 = K k2 then we will just decomopose s1~s2, and it might be better to do so on the spot. An important special case is where s1=s2, and we get just Refl. So canDecomposableTyCon is a fast-path decomposition that uses unifyWanted etc to short-cut that work. Note [Canonicalising type applications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Given (s1 t1) ~ ty2, how should we proceed? The simple things is to see if ty2 is of form (s2 t2), and decompose. By this time s1 and s2 can't be saturated type function applications, because those have been dealt with by an earlier equation in can_eq_nc, so it is always sound to decompose. However, over-eager decomposition gives bad error messages for things like a b ~ Maybe c e f ~ p -> q Suppose (in the first example) we already know a~Array. Then if we decompose the application eagerly, yielding a ~ Maybe b ~ c we get an error "Can't match Array ~ Maybe", but we'd prefer to get "Can't match Array b ~ Maybe c". So instead can_eq_wanted_app flattens the LHS and RHS, in the hope of replacing (a b) by (Array b), before using try_decompose_app to decompose it. Note [Make sure that insolubles are fully rewritten] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When an equality fails, we still want to rewrite the equality all the way down, so that it accurately reflects (a) the mutable reference substitution in force at start of solving (b) any ty-binds in force at this point in solving See Note [Kick out insolubles] in TcSMonad. And if we don't do this there is a bad danger that TcSimplify.applyTyVarDefaulting will find a variable that has in fact been substituted. Note [Do not decompose Given polytype equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider [G] (forall a. t1 ~ forall a. t2). Can we decompose this? No -- what would the evidence look like? So instead we simply discard this given evidence. Note [Combining insoluble constraints] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ As this point we have an insoluble constraint, like Int~Bool. * If it is Wanted, delete it from the cache, so that subsequent Int~Bool constraints give rise to separate error messages * But if it is Derived, DO NOT delete from cache. A class constraint may get kicked out of the inert set, and then have its functional dependency Derived constraints generated a second time. In that case we don't want to get two (or more) error messages by generating two (or more) insoluble fundep constraints from the same class constraint. Note [No top-level newtypes on RHS of representational equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we're in this situation: work item: [W] c1 : a ~R b inert: [G] c2 : b ~R Id a where newtype Id a = Id a We want to make sure canEqTyVar sees [W] a ~R a, after b is flattened and the Id newtype is unwrapped. This is assured by requiring only flat types in canEqTyVar *and* having the newtype-unwrapping check above the tyvar check in can_eq_nc. Note [Occurs check error] ~~~~~~~~~~~~~~~~~~~~~~~~~ If we have an occurs check error, are we necessarily hosed? Say our tyvar is tv1 and the type it appears in is xi2. Because xi2 is function free, then if we're computing w.r.t. nominal equality, then, yes, we're hosed. Nothing good can come from (a ~ [a]). If we're computing w.r.t. representational equality, this is a little subtler. Once again, (a ~R [a]) is a bad thing, but (a ~R N a) for a newtype N might be just fine. This means also that (a ~ b a) might be fine, because `b` might become a newtype. So, we must check: