{-# OPTIONS -fno-warn-tabs #-} -- The above warning supression flag is a temporary kludge. -- While working on this module you are encouraged to remove it and -- detab the module (please do the detabbing in a separate patch). See -- http://hackage.haskell.org/trac/ghc/wiki/Commentary/CodingStyle#TabsvsSpaces -- for details module TcCanonical( canonicalize, flatten, flattenMany, occurCheckExpand, FlattenMode (..), StopOrContinue (..) ) where #include "HsVersions.h" import TcRnTypes import TcType import Type import Kind import TcEvidence import Class import TyCon import TypeRep import Var import VarEnv import Outputable import Control.Monad ( when ) import MonadUtils import Control.Applicative ( (<|>) ) import TrieMap import VarSet import TcSMonad import FastString import Util import TysWiredIn ( eqTyCon ) import Data.Maybe ( isJust, fromMaybe ) -- import Data.List ( zip4 )\end{code} %************************************************************************ %* * %* The Canonicaliser * %* * %************************************************************************ Note [Canonicalization] ~~~~~~~~~~~~~~~~~~~~~~~ Canonicalization converts a flat 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. \begin{code}

-- Informative results of canonicalization data StopOrContinue = ContinueWith Ct -- Either no canonicalization happened, or if some did -- happen, it is still safe to just keep going with this -- work item. | Stop -- Some canonicalization happened, extra work is now in -- the TcS WorkList. instance Outputable StopOrContinue where ppr Stop = ptext (sLit "Stop") ppr (ContinueWith w) = ptext (sLit "ContinueWith") <+> ppr w continueWith :: Ct -> TcS StopOrContinue continueWith = return . ContinueWith andWhenContinue :: TcS StopOrContinue -> (Ct -> TcS StopOrContinue) -> TcS StopOrContinue andWhenContinue tcs1 tcs2 = do { r <- tcs1 ; case r of Stop -> return Stop ContinueWith ct -> tcs2 ct }\end{code} 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. \begin{code}

-- Top-level canonicalization -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ canonicalize :: Ct -> TcS StopOrContinue canonicalize ct@(CNonCanonical { cc_ev = fl, cc_depth = d }) = do { traceTcS "canonicalize (non-canonical)" (ppr ct) ; {-# SCC "canEvVar" #-} canEvVar d fl (classifyPredType (ctPred ct)) } canonicalize (CDictCan { cc_depth = d , cc_ev = fl , cc_class = cls , cc_tyargs = xis }) = {-# SCC "canClass" #-} canClass d fl cls xis -- Do not add any superclasses canonicalize (CTyEqCan { cc_depth = d , cc_ev = fl , cc_tyvar = tv , cc_rhs = xi }) = {-# SCC "canEqLeafTyVarLeftRec" #-} canEqLeafTyVarLeftRec d fl tv xi canonicalize (CFunEqCan { cc_depth = d , cc_ev = fl , cc_fun = fn , cc_tyargs = xis1 , cc_rhs = xi2 }) = {-# SCC "canEqLeafFunEqLeftRec" #-} canEqLeafFunEqLeftRec d fl (fn,xis1) xi2 canonicalize (CIrredEvCan { cc_ev = fl , cc_depth = d , cc_ty = xi }) = canIrred d fl xi canEvVar :: SubGoalDepth -> CtEvidence -> PredTree -> TcS StopOrContinue -- Called only for non-canonical EvVars canEvVar d fl pred_classifier = case pred_classifier of ClassPred cls tys -> canClassNC d fl cls tys EqPred ty1 ty2 -> canEqNC d fl ty1 ty2 IrredPred ev_ty -> canIrred d fl ev_ty TuplePred tys -> canTuple d fl tys\end{code} %************************************************************************ %* * %* Tuple Canonicalization %* * %************************************************************************ \begin{code}

canTuple :: SubGoalDepth -- Depth -> CtEvidence -> [PredType] -> TcS StopOrContinue canTuple d fl tys = do { traceTcS "can_pred" (text "TuplePred!") ; let xcomp = EvTupleMk xdecomp x = zipWith (\_ i -> EvTupleSel x i) tys [0..] ; ctevs <- xCtFlavor fl tys (XEvTerm xcomp xdecomp) ; mapM_ add_to_work ctevs ; return Stop } where add_to_work fl = addToWork $ canEvVar d fl (classifyPredType (ctEvPred fl))\end{code} %************************************************************************ %* * %* Class Canonicalization %* * %************************************************************************ \begin{code}

canClass, canClassNC :: SubGoalDepth -- Depth -> CtEvidence -> Class -> [Type] -> TcS StopOrContinue -- Precondition: EvVar is class evidence -- The canClassNC version is used on non-canonical constraints -- and adds superclasses. The plain canClass version is used -- for already-canonical class constraints (but which might have -- been subsituted or somthing), and hence do not need superclasses canClassNC d fl cls tys = canClass d fl cls tys `andWhenContinue` emitSuperclasses canClass d fl cls tys = do { -- sctx <- getTcSContext ; (xis, cos) <- flattenMany d FMFullFlatten fl tys ; let co = mkTcTyConAppCo (classTyCon cls) cos xi = mkClassPred cls xis ; mb <- rewriteCtFlavor fl xi co ; case mb of Just new_fl -> let (ClassPred cls xis_for_dict) = classifyPredType (ctEvPred new_fl) in continueWith $ CDictCan { cc_ev = new_fl , cc_tyargs = xis_for_dict, cc_class = cls, cc_depth = d } Nothing -> return Stop } emitSuperclasses :: Ct -> TcS StopOrContinue emitSuperclasses ct@(CDictCan { cc_depth = d, cc_ev = fl , cc_tyargs = xis_new, cc_class = cls }) -- Add superclasses of this one here, See Note [Adding superclasses]. -- But only if we are not simplifying the LHS of a rule. = do { newSCWorkFromFlavored d fl cls xis_new -- Arguably we should "seq" the coercions if they are derived, -- as we do below for emit_kind_constraint, to allow errors in -- superclasses to be executed if deferred to runtime! ; continueWith ct } emitSuperclasses _ = panic "emit_superclasses of non-class!"