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 ; return (ccs `extendCCans` CDictCan { cc_id = v_new
253 , cc_tyargs = xis }) }
255 canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts
256 -- See Note [Canonical implicit parameter constraints] to see why we don't
257 -- immediately canonicalize (flatten) IP constraints.
259 = return $ singleCCan $ CIPCan { cc_id = v
265 canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts
267 | tcEqType ty1 ty2 -- Dealing with equality here avoids
268 -- later spurious occurs checks for a~a
269 = do { when (isWanted fl) (setWantedCoBind cv ty1)
272 -- If one side is a variable, orient and flatten,
273 -- WITHOUT expanding type synonyms, so that we tend to
274 -- substitute a ~ Age rather than a ~ Int when @type Age = Int@
275 canEq fl cv ty1@(TyVarTy {}) ty2
276 = do { untch <- getUntouchables
277 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
278 canEq fl cv ty1 ty2@(TyVarTy {})
279 = do { untch <- getUntouchables
280 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
281 -- NB: don't use VarCls directly because tv1 or tv2 may be scolems!
283 canEq fl cv (TyConApp fn tys) ty2
284 | isSynFamilyTyCon fn, length tys == tyConArity fn
285 = do { untch <- getUntouchables
286 ; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }
287 canEq fl cv ty1 (TyConApp fn tys)
288 | isSynFamilyTyCon fn, length tys == tyConArity fn
289 = do { untch <- getUntouchables
290 ; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }
293 | Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1,
294 Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2
295 = do { (v1,v2,v3) <- if isWanted fl then
296 do { v1 <- newWantedCoVar t1a t2a
297 ; v2 <- newWantedCoVar t1b t2b
298 ; v3 <- newWantedCoVar t1c t2c
299 ; let res_co = mkCoPredCo (mkCoVarCoercion v1)
300 (mkCoVarCoercion v2) (mkCoVarCoercion v3)
301 ; setWantedCoBind cv res_co
302 ; return (v1,v2,v3) }
303 else let co_orig = mkCoVarCoercion cv
304 coa = mkCsel1Coercion co_orig
305 cob = mkCsel2Coercion co_orig
306 coc = mkCselRCoercion co_orig
307 in do { v1 <- newGivOrDerCoVar t1a t2a coa
308 ; v2 <- newGivOrDerCoVar t1b t2b cob
309 ; v3 <- newGivOrDerCoVar t1c t2c coc
310 ; return (v1,v2,v3) }
311 ; cc1 <- canEq fl v1 t1a t2a
312 ; cc2 <- canEq fl v2 t1b t2b
313 ; cc3 <- canEq fl v3 t1c t2c
314 ; return (cc1 `andCCan` cc2 `andCCan` cc3) }
317 -- Split up an equality between function types into two equalities.
318 canEq fl cv (FunTy s1 t1) (FunTy s2 t2)
319 = do { (argv, resv) <-
321 do { argv <- newWantedCoVar s1 s2
322 ; resv <- newWantedCoVar t1 t2
323 ; setWantedCoBind cv $
324 mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv)
325 ; return (argv,resv) }
326 else let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv)
327 in do { argv <- newGivOrDerCoVar s1 s2 arg
328 ; resv <- newGivOrDerCoVar t1 t2 res
329 ; return (argv,resv) }
330 ; cc1 <- canEq fl argv s1 s2 -- inherit original kinds and locations
331 ; cc2 <- canEq fl resv t1 t2
332 ; return (cc1 `andCCan` cc2) }
334 canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2))
336 = if isWanted fl then
337 do { v <- newWantedCoVar t1 t2
338 ; setWantedCoBind cv $ mkIParamPredCo n1 (mkCoVarCoercion cv)
340 else return emptyCCan -- DV: How to decompose given IP coercions?
342 canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2))
344 = if isWanted fl then
345 do { vs <- zipWithM newWantedCoVar tys1 tys2
346 ; setWantedCoBind cv $ mkClassPPredCo c1 (map mkCoVarCoercion vs)
347 ; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2
349 else return emptyCCan
350 -- How to decompose given dictionary (and implicit parameter) coercions?
