3 mkCanonical, mkCanonicals, mkCanonicalFEV, canWanteds, canGivens,
7 #include "HsVersions.h"
22 import Control.Monad ( unless, when, zipWithM, zipWithM_ )
24 import Control.Applicative ( (<|>) )
33 Note [Canonicalisation]
34 ~~~~~~~~~~~~~~~~~~~~~~~
35 * Converts (Constraint f) _which_does_not_contain_proper_implications_ to CanonicalCts
36 * Unary: treats individual constraints one at a time
37 * Does not do any zonking
38 * Lives in TcS monad so that it can create new skolem variables
41 %************************************************************************
43 %* Flattening (eliminating all function symbols) *
45 %************************************************************************
49 flatten ty ==> (xi, cc)
51 xi has no type functions
52 cc = Auxiliary given (equality) constraints constraining
53 the fresh type variables in xi. Evidence for these
54 is always the identity coercion, because internally the
55 fresh flattening skolem variables are actually identified
56 with the types they have been generated to stand in for.
58 Note that it is flatten's job to flatten *every type function it sees*.
59 flatten is only called on *arguments* to type functions, by canEqGiven.
61 Recall that in comments we use alpha[flat = ty] to represent a
62 flattening skolem variable alpha which has been generated to stand in
65 ----- Example of flattening a constraint: ------
66 flatten (List (F (G Int))) ==> (xi, cc)
69 cc = { G Int ~ beta[flat = G Int],
70 F beta ~ alpha[flat = F beta] }
72 * alpha and beta are 'flattening skolem variables'.
73 * All the constraints in cc are 'given', and all their coercion terms
76 NB: Flattening Skolems only occur in canonical constraints, which
77 are never zonked, so we don't need to worry about zonking doing
78 accidental unflattening.
80 Note that we prefer to leave type synonyms unexpanded when possible,
81 so when the flattener encounters one, it first asks whether its
82 transitive expansion contains any type function applications. If so,
83 it expands the synonym and proceeds; if not, it simply returns the
86 TODO: caching the information about whether transitive synonym
87 expansions contain any type function applications would speed things
88 up a bit; right now we waste a lot of energy traversing the same types
92 -- Flatten a bunch of types all at once.
93 flattenMany :: CtFlavor -> [Type] -> TcS ([Xi], [Coercion], CanonicalCts)
94 -- Coercions :: Xi ~ Type
96 = do { (xis, cos, cts_s) <- mapAndUnzip3M (flatten ctxt) tys
97 ; return (xis, cos, andCCans cts_s) }
99 -- Flatten a type to get rid of type function applications, returning
100 -- the new type-function-free type, and a collection of new equality
101 -- constraints. See Note [Flattening] for more detail.
102 flatten :: CtFlavor -> TcType -> TcS (Xi, Coercion, CanonicalCts)
103 -- Postcondition: Coercion :: Xi ~ TcType
105 | Just ty' <- tcView ty
106 = do { (xi, co, ccs) <- flatten ctxt ty'
107 -- Preserve type synonyms if possible
108 -- We can tell if ty' is function-free by
109 -- whether there are any floated constraints
110 ; if isEmptyCCan ccs then
111 return (ty, ty, emptyCCan)
113 return (xi, co, ccs) }
115 flatten _ v@(TyVarTy _)
116 = return (v, v, emptyCCan)
118 flatten ctxt (AppTy ty1 ty2)
119 = do { (xi1,co1,c1) <- flatten ctxt ty1
120 ; (xi2,co2,c2) <- flatten ctxt ty2
121 ; return (mkAppTy xi1 xi2, mkAppCoercion co1 co2, c1 `andCCan` c2) }
123 flatten ctxt (FunTy ty1 ty2)
124 = do { (xi1,co1,c1) <- flatten ctxt ty1
125 ; (xi2,co2,c2) <- flatten ctxt ty2
126 ; return (mkFunTy xi1 xi2, mkFunCoercion co1 co2, c1 `andCCan` c2) }
128 flatten fl (TyConApp tc tys)
129 -- For a normal type constructor or data family application, we just
130 -- recursively flatten the arguments.
131 | not (isSynFamilyTyCon tc)
132 = do { (xis,cos,ccs) <- flattenMany fl tys
133 ; return (mkTyConApp tc xis, mkTyConCoercion tc cos, ccs) }
135 -- Otherwise, it's a type function application, and we have to
136 -- flatten it away as well, and generate a new given equality constraint
137 -- between the application and a newly generated flattening skolem variable.
