3 mkCanonical, mkCanonicals, canWanteds, canGivens, canOccursCheck, canEq,
6 #include "HsVersions.h"
21 import Control.Monad ( when, zipWithM )
23 import Control.Applicative ( (<|>) )
30 import Control.Monad ( unless )
31 import TcSMonad -- The TcS Monad
34 Note [Canonicalisation]
35 ~~~~~~~~~~~~~~~~~~~~~~~
36 * Converts (Constraint f) _which_does_not_contain_proper_implications_ to CanonicalCts
37 * Unary: treats individual constraints one at a time
38 * Does not do any zonking
39 * Lives in TcS monad so that it can create new skolem variables
42 %************************************************************************
44 %* Flattening (eliminating all function symbols) *
46 %************************************************************************
50 flatten ty ==> (xi, cc)
52 xi has no type functions
53 cc = Auxiliary given (equality) constraints constraining
54 the fresh type variables in xi. Evidence for these
55 is always the identity coercion, because internally the
56 fresh flattening skolem variables are actually identified
57 with the types they have been generated to stand in for.
59 Note that it is flatten's job to flatten *every type function it sees*.
60 flatten is only called on *arguments* to type functions, by canEqGiven.
62 Recall that in comments we use alpha[flat = ty] to represent a
63 flattening skolem variable alpha which has been generated to stand in
66 ----- Example of flattening a constraint: ------
67 flatten (List (F (G Int))) ==> (xi, cc)
70 cc = { G Int ~ beta[flat = G Int],
71 F beta ~ alpha[flat = F beta] }
73 * alpha and beta are 'flattening skolem variables'.
74 * All the constraints in cc are 'given', and all their coercion terms
77 NB: Flattening Skolems only occur in canonical constraints, which
78 are never zonked, so we don't need to worry about zonking doing
79 accidental unflattening.
81 Note that we prefer to leave type synonyms unexpanded when possible,
82 so when the flattener encounters one, it first asks whether its
83 transitive expansion contains any type function applications. If so,
84 it expands the synonym and proceeds; if not, it simply returns the
87 TODO: caching the information about whether transitive synonym
88 expansions contain any type function applications would speed things
89 up a bit; right now we waste a lot of energy traversing the same types
93 -- Flatten a bunch of types all at once.
94 flattenMany :: CtFlavor -> [Type] -> TcS ([Xi], [Coercion], CanonicalCts)
95 -- Coercions :: Xi ~ Type
97 = do { (xis, cos, cts_s) <- mapAndUnzip3M (flatten ctxt) tys
98 ; return (xis, cos, andCCans cts_s) }
100 -- Flatten a type to get rid of type function applications, returning
101 -- the new type-function-free type, and a collection of new equality
102 -- constraints. See Note [Flattening] for more detail.
103 flatten :: CtFlavor -> TcType -> TcS (Xi, Coercion, CanonicalCts)
104 -- Postcondition: Coercion :: Xi ~ TcType
106 | Just ty' <- tcView ty
107 = do { (xi, co, ccs) <- flatten ctxt ty'
108 -- Preserve type synonyms if possible
109 -- We can tell if ty' is function-free by
110 -- whether there are any floated constraints
111 ; if isEmptyCCan ccs then
112 return (ty, ty, emptyCCan)
114 return (xi, co, ccs) }
116 flatten _ v@(TyVarTy _)
117 = return (v, v, emptyCCan)
119 flatten ctxt (AppTy ty1 ty2)
120 = do { (xi1,co1,c1) <- flatten ctxt ty1
121 ; (xi2,co2,c2) <- flatten ctxt ty2
122 ; return (mkAppTy xi1 xi2, mkAppCoercion co1 co2, c1 `andCCan` c2) }
124 flatten ctxt (FunTy ty1 ty2)
125 = do { (xi1,co1,c1) <- flatten ctxt ty1
126 ; (xi2,co2,c2) <- flatten ctxt ty2
127 ; return (mkFunTy xi1 xi2, mkFunCoercion co1 co2, c1 `andCCan` c2) }
129 flatten fl (TyConApp tc tys)
130 -- For a normal type constructor or data family application, we just
131 -- recursively flatten the arguments.
132 | not (isSynFamilyTyCon tc)
133 = do { (xis,cos,ccs) <- flattenMany fl tys
134 ; return (mkTyConApp tc xis, mkTyConCoercion tc cos, ccs) }
136 -- Otherwise, it's a type function application, and we have to
137 -- flatten it away as well, and generate a new given equality constraint
138 -- between the application and a newly generated flattening skolem variable.