351 -- You may think that the following is right:
352 -- let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
353 -- in zipWith3M newGivOrDerCoVar tys1 tys2 cos
354 -- But this assumes that the coercion is a type constructor-based
355 -- coercion, and not a PredTy (ClassP cn cos) coercion. So we chose
356 -- to not decompose these coercions. We have to get back to this
357 -- when we clean up the Coercion API.
359 canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)
360 | isAlgTyCon tc1 && isAlgTyCon tc2
362 , length tys1 == length tys2
363 = -- Generate equalities for each of the corresponding arguments
364 do { argsv <- if isWanted fl then
365 do { argsv <- zipWithM newWantedCoVar tys1 tys2
366 ; setWantedCoBind cv $ mkTyConCoercion tc1 (map mkCoVarCoercion argsv)
369 let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
370 in zipWith3M newGivOrDerCoVar tys1 tys2 cos
371 ; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 }
373 -- See Note [Equality between type applications]
374 -- Note [Care with type applications] in TcUnify
376 | Just (s1,t1) <- tcSplitAppTy_maybe ty1
377 , Just (s2,t2) <- tcSplitAppTy_maybe ty2
380 then do { cv1 <- newWantedCoVar s1 s2
381 ; cv2 <- newWantedCoVar t1 t2
382 ; setWantedCoBind cv $
383 mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2)
385 else let co1 = mkLeftCoercion $ mkCoVarCoercion cv
386 co2 = mkRightCoercion $ mkCoVarCoercion cv
387 in do { cv1 <- newGivOrDerCoVar s1 s2 co1
388 ; cv2 <- newGivOrDerCoVar t1 t2 co2
390 ; cc1 <- canEq fl cv1 s1 s2
391 ; cc2 <- canEq fl cv2 t1 t2
392 ; return (cc1 `andCCan` cc2) }
394 canEq fl _ s1@(ForAllTy {}) s2@(ForAllTy {})
395 | tcIsForAllTy s1, tcIsForAllTy s2,
397 = canEqFailure fl s1 s2
399 = do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2)
402 -- Finally expand any type synonym applications.
403 canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2
404 canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'
405 canEq fl _ ty1 ty2 = canEqFailure fl ty1 ty2
407 canEqFailure :: CtFlavor -> Type -> Type -> TcS CanonicalCts
408 canEqFailure fl ty1 ty2
409 = do { addErrorTcS MisMatchError fl ty1 ty2
413 Note [Equality between type applications]
414 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
415 If we see an equality of the form s1 t1 ~ s2 t2 we can always split
416 it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type
417 functions (type functions use the TyConApp constructor, which never
418 shows up as the LHS of an AppTy). Other than type functions, types
419 in Haskell are always
421 (1) generative: a b ~ c d implies a ~ c, since different type
422 constructors always generate distinct types
424 (2) injective: a b ~ a d implies b ~ d; we never generate the
425 same type from different type arguments.
428 Note [Canonical ordering for equality constraints]
429 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
430 Implemented as (<+=) below:
432 - Type function applications always come before anything else.
433 - Variables always come before non-variables (other than type
434 function applications).
436 Note that we don't need to unfold type synonyms on the RHS to check
437 the ordering; that is, in the rules above it's OK to consider only
438 whether something is *syntactically* a type function application or
439 not. To illustrate why this is OK, suppose we have an equality of the
440 form 'tv ~ S a b c', where S is a type synonym which expands to a
441 top-level application of the type function F, something like
445 Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's
446 expansion contains type function applications the flattener will do
447 the expansion and then generate a skolem variable for the type
448 function application, so we end up with something like this:
453 where x is the skolem variable. This is one extra equation than
454 absolutely necessary (we could have gotten away with just 'F d e ~ tv'
455 if we had noticed that S expanded to a top-level type function
456 application and flipped it around in the first place) but this way
457 keeps the code simpler.
459 Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the
460 ordering of tv ~ tv constraints. There are several reasons why we
463 (1) In order to be able to extract a substitution that doesn't
464 mention untouchable variables after we are done solving, we might
465 prefer to put touchable variables on the left. However, in and
466 of itself this isn't necessary; we can always re-orient equality
467 constraints at the end if necessary when extracting a substitution.
469 (2) To ensure termination we might think it necessary to put
470 variables in lexicographic order. However, this isn't actually
471 necessary as outlined below.
