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 ; sc_cts <- newSCWorkFromFlavored v_new fl cn xis
253 ; return (sc_cts `andCCan` ccs `extendCCans` CDictCan { cc_id = v_new
256 , cc_tyargs = xis }) }
260 Note [Adding superclasses]
261 ~~~~~~~~~~~~~~~~~~~~~~~~~~
262 Since dictionaries are canonicalized only once in their lifetime, the
263 place to add their superclasses is canonicalisation (The alternative
264 would be to do it during constraint solving, but we'd have to be
265 extremely careful to not repeatedly introduced the same superclass in
266 our worklist). Here is what we do:
269 We add all their superclasses as Givens.
272 Generally speaking, we want to be able to add derived
273 superclasses of unsolved wanteds, and wanteds that have been
274 partially being solved via an instance. This is important to be
275 able to simplify the inferred constraints more (and to allow
276 for recursive dictionaries, less importantly).
278 Example: Inferred wanted constraint is (Eq a, Ord a), but we'd
279 only like to quantify over Ord a, hence we would like to be
280 able to add the superclass of Ord a as Derived and use it to
281 solve the wanted Eq a.
284 Deriveds either arise as wanteds that have been partially
285 solved, or as superclasses of other wanteds or deriveds. Hence,
286 their superclasses must be already there so we must do nothing
289 DV: In fact, it is probably true that the canonicaliser is
290 *never* asked to canonicalise Derived dictionaries
292 There is one disadvantage to this. Suppose the wanted constraints are
293 (Num a, Num a). Then we'll add all the superclasses of both during
294 canonicalisation, only to eliminate them later when they are
295 interacted. That seems like a waste of work. Still, it's simple.
297 Here's an example that demonstrates why we chose to NOT add
298 superclasses during simplification: [Comes from ticket #4497]
300 class Num (RealOf t) => Normed t
303 Assume the generated wanted constraint is:
304 RealOf e ~ e, Normed e
305 If we were to be adding the superclasses during simplification we'd get:
306 Num uf, Normed e, RealOf e ~ e, RealOf e ~ uf
308 e ~ uf, Num uf, Normed e, RealOf e ~ e
309 ==> [Spontaneous solve]
310 Num uf, Normed uf, RealOf uf ~ uf
312 While looks exactly like our original constraint. If we add the superclass again we'd loop.
313 By adding superclasses definitely only once, during canonicalisation, this situation can't
317 newSCWorkFromFlavored :: EvVar -> CtFlavor -> Class -> [Xi] -> TcS CanonicalCts
318 -- Returns superclasses, see Note [Adding superclasses]
319 newSCWorkFromFlavored ev orig_flavor cls xis
320 | Given loc <- orig_flavor -- Very important!
321 , NoScSkol <- ctLocOrigin loc
324 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
325 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
326 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
327 ; mkCanonicals flavor sc_vars }
328 -- NB: Since there is a call to mkCanonicals,
329 -- this will add *recursively* all superclasses
331 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
332 flavor = case orig_flavor of
333 Given loc -> Given loc
334 Wanted loc -> Derived loc DerSC
335 Derived {} -> orig_flavor
336 -- NB: the non-immediate superclasses will show up as
337 -- Derived, and we want their superclasses too!
339 canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts
340 -- See Note [Canonical implicit parameter constraints] to see why we don't
341 -- immediately canonicalize (flatten) IP constraints.
343 = return $ singleCCan $ CIPCan { cc_id = v
349 canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts
351 | tcEqType ty1 ty2 -- Dealing with equality here avoids
352 -- later spurious occurs checks for a~a
353 = do { when (isWanted fl) (setWantedCoBind cv ty1)
356 -- If one side is a variable, orient and flatten,
357 -- WITHOUT expanding type synonyms, so that we tend to
358 -- substitute a ~ Age rather than a ~ Int when @type Age = Int@
359 canEq fl cv ty1@(TyVarTy {}) ty2
360 = do { untch <- getUntouchables
361 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
362 canEq fl cv ty1 ty2@(TyVarTy {})
363 = do { untch <- getUntouchables
364 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
365 -- NB: don't use VarCls directly because tv1 or tv2 may be scolems!