\end{code} Note [Adding superclasses] ~~~~~~~~~~~~~~~~~~~~~~~~~~ Since dictionaries are canonicalized only once in their lifetime, the place to add their superclasses is canonicalisation (The alternative would be to do it during constraint solving, but we'd have to be extremely careful to not repeatedly introduced the same superclass in our worklist). Here is what we do: For Givens: We add all their superclasses as Givens. For Wanteds: Generally speaking we want to be able to add superclasses of wanteds for two reasons: (1) Oportunities for improvement. Example: class (a ~ b) => C a b Wanted constraint is: C alpha beta We'd like to simply have C alpha alpha. Similar situations arise in relation to functional dependencies. (2) To have minimal constraints to quantify over: For instance, if our wanted constraint is (Eq a, Ord a) we'd only like to quantify over Ord a. To deal with (1) above we only add the superclasses of wanteds which may lead to improvement, that is: equality superclasses or superclasses with functional dependencies. We deal with (2) completely independently in TcSimplify. See Note [Minimize by SuperClasses] in TcSimplify. Moreover, in all cases the extra improvement constraints are Derived. Derived constraints have an identity (for now), but we don't do anything with their evidence. For instance they are never used to rewrite other constraints. See also [New Wanted Superclass Work] in TcInteract. For Deriveds: We do nothing. Here's an example that demonstrates why we chose to NOT add superclasses during simplification: [Comes from ticket #4497] class Num (RealOf t) => Normed t type family RealOf x Assume the generated wanted constraint is: RealOf e ~ e, Normed e If we were to be adding the superclasses during simplification we'd get: Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf ==> e ~ uf, Num uf, Normed e, RealOf e ~ e ==> [Spontaneous solve] Num uf, Normed uf, RealOf uf ~ uf While looks exactly like our original constraint. If we add the superclass again we'd loop. By adding superclasses definitely only once, during canonicalisation, this situation can't happen. \begin{code}

newSCWorkFromFlavored :: SubGoalDepth -- Depth -> CtEvidence -> Class -> [Xi] -> TcS () -- Returns superclasses, see Note [Adding superclasses] newSCWorkFromFlavored d flavor cls xis | isDerived flavor = return () -- Deriveds don't yield more superclasses because we will -- add them transitively in the case of wanteds. | isGiven flavor = do { let sc_theta = immSuperClasses cls xis xev_decomp x = zipWith (\_ i -> EvSuperClass x i) sc_theta [0..] xev = XEvTerm { ev_comp = panic "Can't compose for given!" , ev_decomp = xev_decomp } ; ctevs <- xCtFlavor flavor sc_theta xev ; traceTcS "newSCWork/Given" $ ppr "ctevs =" <+> ppr ctevs ; mapM_ emit_non_can ctevs } | isEmptyVarSet (tyVarsOfTypes xis) = return () -- Wanteds with no variables yield no deriveds. -- See Note [Improvement from Ground Wanteds] | otherwise -- Wanted case, just add those SC that can lead to improvement. = do { let sc_rec_theta = transSuperClasses cls xis impr_theta = filter is_improvement_pty sc_rec_theta ; traceTcS "newSCWork/Derived" $ text "impr_theta =" <+> ppr impr_theta ; mapM_ emit_der impr_theta } where emit_der pty = newDerived (ctev_wloc flavor) pty >>= mb_emit mb_emit Nothing = return () mb_emit (Just ctev) = emit_non_can ctev emit_non_can ctev = updWorkListTcS $ extendWorkListCt (CNonCanonical ctev d) is_improvement_pty :: PredType -> Bool -- Either it's an equality, or has some functional dependency is_improvement_pty ty = go (classifyPredType ty) where go (EqPred {}) = True go (ClassPred cls _tys) = not $ null fundeps where (_,fundeps) = classTvsFds cls go (TuplePred ts) = any is_improvement_pty ts go (IrredPred {}) = True -- Might have equalities after reduction?\end{code} %************************************************************************ %* * %* Irreducibles canonicalization %* * %************************************************************************ \begin{code}

canIrred :: SubGoalDepth -- Depth -> CtEvidence -> TcType -> TcS StopOrContinue -- Precondition: ty not a tuple and no other evidence form canIrred d fl ty = do { traceTcS "can_pred" (text "IrredPred = " <+> ppr ty) ; (xi,co) <- flatten d FMFullFlatten fl ty -- co :: xi ~ ty ; let no_flattening = xi `eqType` ty -- In this particular case it is not safe to -- say 'isTcReflCo' because the new constraint may -- be reducible! ; mb <- rewriteCtFlavor fl xi co ; case mb of Just new_fl | no_flattening -> continueWith $ CIrredEvCan { cc_ev = new_fl, cc_ty = xi, cc_depth = d } | otherwise -> canEvVar d new_fl (classifyPredType (ctEvPred new_fl)) Nothing -> return Stop }\end{code} %************************************************************************ %* * %* Flattening (eliminating all function symbols) * %* * %************************************************************************ Note [Flattening] ~~~~~~~~~~~~~~~~~~~~ flatten ty ==> (xi, cc) where xi has no type functions, unless they appear under ForAlls cc = Auxiliary given (equality) constraints constraining the fresh type variables in xi. Evidence for these is always the identity coercion, because internally the fresh flattening skolem variables are actually identified with the types they have been generated to stand in for. Note that it is flatten's job to flatten *every type function it sees*. flatten is only called on *arguments* to type functions, by canEqGiven. Recall that in comments we use alpha[flat = ty] to represent a flattening skolem variable alpha which has been generated to stand in for ty. ----- Example of flattening a constraint: ------ flatten (List (F (G Int))) ==> (xi, cc) where xi = List alpha cc = { G Int ~ beta[flat = G Int], F beta ~ alpha[flat = F beta] } Here * alpha and beta are 'flattening skolem variables'. * All the constraints in cc are 'given', and all their coercion terms are the identity. NB: Flattening Skolems only occur in canonical constraints, which are never zonked, so we don't need to worry about zonking doing accidental unflattening. Note that we prefer to leave type synonyms unexpanded when possible, so when the flattener encounters one, it first asks whether its transitive expansion contains any type function applications. If so, it expands the synonym and proceeds; if not, it simply returns the unexpanded synonym. \begin{code}

data FlattenMode = FMSubstOnly | FMFullFlatten -- Flatten a bunch of types all at once. flattenMany :: SubGoalDepth -- Depth -> FlattenMode -> CtEvidence -> [Type] -> TcS ([Xi], [TcCoercion]) -- Coercions :: Xi ~ Type -- Returns True iff (no flattening happened) -- NB: The EvVar inside the flavor is unused, we merely want Given/Solved/Derived/Wanted info flattenMany d f ctxt tys = -- pprTrace "flattenMany" empty $ go tys where go [] = return ([],[]) go (ty:tys) = do { (xi,co) <- flatten d f ctxt ty ; (xis,cos) <- go tys ; return (xi:xis,co:cos) } -- Flatten a type to get rid of type function applications, returning -- the new type-function-free type, and a collection of new equality -- constraints. See Note [Flattening] for more detail. flatten :: SubGoalDepth -- Depth -> FlattenMode -> CtEvidence -> TcType -> TcS (Xi, TcCoercion) -- Postcondition: Coercion :: Xi ~ TcType flatten d f ctxt ty | Just ty' <- tcView ty = do { (xi, co) <- flatten d f ctxt ty' ; if eqType xi ty then return (ty,co) else return (xi,co) } -- Small tweak for better error messages flatten _ _ _ xi@(LitTy {}) = return (xi, mkTcReflCo xi) flatten d f ctxt (TyVarTy tv) = flattenTyVar d f ctxt tv flatten d f ctxt (AppTy ty1 ty2) = do { (xi1,co1) <- flatten d f ctxt ty1 ; (xi2,co2) <- flatten d f ctxt ty2 ; return (mkAppTy xi1 xi2, mkTcAppCo co1 co2) } flatten d f ctxt (FunTy ty1 ty2) = do { (xi1,co1) <- flatten d f ctxt ty1 ; (xi2,co2) <- flatten d f ctxt ty2 ; return (mkFunTy xi1 xi2, mkTcFunCo co1 co2) } flatten d f fl (TyConApp tc tys) -- For a normal type constructor or data family application, we just -- recursively flatten the arguments. | not (isSynFamilyTyCon tc) = do { (xis,cos) <- flattenMany d f fl tys ; return (mkTyConApp tc xis, mkTcTyConAppCo tc cos) } -- Otherwise, it's a type function application, and we have to -- flatten it away as well, and generate a new given equality constraint -- between the application and a newly generated flattening skolem variable. | otherwise = ASSERT( tyConArity tc <= length tys ) -- Type functions are saturated do { (xis, cos) <- flattenMany d f fl tys ; let (xi_args, xi_rest) = splitAt (tyConArity tc) xis -- The type function might be *over* saturated -- in which case the remaining arguments should -- be dealt with by AppTys fam_ty = mkTyConApp tc xi_args ; (ret_co, rhs_xi, ct) <- case f of FMSubstOnly -> return (mkTcReflCo fam_ty, fam_ty, []) FMFullFlatten -> do { flat_cache <- getFlatCache ; case lookupTM fam_ty flat_cache of Just ct | let ctev = cc_ev ct , ctev `canRewrite` fl -> -- You may think that we can just return (cc_rhs ct) but not so. -- return (mkTcCoVarCo (ctId ct), cc_rhs ct, []) -- The cached constraint resides in the cache so we have to flatten -- the rhs to make sure we have applied any inert substitution to it. -- Alternatively we could be applying the inert substitution to the -- cache as well when we interact an equality with the inert. -- The design choice is: do we keep the flat cache rewritten or not? -- For now I say we don't keep it fully rewritten. do { traceTcS "flatten/flat-cache hit" $ ppr ct ; let rhs_xi = cc_rhs ct ; (flat_rhs_xi,co) <- flatten (cc_depth ct) f ctev rhs_xi ; let final_co = evTermCoercion (ctEvTerm ctev) `mkTcTransCo` mkTcSymCo co ; return (final_co, flat_rhs_xi,[]) } _ | isGiven fl -- Given: make new flatten skolem -> do { traceTcS "flatten/flat-cache miss" $ empty ; rhs_xi_var <- newFlattenSkolemTy fam_ty ; let co = mkTcReflCo fam_ty new_fl = Given { ctev_gloc = ctev_gloc fl , ctev_pred = mkTcEqPred fam_ty rhs_xi_var , ctev_evtm = EvCoercion co } ct = CFunEqCan { cc_ev = new_fl , cc_fun = tc , cc_tyargs = xi_args , cc_rhs = rhs_xi_var , cc_depth = d } -- Update the flat