473 While building up an inert set of canonical constraints, we maintain
474 the invariant that the equality constraints in the inert set form an
475 acyclic rewrite system when viewed as L-R rewrite rules. Moreover,
476 the given constraints form an idempotent substitution (i.e. none of
477 the variables on the LHS occur in any of the RHS's, and type functions
478 never show up in the RHS at all), the wanted constraints also form an
479 idempotent substitution, and finally the LHS of a given constraint
480 never shows up on the RHS of a wanted constraint. There may, however,
481 be a wanted LHS that shows up in a given RHS, since we do not rewrite
482 given constraints with wanted constraints.
484 Suppose we have an inert constraint set
487 tg_1 ~ xig_1 -- givens
490 tw_1 ~ xiw_1 -- wanteds
494 where each t_i can be either a type variable or a type function
495 application. Now suppose we take a new canonical equality constraint,
496 t' ~ xi' (note among other things this means t' does not occur in xi')
497 and try to react it with the existing inert set. We show by induction
498 on the number of t_i which occur in t' ~ xi' that this process will
501 There are several ways t' ~ xi' could react with an existing constraint:
503 TODO: finish this proof. The below was for the case where the entire
504 inert set is an idempotent subustitution...
506 (b) We could have t' = t_j for some j. Then we obtain the new
507 equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We
508 now canonicalize the new equality, which may involve decomposing it
509 into several canonical equalities, and recurse on these. However,
510 none of the new equalities will contain t_j, so they have fewer
511 occurrences of the t_i than the original equation.
513 (a) We could have t_j occurring in xi' for some j, with t' /=
514 t_j. Then we substitute xi_j for t_j in xi' and continue. However,
515 since none of the t_i occur in xi_j, we have decreased the
516 number of t_i that occur in xi', since we eliminated t_j and did not
517 introduce any new ones.
521 = FskCls TcTyVar -- ^ Flatten skolem
522 | VarCls TcTyVar -- ^ Non-flatten-skolem variable
523 | FunCls TyCon [Type] -- ^ Type function, exactly saturated
524 | OtherCls TcType -- ^ Neither of the above
526 unClassify :: TypeClassifier -> TcType
527 unClassify (VarCls tv) = TyVarTy tv
528 unClassify (FskCls tv) = TyVarTy tv
529 unClassify (FunCls fn tys) = TyConApp fn tys
530 unClassify (OtherCls ty) = ty
532 classify :: TcType -> TypeClassifier
534 classify (TyVarTy tv)
536 FlatSkol {} <- tcTyVarDetails tv = FskCls tv
537 | otherwise = VarCls tv
538 classify (TyConApp tc tys) | isSynFamilyTyCon tc
539 , tyConArity tc == length tys
541 classify ty | Just ty' <- tcView ty
542 = case classify ty' of
543 OtherCls {} -> OtherCls ty
544 var_or_fn -> var_or_fn
548 -- See note [Canonical ordering for equality constraints].
549 reOrient :: TcsUntouchables -> TypeClassifier -> TypeClassifier -> Bool
550 -- (t1 `reOrient` t2) responds True
551 -- iff we should flip to (t2~t1)
552 -- We try to say False if possible, to minimise evidence generation
554 -- Postcondition: After re-orienting, first arg is not OTherCls
555 reOrient _untch (OtherCls {}) (FunCls {}) = True
556 reOrient _untch (OtherCls {}) (FskCls {}) = True
557 reOrient _untch (OtherCls {}) (VarCls {}) = True
558 reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun
560 reOrient _untch (FunCls {}) (VarCls {}) = False
561 -- See Note [No touchables as FunEq RHS] in TcSMonad
562 reOrient _untch (FunCls {}) _ = False -- Fun/Other on rhs
564 reOrient _untch (VarCls {}) (FunCls {}) = True
566 reOrient _untch (VarCls {}) (FskCls {}) = False
568 reOrient _untch (VarCls {}) (OtherCls {}) = False
569 reOrient _untch (VarCls tv1) (VarCls tv2)
570 | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True
572 -- Just for efficiency, see CTyEqCan invariants
574 reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2
575 -- Just for efficiency, see CTyEqCan invariants
577 reOrient _untch (FskCls {}) (FskCls {}) = False
578 reOrient _untch (FskCls {}) (FunCls {}) = True
579 reOrient _untch (FskCls {}) (OtherCls {}) = False
582 canEqLeaf :: TcsUntouchables
584 -> TypeClassifier -> TypeClassifier -> TcS CanonicalCts
585 -- Canonicalizing "leaf" equality constraints which cannot be
586 -- decomposed further (ie one of the types is a variable or
587 -- saturated type function application).