does tv1 appear in xi2 under any type constructor that is generative w.r.t. representational equality? That's what isTyVarUnderDatatype does. (The other name I considered, isTyVarUnderTyConGenerativeWrtReprEq was a bit verbose. And the shorter name gets the point across.) See also #10715, which induced this addition. Note [No derived kind equalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When we're working with a heterogeneous derived equality [D] (t1 :: k1) ~ (t2 :: k2) we want to homogenise to establish the kind invariant on CTyEqCans. But we can't emit [D] k1 ~ k2 because we wouldn't then be able to use the evidence in the homogenised types. So we emit a wanted constraint, because we do really need the evidence here. Thus: no derived kind equalities. -} canCFunEqCan :: CtEvidence -> TyCon -> [TcType] -- LHS -> TcTyVar -- RHS -> TcS (StopOrContinue Ct) -- ^ Canonicalise a CFunEqCan. We know that -- the arg types are already flat, -- and the RHS is a fsk, which we must *not* substitute. -- So just substitute in the LHS canCFunEqCan ev fn tys fsk = do { (tys', cos) <- flattenManyNom ev tys -- cos :: tys' ~ tys ; let lhs_co = mkTcTyConAppCo Nominal fn cos -- :: F tys' ~ F tys new_lhs = mkTyConApp fn tys' fsk_ty = mkTyVarTy fsk ; rewriteEqEvidence ev NotSwapped new_lhs fsk_ty lhs_co (mkTcNomReflCo fsk_ty) `andWhenContinue` \ ev' -> do { extendFlatCache fn tys' (ctEvCoercion ev', fsk_ty, ctEvFlavour ev') ; continueWith (CFunEqCan { cc_ev = ev', cc_fun = fn , cc_tyargs = tys', cc_fsk = fsk }) } } --------------------- canEqTyVar :: CtEvidence -> EqRel -> SwapFlag -> TcTyVar -- already flat -> TcType -- already flat -> TcS (StopOrContinue Ct) -- A TyVar on LHS, but so far un-zonked canEqTyVar ev eq_rel swapped tv1 ps_ty2 -- ev :: tv ~ s2 = do { traceTcS "canEqTyVar" (ppr tv1 $$ ppr ps_ty2 $$ ppr swapped) -- FM_Avoid commented out: see Note [Lazy flattening] in TcFlatten -- let fmode = FE { fe_ev = ev, fe_mode = FM_Avoid tv1' True } -- Flatten the RHS less vigorously, to avoid gratuitous flattening -- True <=> xi2 should not itself be a type-function application ; dflags <- getDynFlags ; canEqTyVar2 dflags ev eq_rel swapped tv1 ps_ty2 } canEqTyVar2 :: DynFlags -> CtEvidence -- lhs ~ rhs (or, if swapped, orhs ~ olhs) -> EqRel -> SwapFlag -> TcTyVar -- lhs, flat -> TcType -- rhs, flat -> TcS (StopOrContinue Ct) -- LHS is an inert type variable, -- and RHS is fully rewritten, but with type synonyms -- preserved as much as possible canEqTyVar2 dflags ev eq_rel swapped tv1 xi2 | Just (tv2, kco2) <- getCastedTyVar_maybe xi2 = canEqTyVarTyVar ev eq_rel swapped tv1 tv2 kco2 | OC_OK xi2' <- occurCheckExpand dflags tv1 xi2 -- No occurs check -- We use xi2' on the RHS of the new CTyEqCan, a ~ xi2' -- to establish the invariant that a does not appear in the -- rhs of the CTyEqCan. This is guaranteed by occurCheckExpand; -- see Note [Occurs check expansion] in TcType = rewriteEqEvidence ev swapped xi1 xi2' co1 (mkTcReflCo role xi2') `andWhenContinue` \ new_ev -> homogeniseRhsKind new_ev eq_rel xi1 xi2' $ \new_new_ev xi2'' -> CTyEqCan { cc_ev = new_new_ev, cc_tyvar = tv1 , cc_rhs = xi2'', cc_eq_rel = eq_rel } | otherwise -- Occurs check error = do { traceTcS "canEqTyVar2 occurs check error" (ppr tv1 $$ ppr xi2) ; rewriteEqEvidence ev swapped xi1 xi2 co1 co2 `andWhenContinue` \ new_ev -> if eq_rel == NomEq || isTyVarUnderDatatype tv1 xi2 then do { emitInsoluble (mkNonCanonical new_ev) -- If we have a ~ [a], it is not canonical, and in particular -- we don't want to rewrite existing