cache ; updFlatCache ct ; return (co, rhs_xi_var, [ct]) } | otherwise -- Wanted or Derived: make new unification variable -> do { traceTcS "flatten/flat-cache miss" $ empty ; rhs_xi_var <- newFlexiTcSTy (typeKind fam_ty) ; let pred = mkTcEqPred fam_ty rhs_xi_var wloc = ctev_wloc fl ; mw <- newWantedEvVar wloc pred ; case mw of Fresh ctev -> do { let ct = CFunEqCan { cc_ev = ctev , cc_fun = tc , cc_tyargs = xi_args , cc_rhs = rhs_xi_var , cc_depth = d } -- Update the flat cache: just an optimisation! ; updFlatCache ct ; return (evTermCoercion (ctEvTerm ctev), rhs_xi_var, [ct]) } Cached {} -> panic "flatten TyConApp, var must be fresh!" } } -- Emit the flat constraints ; updWorkListTcS $ appendWorkListEqs ct ; let (cos_args, cos_rest) = splitAt (tyConArity tc) cos ; return ( mkAppTys rhs_xi xi_rest -- NB mkAppTys: rhs_xi might not be a type variable -- cf Trac #5655 , mkTcAppCos (mkTcSymCo ret_co `mkTcTransCo` mkTcTyConAppCo tc cos_args) $ cos_rest ) } flatten d _f ctxt ty@(ForAllTy {}) -- We allow for-alls when, but only when, no type function -- applications inside the forall involve the bound type variables. = do { let (tvs, rho) = splitForAllTys ty ; (rho', co) <- flatten d FMSubstOnly ctxt rho ; return (mkForAllTys tvs rho', foldr mkTcForAllCo co tvs) }\end{code} \begin{code}

flattenTyVar :: SubGoalDepth -> FlattenMode -> CtEvidence -> TcTyVar -> TcS (Xi, TcCoercion) -- "Flattening" a type variable means to apply the substitution to it flattenTyVar d f ctxt tv = do { ieqs <- getInertEqs ; let mco = tv_eq_subst (fst ieqs) tv -- co : v ~ ty ; case mco of -- Done, but make sure the kind is zonked Nothing -> do { let knd = tyVarKind tv ; (new_knd,_kind_co) <- flatten d f ctxt knd ; let ty = mkTyVarTy (setVarType tv new_knd) ; return (ty, mkTcReflCo ty) } -- NB recursive call. -- Why? Because inert subst. non-idempotent, Note [Detailed InertCans Invariants] -- In fact, because of flavors, it couldn't possibly be idempotent, -- this is explained in Note [Non-idempotent inert substitution] Just (co,ty) -> do { (ty_final,co') <- flatten d f ctxt ty ; return (ty_final, co' `mkTcTransCo` mkTcSymCo co) } } where tv_eq_subst subst tv | Just ct <- lookupVarEnv subst tv , let ctev = cc_ev ct , ctev `canRewrite` ctxt = Just (evTermCoercion (ctEvTerm ctev), cc_rhs ct) -- NB: even if ct is Derived we are not going to -- touch the actual coercion so we are fine. | otherwise = Nothing\end{code} Note [Non-idempotent inert substitution] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The inert substitution is not idempotent in the broad sense. It is only idempotent in that it cannot rewrite the RHS of other inert equalities any further. An example of such an inert substitution is: [G] g1 : ta8 ~ ta4 [W] g2 : ta4 ~ a5Fj Observe that the wanted cannot rewrite the solved goal, despite the fact that ta4 appears on an RHS of an equality. Now, imagine a constraint: [W] g3: ta8 ~ Int coming in. If we simply apply once the inert substitution we will get: [W] g3_1: ta4 ~ Int and because potentially ta4 is untouchable we will try to insert g3_1 in the inert set, getting a panic since the inert only allows ONE equation per LHS type variable (as it should). For this reason, when we reach to flatten a type variable, we flatten it recursively, so that we can make sure that the inert substitution /is/ fully applied. Insufficient (non-recursive) rewriting was the reason for #5668. \begin{code}

----------------- addToWork :: TcS StopOrContinue -> TcS () addToWork tcs_action = tcs_action >>= stop_or_emit where stop_or_emit Stop = return () stop_or_emit (ContinueWith ct) = updWorkListTcS $ extendWorkListCt ct\end{code} %************************************************************************ %* * %* Equalities %* * %************************************************************************ \begin{code}

canEqEvVarsCreated :: SubGoalDepth -> [CtEvidence] -> TcS StopOrContinue canEqEvVarsCreated _d [] = return Stop canEqEvVarsCreated d (quad:quads) = mapM_ (addToWork . do_quad) quads >> do_quad quad -- Add all but one to the work list -- and return the first (if any) for futher processing where do_quad fl = let EqPred ty1 ty2 = classifyPredType $ ctEvPred fl in canEqNC d fl ty1 ty2 -- Note the "NC": these are fresh equalities so we must be -- careful to add their kind constraints ------------------------- canEqNC, canEq :: SubGoalDepth -> CtEvidence -> Type -> Type -> TcS StopOrContinue canEqNC d fl ty1 ty2 = canEq d fl ty1 ty2 `andWhenContinue` emitKindConstraint canEq _d fl ty1 ty2 | eqType ty1 ty2 -- Dealing with equality here avoids -- later spurious occurs checks for a~a = if isWanted fl then setEvBind (ctev_evar fl) (EvCoercion (mkTcReflCo ty1)) >> return Stop else return Stop -- If one side is a variable, orient and flatten, -- WITHOUT expanding type synonyms, so that we tend to -- substitute a ~ Age rather than a ~ Int when @type Age = Int@ canEq d fl ty1@(TyVarTy {}) ty2 = canEqLeaf d fl ty1 ty2 canEq d fl ty1 ty2@(TyVarTy {}) = canEqLeaf d fl ty1 ty2 -- See Note [Naked given applications] canEq d fl ty1 ty2 | Just ty1' <- tcView ty1 = canEq d fl ty1' ty2 | Just ty2' <- tcView ty2 = canEq d fl ty1 ty2' canEq d fl ty1@(TyConApp fn tys) ty2 | isSynFamilyTyCon fn, length tys == tyConArity fn = canEqLeaf d fl ty1 ty2 canEq d fl ty1 ty2@(TyConApp fn tys) | isSynFamilyTyCon fn, length tys == tyConArity fn = canEqLeaf d fl ty1 ty2 canEq d fl ty1 ty2 | Just (tc1,tys1) <- tcSplitTyConApp_maybe ty1 , Just (tc2,tys2) <- tcSplitTyConApp_maybe ty2 , isDecomposableTyCon tc1 && isDecomposableTyCon tc2 = -- Generate equalities for each of the corresponding arguments if (tc1 /= tc2 || length tys1 /= length tys2) -- Fail straight away for better error messages then canEqFailure d fl else do { let xcomp xs = EvCoercion (mkTcTyConAppCo tc1 (map evTermCoercion xs)) xdecomp x = zipWith (\_ i -> EvCoercion $ mkTcNthCo i (evTermCoercion x)) tys1 [0..] xev = XEvTerm xcomp xdecomp ; ctevs <- xCtFlavor fl (zipWith mkTcEqPred tys1 tys2) xev ; canEqEvVarsCreated d ctevs } -- See Note [Equality between type applications] -- Note [Care with type applications] in TcUnify canEq d fl ty1 ty2 -- e.g. F a b ~ Maybe c -- where F has arity 1 | Just (s1,t1) <- tcSplitAppTy_maybe ty1 , Just (s2,t2) <- tcSplitAppTy_maybe ty2 = canEqAppTy d fl s1 t1 s2 t2 canEq d fl s1@(ForAllTy {}) s2@(ForAllTy {}) | tcIsForAllTy s1, tcIsForAllTy s2 , Wanted { ctev_wloc = loc, ctev_evar = orig_ev } <- fl = do { let (tvs1,body1) = tcSplitForAllTys s1 (tvs2,body2) = tcSplitForAllTys s2 ; if not (equalLength tvs1 tvs2) then canEqFailure d fl else do { traceTcS "Creating implication for polytype equality" $ ppr fl ; deferTcSForAllEq (loc,orig_ev) (tvs1,body1) (tvs2,body2) ; return Stop } } | otherwise = do { traceTcS "Ommitting decomposition of given polytype equality" $ pprEq s1 s2 ; return Stop } canEq d fl _ _ = canEqFailure d fl ------------------------ -- Type application canEqAppTy :: SubGoalDepth -> CtEvidence -> Type -> Type -> Type -> Type -> TcS StopOrContinue canEqAppTy d fl s1 t1 s2 t2 = ASSERT( not (isKind t1) && not (isKind t2) ) if isGiven fl then do { traceTcS "canEq (app case)" $ text "Ommitting decomposition of given equality between: " <+> ppr (AppTy s1 t1) <+> text "and" <+> ppr (AppTy s2 t2) -- We cannot decompose given applications -- because we no longer have 'left' and 'right' ; return Stop } else do { let xevcomp [x,y] = EvCoercion (mkTcAppCo (evTermCoercion x) (evTermCoercion y)) xevcomp _ = error "canEqAppTy: can't happen" -- Can't happen xev = XEvTerm { ev_comp = xevcomp , ev_decomp = error "canEqAppTy: can't happen" } ; ctevs <- xCtFlavor fl [mkTcEqPred s1 s2, mkTcEqPred t1 t2] xev ; canEqEvVarsCreated d ctevs } canEqFailure :: SubGoalDepth -> CtEvidence -> TcS StopOrContinue canEqFailure d fl = emitFrozenError fl d >> return Stop ------------------------ emitKindConstraint :: Ct -> TcS StopOrContinue emitKindConstraint ct = case ct of CTyEqCan { cc_depth = d , cc_ev = fl, cc_tyvar = tv , cc_rhs = ty } -> emit_kind_constraint d fl (mkTyVarTy tv) ty CFunEqCan { cc_depth = d , cc_ev = fl , cc_fun = fn, cc_tyargs = xis1 , cc_rhs = xi2 } -> emit_kind_constraint d fl (mkTyConApp fn xis1) xi2 _ -> continueWith ct where emit_kind_constraint d fl ty1 ty2 | compatKind k1 k2 -- True when ty1,ty2 are themselves kinds, = continueWith ct -- because then k1, k2 are BOX | otherwise = ASSERT( isKind k1 && isKind k2 ) do { kev <- do { mw <- newWantedEvVar kind_co_wloc (mkEqPred k1 k2) ; case mw of Cached ev_tm -> return ev_tm Fresh ctev -> do { addToWork (canEq d ctev k1 k2) ; return (ctEvTerm ctev) } } ; let xcomp [x] = mkEvKindCast x (evTermCoercion kev) xcomp _ = panic "emit_kind_constraint:can't happen" xdecomp x = [mkEvKindCast x (evTermCoercion kev)] xev = XEvTerm xcomp xdecomp ; ctevs <- xCtFlavor_cache False fl [mkTcEqPred ty1 ty2] xev -- Important: Do not cache original as Solved since we are supposed to -- solve /exactly/ the same constraint later! Example: -- (alpha :: kappa0) -- (T :: *) -- Equality is: (alpha ~ T), so we will emitConstraint (kappa0 ~ *) but -- we don't want to say that (alpha ~ T) is now Solved! ; case ctevs of [] -> return Stop [new_ctev] -> continueWith (ct { cc_ev = new_ctev }) _ -> panic "emitKindConstraint" } where k1 = typeKind ty1 k2 = typeKind ty2 ctxt = mkKindErrorCtxtTcS ty1 k1 ty2 k2 -- Always create a Wanted kind equality even if -- you are decomposing a given constraint. -- NB: DV finds this reasonable for now. Maybe we have to revisit. kind_co_wloc = pushErrCtxtSameOrigin ctxt wanted_loc wanted_loc = case fl of Wanted { ctev_wloc = wloc } -> wloc Derived { ctev_wloc = wloc } -> wloc Given { ctev_gloc = gloc } -> setCtLocOrigin gloc orig orig = TypeEqOrigin (UnifyOrigin ty1 ty2)\end{code} 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 [Naked given applications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider: data A a type T a = A a and the given equality: [G] A a ~ T Int We will reach the case canEq where we do a tcSplitAppTy_maybe, but if we dont have the guards (Nothing <- tcView ty1) (Nothing <- tcView ty2) then the given equation is going to fall through and get completely forgotten! What we want instead is this clause to apply only when there is no immediate top-level synonym; if there is one it will be later on unfolded by the later stages of canEq. Test-case is in typecheck/should_compile/GivenTypeSynonym.hs Note [Equality between type