590 -- * one of the two arguments is not OtherCls
591 -- * the two types are not equal (looking through synonyms)
592 canEqLeaf untch fl cv cls1 cls2
593 | cls1 `re_orient` cls2
594 = do { cv' <- if isWanted fl
595 then do { cv' <- newWantedCoVar s2 s1
596 ; setWantedCoBind cv $ mkSymCoercion (mkCoVarCoercion cv')
598 else newGivOrDerCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv))
599 ; canEqLeafOriented fl cv' cls2 s1 }
602 = canEqLeafOriented fl cv cls1 s2
604 re_orient = reOrient untch
609 canEqLeafOriented :: CtFlavor -> CoVar
610 -> TypeClassifier -> TcType -> TcS CanonicalCts
611 -- First argument is not OtherCls
612 canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2 -- cv : F tys1
613 | let k1 = kindAppResult (tyConKind fn) tys1,
614 let k2 = typeKind s2,
615 isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CFunEqCan
616 = addErrorTcS KindError fl (unClassify cls1) s2 >> return emptyCCan
617 -- Eagerly fails, see Note [Kind errors] in TcInteract
620 = ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )
621 do { (xis1,cos1,ccs1) <- flattenMany fl tys1 -- Flatten type function arguments
622 -- cos1 :: xis1 ~ tys1
623 ; (xi2, co2, ccs2) <- flatten fl s2 -- Flatten entire RHS
625 ; let ccs = ccs1 `andCCan` ccs2
626 no_flattening_happened = isEmptyCCan ccs
627 ; cv_new <- if no_flattening_happened then return cv
628 else if isGiven fl then return cv
629 else do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2
631 ; let -- fun_co :: F xis1 ~ F tys1
632 fun_co = mkTyConCoercion fn cos1
633 -- want_co :: F tys1 ~ s2
634 want_co = mkSymCoercion fun_co
635 `mkTransCoercion` mkCoVarCoercion cv'
636 `mkTransCoercion` co2
637 -- der_co :: F xis1 ~ xi2
639 `mkTransCoercion` mkCoVarCoercion cv
640 `mkTransCoercion` mkSymCoercion co2
642 then setWantedCoBind cv want_co
643 else setWantedCoBind cv' der_co
646 ; let final_cc = CFunEqCan { cc_id = cv_new
651 ; return $ ccs `extendCCans` final_cc }
653 -- Otherwise, we have a variable on the left, so call canEqLeafTyVarLeft
654 canEqLeafOriented fl cv (FskCls tv) s2
655 = canEqLeafTyVarLeft fl cv tv s2
656 canEqLeafOriented fl cv (VarCls tv) s2
657 = canEqLeafTyVarLeft fl cv tv s2
658 canEqLeafOriented _ cv (OtherCls ty1) ty2
659 = pprPanic "canEqLeaf" (ppr cv $$ ppr ty1 $$ ppr ty2)
661 canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts
662 -- Establish invariants of CTyEqCans
663 canEqLeafTyVarLeft fl cv tv s2 -- cv : tv ~ s2
664 | isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CTyEqCan
665 = addErrorTcS KindError fl (mkTyVarTy tv) s2 >> return emptyCCan
666 -- Eagerly fails, see Note [Kind errors] in TcInteract
668 = do { (xi2, co, ccs2) <- flatten fl s2 -- Flatten RHS co : xi2 ~ s2
669 ; mxi2' <- canOccursCheck fl tv xi2 -- Do an occurs check, and return a possibly
670 -- unfolded version of the RHS, if we had to
671 -- unfold any type synonyms to get rid of tv.