140 = ASSERT( tyConArity tc <= length tys ) -- Type functions are saturated
141 do { (xis, cos, ccs) <- flattenMany fl tys
142 ; let (xi_args, xi_rest) = splitAt (tyConArity tc) xis
143 (cos_args, cos_rest) = splitAt (tyConArity tc) cos
144 -- The type function might be *over* saturated
145 -- in which case the remaining arguments should
146 -- be dealt with by AppTys
147 fam_ty = mkTyConApp tc xi_args
148 fam_co = fam_ty -- identity
150 ; (ret_co, rhs_var, ct) <-
152 do { rhs_var <- newFlattenSkolemTy fam_ty
153 ; cv <- newGivOrDerCoVar fam_ty rhs_var fam_co
154 ; let ct = CFunEqCan { cc_id = cv
155 , cc_flavor = fl -- Given
157 , cc_tyargs = xi_args
159 ; return $ (mkCoVarCoercion cv, rhs_var, ct) }
160 else -- Derived or Wanted: make a new *unification* flatten variable
161 do { rhs_var <- newFlexiTcSTy (typeKind fam_ty)
162 ; cv <- newWantedCoVar fam_ty rhs_var
163 ; let ct = CFunEqCan { cc_id = cv
164 , cc_flavor = mkWantedFlavor fl
165 -- Always Wanted, not Derived
167 , cc_tyargs = xi_args
169 ; return $ (mkCoVarCoercion cv, rhs_var, ct) }
171 ; return ( foldl AppTy rhs_var xi_rest
172 , foldl AppTy (mkSymCoercion ret_co
173 `mkTransCoercion` mkTyConCoercion tc cos_args) cos_rest
174 , ccs `extendCCans` ct) }
177 flatten ctxt (PredTy pred)
178 = do { (pred', co, ccs) <- flattenPred ctxt pred
179 ; return (PredTy pred', co, ccs) }
181 flatten ctxt ty@(ForAllTy {})
182 -- We allow for-alls when, but only when, no type function
183 -- applications inside the forall involve the bound type variables
184 -- TODO: What if it is a (t1 ~ t2) => t3
185 -- Must revisit when the New Coercion API is here!
186 = do { let (tvs, rho) = splitForAllTys ty
187 ; (rho', co, ccs) <- flatten ctxt rho
188 ; let bad_eqs = filterBag is_bad ccs
189 is_bad c = tyVarsOfCanonical c `intersectsVarSet` tv_set
190 tv_set = mkVarSet tvs
191 ; unless (isEmptyBag bad_eqs)
192 (flattenForAllErrorTcS ctxt ty bad_eqs)
193 ; return (mkForAllTys tvs rho', mkForAllTys tvs co, ccs) }
196 flattenPred :: CtFlavor -> TcPredType -> TcS (TcPredType, Coercion, CanonicalCts)
197 flattenPred ctxt (ClassP cls tys)
198 = do { (tys', cos, ccs) <- flattenMany ctxt tys
199 ; return (ClassP cls tys', mkClassPPredCo cls cos, ccs) }
200 flattenPred ctxt (IParam nm ty)
201 = do { (ty', co, ccs) <- flatten ctxt ty
202 ; return (IParam nm ty', mkIParamPredCo nm co, ccs) }
203 -- TODO: Handling of coercions between EqPreds must be revisited once the New Coercion API is ready!