applications] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If we see an equality of the form s1 t1 ~ s2 t2 we can always split it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type functions (type functions use the TyConApp constructor, which never shows up as the LHS of an AppTy). Other than type functions, types in Haskell are always (1) generative: a b ~ c d implies a ~ c, since different type constructors always generate distinct types (2) injective: a b ~ a d implies b ~ d; we never generate the same type from different type arguments. Note [Canonical ordering for equality constraints] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Implemented as (<+=) below: - Type function applications always come before anything else. - Variables always come before non-variables (other than type function applications). Note that we don't need to unfold type synonyms on the RHS to check the ordering; that is, in the rules above it's OK to consider only whether something is *syntactically* a type function application or not. To illustrate why this is OK, suppose we have an equality of the form 'tv ~ S a b c', where S is a type synonym which expands to a top-level application of the type function F, something like type S a b c = F d e Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's expansion contains type function applications the flattener will do the expansion and then generate a skolem variable for the type function application, so we end up with something like this: tv ~ x F d e ~ x where x is the skolem variable. This is one extra equation than absolutely necessary (we could have gotten away with just 'F d e ~ tv' if we had noticed that S expanded to a top-level type function application and flipped it around in the first place) but this way keeps the code simpler. Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the ordering of tv ~ tv constraints. There are several reasons why we might: (1) In order to be able to extract a substitution that doesn't mention untouchable variables after we are done solving, we might prefer to put touchable variables on the left. However, in and of itself this isn't necessary; we can always re-orient equality constraints at the end if necessary when extracting a substitution. (2) To ensure termination we might think it necessary to put variables in lexicographic order. However, this isn't actually necessary as outlined below. While building up an inert set of canonical constraints, we maintain the invariant that the equality constraints in the inert set form an acyclic rewrite system when viewed as L-R rewrite rules. Moreover, the given constraints form an idempotent substitution (i.e. none of the variables on the LHS occur in any of the RHS's, and type functions never show up in the RHS at all), the wanted constraints also form an idempotent substitution, and finally the LHS of a given constraint never shows up on the RHS of a wanted constraint. There may, however, be a wanted LHS that shows up in a given RHS, since we do not rewrite given constraints with wanted constraints. Suppose we have an inert constraint set tg_1 ~ xig_1 -- givens tg_2 ~ xig_2 ... tw_1 ~ xiw_1 -- wanteds tw_2 ~ xiw_2 ... where each t_i can be either a type variable or a type function application. Now suppose we take a new canonical equality constraint, t' ~ xi' (note among other things this means t' does not occur in xi') and try to react it with the existing inert set. We show by induction on the number of t_i which occur in t' ~ xi' that this process will terminate. There are several ways t' ~ xi' could react with an existing constraint: TODO: finish this proof. The below was for the case where the entire inert set is an idempotent subustitution... (b) We could have t' = t_j for some j. Then we obtain the new equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We now canonicalize the new equality, which may involve decomposing it into several canonical equalities, and recurse on these. However, none of the new equalities will contain t_j, so they have fewer occurrences of the t_i than the original equation. (a) We could have t_j occurring in xi' for some j, with t' /= t_j. Then we substitute xi_j for t_j in xi' and continue. However, since none of the t_i occur in xi_j, we have decreased the number of t_i that occur in xi', since we eliminated t_j and did not introduce any new ones. \begin{code}

data TypeClassifier = FskCls TcTyVar -- ^ Flatten skolem | VarCls TcTyVar -- ^ Non-flatten-skolem variable | FunCls TyCon [Type] -- ^ Type function, exactly saturated | OtherCls TcType -- ^ Neither of the above classify :: TcType -> TypeClassifier classify (TyVarTy tv) | isTcTyVar tv, FlatSkol {} <- tcTyVarDetails tv = FskCls tv | otherwise = VarCls tv classify (TyConApp tc tys) | isSynFamilyTyCon tc , tyConArity tc == length tys = FunCls tc tys classify ty | Just ty' <- tcView ty = case classify ty' of OtherCls {} -> OtherCls ty var_or_fn -> var_or_fn | otherwise = OtherCls ty -- See note [Canonical ordering for equality constraints]. reOrient :: CtEvidence -> TypeClassifier -> TypeClassifier -> Bool -- (t1 `reOrient` t2) responds True -- iff we should flip to (t2~t1) -- We try to say False