inerts with it, otherwise -- we'd risk divergence in the constraint solver ; stopWith new_ev "Occurs check" } -- A representational equality with an occurs-check problem isn't -- insoluble! For example: -- a ~R b a -- We might learn that b is the newtype Id. -- But, the occurs-check certainly prevents the equality from being -- canonical, and we might loop if we were to use it in rewriting. else do { traceTcS "Occurs-check in representational equality" (ppr xi1 $$ ppr xi2) ; continueWith (CIrredEvCan { cc_ev = new_ev }) } } where role = eqRelRole eq_rel xi1 = mkTyVarTy tv1 co1 = mkTcReflCo role xi1 co2 = mkTcReflCo role xi2 canEqTyVarTyVar :: CtEvidence -- tv1 ~ rhs (or rhs ~ tv1, if swapped) -> EqRel -> SwapFlag -> TcTyVar -> TcTyVar -- tv1, tv2 -> Coercion -- the co in (rhs = tv2 |> co) -> TcS (StopOrContinue Ct) -- Both LHS and RHS rewrote to a type variable -- See Note [Canonical orientation for tyvar/tyvar equality constraints] canEqTyVarTyVar ev eq_rel swapped tv1 tv2 kco2 | tv1 == tv2 = do { let mk_coh = case swapped of IsSwapped -> mkTcCoherenceLeftCo NotSwapped -> mkTcCoherenceRightCo ; setEvBindIfWanted ev (EvCoercion $ mkTcReflCo role xi1 `mk_coh` kco2) ; stopWith ev "Equal tyvars" } -- We don't do this any more -- See Note [Orientation of equalities with fmvs] in TcFlatten -- | isFmvTyVar tv1 = do_fmv swapped tv1 xi1 xi2 co1 co2 -- | isFmvTyVar tv2 = do_fmv (flipSwap swapped) tv2 xi2 xi1 co2 co1 | swap_over = do_swap | otherwise = no_swap where role = eqRelRole eq_rel xi1 = mkTyVarTy tv1 co1 = mkTcReflCo role xi1 xi2 = mkTyVarTy tv2 co2 = mkTcReflCo role xi2 `mkTcCoherenceRightCo` kco2 no_swap = canon_eq swapped tv1 xi1 xi2 co1 co2 do_swap = canon_eq (flipSwap swapped) tv2 xi2 xi1 co2 co1 canon_eq swapped tv1 ty1 ty2 co1 co2 -- ev : tv1 ~ orhs (not swapped) or orhs ~ tv1 (swapped) -- co1 : xi1 ~ tv1 -- co2 : xi2 ~ tv2 = do { traceTcS "canEqTyVarTyVar" (vcat [ ppr swapped , ppr tv1 <+> dcolon <+> ppr (tyVarKind tv1) , ppr ty1 <+> dcolon <+> ppr (typeKind ty1) , ppr ty2 <+> dcolon <+> ppr (typeKind ty2) , ppr co1 <+> dcolon <+> ppr (tcCoercionKind co1) , ppr co2 <+> dcolon <+> ppr (tcCoercionKind co2) ]) ; rewriteEqEvidence ev swapped ty1 ty2 co1 co2 `andWhenContinue` \ new_ev -> homogeniseRhsKind new_ev eq_rel ty1 ty2 $ \new_new_ev ty2' -> CTyEqCan { cc_ev = new_new_ev, cc_tyvar = tv1 , cc_rhs = ty2', cc_eq_rel = eq_rel } } {- We don't do this any more See Note [Orientation of equalities with fmvs] in TcFlatten -- tv1 is the flatten meta-var do_fmv swapped tv1 xi1 xi2 co1 co2 | same_kind = canon_eq swapped tv1 xi1 xi2 co1 co2 | otherwise -- Presumably tv1 :: *, since it is a flatten meta-var, -- at a kind that has some interesting sub-kind structure. -- Since the two kinds are not the same, we must have -- tv1 `subKind` tv2, which is the wrong way round -- e.g. (fmv::*) ~ (a::OpenKind) -- So make a new meta-var and use that: -- fmv ~ (beta::*) -- (a::OpenKind) ~ (beta::*) = ASSERT2( k1_sub_k2, ppr tv1 <+> dcolon <+> ppr (tyVarKind tv1) $$ ppr xi2 <+> dcolon <+> ppr (typeKind xi2) ) ASSERT2( isWanted ev, ppr ev ) -- Only wanteds have flatten meta-vars do { tv_ty <- newFlexiTcSTy (tyVarKind tv1) ; new_ev <- newWantedEvVarNC (ctEvLoc ev) (mkPrimEqPredRole (eqRelRole eq_rel) g tv_ty xi2) ; emitWorkNC [new_ev] ; canon_eq swapped tv1 xi1 tv_ty co1 (ctEvCoercion new_ev) } -} swap_over -- If tv1 is touchable, swap only if tv2 is also -- touchable and it's strictly better to update the latter -- But see Note [Avoid unnecessary swaps] | Just lvl1 <- metaTyVarTcLevel_maybe