139 = ASSERT( tyConArity tc <= length tys ) -- Type functions are saturated
140 do { (xis, cos, ccs) <- flattenMany fl tys
141 ; let (xi_args, xi_rest) = splitAt (tyConArity tc) xis
142 (cos_args, cos_rest) = splitAt (tyConArity tc) cos
143 -- The type function might be *over* saturated
144 -- in which case the remaining arguments should
145 -- be dealt with by AppTys
146 fam_ty = mkTyConApp tc xi_args
147 fam_co = fam_ty -- identity
149 ; (ret_co, rhs_var, ct) <-
151 do { rhs_var <- newFlattenSkolemTy fam_ty
152 ; cv <- newGivenCoVar fam_ty rhs_var fam_co
153 ; let ct = CFunEqCan { cc_id = cv
154 , cc_flavor = fl -- Given
156 , cc_tyargs = xi_args
158 ; return $ (mkCoVarCoercion cv, rhs_var, ct) }
159 else -- Derived or Wanted: make a new *unification* flatten variable
160 do { rhs_var <- newFlexiTcSTy (typeKind fam_ty)
161 ; cv <- newWantedCoVar fam_ty rhs_var
162 ; let ct = CFunEqCan { cc_id = cv
163 , cc_flavor = mkWantedFlavor fl
164 -- Always Wanted, not Derived
166 , cc_tyargs = xi_args
168 ; return $ (mkCoVarCoercion cv, rhs_var, ct) }
170 ; return ( foldl AppTy rhs_var xi_rest
171 , foldl AppTy (mkSymCoercion ret_co
172 `mkTransCoercion` mkTyConCoercion tc cos_args) cos_rest
173 , ccs `extendCCans` ct) }
176 flatten ctxt (PredTy pred)
177 = do { (pred', co, ccs) <- flattenPred ctxt pred
178 ; return (PredTy pred', co, ccs) }
180 flatten ctxt ty@(ForAllTy {})
181 -- We allow for-alls when, but only when, no type function
182 -- applications inside the forall involve the bound type variables
183 -- TODO: What if it is a (t1 ~ t2) => t3
184 -- Must revisit when the New Coercion API is here!
185 = do { let (tvs, rho) = splitForAllTys ty
186 ; (rho', co, ccs) <- flatten ctxt rho
187 ; let bad_eqs = filterBag is_bad ccs
188 is_bad c = tyVarsOfCanonical c `intersectsVarSet` tv_set
189 tv_set = mkVarSet tvs
190 ; unless (isEmptyBag bad_eqs)
191 (flattenForAllErrorTcS ctxt ty bad_eqs)
192 ; return (mkForAllTys tvs rho', mkForAllTys tvs co, ccs) }
195 flattenPred :: CtFlavor -> TcPredType -> TcS (TcPredType, Coercion, CanonicalCts)
196 flattenPred ctxt (ClassP cls tys)
197 = do { (tys', cos, ccs) <- flattenMany ctxt tys
198 ; return (ClassP cls tys', mkClassPPredCo cls cos, ccs) }
199 flattenPred ctxt (IParam nm ty)
200 = do { (ty', co, ccs) <- flatten ctxt ty
201 ; return (IParam nm ty', mkIParamPredCo nm co, ccs) }
202 -- TODO: Handling of coercions between EqPreds must be revisited once the New Coercion API is ready!
203 flattenPred ctxt (EqPred ty1 ty2)
204 = do { (ty1', co1, ccs1) <- flatten ctxt ty1
205 ; (ty2', co2, ccs2) <- flatten ctxt ty2
206 ; return (EqPred ty1' ty2', mkEqPredCo co1 co2, ccs1 `andCCan` ccs2) }
210 %************************************************************************
212 %* Canonicalising given constraints *
214 %************************************************************************
217 canWanteds :: [WantedEvVar] -> TcS CanonicalCts
218 canWanteds = fmap andCCans . mapM (\(EvVarX ev loc) -> mkCanonical (Wanted loc) ev)
220 canGivens :: GivenLoc -> [EvVar] -> TcS CanonicalCts
221 canGivens loc givens = do { ccs <- mapM (mkCanonical (Given loc)) givens
222 ; return (andCCans ccs) }
224 mkCanonicals :: CtFlavor -> [EvVar] -> TcS CanonicalCts
225 mkCanonicals fl vs = fmap andCCans (mapM (mkCanonical fl) vs)
227 mkCanonicalFEV :: FlavoredEvVar -> TcS CanonicalCts
228 mkCanonicalFEV (EvVarX ev fl) = mkCanonical fl ev
230 mkCanonical :: CtFlavor -> EvVar -> TcS CanonicalCts
231 mkCanonical fl ev = case evVarPred ev of
232 ClassP clas tys -> canClass fl ev clas tys
233 IParam ip ty -> canIP fl ev ip ty
234 EqPred ty1 ty2 -> canEq fl ev ty1 ty2
237 canClass :: CtFlavor -> EvVar -> Class -> [TcType] -> TcS CanonicalCts
239 = do { (xis,cos,ccs) <- flattenMany fl tys -- cos :: xis ~ tys
240 ; let no_flattening_happened = isEmptyCCan ccs
241 dict_co = mkTyConCoercion (classTyCon cn) cos
242 ; v_new <- if no_flattening_happened then return v
243 else if isGiven fl then return v
244 -- The cos are all identities if fl=Given,
245 -- hence nothing to do
246 else do { v' <- newDictVar cn xis -- D xis
247 ; when (isWanted fl) $ setDictBind v (EvCast v' dict_co)
248 ; when (isGiven fl) $ setDictBind v' (EvCast v (mkSymCoercion dict_co))
249 -- NB: No more setting evidence for derived now
252 -- Add the superclasses of this one here, See Note [Adding superclasses].