204 flattenPred ctxt (EqPred ty1 ty2)
205 = do { (ty1', co1, ccs1) <- flatten ctxt ty1
206 ; (ty2', co2, ccs2) <- flatten ctxt ty2
207 ; return (EqPred ty1' ty2', mkEqPredCo co1 co2, ccs1 `andCCan` ccs2) }
211 %************************************************************************
213 %* Canonicalising given constraints *
215 %************************************************************************
218 canWanteds :: [WantedEvVar] -> TcS CanonicalCts
219 canWanteds = fmap andCCans . mapM (\(WantedEvVar ev loc) -> mkCanonical (Wanted loc) ev)
221 canGivens :: GivenLoc -> [EvVar] -> TcS CanonicalCts
222 canGivens loc givens = do { ccs <- mapM (mkCanonical (Given loc)) givens
223 ; return (andCCans ccs) }
225 mkCanonicals :: CtFlavor -> [EvVar] -> TcS CanonicalCts
226 mkCanonicals fl vs = fmap andCCans (mapM (mkCanonical fl) vs)
228 mkCanonical :: CtFlavor -> EvVar -> TcS CanonicalCts
229 mkCanonical fl ev = case evVarPred ev of
230 ClassP clas tys -> canClass fl ev clas tys
231 IParam ip ty -> canIP fl ev ip ty
232 EqPred ty1 ty2 -> canEq fl ev ty1 ty2
235 canClass :: CtFlavor -> EvVar -> Class -> [TcType] -> TcS CanonicalCts
237 = do { (xis,cos,ccs) <- flattenMany fl tys -- cos :: xis ~ tys
238 ; let no_flattening_happened = isEmptyCCan ccs
239 dict_co = mkTyConCoercion (classTyCon cn) cos
240 ; v_new <- if no_flattening_happened then return v
241 else if isGiven fl then return v
242 -- The cos are all identities if fl=Given,
243 -- hence nothing to do
244 else do { v' <- newDictVar cn xis -- D xis
246 then setDictBind v (EvCast v' dict_co)
247 else setDictBind v' (EvCast v (mkSymCoercion dict_co))
250 -- Add the superclasses of this one here, See Note [Adding superclasses].
251 -- But only if we are not simplifying the LHS of a rule.
252 ; sctx <- getTcSContext
253 ; sc_cts <- if simplEqsOnly sctx then return emptyCCan
254 else newSCWorkFromFlavored v_new fl cn xis
256 ; return (sc_cts `andCCan` ccs `extendCCans` CDictCan { cc_id = v_new
259 , cc_tyargs = xis }) }
263 Note [Adding superclasses]
264 ~~~~~~~~~~~~~~~~~~~~~~~~~~
265 Since dictionaries are canonicalized only once in their lifetime, the
266 place to add their superclasses is canonicalisation (The alternative
267 would be to do it during constraint solving, but we'd have to be
268 extremely careful to not repeatedly introduced the same superclass in
269 our worklist). Here is what we do:
272 We add all their superclasses as Givens.
275 Generally speaking, we want to be able to add derived
276 superclasses of unsolved wanteds, and wanteds that have been
277 partially being solved via an instance. This is important to be
278 able to simplify the inferred constraints more (and to allow
279 for recursive dictionaries, less importantly).
281 Example: Inferred wanted constraint is (Eq a, Ord a), but we'd
282 only like to quantify over Ord a, hence we would like to be
283 able to add the superclass of Ord a as Derived and use it to
284 solve the wanted Eq a.
287 Deriveds either arise as wanteds that have been partially
288 solved, or as superclasses of other wanteds or deriveds. Hence,
289 their superclasses must be already there so we must do nothing
292 DV: In fact, it is probably true that the canonicaliser is
293 *never* asked to canonicalise Derived dictionaries
295 There is one disadvantage to this. Suppose the wanted constraints are
296 (Num a, Num a). Then we'll add all the superclasses of both during
297 canonicalisation, only to eliminate them later when they are
298 interacted. That seems like a waste of work. Still, it's simple.
300 Here's an example that demonstrates why we chose to NOT add
301 superclasses during simplification: [Comes from ticket #4497]
303 class Num (RealOf t) => Normed t
306 Assume the generated wanted constraint is:
307 RealOf e ~ e, Normed e
308 If we were to be adding the superclasses during simplification we'd get:
309 Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf
311 e ~ uf, Num uf, Normed e, RealOf e ~ e
312 ==> [Spontaneous solve]
313 Num uf, Normed uf, RealOf uf ~ uf
315 While looks exactly like our original constraint. If we add the superclass again we'd loop.
316 By adding superclasses definitely only once, during canonicalisation, this situation can't
320 newSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS CanonicalCts
321 -- Returns superclasses, see Note [Adding superclasses]
322 newSCWorkFromFlavored ev orig_flavor cls xis
323 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
324 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
325 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
326 ; mkCanonicals flavor sc_vars }
327 -- NB: Since there is a call to mkCanonicals,
328 -- this will add *recursively* all superclasses
330 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
331 flavor = case orig_flavor of
332 Given loc -> Given loc
333 Wanted loc -> Derived loc DerSC
334 Derived {} -> orig_flavor
335 -- NB: the non-immediate superclasses will show up as
336 -- Derived, and we want their superclasses too!
338 canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts
339 -- See Note [Canonical implicit parameter constraints] to see why we don't
340 -- immediately canonicalize (flatten) IP constraints.