tv1 = case metaTyVarTcLevel_maybe tv2 of Nothing -> False Just lvl2 | lvl2 `strictlyDeeperThan` lvl1 -> True | lvl1 `strictlyDeeperThan` lvl2 -> False | otherwise -> nicer_to_update_tv2 -- So tv1 is not a meta tyvar -- If only one is a meta tyvar, put it on the left -- This is not because it'll be solved; but because -- the floating step looks for meta tyvars on the left | isMetaTyVar tv2 = True -- So neither is a meta tyvar (including FlatMetaTv) -- If only one is a flatten skolem, put it on the left -- See Note [Eliminate flat-skols] | not (isFlattenTyVar tv1), isFlattenTyVar tv2 = True | otherwise = False nicer_to_update_tv2 = (isSigTyVar tv1 && not (isSigTyVar tv2)) || (isSystemName (Var.varName tv2) && not (isSystemName (Var.varName tv1))) -- | Solve a reflexive equality constraint canEqReflexive :: CtEvidence -- ty ~ ty -> EqRel -> TcType -- ty -> TcS (StopOrContinue Ct) -- always Stop canEqReflexive ev eq_rel ty = do { setEvBindIfWanted ev (EvCoercion $ mkTcReflCo (eqRelRole eq_rel) ty) ; stopWith ev "Solved by reflexivity" } -- See Note [Equalities with incompatible kinds] homogeniseRhsKind :: CtEvidence -- ^ the evidence to homogenise -> EqRel -> TcType -- ^ original LHS -> Xi -- ^ original RHS -> (CtEvidence -> Xi -> Ct) -- ^ how to build the homogenised constraint; -- the 'Xi' is the new RHS -> TcS (StopOrContinue Ct) homogeniseRhsKind ev eq_rel lhs rhs build_ct | k1 `tcEqType` k2 = continueWith (build_ct ev rhs) | CtGiven { ctev_evar = evar } <- ev -- tm :: (lhs :: k1) ~ (rhs :: k2) = do { kind_ev_id <- newBoundEvVarId kind_pty (EvCoercion $ mkTcKindCo $ mkTcCoVarCo evar) -- kind_ev_id :: (k1 :: *) ~# (k2 :: *) ; let kind_ev = CtGiven { ctev_pred = kind_pty , ctev_evar = kind_ev_id , ctev_loc = kind_loc } homo_co = mkSymCo $ mkCoVarCo kind_ev_id rhs' = mkCastTy rhs homo_co ; traceTcS "Hetero equality gives rise to given kind equality" (ppr kind_ev_id <+> dcolon <+> ppr kind_pty) ; emitWorkNC [kind_ev] ; type_ev <- newGivenEvVar loc ( mkTcEqPredLikeEv ev lhs rhs' , EvCoercion $ mkTcCoherenceRightCo (mkTcCoVarCo evar) homo_co ) -- type_ev :: (lhs :: k1) ~ ((rhs |> sym kind_ev_id) :: k1) ; continueWith (build_ct type_ev rhs') } | otherwise -- Wanted and Derived. See Note [No derived kind equalities] -- evar :: (lhs :: k1) ~ (rhs :: k2) = do { (kind_ev, kind_co) <- newWantedEq kind_loc Nominal k1 k2 -- kind_ev :: (k1 :: *) ~ (k2 :: *) ; traceTcS "Hetero equality gives rise to wanted kind equality" $ ppr (kind_ev) ; emitWorkNC [kind_ev] ; let homo_co = mkSymCo kind_co -- homo_co :: k2 ~ k1 rhs' = mkCastTy rhs homo_co ; case ev of CtGiven {} -> panic "homogeniseRhsKind" CtDerived {} -> continueWith (build_ct (ev { ctev_pred = homo_pred }) rhs') where homo_pred = mkTcEqPredLikeEv ev lhs rhs' CtWanted { ctev_dest = dest } -> do { (type_ev, hole_co) <- newWantedEq loc role lhs rhs' -- type_ev :: (lhs :: k1) ~ (rhs |> sym kind_ev :: k1) ; setWantedEq dest (hole_co `mkTransCo` (mkReflCo role rhs `mkCoherenceLeftCo` homo_co)) -- dest := hole ; <rhs> |> homo_co :: (lhs :: k1) ~ (rhs :: k2) ; continueWith (build_ct type_ev rhs') }} where k1 = typeKind lhs k2 = typeKind rhs kind_pty = mkHeteroPrimEqPred liftedTypeKind liftedTypeKind k1 k2 kind_loc = mkKindLoc lhs rhs loc loc = ctev_loc ev role = eqRelRole eq_rel {- Note [Canonical orientation for tyvar/tyvar equality constraints] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When we have a ~ b where both 'a' and 'b' are TcTyVars, which way round should be oriented in the CTyEqCan? The rules, implemented by canEqTyVarTyVar, are