253 -- But only if we are not simplifying the LHS of a rule.
254 ; sctx <- getTcSContext
255 ; sc_cts <- if simplEqsOnly sctx then return emptyCCan
256 else newSCWorkFromFlavored v_new fl cn xis
258 ; return (sc_cts `andCCan` ccs `extendCCans` CDictCan { cc_id = v_new
261 , cc_tyargs = xis }) }
264 Note [Adding superclasses]
265 ~~~~~~~~~~~~~~~~~~~~~~~~~~
266 Since dictionaries are canonicalized only once in their lifetime, the
267 place to add their superclasses is canonicalisation (The alternative
268 would be to do it during constraint solving, but we'd have to be
269 extremely careful to not repeatedly introduced the same superclass in
270 our worklist). Here is what we do:
273 We add all their superclasses as Givens.
276 Generally speaking we want to be able to add superclasses of
277 wanteds for two reasons:
279 (1) Oportunities for improvement. Example:
280 class (a ~ b) => C a b
281 Wanted constraint is: C alpha beta
282 We'd like to simply have C alpha alpha. Similar
283 situations arise in relation to functional dependencies.
285 (2) To have minimal constraints to quantify over:
286 For instance, if our wanted constraint is (Eq a, Ord a)
287 we'd only like to quantify over Ord a.
289 To deal with (1) above we only add the superclasses of wanteds
290 which may lead to improvement, that is: equality superclasses or
291 superclasses with functional dependencies.
293 We deal with (2) completely independently in TcSimplify. See
294 Note [Minimize by SuperClasses] in TcSimplify.
297 Moreover, in all cases the extra improvement constraints are
298 Derived. Derived constraints have an identity (for now), but
299 we don't do anything with their evidence. For instance they
300 are never used to rewrite other constraints.
302 See also [New Wanted Superclass Work] in TcInteract.
308 Here's an example that demonstrates why we chose to NOT add
309 superclasses during simplification: [Comes from ticket #4497]
311 class Num (RealOf t) => Normed t
314 Assume the generated wanted constraint is:
315 RealOf e ~ e, Normed e
316 If we were to be adding the superclasses during simplification we'd get:
317 Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf
319 e ~ uf, Num uf, Normed e, RealOf e ~ e
320 ==> [Spontaneous solve]
321 Num uf, Normed uf, RealOf uf ~ uf
323 While looks exactly like our original constraint. If we add the superclass again we'd loop.
324 By adding superclasses definitely only once, during canonicalisation, this situation can't
329 newSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS CanonicalCts
330 -- Returns superclasses, see Note [Adding superclasses]
331 newSCWorkFromFlavored ev orig_flavor cls xis
332 | isDerived orig_flavor
333 = return emptyCCan -- Deriveds don't yield more superclasses because we will
334 -- add them transitively in the case of wanteds.
336 | isGiven orig_flavor
337 = do { let sc_theta = immSuperClasses cls xis
339 ; sc_vars <- mapM newEvVar sc_theta
340 ; _ <- zipWithM_ setEvBind sc_vars [EvSuperClass ev n | n <- [0..]]
341 ; mkCanonicals flavor sc_vars }
343 | isEmptyVarSet (tyVarsOfTypes xis)
344 = return emptyCCan -- Wanteds with no variables yield no deriveds.
345 -- See Note [Improvement from Ground Wanteds]
347 | otherwise -- Wanted case, just add those SC that can lead to improvement.
348 = do { let sc_rec_theta = transSuperClasses cls xis
349 impr_theta = filter is_improvement_pty sc_rec_theta
350 Wanted wloc = orig_flavor
351 ; der_ids <- mapM newDerivedId impr_theta
352 ; mkCanonicals (Derived wloc) der_ids }
355 is_improvement_pty :: PredType -> Bool
356 -- Either it's an equality, or has some functional dependency
357 is_improvement_pty (EqPred {}) = True
358 is_improvement_pty (ClassP cls _ty) = not $ null fundeps
359 where (_,fundeps,_,_,_,_) = classExtraBigSig cls
360 is_improvement_pty _ = False
365 canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts
366 -- See Note [Canonical implicit parameter constraints] to see why we don't
367 -- immediately canonicalize (flatten) IP constraints.