342 = return $ singleCCan $ CIPCan { cc_id = v
348 canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts
350 | tcEqType ty1 ty2 -- Dealing with equality here avoids
351 -- later spurious occurs checks for a~a
352 = do { when (isWanted fl) (setWantedCoBind cv ty1)
355 -- If one side is a variable, orient and flatten,
356 -- WITHOUT expanding type synonyms, so that we tend to
357 -- substitute a ~ Age rather than a ~ Int when @type Age = Int@
358 canEq fl cv ty1@(TyVarTy {}) ty2
359 = do { untch <- getUntouchables
360 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
361 canEq fl cv ty1 ty2@(TyVarTy {})
362 = do { untch <- getUntouchables
363 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
364 -- NB: don't use VarCls directly because tv1 or tv2 may be scolems!
366 canEq fl cv (TyConApp fn tys) ty2
367 | isSynFamilyTyCon fn, length tys == tyConArity fn
368 = do { untch <- getUntouchables
369 ; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }
370 canEq fl cv ty1 (TyConApp fn tys)
371 | isSynFamilyTyCon fn, length tys == tyConArity fn
372 = do { untch <- getUntouchables
373 ; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }
376 | Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1,
377 Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2
378 = do { (v1,v2,v3) <- if isWanted fl then
379 do { v1 <- newWantedCoVar t1a t2a
380 ; v2 <- newWantedCoVar t1b t2b
381 ; v3 <- newWantedCoVar t1c t2c
382 ; let res_co = mkCoPredCo (mkCoVarCoercion v1)
383 (mkCoVarCoercion v2) (mkCoVarCoercion v3)
384 ; setWantedCoBind cv res_co
385 ; return (v1,v2,v3) }
386 else let co_orig = mkCoVarCoercion cv
387 coa = mkCsel1Coercion co_orig
388 cob = mkCsel2Coercion co_orig
389 coc = mkCselRCoercion co_orig
390 in do { v1 <- newGivOrDerCoVar t1a t2a coa
391 ; v2 <- newGivOrDerCoVar t1b t2b cob
392 ; v3 <- newGivOrDerCoVar t1c t2c coc
393 ; return (v1,v2,v3) }
394 ; cc1 <- canEq fl v1 t1a t2a
395 ; cc2 <- canEq fl v2 t1b t2b
396 ; cc3 <- canEq fl v3 t1c t2c
397 ; return (cc1 `andCCan` cc2 `andCCan` cc3) }
400 -- Split up an equality between function types into two equalities.
401 canEq fl cv (FunTy s1 t1) (FunTy s2 t2)
402 = do { (argv, resv) <-
404 do { argv <- newWantedCoVar s1 s2
405 ; resv <- newWantedCoVar t1 t2
406 ; setWantedCoBind cv $
407 mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv)
408 ; return (argv,resv) }
409 else let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv)
410 in do { argv <- newGivOrDerCoVar s1 s2 arg
411 ; resv <- newGivOrDerCoVar t1 t2 res
412 ; return (argv,resv) }
413 ; cc1 <- canEq fl argv s1 s2 -- inherit original kinds and locations
414 ; cc2 <- canEq fl resv t1 t2
415 ; return (cc1 `andCCan` cc2) }
417 canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2))
419 = if isWanted fl then
420 do { v <- newWantedCoVar t1 t2
421 ; setWantedCoBind cv $ mkIParamPredCo n1 (mkCoVarCoercion cv)
423 else return emptyCCan -- DV: How to decompose given IP coercions?
425 canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2))
427 = if isWanted fl then
428 do { vs <- zipWithM newWantedCoVar tys1 tys2
429 ; setWantedCoBind cv $ mkClassPPredCo c1 (map mkCoVarCoercion vs)
430 ; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2
432 else return emptyCCan
433 -- How to decompose given dictionary (and implicit parameter) coercions?
434 -- You may think that the following is right:
435 -- let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
436 -- in zipWith3M newGivOrDerCoVar tys1 tys2 cos
437 -- But this assumes that the coercion is a type constructor-based
438 -- coercion, and not a PredTy (ClassP cn cos) coercion. So we chose
439 -- to not decompose these coercions. We have to get back to this
440 -- when we clean up the Coercion API.