367 canEq fl cv (TyConApp fn tys) ty2
368 | isSynFamilyTyCon fn, length tys == tyConArity fn
369 = do { untch <- getUntouchables
370 ; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }
371 canEq fl cv ty1 (TyConApp fn tys)
372 | isSynFamilyTyCon fn, length tys == tyConArity fn
373 = do { untch <- getUntouchables
374 ; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }
377 | Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1,
378 Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2
379 = do { (v1,v2,v3) <- if isWanted fl then
380 do { v1 <- newWantedCoVar t1a t2a
381 ; v2 <- newWantedCoVar t1b t2b
382 ; v3 <- newWantedCoVar t1c t2c
383 ; let res_co = mkCoPredCo (mkCoVarCoercion v1)
384 (mkCoVarCoercion v2) (mkCoVarCoercion v3)
385 ; setWantedCoBind cv res_co
386 ; return (v1,v2,v3) }
387 else let co_orig = mkCoVarCoercion cv
388 coa = mkCsel1Coercion co_orig
389 cob = mkCsel2Coercion co_orig
390 coc = mkCselRCoercion co_orig
391 in do { v1 <- newGivOrDerCoVar t1a t2a coa
392 ; v2 <- newGivOrDerCoVar t1b t2b cob
393 ; v3 <- newGivOrDerCoVar t1c t2c coc
394 ; return (v1,v2,v3) }
395 ; cc1 <- canEq fl v1 t1a t2a
396 ; cc2 <- canEq fl v2 t1b t2b
397 ; cc3 <- canEq fl v3 t1c t2c
398 ; return (cc1 `andCCan` cc2 `andCCan` cc3) }
401 -- Split up an equality between function types into two equalities.
402 canEq fl cv (FunTy s1 t1) (FunTy s2 t2)
403 = do { (argv, resv) <-
405 do { argv <- newWantedCoVar s1 s2
406 ; resv <- newWantedCoVar t1 t2
407 ; setWantedCoBind cv $
408 mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv)
409 ; return (argv,resv) }
410 else let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv)
411 in do { argv <- newGivOrDerCoVar s1 s2 arg
412 ; resv <- newGivOrDerCoVar t1 t2 res
413 ; return (argv,resv) }
414 ; cc1 <- canEq fl argv s1 s2 -- inherit original kinds and locations
415 ; cc2 <- canEq fl resv t1 t2
416 ; return (cc1 `andCCan` cc2) }
418 canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2))
420 = if isWanted fl then
421 do { v <- newWantedCoVar t1 t2
422 ; setWantedCoBind cv $ mkIParamPredCo n1 (mkCoVarCoercion cv)
424 else return emptyCCan -- DV: How to decompose given IP coercions?
426 canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2))
428 = if isWanted fl then
429 do { vs <- zipWithM newWantedCoVar tys1 tys2
430 ; setWantedCoBind cv $ mkClassPPredCo c1 (map mkCoVarCoercion vs)
431 ; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2
433 else return emptyCCan
434 -- How to decompose given dictionary (and implicit parameter) coercions?
435 -- You may think that the following is right:
436 -- let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
437 -- in zipWith3M newGivOrDerCoVar tys1 tys2 cos
438 -- But this assumes that the coercion is a type constructor-based
439 -- coercion, and not a PredTy (ClassP cn cos) coercion. So we chose
440 -- to not decompose these coercions. We have to get back to this
441 -- when we clean up the Coercion API.
443 canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)
444 | isAlgTyCon tc1 && isAlgTyCon tc2
446 , length tys1 == length tys2
447 = -- Generate equalities for each of the corresponding arguments
448 do { argsv <- if isWanted fl then
449 do { argsv <- zipWithM newWantedCoVar tys1 tys2
450 ; setWantedCoBind cv $ mkTyConCoercion tc1 (map mkCoVarCoercion argsv)
453 let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
454 in zipWith3M newGivOrDerCoVar tys1 tys2 cos
455 ; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 }
457 -- See Note [Equality between type applications]
458 -- Note [Care with type applications] in TcUnify
460 | Just (s1,t1) <- tcSplitAppTy_maybe ty1
461 , Just (s2,t2) <- tcSplitAppTy_maybe ty2
464 then do { cv1 <- newWantedCoVar s1 s2
465 ; cv2 <- newWantedCoVar t1 t2
466 ; setWantedCoBind cv $
467 mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2)
469 else let co1 = mkLeftCoercion $ mkCoVarCoercion cv
470 co2 = mkRightCoercion $ mkCoVarCoercion cv
471 in do { cv1 <- newGivOrDerCoVar s1 s2 co1
472 ; cv2 <- newGivOrDerCoVar t1 t2 co2
474 ; cc1 <- canEq fl cv1 s1 s2
475 ; cc2 <- canEq fl cv2 t1 t2
476 ; return (cc1 `andCCan` cc2) }
478 canEq fl _ s1@(ForAllTy {}) s2@(ForAllTy {})
479 | tcIsForAllTy s1, tcIsForAllTy s2,
481 = canEqFailure fl s1 s2
483 = do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2)
486 -- Finally expand any type synonym applications.