369 = return $ singleCCan $ CIPCan { cc_id = v
375 canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts
377 | tcEqType ty1 ty2 -- Dealing with equality here avoids
378 -- later spurious occurs checks for a~a
379 = do { when (isWanted fl) (setWantedCoBind cv ty1)
382 -- If one side is a variable, orient and flatten,
383 -- WITHOUT expanding type synonyms, so that we tend to
384 -- substitute a ~ Age rather than a ~ Int when @type Age = Int@
385 canEq fl cv ty1@(TyVarTy {}) ty2
386 = do { untch <- getUntouchables
387 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
388 canEq fl cv ty1 ty2@(TyVarTy {})
389 = do { untch <- getUntouchables
390 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
391 -- NB: don't use VarCls directly because tv1 or tv2 may be scolems!
393 canEq fl cv (TyConApp fn tys) ty2
394 | isSynFamilyTyCon fn, length tys == tyConArity fn
395 = do { untch <- getUntouchables
396 ; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }
397 canEq fl cv ty1 (TyConApp fn tys)
398 | isSynFamilyTyCon fn, length tys == tyConArity fn
399 = do { untch <- getUntouchables
400 ; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }
403 | Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1,
404 Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2
406 <- if isWanted fl then -- Wanted
407 do { v1 <- newWantedCoVar t1a t2a
408 ; v2 <- newWantedCoVar t1b t2b
409 ; v3 <- newWantedCoVar t1c t2c
410 ; let res_co = mkCoPredCo (mkCoVarCoercion v1)
411 (mkCoVarCoercion v2) (mkCoVarCoercion v3)
412 ; setWantedCoBind cv res_co
413 ; return (v1,v2,v3) }
414 else if isGiven fl then -- Given
415 let co_orig = mkCoVarCoercion cv
416 coa = mkCsel1Coercion co_orig
417 cob = mkCsel2Coercion co_orig
418 coc = mkCselRCoercion co_orig
419 in do { v1 <- newGivenCoVar t1a t2a coa
420 ; v2 <- newGivenCoVar t1b t2b cob
421 ; v3 <- newGivenCoVar t1c t2c coc
422 ; return (v1,v2,v3) }
424 do { v1 <- newDerivedId (EqPred t1a t2a)
425 ; v2 <- newDerivedId (EqPred t1b t2b)
426 ; v3 <- newDerivedId (EqPred t1c t2c)
427 ; return (v1,v2,v3) }
428 ; cc1 <- canEq fl v1 t1a t2a
429 ; cc2 <- canEq fl v2 t1b t2b
430 ; cc3 <- canEq fl v3 t1c t2c
431 ; return (cc1 `andCCan` cc2 `andCCan` cc3) }
434 -- Split up an equality between function types into two equalities.
435 canEq fl cv (FunTy s1 t1) (FunTy s2 t2)
436 = do { (argv, resv) <-
438 do { argv <- newWantedCoVar s1 s2
439 ; resv <- newWantedCoVar t1 t2
440 ; setWantedCoBind cv $
441 mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv)
442 ; return (argv,resv) }
444 else if isGiven fl then
445 let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv)
446 in do { argv <- newGivenCoVar s1 s2 arg
447 ; resv <- newGivenCoVar t1 t2 res
448 ; return (argv,resv) }
451 do { argv <- newDerivedId (EqPred s1 s2)
452 ; resv <- newDerivedId (EqPred t1 t2)
453 ; return (argv,resv) }
455 ; cc1 <- canEq fl argv s1 s2 -- inherit original kinds and locations
456 ; cc2 <- canEq fl resv t1 t2
457 ; return (cc1 `andCCan` cc2) }
459 canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2))
461 = if isWanted fl then
462 do { v <- newWantedCoVar t1 t2
463 ; setWantedCoBind cv $ mkIParamPredCo n1 (mkCoVarCoercion cv)
465 else return emptyCCan -- DV: How to decompose given IP coercions?
467 canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2))
469 = if isWanted fl then
470 do { vs <- zipWithM newWantedCoVar tys1 tys2
471 ; setWantedCoBind cv $ mkClassPPredCo c1 (map mkCoVarCoercion vs)
472 ; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2
474 else return emptyCCan
475 -- How to decompose given dictionary (and implicit parameter) coercions?