442 canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)
443 | isAlgTyCon tc1 && isAlgTyCon tc2
445 , length tys1 == length tys2
446 = -- Generate equalities for each of the corresponding arguments
447 do { argsv <- if isWanted fl then
448 do { argsv <- zipWithM newWantedCoVar tys1 tys2
449 ; setWantedCoBind cv $ mkTyConCoercion tc1 (map mkCoVarCoercion argsv)
452 let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
453 in zipWith3M newGivOrDerCoVar tys1 tys2 cos
454 ; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 }
456 -- See Note [Equality between type applications]
457 -- Note [Care with type applications] in TcUnify
459 | Just (s1,t1) <- tcSplitAppTy_maybe ty1
460 , Just (s2,t2) <- tcSplitAppTy_maybe ty2
463 then do { cv1 <- newWantedCoVar s1 s2
464 ; cv2 <- newWantedCoVar t1 t2
465 ; setWantedCoBind cv $
466 mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2)
468 else let co1 = mkLeftCoercion $ mkCoVarCoercion cv
469 co2 = mkRightCoercion $ mkCoVarCoercion cv
470 in do { cv1 <- newGivOrDerCoVar s1 s2 co1
471 ; cv2 <- newGivOrDerCoVar t1 t2 co2
473 ; cc1 <- canEq fl cv1 s1 s2
474 ; cc2 <- canEq fl cv2 t1 t2
475 ; return (cc1 `andCCan` cc2) }
477 canEq fl _ s1@(ForAllTy {}) s2@(ForAllTy {})
478 | tcIsForAllTy s1, tcIsForAllTy s2,
480 = canEqFailure fl s1 s2
482 = do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2)
485 -- Finally expand any type synonym applications.
486 canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2
487 canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'
488 canEq fl _ ty1 ty2 = canEqFailure fl ty1 ty2
490 canEqFailure :: CtFlavor -> Type -> Type -> TcS CanonicalCts
491 canEqFailure fl ty1 ty2
492 = do { addErrorTcS MisMatchError fl ty1 ty2
496 Note [Equality between type applications]
497 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
498 If we see an equality of the form s1 t1 ~ s2 t2 we can always split
499 it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type
500 functions (type functions use the TyConApp constructor, which never
501 shows up as the LHS of an AppTy). Other than type functions, types
502 in Haskell are always
504 (1) generative: a b ~ c d implies a ~ c, since different type
505 constructors always generate distinct types
507 (2) injective: a b ~ a d implies b ~ d; we never generate the
508 same type from different type arguments.
511 Note [Canonical ordering for equality constraints]
512 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
513 Implemented as (<+=) below:
515 - Type function applications always come before anything else.
516 - Variables always come before non-variables (other than type
517 function applications).
519 Note that we don't need to unfold type synonyms on the RHS to check
520 the ordering; that is, in the rules above it's OK to consider only
521 whether something is *syntactically* a type function application or
522 not. To illustrate why this is OK, suppose we have an equality of the
523 form 'tv ~ S a b c', where S is a type synonym which expands to a
524 top-level application of the type function F, something like
528 Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's
529 expansion contains type function applications the flattener will do
530 the expansion and then generate a skolem variable for the type
531 function application, so we end up with something like this:
536 where x is the skolem variable. This is one extra equation than
537 absolutely necessary (we could have gotten away with just 'F d e ~ tv'
538 if we had noticed that S expanded to a top-level type function
539 application and flipped it around in the first place) but this way
540 keeps the code simpler.
542 Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the
543 ordering of tv ~ tv constraints. There are several reasons why we
546 (1) In order to be able to extract a substitution that doesn't
547 mention untouchable variables after we are done solving, we might
548 prefer to put touchable variables on the left. However, in and
549 of itself this isn't necessary; we can always re-orient equality
550 constraints at the end if necessary when extracting a substitution.
552 (2) To ensure termination we might think it necessary to put
553 variables in lexicographic order. However, this isn't actually
554 necessary as outlined below.
556 While building up an inert set of canonical constraints, we maintain
557 the invariant that the equality constraints in the inert set form an
558 acyclic rewrite system when viewed as L-R rewrite rules. Moreover,
559 the given constraints form an idempotent substitution (i.e. none of
560 the variables on the LHS occur in any of the RHS's, and type functions
561 never show up in the RHS at all), the wanted constraints also form an
562 idempotent substitution, and finally the LHS of a given constraint
563 never shows up on the RHS of a wanted constraint. There may, however,
564 be a wanted LHS that shows up in a given RHS, since we do not rewrite
565 given constraints with wanted constraints.
567 Suppose we have an inert constraint set
570 tg_1 ~ xig_1 -- givens
573 tw_1 ~ xiw_1 -- wanteds
577 where each t_i can be either a type variable or a type function
578 application. Now suppose we take a new canonical equality constraint,
579 t' ~ xi' (note among other things this means t' does not occur in xi')
580 and try to react it with the existing inert set. We show by induction
581 on the number of t_i which occur in t' ~ xi' that this process will
584 There are several ways t' ~ xi' could react with an existing constraint:
586 TODO: finish this proof. The below was for the case where the entire
587 inert set is an idempotent subustitution...