487 canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2
488 canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'
489 canEq fl _ ty1 ty2 = canEqFailure fl ty1 ty2
491 canEqFailure :: CtFlavor -> Type -> Type -> TcS CanonicalCts
492 canEqFailure fl ty1 ty2
493 = do { addErrorTcS MisMatchError fl ty1 ty2
497 Note [Equality between type applications]
498 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
499 If we see an equality of the form s1 t1 ~ s2 t2 we can always split
500 it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type
501 functions (type functions use the TyConApp constructor, which never
502 shows up as the LHS of an AppTy). Other than type functions, types
503 in Haskell are always
505 (1) generative: a b ~ c d implies a ~ c, since different type
506 constructors always generate distinct types
508 (2) injective: a b ~ a d implies b ~ d; we never generate the
509 same type from different type arguments.
512 Note [Canonical ordering for equality constraints]
513 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
514 Implemented as (<+=) below:
516 - Type function applications always come before anything else.
517 - Variables always come before non-variables (other than type
518 function applications).
520 Note that we don't need to unfold type synonyms on the RHS to check
521 the ordering; that is, in the rules above it's OK to consider only
522 whether something is *syntactically* a type function application or
523 not. To illustrate why this is OK, suppose we have an equality of the
524 form 'tv ~ S a b c', where S is a type synonym which expands to a
525 top-level application of the type function F, something like
529 Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's
530 expansion contains type function applications the flattener will do
531 the expansion and then generate a skolem variable for the type
532 function application, so we end up with something like this:
537 where x is the skolem variable. This is one extra equation than
538 absolutely necessary (we could have gotten away with just 'F d e ~ tv'
539 if we had noticed that S expanded to a top-level type function
540 application and flipped it around in the first place) but this way
541 keeps the code simpler.
543 Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the
544 ordering of tv ~ tv constraints. There are several reasons why we
547 (1) In order to be able to extract a substitution that doesn't
548 mention untouchable variables after we are done solving, we might
549 prefer to put touchable variables on the left. However, in and
550 of itself this isn't necessary; we can always re-orient equality
551 constraints at the end if necessary when extracting a substitution.
553 (2) To ensure termination we might think it necessary to put
554 variables in lexicographic order. However, this isn't actually
555 necessary as outlined below.
557 While building up an inert set of canonical constraints, we maintain
558 the invariant that the equality constraints in the inert set form an
559 acyclic rewrite system when viewed as L-R rewrite rules. Moreover,
560 the given constraints form an idempotent substitution (i.e. none of
561 the variables on the LHS occur in any of the RHS's, and type functions
562 never show up in the RHS at all), the wanted constraints also form an
563 idempotent substitution, and finally the LHS of a given constraint
564 never shows up on the RHS of a wanted constraint. There may, however,
565 be a wanted LHS that shows up in a given RHS, since we do not rewrite
566 given constraints with wanted constraints.
568 Suppose we have an inert constraint set
571 tg_1 ~ xig_1 -- givens
574 tw_1 ~ xiw_1 -- wanteds
578 where each t_i can be either a type variable or a type function
579 application. Now suppose we take a new canonical equality constraint,
580 t' ~ xi' (note among other things this means t' does not occur in xi')
581 and try to react it with the existing inert set. We show by induction
582 on the number of t_i which occur in t' ~ xi' that this process will
585 There are several ways t' ~ xi' could react with an existing constraint:
587 TODO: finish this proof. The below was for the case where the entire
588 inert set is an idempotent subustitution...
590 (b) We could have t' = t_j for some j. Then we obtain the new
591 equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We
592 now canonicalize the new equality, which may involve decomposing it
593 into several canonical equalities, and recurse on these. However,
594 none of the new equalities will contain t_j, so they have fewer
595 occurrences of the t_i than the original equation.