476 -- You may think that the following is right:
477 -- let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
478 -- in zipWith3M newGivOrDerCoVar tys1 tys2 cos
479 -- But this assumes that the coercion is a type constructor-based
480 -- coercion, and not a PredTy (ClassP cn cos) coercion. So we chose
481 -- to not decompose these coercions. We have to get back to this
482 -- when we clean up the Coercion API.
484 canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)
485 | isAlgTyCon tc1 && isAlgTyCon tc2
487 , length tys1 == length tys2
488 = -- Generate equalities for each of the corresponding arguments
490 <- if isWanted fl then
491 do { argsv <- zipWithM newWantedCoVar tys1 tys2
492 ; setWantedCoBind cv $
493 mkTyConCoercion tc1 (map mkCoVarCoercion argsv)
496 else if isGiven fl then
497 let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
498 in zipWith3M newGivenCoVar tys1 tys2 cos
501 zipWithM (\t1 t2 -> newDerivedId (EqPred t1 t2)) tys1 tys2
503 ; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 }
505 -- See Note [Equality between type applications]
506 -- Note [Care with type applications] in TcUnify
508 | Just (s1,t1) <- tcSplitAppTy_maybe ty1
509 , Just (s2,t2) <- tcSplitAppTy_maybe ty2
512 then do { cv1 <- newWantedCoVar s1 s2
513 ; cv2 <- newWantedCoVar t1 t2
514 ; setWantedCoBind cv $
515 mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2)
518 else if isGiven fl then
519 let co1 = mkLeftCoercion $ mkCoVarCoercion cv
520 co2 = mkRightCoercion $ mkCoVarCoercion cv
521 in do { cv1 <- newGivenCoVar s1 s2 co1
522 ; cv2 <- newGivenCoVar t1 t2 co2
525 do { cv1 <- newDerivedId (EqPred s1 s2)
526 ; cv2 <- newDerivedId (EqPred t1 t2)
529 ; cc1 <- canEq fl cv1 s1 s2
530 ; cc2 <- canEq fl cv2 t1 t2
531 ; return (cc1 `andCCan` cc2) }
533 canEq fl cv s1@(ForAllTy {}) s2@(ForAllTy {})
534 | tcIsForAllTy s1, tcIsForAllTy s2,
538 = do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2)
541 -- Finally expand any type synonym applications.
542 canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2
543 canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'
544 canEq fl cv _ _ = canEqFailure fl cv
546 canEqFailure :: CtFlavor -> EvVar -> TcS CanonicalCts
547 canEqFailure fl cv = return (singleCCan (mkFrozenError fl cv))
550 Note [Equality between type applications]
551 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
552 If we see an equality of the form s1 t1 ~ s2 t2 we can always split
553 it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type
554 functions (type functions use the TyConApp constructor, which never
555 shows up as the LHS of an AppTy). Other than type functions, types
556 in Haskell are always
558 (1) generative: a b ~ c d implies a ~ c, since different type
559 constructors always generate distinct types
561 (2) injective: a b ~ a d implies b ~ d; we never generate the
562 same type from different type arguments.
565 Note [Canonical ordering for equality constraints]
566 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
567 Implemented as (<+=) below:
569 - Type function applications always come before anything else.
570 - Variables always come before non-variables (other than type
571 function applications).
573 Note that we don't need to unfold type synonyms on the RHS to check
574 the ordering; that is, in the rules above it's OK to consider only
575 whether something is *syntactically* a type function application or
576 not. To illustrate why this is OK, suppose we have an equality of the
577 form 'tv ~ S a b c', where S is a type synonym which expands to a
578 top-level application of the type function F, something like
582 Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's
583 expansion contains type function applications the flattener will do
584 the expansion and then generate a skolem variable for the type
585 function application, so we end up with something like this:
590 where x is the skolem variable. This is one extra equation than
591 absolutely necessary (we could have gotten away with just 'F d e ~ tv'
592 if we had noticed that S expanded to a top-level type function
593 application and flipped it around in the first place) but this way
594 keeps the code simpler.
596 Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the
597 ordering of tv ~ tv constraints. There are several reasons why we
600 (1) In order to be able to extract a substitution that doesn't
601 mention untouchable variables after we are done solving, we might
602 prefer to put touchable variables on the left. However, in and
603 of itself this isn't necessary; we can always re-orient equality
604 constraints at the end if necessary when extracting a substitution.
606 (2) To ensure termination we might think it necessary to put
607 variables in lexicographic order. However, this isn't actually
608 necessary as outlined below.