589 (b) We could have t' = t_j for some j. Then we obtain the new
590 equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We
591 now canonicalize the new equality, which may involve decomposing it
592 into several canonical equalities, and recurse on these. However,
593 none of the new equalities will contain t_j, so they have fewer
594 occurrences of the t_i than the original equation.
596 (a) We could have t_j occurring in xi' for some j, with t' /=
597 t_j. Then we substitute xi_j for t_j in xi' and continue. However,
598 since none of the t_i occur in xi_j, we have decreased the
599 number of t_i that occur in xi', since we eliminated t_j and did not
600 introduce any new ones.
604 = FskCls TcTyVar -- ^ Flatten skolem
605 | VarCls TcTyVar -- ^ Non-flatten-skolem variable
606 | FunCls TyCon [Type] -- ^ Type function, exactly saturated
607 | OtherCls TcType -- ^ Neither of the above
609 unClassify :: TypeClassifier -> TcType
610 unClassify (VarCls tv) = TyVarTy tv
611 unClassify (FskCls tv) = TyVarTy tv
612 unClassify (FunCls fn tys) = TyConApp fn tys
613 unClassify (OtherCls ty) = ty
615 classify :: TcType -> TypeClassifier
617 classify (TyVarTy tv)
619 FlatSkol {} <- tcTyVarDetails tv = FskCls tv
620 | otherwise = VarCls tv
621 classify (TyConApp tc tys) | isSynFamilyTyCon tc
622 , tyConArity tc == length tys
624 classify ty | Just ty' <- tcView ty
625 = case classify ty' of
626 OtherCls {} -> OtherCls ty
627 var_or_fn -> var_or_fn
631 -- See note [Canonical ordering for equality constraints].
632 reOrient :: TcsUntouchables -> TypeClassifier -> TypeClassifier -> Bool
633 -- (t1 `reOrient` t2) responds True
634 -- iff we should flip to (t2~t1)
635 -- We try to say False if possible, to minimise evidence generation
637 -- Postcondition: After re-orienting, first arg is not OTherCls
638 reOrient _untch (OtherCls {}) (FunCls {}) = True
639 reOrient _untch (OtherCls {}) (FskCls {}) = True
640 reOrient _untch (OtherCls {}) (VarCls {}) = True
641 reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun
643 reOrient _untch (FunCls {}) (VarCls {}) = False
644 -- See Note [No touchables as FunEq RHS] in TcSMonad
645 reOrient _untch (FunCls {}) _ = False -- Fun/Other on rhs
647 reOrient _untch (VarCls {}) (FunCls {}) = True
649 reOrient _untch (VarCls {}) (FskCls {}) = False
651 reOrient _untch (VarCls {}) (OtherCls {}) = False
652 reOrient _untch (VarCls tv1) (VarCls tv2)
653 | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True
655 -- Just for efficiency, see CTyEqCan invariants
657 reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2
658 -- Just for efficiency, see CTyEqCan invariants
660 reOrient _untch (FskCls {}) (FskCls {}) = False
661 reOrient _untch (FskCls {}) (FunCls {}) = True
662 reOrient _untch (FskCls {}) (OtherCls {}) = False
665 canEqLeaf :: TcsUntouchables
667 -> TypeClassifier -> TypeClassifier -> TcS CanonicalCts
668 -- Canonicalizing "leaf" equality constraints which cannot be
669 -- decomposed further (ie one of the types is a variable or
670 -- saturated type function application).