597 (a) We could have t_j occurring in xi' for some j, with t' /=
598 t_j. Then we substitute xi_j for t_j in xi' and continue. However,
599 since none of the t_i occur in xi_j, we have decreased the
600 number of t_i that occur in xi', since we eliminated t_j and did not
601 introduce any new ones.
605 = FskCls TcTyVar -- ^ Flatten skolem
606 | VarCls TcTyVar -- ^ Non-flatten-skolem variable
607 | FunCls TyCon [Type] -- ^ Type function, exactly saturated
608 | OtherCls TcType -- ^ Neither of the above
610 unClassify :: TypeClassifier -> TcType
611 unClassify (VarCls tv) = TyVarTy tv
612 unClassify (FskCls tv) = TyVarTy tv
613 unClassify (FunCls fn tys) = TyConApp fn tys
614 unClassify (OtherCls ty) = ty
616 classify :: TcType -> TypeClassifier
618 classify (TyVarTy tv)
620 FlatSkol {} <- tcTyVarDetails tv = FskCls tv
621 | otherwise = VarCls tv
622 classify (TyConApp tc tys) | isSynFamilyTyCon tc
623 , tyConArity tc == length tys
625 classify ty | Just ty' <- tcView ty
626 = case classify ty' of
627 OtherCls {} -> OtherCls ty
628 var_or_fn -> var_or_fn
632 -- See note [Canonical ordering for equality constraints].
633 reOrient :: TcsUntouchables -> TypeClassifier -> TypeClassifier -> Bool
634 -- (t1 `reOrient` t2) responds True
635 -- iff we should flip to (t2~t1)
636 -- We try to say False if possible, to minimise evidence generation
638 -- Postcondition: After re-orienting, first arg is not OTherCls
639 reOrient _untch (OtherCls {}) (FunCls {}) = True
640 reOrient _untch (OtherCls {}) (FskCls {}) = True
641 reOrient _untch (OtherCls {}) (VarCls {}) = True
642 reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun
644 reOrient _untch (FunCls {}) (VarCls {}) = False
645 -- See Note [No touchables as FunEq RHS] in TcSMonad
646 reOrient _untch (FunCls {}) _ = False -- Fun/Other on rhs
648 reOrient _untch (VarCls {}) (FunCls {}) = True
650 reOrient _untch (VarCls {}) (FskCls {}) = False
652 reOrient _untch (VarCls {}) (OtherCls {}) = False
653 reOrient _untch (VarCls tv1) (VarCls tv2)
654 | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True
656 -- Just for efficiency, see CTyEqCan invariants
658 reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2
659 -- Just for efficiency, see CTyEqCan invariants
661 reOrient _untch (FskCls {}) (FskCls {}) = False
662 reOrient _untch (FskCls {}) (FunCls {}) = True
663 reOrient _untch (FskCls {}) (OtherCls {}) = False
666 canEqLeaf :: TcsUntouchables
668 -> TypeClassifier -> TypeClassifier -> TcS CanonicalCts
669 -- Canonicalizing "leaf" equality constraints which cannot be
670 -- decomposed further (ie one of the types is a variable or
671 -- saturated type function application).