610 While building up an inert set of canonical constraints, we maintain
611 the invariant that the equality constraints in the inert set form an
612 acyclic rewrite system when viewed as L-R rewrite rules. Moreover,
613 the given constraints form an idempotent substitution (i.e. none of
614 the variables on the LHS occur in any of the RHS's, and type functions
615 never show up in the RHS at all), the wanted constraints also form an
616 idempotent substitution, and finally the LHS of a given constraint
617 never shows up on the RHS of a wanted constraint. There may, however,
618 be a wanted LHS that shows up in a given RHS, since we do not rewrite
619 given constraints with wanted constraints.
621 Suppose we have an inert constraint set
624 tg_1 ~ xig_1 -- givens
627 tw_1 ~ xiw_1 -- wanteds
631 where each t_i can be either a type variable or a type function
632 application. Now suppose we take a new canonical equality constraint,
633 t' ~ xi' (note among other things this means t' does not occur in xi')
634 and try to react it with the existing inert set. We show by induction
635 on the number of t_i which occur in t' ~ xi' that this process will
638 There are several ways t' ~ xi' could react with an existing constraint:
640 TODO: finish this proof. The below was for the case where the entire
641 inert set is an idempotent subustitution...
643 (b) We could have t' = t_j for some j. Then we obtain the new
644 equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We
645 now canonicalize the new equality, which may involve decomposing it
646 into several canonical equalities, and recurse on these. However,
647 none of the new equalities will contain t_j, so they have fewer
648 occurrences of the t_i than the original equation.
650 (a) We could have t_j occurring in xi' for some j, with t' /=
651 t_j. Then we substitute xi_j for t_j in xi' and continue. However,
652 since none of the t_i occur in xi_j, we have decreased the
653 number of t_i that occur in xi', since we eliminated t_j and did not
654 introduce any new ones.
658 = FskCls TcTyVar -- ^ Flatten skolem
659 | VarCls TcTyVar -- ^ Non-flatten-skolem variable
660 | FunCls TyCon [Type] -- ^ Type function, exactly saturated
661 | OtherCls TcType -- ^ Neither of the above
663 unClassify :: TypeClassifier -> TcType
664 unClassify (VarCls tv) = TyVarTy tv
665 unClassify (FskCls tv) = TyVarTy tv
666 unClassify (FunCls fn tys) = TyConApp fn tys
667 unClassify (OtherCls ty) = ty
669 classify :: TcType -> TypeClassifier
671 classify (TyVarTy tv)
673 FlatSkol {} <- tcTyVarDetails tv = FskCls tv
674 | otherwise = VarCls tv
675 classify (TyConApp tc tys) | isSynFamilyTyCon tc
676 , tyConArity tc == length tys
678 classify ty | Just ty' <- tcView ty
679 = case classify ty' of
680 OtherCls {} -> OtherCls ty
681 var_or_fn -> var_or_fn
685 -- See note [Canonical ordering for equality constraints].
686 reOrient :: TcsUntouchables -> TypeClassifier -> TypeClassifier -> Bool
687 -- (t1 `reOrient` t2) responds True
688 -- iff we should flip to (t2~t1)
689 -- We try to say False if possible, to minimise evidence generation
691 -- Postcondition: After re-orienting, first arg is not OTherCls
692 reOrient _untch (OtherCls {}) (FunCls {}) = True
693 reOrient _untch (OtherCls {}) (FskCls {}) = True
694 reOrient _untch (OtherCls {}) (VarCls {}) = True
695 reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun
697 reOrient _untch (FunCls {}) (VarCls {}) = False
698 -- See Note [No touchables as FunEq RHS] in TcSMonad
699 reOrient _untch (FunCls {}) _ = False -- Fun/Other on rhs
701 reOrient _untch (VarCls {}) (FunCls {}) = True
703 reOrient _untch (VarCls {}) (FskCls {}) = False
705 reOrient _untch (VarCls {}) (OtherCls {}) = False
706 reOrient _untch (VarCls tv1) (VarCls tv2)
707 | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True
709 -- Just for efficiency, see CTyEqCan invariants
711 reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2
712 -- Just for efficiency, see CTyEqCan invariants
714 reOrient _untch (FskCls {}) (FskCls {}) = False
715 reOrient _untch (FskCls {}) (FunCls {}) = True
716 reOrient _untch (FskCls {}) (OtherCls {}) = False
719 canEqLeaf :: TcsUntouchables
721 -> TypeClassifier -> TypeClassifier -> TcS CanonicalCts
722 -- Canonicalizing "leaf" equality constraints which cannot be
723 -- decomposed further (ie one of the types is a variable or
724 -- saturated type function application).