these * If either is a flatten-meta-variables, it goes on the left. * If one is a strict sub-kind of the other e.g. (alpha::?) ~ (beta::*) orient them so RHS is a subkind of LHS. That way we will replace 'a' with 'b', correctly narrowing the kind. This establishes the subkind invariant of CTyEqCan. * Put a meta-tyvar on the left if possible alpha[3] ~ r * If both are meta-tyvars, put the more touchable one (deepest level number) on the left, so there is the best chance of unifying it alpha[3] ~ beta[2] * If both are meta-tyvars and both at the same level, put a SigTv on the right if possible alpha[2] ~ beta[2](sig-tv) That way, when we unify alpha := beta, we don't lose the SigTv flag. * Put a meta-tv with a System Name on the left if possible so it gets eliminated (improves error messages) * If one is a flatten-skolem, put it on the left so that it is substituted out Note [Elminate flat-skols] fsk ~ a Note [Avoid unnecessary swaps] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If we swap without actually improving matters, we can get an infnite loop. Consider work item: a ~ b inert item: b ~ c We canonicalise the work-time to (a ~ c). If we then swap it before aeding to the inert set, we'll add (c ~ a), and therefore kick out the inert guy, so we get new work item: b ~ c inert item: c ~ a And now the cycle just repeats Note [Eliminate flat-skols] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have [G] Num (F [a]) then we flatten to [G] Num fsk [G] F [a] ~ fsk where fsk is a flatten-skolem (FlatSkol). Suppose we have type instance F [a] = a then we'll reduce the second constraint to [G] a ~ fsk and then replace all uses of 'a' with fsk. That's bad because in error messages intead of saying 'a' we'll say (F [a]). In all places, including those where the programmer wrote 'a' in the first place. Very confusing! See Trac #7862. Solution: re-orient a~fsk to fsk~a, so that we preferentially eliminate the fsk. Note [Equalities with incompatible kinds] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ canEqLeaf is about to make a CTyEqCan or CFunEqCan; but both have the invariant that LHS and RHS satisfy the kind invariants for CTyEqCan, CFunEqCan. What if we try to unify two things with incompatible kinds? eg a ~ b where a::*, b::*->* or a ~ b where a::*, b::k, k is a kind variable The CTyEqCan compatKind invariant is important. If we make a CTyEqCan for a~b, then we might well *substitute* 'b' for 'a', and that might make a well-kinded type ill-kinded; and that is bad (eg typeKind can crash, see Trac #7696). So instead for these ill-kinded equalities we homogenise the RHS of the equality, emitting new constraints as necessary. Note [Type synonyms and canonicalization] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We treat type synonym applications as xi types, that is, they do not count as type function applications. However, we do need to be a bit careful with type synonyms: like type functions they may not be generative or injective. However, unlike type functions, they are parametric, so there is no problem in expanding them whenever we see them, since we do not need to know anything about their arguments in order to expand them; this is what justifies not having to treat them as specially as type function applications. The thing that causes some subtleties is that we prefer to leave type synonym applications *unexpanded* whenever possible, in order to generate better error messages. If we encounter an equality constraint with type synonym applications