if possible, to minimise evidence generation -- -- Postcondition: After re-orienting, first arg is not OTherCls reOrient _fl (OtherCls {}) (FunCls {}) = True reOrient _fl (OtherCls {}) (FskCls {}) = True reOrient _fl (OtherCls {}) (VarCls {}) = True reOrient _fl (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun reOrient _fl (FunCls {}) (VarCls _tv) = False -- But consider the following variation: isGiven fl && isMetaTyVar tv -- See Note [No touchables as FunEq RHS] in TcSMonad reOrient _fl (FunCls {}) _ = False -- Fun/Other on rhs reOrient _fl (VarCls {}) (FunCls {}) = True reOrient _fl (VarCls {}) (FskCls {}) = False reOrient _fl (VarCls {}) (OtherCls {}) = False reOrient _fl (VarCls tv1) (VarCls tv2) | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True | otherwise = False -- Just for efficiency, see CTyEqCan invariants reOrient _fl (FskCls {}) (VarCls tv2) = isMetaTyVar tv2 -- Just for efficiency, see CTyEqCan invariants reOrient _fl (FskCls {}) (FskCls {}) = False reOrient _fl (FskCls {}) (FunCls {}) = True reOrient _fl (FskCls {}) (OtherCls {}) = False ------------------ canEqLeaf :: SubGoalDepth -- Depth -> CtEvidence -> Type -> Type -> TcS StopOrContinue -- Canonicalizing "leaf" equality constraints which cannot be -- decomposed further (ie one of the types is a variable or -- saturated type function application). -- Preconditions: -- * one of the two arguments is variable or family applications -- * the two types are not equal (looking through synonyms) canEqLeaf d fl s1 s2 | cls1 `re_orient` cls2 = do { traceTcS "canEqLeaf (reorienting)" $ ppr fl <+> dcolon <+> pprEq s1 s2 ; let xcomp [x] = EvCoercion (mkTcSymCo (evTermCoercion x)) xcomp _ = panic "canEqLeaf: can't happen" xdecomp x = [EvCoercion (mkTcSymCo (evTermCoercion x))] xev = XEvTerm xcomp xdecomp ; ctevs <- xCtFlavor fl [mkTcEqPred s2 s1] xev ; case ctevs of [] -> return Stop [ctev] -> canEqLeafOriented d ctev s2 s1 _ -> panic "canEqLeaf" } | otherwise = do { traceTcS "canEqLeaf" $ ppr (mkTcEqPred s1 s2) ; canEqLeafOriented d fl s1 s2 } where re_orient = reOrient fl cls1 = classify s1 cls2 = classify s2 canEqLeafOriented :: SubGoalDepth -- Depth -> CtEvidence -> TcType -> TcType -> TcS StopOrContinue -- By now s1 will either be a variable or a type family application canEqLeafOriented d fl s1 s2 = can_eq_split_lhs d fl s1 s2 where can_eq_split_lhs d fl s1 s2 | Just (fn,tys1) <- splitTyConApp_maybe s1 = canEqLeafFunEqLeftRec d fl (fn,tys1) s2 | Just tv <- getTyVar_maybe s1 = canEqLeafTyVarLeftRec d fl tv s2 | otherwise = pprPanic "canEqLeafOriented" $ text "Non-variable or non-family equality LHS" <+> ppr (ctEvPred fl) canEqLeafFunEqLeftRec :: SubGoalDepth -> CtEvidence -> (TyCon,[TcType]) -> TcType -> TcS StopOrContinue canEqLeafFunEqLeftRec d fl (fn,tys1) ty2 -- fl :: F tys1 ~ ty2 = do { traceTcS "canEqLeafFunEqLeftRec" $ pprEq (mkTyConApp fn tys1) ty2 ; (xis1,cos1) <- {-# SCC "flattenMany" #-} flattenMany d FMFullFlatten fl tys1 -- Flatten type function arguments -- cos1 :: xis1 ~ tys1 ; let fam_head = mkTyConApp fn xis1 -- Fancy higher-dimensional coercion between equalities! ; let co = mkTcTyConAppCo eqTyCon $ [mkTcReflCo (defaultKind $ typeKind ty2), mkTcTyConAppCo fn cos1, mkTcReflCo ty2] -- Why defaultKind? Same reason as the comment on TcType/mkTcEqPred. I trully hate this (DV) -- co :: (F xis1 ~ ty2) ~ (F tys1 ~ ty2) ; mb <- rewriteCtFlavor fl (mkTcEqPred fam_head ty2) co ; case mb of Nothing -> return Stop Just new_fl -> canEqLeafFunEqLeft d new_fl (fn,xis1) ty2 } canEqLeafFunEqLeft :: SubGoalDepth -- Depth -> CtEvidence -> (TyCon,[Xi]) -> TcType -> TcS StopOrContinue -- Precondition: No more flattening is needed for the LHS canEqLeafFunEqLeft d fl (fn,xis1) s2 = {-# SCC "canEqLeafFunEqLeft" #-} do { traceTcS "canEqLeafFunEqLeft" $ pprEq (mkTyConApp fn xis1) s2 ; (xi2,co2) <- {-# SCC "flatten" #-} flatten d FMFullFlatten fl s2 -- co2 :: xi2 ~ s2 ; let fam_head = mkTyConApp fn xis1 -- Fancy coercion between equalities! But it should just work! ; let co = mkTcTyConAppCo eqTyCon $ [ mkTcReflCo (defaultKind $ typeKind s2) , mkTcReflCo fam_head, co2 ] -- Why defaultKind? Same reason as the comment at TcType/mkTcEqPred -- co :: (F xis1 ~ xi2) ~ (F xis1 ~ s2) -- new pred old pred ; mb <- rewriteCtFlavor fl (mkTcEqPred fam_head xi2) co ; case mb of Nothing -> return Stop Just new_fl -> continueWith $ CFunEqCan { cc_ev = new_fl, cc_depth = d , cc_fun = fn, cc_tyargs = xis1, cc_rhs = xi2 } } canEqLeafTyVarLeftRec :: SubGoalDepth -> CtEvidence -> TcTyVar -> TcType -> TcS StopOrContinue canEqLeafTyVarLeftRec d fl tv s2 -- fl :: tv ~ s2 = do { traceTcS "canEqLeafTyVarLeftRec" $ pprEq (mkTyVarTy tv) s2 ; (xi1,co1) <- flattenTyVar d FMFullFlatten fl tv -- co1 :: xi1 ~ tv ; let is_still_var = isJust (getTyVar_maybe xi1) ; traceTcS "canEqLeafTyVarLeftRec2" $ empty ; let co = mkTcTyConAppCo eqTyCon $ [ mkTcReflCo (defaultKind $ typeKind s2) , co1, mkTcReflCo s2] -- co :: (xi1 ~ s2) ~ (tv ~ s2) ; mb <- rewriteCtFlavor_cache (if is_still_var then False else True) fl (mkTcEqPred xi1 s2) co -- See Note [Caching loops] ; traceTcS "canEqLeafTyVarLeftRec3" $ empty ; case mb of Nothing -> return Stop Just new_fl -> case getTyVar_maybe xi1 of Just