727 -- * one of the two arguments is not OtherCls
728 -- * the two types are not equal (looking through synonyms)
729 canEqLeaf untch fl cv cls1 cls2
730 | cls1 `re_orient` cls2
731 = do { cv' <- if isWanted fl
732 then do { cv' <- newWantedCoVar s2 s1
733 ; setWantedCoBind cv $ mkSymCoercion (mkCoVarCoercion cv')
735 else if isGiven fl then
736 newGivenCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv))
738 newDerivedId (EqPred s2 s1)
739 ; canEqLeafOriented fl cv' cls2 s1 }
742 = do { traceTcS "canEqLeaf" (ppr (unClassify cls1) $$ ppr (unClassify cls2))
743 ; canEqLeafOriented fl cv cls1 s2 }
745 re_orient = reOrient untch
750 canEqLeafOriented :: CtFlavor -> CoVar
751 -> TypeClassifier -> TcType -> TcS CanonicalCts
752 -- First argument is not OtherCls
753 canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2 -- cv : F tys1
754 | let k1 = kindAppResult (tyConKind fn) tys1,
755 let k2 = typeKind s2,
756 not (k1 `compatKind` k2) -- Establish the kind invariant for CFunEqCan
758 -- Eagerly fails, see Note [Kind errors] in TcInteract
761 = ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )
762 do { (xis1,cos1,ccs1) <- flattenMany fl tys1 -- Flatten type function arguments
763 -- cos1 :: xis1 ~ tys1
764 ; (xi2, co2, ccs2) <- flatten fl s2 -- Flatten entire RHS
766 ; let ccs = ccs1 `andCCan` ccs2
767 no_flattening_happened = isEmptyCCan ccs
768 ; cv_new <- if no_flattening_happened then return cv
769 else if isGiven fl then return cv
770 else if isWanted fl then
771 do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2
773 ; let -- fun_co :: F xis1 ~ F tys1
774 fun_co = mkTyConCoercion fn cos1
775 -- want_co :: F tys1 ~ s2
776 want_co = mkSymCoercion fun_co
777 `mkTransCoercion` mkCoVarCoercion cv'
778 `mkTransCoercion` co2
779 ; setWantedCoBind cv want_co
782 newDerivedId (EqPred (unClassify (FunCls fn xis1)) xi2)
784 ; let final_cc = CFunEqCan { cc_id = cv_new
789 ; return $ ccs `extendCCans` final_cc }
791 -- Otherwise, we have a variable on the left, so call canEqLeafTyVarLeft
792 canEqLeafOriented fl cv (FskCls tv) s2
793 = canEqLeafTyVarLeft fl cv tv s2
794 canEqLeafOriented fl cv (VarCls tv) s2
795 = canEqLeafTyVarLeft fl cv tv s2
796 canEqLeafOriented _ cv (OtherCls ty1) ty2
797 = pprPanic "canEqLeaf" (ppr cv $$ ppr ty1 $$ ppr ty2)
799 canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts
800 -- Establish invariants of CTyEqCans
801 canEqLeafTyVarLeft fl cv tv s2 -- cv : tv ~ s2
802 | not (k1 `compatKind` k2) -- Establish the kind invariant for CTyEqCan
804 -- Eagerly fails, see Note [Kind errors] in TcInteract
806 = do { (xi2, co, ccs2) <- flatten fl s2 -- Flatten RHS co : xi2 ~ s2
807 ; mxi2' <- canOccursCheck fl tv xi2 -- Do an occurs check, and return a possibly
808 -- unfolded version of the RHS, if we had to
809 -- unfold any type synonyms to get rid of tv.
811 Nothing -> canEqFailure fl cv ;
813 do { let no_flattening_happened = isEmptyCCan ccs2
814 ; cv_new <- if no_flattening_happened then return cv
815 else if isGiven fl then return cv
816 else if isWanted fl then
817 do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2' -- cv' : tv ~ xi2
818 ; setWantedCoBind cv (mkCoVarCoercion cv' `mkTransCoercion` co)
821 newDerivedId (EqPred (mkTyVarTy tv) xi2')
823 ; return $ ccs2 `extendCCans` CTyEqCan { cc_id = cv_new
826 , cc_rhs = xi2' } } } }
831 -- See Note [Type synonyms and canonicalization].
832 -- Check whether the given variable occurs in the given type. We may
833 -- have needed to do some type synonym unfolding in order to get rid
834 -- of the variable, so we also return the unfolded version of the
835 -- type, which is guaranteed to be syntactically free of the given
836 -- type variable. If the type is already syntactically free of the
837 -- variable, then the same type is returned.
839 -- Precondition: the two types are not equal (looking though synonyms)
840 canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi)
841 canOccursCheck _gw tv xi = return (expandAway tv xi)
844 @expandAway tv xi@ expands synonyms in xi just enough to get rid of
845 occurrences of tv, if that is possible; otherwise, it returns Nothing.