on both sides, or a type synonym application on one side and some sort of type application on the other, we simply must expand out the type synonyms in order to continue decomposing the equality constraint into primitive equality constraints. For example, suppose we have type F a = [Int] and we encounter the equality F a ~ [b] In order to continue we must expand F a into [Int], giving us the equality [Int] ~ [b] which we can then decompose into the more primitive equality constraint Int ~ b. However, if we encounter an equality constraint with a type synonym application on one side and a variable on the other side, we should NOT (necessarily) expand the type synonym, since for the purpose of good error messages we want to leave type synonyms unexpanded as much as possible. Hence the ps_ty1, ps_ty2 argument passed to canEqTyVar. -} {- ************************************************************************ * * Evidence transformation * * ************************************************************************ -} data StopOrContinue a = ContinueWith a -- The constraint was not solved, although it may have -- been rewritten | Stop CtEvidence -- The (rewritten) constraint was solved SDoc -- Tells how it was solved -- Any new sub-goals have been put on the work list instance Functor StopOrContinue where fmap f (ContinueWith x) = ContinueWith (f x) fmap _ (Stop ev s) = Stop ev s instance Outputable a => Outputable (StopOrContinue a) where ppr (Stop ev s) = text "Stop" <> parens s <+> ppr ev ppr (ContinueWith w) = text "ContinueWith" <+> ppr w continueWith :: a -> TcS (StopOrContinue a) continueWith = return . ContinueWith stopWith :: CtEvidence -> String -> TcS (StopOrContinue a) stopWith ev s = return (Stop ev (text s)) andWhenContinue :: TcS (StopOrContinue a) -> (a -> TcS (StopOrContinue b)) -> TcS (StopOrContinue b) andWhenContinue tcs1 tcs2 = do { r <- tcs1 ; case r of Stop ev s -> return (Stop ev s) ContinueWith ct -> tcs2 ct } infixr 0 `andWhenContinue` -- allow chaining with ($) rewriteEvidence :: CtEvidence -- old evidence -> TcPredType -- new predicate -> TcCoercion -- Of type :: new predicate ~ <type of old evidence> -> TcS (StopOrContinue CtEvidence) -- Returns Just new_ev iff either (i) 'co' is reflexivity -- or (ii) 'co' is not reflexivity, and 'new_pred' not cached -- In either case, there is nothing new to do with new_ev {- rewriteEvidence old_ev new_pred co Main purpose: create new evidence for new_pred; unless new_pred is cached already * Returns a new_ev : new_pred, with same wanted/given/derived flag as old_ev * If old_ev was wanted, create a binding for old_ev, in terms of new_ev * If old_ev was given, AND not cached, create a binding for new_ev, in terms of old_ev * Returns Nothing if new_ev is already cached Old evidence New predicate is Return new evidence flavour of same flavor ------------------------------------------------------------------- Wanted Already solved or in inert Nothing or Derived Not Just new_evidence Given Already in inert Nothing Not Just new_evidence Note [Rewriting with Refl] ~~~~~~~~~~~~~~~~~~~~~~~~~~ If the coercion is just reflexivity then you may re-use the same variable. But be careful! Although the coercion is Refl, new_pred may reflect the result of unification alpha := ty, so new_pred might not _look_ the same as old_pred, and it's vital to proceed from now on using new_pred. The flattener preserves type synonyms, so they should appear in new_pred as well as in old_pred; that is important for good error messages. -} rewriteEvidence