tv' -> canEqLeafTyVarLeft d new_fl tv' s2 Nothing -> canEq d new_fl xi1 s2 } canEqLeafTyVarLeft :: SubGoalDepth -- Depth -> CtEvidence -> TcTyVar -> TcType -> TcS StopOrContinue -- Precondition LHS is fully rewritten from inerts (but not RHS) canEqLeafTyVarLeft d fl tv s2 -- eqv : tv ~ s2 = do { let tv_ty = mkTyVarTy tv ; traceTcS "canEqLeafTyVarLeft" (pprEq tv_ty s2) ; (xi2, co2) <- flatten d FMFullFlatten fl s2 -- Flatten RHS co:xi2 ~ s2 ; traceTcS "canEqLeafTyVarLeft" (nest 2 (vcat [ text "tv =" <+> ppr tv , text "s2 =" <+> ppr s2 , text "xi2 =" <+> ppr xi2])) -- Reflexivity exposed through flattening ; if tv_ty `eqType` xi2 then when (isWanted fl) (setEvBind (ctev_evar fl) (EvCoercion co2)) >> return Stop else do -- Not reflexivity but maybe an occurs error { let occ_check_result = occurCheckExpand tv xi2 xi2' = fromMaybe xi2 occ_check_result not_occ_err = isJust occ_check_result -- Delicate: don't want to cache as solved a constraint with occurs error! co = mkTcTyConAppCo eqTyCon $ [mkTcReflCo (defaultKind $ typeKind s2), mkTcReflCo tv_ty, co2] ; mb <- rewriteCtFlavor_cache not_occ_err fl (mkTcEqPred tv_ty xi2') co ; case mb of Just new_fl -> if not_occ_err then continueWith $ CTyEqCan { cc_ev = new_fl, cc_depth = d , cc_tyvar = tv, cc_rhs = xi2' } else canEqFailure d new_fl Nothing -> return Stop } }\end{code} Note [Occurs check expansion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ @occurCheckExpand tv xi@ expands synonyms in xi just enough to get rid of occurrences of tv outside type function arguments, if that is possible; otherwise, it returns Nothing. For example, suppose we have type F a b = [a] Then occurCheckExpand b (F Int b) = Just [Int] but occurCheckExpand a (F a Int) = Nothing We don't promise to do the absolute minimum amount of expanding necessary, but we try not to do expansions we don't need to. We prefer doing inner expansions first. For example, type F a b = (a, Int, a, [a]) type G b = Char We have occurCheckExpand b (F (G b)) = F Char even though we could also expand F to get rid of b. See also Note [Type synonyms and canonicalization]. \begin{code}

occurCheckExpand :: TcTyVar -> Type -> Maybe Type -- Check whether the given variable occurs in the given type. We may -- have needed to do some type synonym unfolding in order to get rid -- of the variable, so we also return the unfolded version of the -- type, which is guaranteed to be syntactically free of the given -- type variable. If the type is already syntactically free of the -- variable, then the same type is returned. occurCheckExpand tv ty | not (tv `elemVarSet` tyVarsOfType ty) = Just ty | otherwise = go ty where go t@(TyVarTy tv') | tv == tv' = Nothing | otherwise = Just t go ty@(LitTy {}) = return ty go (AppTy ty1 ty2) = do { ty1' <- go ty1 ; ty2' <- go ty2 ; return (mkAppTy ty1' ty2') } -- mkAppTy <$> go ty1 <*> go ty2 go (FunTy ty1 ty2) = do { ty1' <- go ty1 ; ty2' <- go ty2 ; return (mkFunTy ty1' ty2') } -- mkFunTy <$> go ty1 <*> go ty2 go ty@(ForAllTy {}) | tv `elemVarSet` tyVarsOfTypes tvs_knds = Nothing -- Can't expand away the kinds unless we create -- fresh variables which we don't want to do at this point. | otherwise = do { rho' <- go rho ; return (mkForAllTys tvs rho') } where (tvs,rho) = splitForAllTys ty tvs_knds = map tyVarKind tvs -- For a type constructor application, first try expanding away the -- offending variable from the arguments. If that doesn't work, next -- see if the type constructor is a type synonym, and if so, expand -- it and try again. go ty@(TyConApp tc tys) | isSynFamilyTyCon tc -- It's ok for tv to occur under a type family application = return ty -- Eg. (a ~ F a) is not an occur-check error -- NB This case can't occur during canonicalisation, -- because the arg is a Xi-type, but can occur in the -- call from TcErrors | otherwise = (mkTyConApp tc <$> mapM go tys) <|> (tcView ty >>= go)\end{code} 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. However, there is a subtle point with type synonyms and the occurs check that takes place for equality constraints of the form tv ~ xi. As an example, suppose we have type F a = Int and we come across the equality constraint a ~ F a This should not actually fail the occurs check, since expanding out the type synonym results in the legitimate equality constraint a ~ Int. We must actually do this expansion, because unifying a with F a will lead the type checker into infinite loops later. Put another way, canonical equality constraints should never *syntactically* contain the LHS variable in the RHS type. However, we don't always need to expand type synonyms when doing an occurs check; for example, the constraint a ~ F b is obviously fine no matter what F expands to. And in this case we would rather unify a with F b (rather than F b's expansion) in order to get better error messages later. So, when doing an occurs check with a type synonym application on the RHS, we use some heuristics to find an expansion of the RHS which does not contain the variable from the LHS. In particular, given a ~ F t1 ... tn we first try expanding each of the ti to types which no longer contain a. If this turns out to be impossible, we next try expanding F itself, and so on.