674 -- * one of the two arguments is not OtherCls
675 -- * the two types are not equal (looking through synonyms)
676 canEqLeaf untch fl cv cls1 cls2
677 | cls1 `re_orient` cls2
678 = do { cv' <- if isWanted fl
679 then do { cv' <- newWantedCoVar s2 s1
680 ; setWantedCoBind cv $ mkSymCoercion (mkCoVarCoercion cv')
682 else newGivOrDerCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv))
683 ; canEqLeafOriented fl cv' cls2 s1 }
686 = canEqLeafOriented fl cv cls1 s2
688 re_orient = reOrient untch
693 canEqLeafOriented :: CtFlavor -> CoVar
694 -> TypeClassifier -> TcType -> TcS CanonicalCts
695 -- First argument is not OtherCls
696 canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2 -- cv : F tys1
697 | let k1 = kindAppResult (tyConKind fn) tys1,
698 let k2 = typeKind s2,
699 isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CFunEqCan
700 = addErrorTcS KindError fl (unClassify cls1) s2 >> return emptyCCan
701 -- Eagerly fails, see Note [Kind errors] in TcInteract
704 = ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )
705 do { (xis1,cos1,ccs1) <- flattenMany fl tys1 -- Flatten type function arguments
706 -- cos1 :: xis1 ~ tys1
707 ; (xi2, co2, ccs2) <- flatten fl s2 -- Flatten entire RHS
709 ; let ccs = ccs1 `andCCan` ccs2
710 no_flattening_happened = isEmptyCCan ccs
711 ; cv_new <- if no_flattening_happened then return cv
712 else if isGiven fl then return cv
713 else do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2
715 ; let -- fun_co :: F xis1 ~ F tys1
716 fun_co = mkTyConCoercion fn cos1
717 -- want_co :: F tys1 ~ s2
718 want_co = mkSymCoercion fun_co
719 `mkTransCoercion` mkCoVarCoercion cv'
720 `mkTransCoercion` co2
721 -- der_co :: F xis1 ~ xi2
723 `mkTransCoercion` mkCoVarCoercion cv
724 `mkTransCoercion` mkSymCoercion co2
726 then setWantedCoBind cv want_co
727 else setWantedCoBind cv' der_co
730 ; let final_cc = CFunEqCan { cc_id = cv_new
735 ; return $ ccs `extendCCans` final_cc }
737 -- Otherwise, we have a variable on the left, so call canEqLeafTyVarLeft
738 canEqLeafOriented fl cv (FskCls tv) s2
739 = canEqLeafTyVarLeft fl cv tv s2
740 canEqLeafOriented fl cv (VarCls tv) s2
741 = canEqLeafTyVarLeft fl cv tv s2
742 canEqLeafOriented _ cv (OtherCls ty1) ty2
743 = pprPanic "canEqLeaf" (ppr cv $$ ppr ty1 $$ ppr ty2)
745 canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts
746 -- Establish invariants of CTyEqCans
747 canEqLeafTyVarLeft fl cv tv s2 -- cv : tv ~ s2
748 | isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CTyEqCan
749 = addErrorTcS KindError fl (mkTyVarTy tv) s2 >> return emptyCCan
750 -- Eagerly fails, see Note [Kind errors] in TcInteract
752 = do { (xi2, co, ccs2) <- flatten fl s2 -- Flatten RHS co : xi2 ~ s2
753 ; mxi2' <- canOccursCheck fl tv xi2 -- Do an occurs check, and return a possibly
754 -- unfolded version of the RHS, if we had to
755 -- unfold any type synonyms to get rid of tv.
757 Nothing -> addErrorTcS OccCheckError fl (mkTyVarTy tv) xi2 >> return emptyCCan ;
759 do { let no_flattening_happened = isEmptyCCan ccs2
760 ; cv_new <- if no_flattening_happened then return cv
761 else if isGiven fl then return cv
762 else do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2' -- cv' : tv ~ xi2
764 then setWantedCoBind cv (mkCoVarCoercion cv' `mkTransCoercion` co)
765 else setWantedCoBind cv' (mkCoVarCoercion cv `mkTransCoercion`
769 ; return $ ccs2 `extendCCans` CTyEqCan { cc_id = cv_new
772 , cc_rhs = xi2' } } } }
777 -- See Note [Type synonyms and canonicalization].
778 -- Check whether the given variable occurs in the given type. We may
779 -- have needed to do some type synonym unfolding in order to get rid
780 -- of the variable, so we also return the unfolded version of the
781 -- type, which is guaranteed to be syntactically free of the given
782 -- type variable. If the type is already syntactically free of the
783 -- variable, then the same type is returned.
785 -- Precondition: the two types are not equal (looking though synonyms)
786 canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi)
787 canOccursCheck _gw tv xi = return (expandAway tv xi)
790 @expandAway tv xi@ expands synonyms in xi just enough to get rid of
791 occurrences of tv, if that is possible; otherwise, it returns Nothing.
792 For example, suppose we have
795 expandAway b (F Int b) = Just [Int]
797 expandAway a (F a Int) = Nothing
799 We don't promise to do the absolute minimum amount of expanding
800 necessary, but we try not to do expansions we don't need to. We
801 prefer doing inner expansions first. For example,
802 type F a b = (a, Int, a, [a])
805 expandAway b (F (G b)) = F Char
806 even though we could also expand F to get rid of b.