673 -- * one of the two arguments is not OtherCls
674 -- * the two types are not equal (looking through synonyms)
675 canEqLeaf untch fl cv cls1 cls2
676 | cls1 `re_orient` cls2
677 = do { cv' <- if isWanted fl
678 then do { cv' <- newWantedCoVar s2 s1
679 ; setWantedCoBind cv $ mkSymCoercion (mkCoVarCoercion cv')
681 else newGivOrDerCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv))
682 ; canEqLeafOriented fl cv' cls2 s1 }
685 = canEqLeafOriented fl cv cls1 s2
687 re_orient = reOrient untch
692 canEqLeafOriented :: CtFlavor -> CoVar
693 -> TypeClassifier -> TcType -> TcS CanonicalCts
694 -- First argument is not OtherCls
695 canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2 -- cv : F tys1
696 | let k1 = kindAppResult (tyConKind fn) tys1,
697 let k2 = typeKind s2,
698 isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CFunEqCan
699 = addErrorTcS KindError fl (unClassify cls1) s2 >> return emptyCCan
700 -- Eagerly fails, see Note [Kind errors] in TcInteract
703 = ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )
704 do { (xis1,cos1,ccs1) <- flattenMany fl tys1 -- Flatten type function arguments
705 -- cos1 :: xis1 ~ tys1
706 ; (xi2, co2, ccs2) <- flatten fl s2 -- Flatten entire RHS
708 ; let ccs = ccs1 `andCCan` ccs2
709 no_flattening_happened = isEmptyCCan ccs
710 ; cv_new <- if no_flattening_happened then return cv
711 else if isGiven fl then return cv
712 else do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2
714 ; let -- fun_co :: F xis1 ~ F tys1
715 fun_co = mkTyConCoercion fn cos1
716 -- want_co :: F tys1 ~ s2
717 want_co = mkSymCoercion fun_co
718 `mkTransCoercion` mkCoVarCoercion cv'
719 `mkTransCoercion` co2
720 -- der_co :: F xis1 ~ xi2
722 `mkTransCoercion` mkCoVarCoercion cv
723 `mkTransCoercion` mkSymCoercion co2
725 then setWantedCoBind cv want_co
726 else setWantedCoBind cv' der_co
729 ; let final_cc = CFunEqCan { cc_id = cv_new
734 ; return $ ccs `extendCCans` final_cc }
736 -- Otherwise, we have a variable on the left, so call canEqLeafTyVarLeft
737 canEqLeafOriented fl cv (FskCls tv) s2
738 = canEqLeafTyVarLeft fl cv tv s2
739 canEqLeafOriented fl cv (VarCls tv) s2
740 = canEqLeafTyVarLeft fl cv tv s2
741 canEqLeafOriented _ cv (OtherCls ty1) ty2
742 = pprPanic "canEqLeaf" (ppr cv $$ ppr ty1 $$ ppr ty2)
744 canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts
745 -- Establish invariants of CTyEqCans
746 canEqLeafTyVarLeft fl cv tv s2 -- cv : tv ~ s2
747 | isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CTyEqCan
748 = addErrorTcS KindError fl (mkTyVarTy tv) s2 >> return emptyCCan
749 -- Eagerly fails, see Note [Kind errors] in TcInteract
751 = do { (xi2, co, ccs2) <- flatten fl s2 -- Flatten RHS co : xi2 ~ s2
752 ; mxi2' <- canOccursCheck fl tv xi2 -- Do an occurs check, and return a possibly
753 -- unfolded version of the RHS, if we had to
754 -- unfold any type synonyms to get rid of tv.
756 Nothing -> addErrorTcS OccCheckError fl (mkTyVarTy tv) xi2 >> return emptyCCan ;
758 do { let no_flattening_happened = isEmptyCCan ccs2
759 ; cv_new <- if no_flattening_happened then return cv
760 else if isGiven fl then return cv
761 else do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2' -- cv' : tv ~ xi2
763 then setWantedCoBind cv (mkCoVarCoercion cv' `mkTransCoercion` co)
764 else setWantedCoBind cv' (mkCoVarCoercion cv `mkTransCoercion`
768 ; return $ ccs2 `extendCCans` CTyEqCan { cc_id = cv_new
771 , cc_rhs = xi2' } } } }
776 -- See Note [Type synonyms and canonicalization].
777 -- Check whether the given variable occurs in the given type. We may
778 -- have needed to do some type synonym unfolding in order to get rid
779 -- of the variable, so we also return the unfolded version of the
780 -- type, which is guaranteed to be syntactically free of the given
781 -- type variable. If the type is already syntactically free of the
782 -- variable, then the same type is returned.
784 -- Precondition: the two types are not equal (looking though synonyms)
785 canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi)
786 canOccursCheck _gw tv xi = return (expandAway tv xi)
789 @expandAway tv xi@ expands synonyms in xi just enough to get rid of
790 occurrences of tv, if that is possible; otherwise, it returns Nothing.
791 For example, suppose we have
794 expandAway b (F Int b) = Just [Int]
796 expandAway a (F a Int) = Nothing
798 We don't promise to do the absolute minimum amount of expanding
799 necessary, but we try not to do expansions we don't need to. We
800 prefer doing inner expansions first. For example,
801 type F a b = (a, Int, a, [a])
804 expandAway b (F (G b)) = F Char
805 even though we could also expand F to get rid of b.