846 For example, suppose we have
849 expandAway b (F Int b) = Just [Int]
851 expandAway a (F a Int) = Nothing
853 We don't promise to do the absolute minimum amount of expanding
854 necessary, but we try not to do expansions we don't need to. We
855 prefer doing inner expansions first. For example,
856 type F a b = (a, Int, a, [a])
859 expandAway b (F (G b)) = F Char
860 even though we could also expand F to get rid of b.
863 expandAway :: TcTyVar -> Xi -> Maybe Xi
864 expandAway tv t@(TyVarTy tv')
865 | tv == tv' = Nothing
868 | not (tv `elemVarSet` tyVarsOfType xi) = Just xi
869 expandAway tv (AppTy ty1 ty2)
870 = do { ty1' <- expandAway tv ty1
871 ; ty2' <- expandAway tv ty2
872 ; return (mkAppTy ty1' ty2') }
873 -- mkAppTy <$> expandAway tv ty1 <*> expandAway tv ty2
874 expandAway tv (FunTy ty1 ty2)
875 = do { ty1' <- expandAway tv ty1
876 ; ty2' <- expandAway tv ty2
877 ; return (mkFunTy ty1' ty2') }
878 -- mkFunTy <$> expandAway tv ty1 <*> expandAway tv ty2
879 expandAway tv ty@(ForAllTy {})
880 = let (tvs,rho) = splitForAllTys ty
881 tvs_knds = map tyVarKind tvs
882 in if tv `elemVarSet` tyVarsOfTypes tvs_knds then
883 -- Can't expand away the kinds unless we create
884 -- fresh variables which we don't want to do at this point.
886 else do { rho' <- expandAway tv rho
887 ; return (mkForAllTys tvs rho') }
888 expandAway tv (PredTy pred)
889 = do { pred' <- expandAwayPred tv pred
890 ; return (PredTy pred') }
891 -- For a type constructor application, first try expanding away the
892 -- offending variable from the arguments. If that doesn't work, next
893 -- see if the type constructor is a type synonym, and if so, expand
895 expandAway tv ty@(TyConApp tc tys)
896 = (mkTyConApp tc <$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv)
898 expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType
899 expandAwayPred tv (ClassP cls tys)
900 = do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') }
901 expandAwayPred tv (EqPred ty1 ty2)
902 = do { ty1' <- expandAway tv ty1
903 ; ty2' <- expandAway tv ty2
904 ; return (EqPred ty1' ty2') }
905 expandAwayPred tv (IParam nm ty)
906 = do { ty' <- expandAway tv ty
907 ; return (IParam nm ty') }
913 Note [Type synonyms and canonicalization]
914 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
916 We treat type synonym applications as xi types, that is, they do not
917 count as type function applications. However, we do need to be a bit
918 careful with type synonyms: like type functions they may not be
919 generative or injective. However, unlike type functions, they are
920 parametric, so there is no problem in expanding them whenever we see
921 them, since we do not need to know anything about their arguments in
922 order to expand them; this is what justifies not having to treat them
923 as specially as type function applications. The thing that causes
924 some subtleties is that we prefer to leave type synonym applications
925 *unexpanded* whenever possible, in order to generate better error
928 If we encounter an equality constraint with type synonym applications
929 on both sides, or a type synonym application on one side and some sort
930 of type application on the other, we simply must expand out the type
931 synonyms in order to continue decomposing the equality constraint into
932 primitive equality constraints. For example, suppose we have
936 and we encounter the equality
940 In order to continue we must expand F a into [Int], giving us the
945 which we can then decompose into the more primitive equality
950 However, if we encounter an equality constraint with a type synonym
951 application on one side and a variable on the other side, we should
952 NOT (necessarily) expand the type synonym, since for the purpose of
953 good error messages we want to leave type synonyms unexpanded as much
956 However, there is a subtle point with type synonyms and the occurs
957 check that takes place for equality constraints of the form tv ~ xi.
958 As an example, suppose we have
962 and we come across the equality constraint
966 This should not actually fail the occurs check, since expanding out
967 the type synonym results in the legitimate equality constraint a ~
968 Int. We must actually do this expansion, because unifying a with F a
969 will lead the type checker into infinite loops later. Put another
970 way, canonical equality constraints should never *syntactically*
971 contain the LHS variable in the RHS type. However, we don't always
972 need to expand type synonyms when doing an occurs check; for example,
977 is obviously fine no matter what F expands to. And in this case we
978 would rather unify a with F b (rather than F b's expansion) in order
979 to get better error messages later.
981 So, when doing an occurs check with a type synonym application on the
982 RHS, we use some heuristics to find an expansion of the RHS which does
983 not contain the variable from the LHS. In particular, given
987 we first try expanding each of the ti to types which no longer contain
988 a. If this turns out to be impossible, we next try expanding F