809 expandAway :: TcTyVar -> Xi -> Maybe Xi
810 expandAway tv t@(TyVarTy tv')
811 | tv == tv' = Nothing
814 | not (tv `elemVarSet` tyVarsOfType xi) = Just xi
815 expandAway tv (AppTy ty1 ty2)
816 = do { ty1' <- expandAway tv ty1
817 ; ty2' <- expandAway tv ty2
818 ; return (mkAppTy ty1' ty2') }
819 -- mkAppTy <$> expandAway tv ty1 <*> expandAway tv ty2
820 expandAway tv (FunTy ty1 ty2)
821 = do { ty1' <- expandAway tv ty1
822 ; ty2' <- expandAway tv ty2
823 ; return (mkFunTy ty1' ty2') }
824 -- mkFunTy <$> expandAway tv ty1 <*> expandAway tv ty2
825 expandAway tv ty@(ForAllTy {})
826 = let (tvs,rho) = splitForAllTys ty
827 tvs_knds = map tyVarKind tvs
828 in if tv `elemVarSet` tyVarsOfTypes tvs_knds then
829 -- Can't expand away the kinds unless we create
830 -- fresh variables which we don't want to do at this point.
832 else do { rho' <- expandAway tv rho
833 ; return (mkForAllTys tvs rho') }
834 expandAway tv (PredTy pred)
835 = do { pred' <- expandAwayPred tv pred
836 ; return (PredTy pred') }
837 -- For a type constructor application, first try expanding away the
838 -- offending variable from the arguments. If that doesn't work, next
839 -- see if the type constructor is a type synonym, and if so, expand
841 expandAway tv ty@(TyConApp tc tys)
842 = (mkTyConApp tc <$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv)
844 expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType
845 expandAwayPred tv (ClassP cls tys)
846 = do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') }
847 expandAwayPred tv (EqPred ty1 ty2)
848 = do { ty1' <- expandAway tv ty1
849 ; ty2' <- expandAway tv ty2
850 ; return (EqPred ty1' ty2') }
851 expandAwayPred tv (IParam nm ty)
852 = do { ty' <- expandAway tv ty
853 ; return (IParam nm ty') }
859 Note [Type synonyms and canonicalization]
860 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
862 We treat type synonym applications as xi types, that is, they do not
863 count as type function applications. However, we do need to be a bit
864 careful with type synonyms: like type functions they may not be
865 generative or injective. However, unlike type functions, they are
866 parametric, so there is no problem in expanding them whenever we see
867 them, since we do not need to know anything about their arguments in
868 order to expand them; this is what justifies not having to treat them
869 as specially as type function applications. The thing that causes
870 some subtleties is that we prefer to leave type synonym applications
871 *unexpanded* whenever possible, in order to generate better error
874 If we encounter an equality constraint with type synonym applications
875 on both sides, or a type synonym application on one side and some sort
876 of type application on the other, we simply must expand out the type
877 synonyms in order to continue decomposing the equality constraint into
878 primitive equality constraints. For example, suppose we have
882 and we encounter the equality
886 In order to continue we must expand F a into [Int], giving us the
891 which we can then decompose into the more primitive equality
896 However, if we encounter an equality constraint with a type synonym
897 application on one side and a variable on the other side, we should
898 NOT (necessarily) expand the type synonym, since for the purpose of
899 good error messages we want to leave type synonyms unexpanded as much
902 However, there is a subtle point with type synonyms and the occurs
903 check that takes place for equality constraints of the form tv ~ xi.
904 As an example, suppose we have
908 and we come across the equality constraint
912 This should not actually fail the occurs check, since expanding out
913 the type synonym results in the legitimate equality constraint a ~
914 Int. We must actually do this expansion, because unifying a with F a
915 will lead the type checker into infinite loops later. Put another
916 way, canonical equality constraints should never *syntactically*
917 contain the LHS variable in the RHS type. However, we don't always
918 need to expand type synonyms when doing an occurs check; for example,
923 is obviously fine no matter what F expands to. And in this case we
924 would rather unify a with F b (rather than F b's expansion) in order
925 to get better error messages later.
927 So, when doing an occurs check with a type synonym application on the
928 RHS, we use some heuristics to find an expansion of the RHS which does
929 not contain the variable from the LHS. In particular, given
933 we first try expanding each of the ti to types which no longer contain
934 a. If this turns out to be impossible, we next try expanding F