808 expandAway :: TcTyVar -> Xi -> Maybe Xi
809 expandAway tv t@(TyVarTy tv')
810 | tv == tv' = Nothing
813 | not (tv `elemVarSet` tyVarsOfType xi) = Just xi
814 expandAway tv (AppTy ty1 ty2)
815 = do { ty1' <- expandAway tv ty1
816 ; ty2' <- expandAway tv ty2
817 ; return (mkAppTy ty1' ty2') }
818 -- mkAppTy <$> expandAway tv ty1 <*> expandAway tv ty2
819 expandAway tv (FunTy ty1 ty2)
820 = do { ty1' <- expandAway tv ty1
821 ; ty2' <- expandAway tv ty2
822 ; return (mkFunTy ty1' ty2') }
823 -- mkFunTy <$> expandAway tv ty1 <*> expandAway tv ty2
824 expandAway tv ty@(ForAllTy {})
825 = let (tvs,rho) = splitForAllTys ty
826 tvs_knds = map tyVarKind tvs
827 in if tv `elemVarSet` tyVarsOfTypes tvs_knds then
828 -- Can't expand away the kinds unless we create
829 -- fresh variables which we don't want to do at this point.
831 else do { rho' <- expandAway tv rho
832 ; return (mkForAllTys tvs rho') }
833 expandAway tv (PredTy pred)
834 = do { pred' <- expandAwayPred tv pred
835 ; return (PredTy pred') }
836 -- For a type constructor application, first try expanding away the
837 -- offending variable from the arguments. If that doesn't work, next
838 -- see if the type constructor is a type synonym, and if so, expand
840 expandAway tv ty@(TyConApp tc tys)
841 = (mkTyConApp tc <$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv)
843 expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType
844 expandAwayPred tv (ClassP cls tys)
845 = do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') }
846 expandAwayPred tv (EqPred ty1 ty2)
847 = do { ty1' <- expandAway tv ty1
848 ; ty2' <- expandAway tv ty2
849 ; return (EqPred ty1' ty2') }
850 expandAwayPred tv (IParam nm ty)
851 = do { ty' <- expandAway tv ty
852 ; return (IParam nm ty') }
858 Note [Type synonyms and canonicalization]
859 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
861 We treat type synonym applications as xi types, that is, they do not
862 count as type function applications. However, we do need to be a bit
863 careful with type synonyms: like type functions they may not be
864 generative or injective. However, unlike type functions, they are
865 parametric, so there is no problem in expanding them whenever we see
866 them, since we do not need to know anything about their arguments in
867 order to expand them; this is what justifies not having to treat them
868 as specially as type function applications. The thing that causes
869 some subtleties is that we prefer to leave type synonym applications
870 *unexpanded* whenever possible, in order to generate better error
873 If we encounter an equality constraint with type synonym applications
874 on both sides, or a type synonym application on one side and some sort
875 of type application on the other, we simply must expand out the type
876 synonyms in order to continue decomposing the equality constraint into
877 primitive equality constraints. For example, suppose we have
881 and we encounter the equality
885 In order to continue we must expand F a into [Int], giving us the
890 which we can then decompose into the more primitive equality
895 However, if we encounter an equality constraint with a type synonym
896 application on one side and a variable on the other side, we should
897 NOT (necessarily) expand the type synonym, since for the purpose of
898 good error messages we want to leave type synonyms unexpanded as much
901 However, there is a subtle point with type synonyms and the occurs
902 check that takes place for equality constraints of the form tv ~ xi.
903 As an example, suppose we have
907 and we come across the equality constraint
911 This should not actually fail the occurs check, since expanding out
912 the type synonym results in the legitimate equality constraint a ~
913 Int. We must actually do this expansion, because unifying a with F a
914 will lead the type checker into infinite loops later. Put another
915 way, canonical equality constraints should never *syntactically*
916 contain the LHS variable in the RHS type. However, we don't always
917 need to expand type synonyms when doing an occurs check; for example,
922 is obviously fine no matter what F expands to. And in this case we
923 would rather unify a with F b (rather than F b's expansion) in order
924 to get better error messages later.
926 So, when doing an occurs check with a type synonym application on the
927 RHS, we use some heuristics to find an expansion of the RHS which does
928 not contain the variable from the LHS. In particular, given
932 we first try expanding each of the ti to types which no longer contain
933 a. If this turns out to be impossible, we next try expanding F