old_ev@(CtDerived {}) new_pred _co = -- If derived, don't even look at the coercion. -- This is very important, DO NOT re-order the equations for -- rewriteEvidence to put the isTcReflCo test first! -- Why? Because for *Derived* constraints, c, the coercion, which -- was produced by flattening, may contain suspended calls to -- (ctEvTerm c), which fails for Derived constraints. -- (Getting this wrong caused Trac #7384.) continueWith (old_ev { ctev_pred = new_pred }) rewriteEvidence old_ev new_pred co | isTcReflCo co -- See Note [Rewriting with Refl] = continueWith (old_ev { ctev_pred = new_pred }) rewriteEvidence ev@(CtGiven { ctev_evar = old_evar , ctev_loc = loc }) new_pred co = do { new_ev <- newGivenEvVar loc (new_pred, new_tm) ; continueWith new_ev } where -- mkEvCast optimises ReflCo new_tm = mkEvCast (EvId old_evar) (tcDowngradeRole Representational (ctEvRole ev) (mkTcSymCo co)) rewriteEvidence ev@(CtWanted { ctev_dest = dest , ctev_loc = loc }) new_pred co = do { mb_new_ev <- newWanted loc new_pred ; MASSERT( tcCoercionRole co == ctEvRole ev ) ; setWantedEvTerm dest (mkEvCast (getEvTerm mb_new_ev) (tcDowngradeRole Representational (ctEvRole ev) co)) ; case mb_new_ev of Fresh new_ev -> continueWith new_ev Cached _ -> stopWith ev "Cached wanted" } rewriteEqEvidence :: CtEvidence -- Old evidence :: olhs ~ orhs (not swapped) -- or orhs ~ olhs (swapped) -> SwapFlag -> TcType -> TcType -- New predicate nlhs ~ nrhs -- Should be zonked, because we use typeKind on nlhs/nrhs -> TcCoercion -- lhs_co, of type :: nlhs ~ olhs -> TcCoercion -- rhs_co, of type :: nrhs ~ orhs -> TcS (StopOrContinue CtEvidence) -- Of type nlhs ~ nrhs -- For (rewriteEqEvidence (Given g olhs orhs) False nlhs nrhs lhs_co rhs_co) -- we generate -- If not swapped -- g1 : nlhs ~ nrhs = lhs_co ; g ; sym rhs_co -- If 'swapped' -- g1 : nlhs ~ nrhs = lhs_co ; Sym g ; sym rhs_co -- -- For (Wanted w) we do the dual thing. -- New w1 : nlhs ~ nrhs -- If not swapped -- w : olhs ~ orhs = sym lhs_co ; w1 ; rhs_co -- If swapped -- w : orhs ~ olhs = sym rhs_co ; sym w1 ; lhs_co -- -- It's all a form of rewwriteEvidence, specialised for equalities rewriteEqEvidence old_ev swapped nlhs nrhs lhs_co rhs_co | CtDerived {} <- old_ev -- Don't force the evidence for a Derived = continueWith (old_ev { ctev_pred = new_pred }) | NotSwapped <- swapped , isTcReflCo lhs_co -- See Note [Rewriting with Refl] , isTcReflCo rhs_co = continueWith (old_ev { ctev_pred = new_pred }) | CtGiven { ctev_evar = old_evar } <- old_ev = do { let new_tm = EvCoercion (lhs_co `mkTcTransCo` maybeSym swapped (mkTcCoVarCo old_evar) `mkTcTransCo` mkTcSymCo rhs_co) ; new_ev <- newGivenEvVar loc' (new_pred, new_tm) ; continueWith new_ev } | CtWanted { ctev_dest = dest } <- old_ev = do { (new_ev, hole_co) <- newWantedEq loc' (ctEvRole old_ev) nlhs nrhs ; let co = maybeSym swapped $ mkSymCo lhs_co `mkTransCo` hole_co `mkTransCo` rhs_co ; setWantedEq dest co ; traceTcS "rewriteEqEvidence" (vcat [ppr old_ev, ppr nlhs, ppr nrhs, ppr co]) ; continueWith new_ev } | otherwise = panic "rewriteEvidence" where new_pred = mkTcEqPredLikeEv old_ev nlhs nrhs -- equality is like a type class. Bumping the depth is necessary because -- of recursive newtypes, where "reducing" a newtype can actually make -- it bigger. See Note [Newtypes can blow the stack]. loc = ctEvLoc old_ev loc' = bumpCtLocDepth loc {- Note [unifyWanted and unifyDerived] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When decomposing equalities we often create new wanted constraints for (s ~ t). But what if s=t? Then it'd be faster to return Refl right away. Similar remarks apply for Derived. Rather than making an equality test (which traverses the structure of the type, perhaps fruitlessly, unifyWanted traverses the common structure, and bales out when it finds a difference by creating a new Wanted constraint. But where it succeeds in finding common structure, it just builds a coercion to reflect it. -} unifyWanted :: CtLoc -> Role -> TcType -> TcType -> TcS Coercion -- Return coercion witnessing the equality of the two types, -- emitting new work equalities where necessary to achieve that -- Very good short-cut when the two types are equal, or nearly so -- See Note [unifyWanted and unifyDerived] -- The returned coercion's role matches the input parameter unifyWanted loc Phantom ty1 ty2 = do { kind_co <- unifyWanted loc Nominal (typeKind ty1) (typeKind ty2) ; return (mkPhantomCo kind_co ty1 ty2) } unifyWanted loc role orig_ty1 orig_ty2 = go orig_ty1 orig_ty2 where go ty1 ty2 | Just ty1' <- coreView ty1 = go ty1' ty2 go ty1 ty2 | Just ty2' <- coreView ty2 = go ty1 ty2' go (ForAllTy (Anon s1) t1) (ForAllTy (Anon s2) t2) = do { co_s <- unifyWanted loc role s1 s2 ; co_t <- unifyWanted loc role t1 t2 ; return (mkTyConAppCo role funTyCon [co_s,co_t]) } go (TyConApp tc1 tys1) (TyConApp tc2 tys2) | tc1 == tc2, tys1 `equalLength` tys2 , isInjectiveTyCon tc1 role -- don't look under newtypes at Rep equality = do { cos <- zipWith3M (unifyWanted loc) (tyConRolesX role tc1) tys1 tys2 ; return (mkTyConAppCo role tc1 cos) } go (TyVarTy tv) ty2 = do { mb_ty <- isFilledMetaTyVar_maybe tv ; case mb_ty of Just ty1' -> go ty1' ty2 Nothing -> bale_out } go ty1 (TyVarTy tv) = do { mb_ty <- isFilledMetaTyVar_maybe tv ; case mb_ty of Just ty2' -> go ty1 ty2' Nothing -> bale_out } go ty1@(CoercionTy {}) (CoercionTy {}) = return (mkReflCo role ty1) -- we just don't care about coercions! go _ _ = bale_out bale_out = do { (new_ev, co) <- newWantedEq loc role orig_ty1 orig_ty2 ; emitWorkNC [new_ev] ; return co } unifyDeriveds :: CtLoc -> [Role] -> [TcType] -> [TcType] -> TcS () -- See Note [unifyWanted and unifyDerived] unifyDeriveds loc roles tys1 tys2 = zipWith3M_ (unify_derived loc) roles tys1 tys2 unifyDerived :: CtLoc -> Role -> Pair TcType -> TcS () -- See Note [unifyWanted and unifyDerived] unifyDerived loc role (Pair ty1 ty2) = unify_derived loc role ty1 ty2 unify_derived :: CtLoc -> Role -> TcType -> TcType -> TcS () -- Create new Derived and put it in the work list -- Should do nothing if the two types are equal -- See Note [unifyWanted and unifyDerived] unify_derived _ Phantom _ _ = return () unify_derived loc role orig_ty1 orig_ty2 = go orig_ty1 orig_ty2 where go ty1 ty2 | Just ty1' <- coreView ty1 = go ty1' ty2 go ty1 ty2 | Just ty2' <- coreView ty2 = go ty1 ty2' go (ForAllTy (Anon s1) t1) (ForAllTy (Anon s2) t2) = do { unify_derived loc role s1 s2 ; unify_derived loc role t1 t2 } go (TyConApp tc1 tys1) (TyConApp tc2 tys2) | tc1 == tc2, tys1 `equalLength` tys2 , isInjectiveTyCon tc1 role = unifyDeriveds loc (tyConRolesX role tc1) tys1 tys2 go (TyVarTy tv) ty2 = do { mb_ty <- isFilledMetaTyVar_maybe tv ; case mb_ty of Just ty1' -> go ty1' ty2 Nothing -> bale_out } go ty1 (TyVarTy tv) = do { mb_ty <- isFilledMetaTyVar_maybe tv ; case mb_ty of Just ty2' -> go ty1 ty2' Nothing -> bale_out } go _ _ = bale_out bale_out = emitNewDerivedEq loc role orig_ty1 orig_ty2 maybeSym :: SwapFlag -> TcCoercion -> TcCoercion maybeSym IsSwapped co = mkTcSymCo co maybeSym NotSwapped co = co