673 Nothing -> addErrorTcS OccCheckError fl (mkTyVarTy tv) xi2 >> return emptyCCan ;
675 do { let no_flattening_happened = isEmptyCCan ccs2
676 ; cv_new <- if no_flattening_happened then return cv
677 else if isGiven fl then return cv
678 else do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2' -- cv' : tv ~ xi2
680 then setWantedCoBind cv (mkCoVarCoercion cv' `mkTransCoercion` co)
681 else setWantedCoBind cv' (mkCoVarCoercion cv `mkTransCoercion`
685 ; return $ ccs2 `extendCCans` CTyEqCan { cc_id = cv_new
688 , cc_rhs = xi2' } } } }
693 -- See Note [Type synonyms and canonicalization].
694 -- Check whether the given variable occurs in the given type. We may
695 -- have needed to do some type synonym unfolding in order to get rid
696 -- of the variable, so we also return the unfolded version of the
697 -- type, which is guaranteed to be syntactically free of the given
698 -- type variable. If the type is already syntactically free of the
699 -- variable, then the same type is returned.
701 -- Precondition: the two types are not equal (looking though synonyms)
702 canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi)
703 canOccursCheck _gw tv xi = return (expandAway tv xi)
706 @expandAway tv xi@ expands synonyms in xi just enough to get rid of
707 occurrences of tv, if that is possible; otherwise, it returns Nothing.
708 For example, suppose we have
711 expandAway b (F Int b) = Just [Int]
713 expandAway a (F a Int) = Nothing
715 We don't promise to do the absolute minimum amount of expanding
716 necessary, but we try not to do expansions we don't need to. We
717 prefer doing inner expansions first. For example,
718 type F a b = (a, Int, a, [a])
721 expandAway b (F (G b)) = F Char
722 even though we could also expand F to get rid of b.
725 expandAway :: TcTyVar -> Xi -> Maybe Xi
726 expandAway tv t@(TyVarTy tv')
727 | tv == tv' = Nothing
730 | not (tv `elemVarSet` tyVarsOfType xi) = Just xi
731 expandAway tv (AppTy ty1 ty2)
732 = do { ty1' <- expandAway tv ty1
733 ; ty2' <- expandAway tv ty2
734 ; return (mkAppTy ty1' ty2') }
735 -- mkAppTy <$> expandAway tv ty1 <*> expandAway tv ty2
736 expandAway tv (FunTy ty1 ty2)
737 = do { ty1' <- expandAway tv ty1
738 ; ty2' <- expandAway tv ty2
739 ; return (mkFunTy ty1' ty2') }
740 -- mkFunTy <$> expandAway tv ty1 <*> expandAway tv ty2
741 expandAway tv ty@(ForAllTy {})
742 = let (tvs,rho) = splitForAllTys ty
743 tvs_knds = map tyVarKind tvs
744 in if tv `elemVarSet` tyVarsOfTypes tvs_knds then
745 -- Can't expand away the kinds unless we create
746 -- fresh variables which we don't want to do at this point.
748 else do { rho' <- expandAway tv rho
749 ; return (mkForAllTys tvs rho') }
750 expandAway tv (PredTy pred)
751 = do { pred' <- expandAwayPred tv pred
752 ; return (PredTy pred') }
753 -- For a type constructor application, first try expanding away the
754 -- offending variable from the arguments. If that doesn't work, next
755 -- see if the type constructor is a type synonym, and if so, expand
757 expandAway tv ty@(TyConApp tc tys)
758 = (mkTyConApp tc <$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv)
760 expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType
761 expandAwayPred tv (ClassP cls tys)
762 = do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') }
763 expandAwayPred tv (EqPred ty1 ty2)
764 = do { ty1' <- expandAway tv ty1
765 ; ty2' <- expandAway tv ty2
766 ; return (EqPred ty1' ty2') }
767 expandAwayPred tv (IParam nm ty)
768 = do { ty' <- expandAway tv ty
769 ; return (IParam nm ty') }
775 Note [Type synonyms and canonicalization]
776 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
778 We treat type synonym applications as xi types, that is, they do not
779 count as type function applications. However, we do need to be a bit
780 careful with type synonyms: like type functions they may not be
781 generative or injective. However, unlike type functions, they are
782 parametric, so there is no problem in expanding them whenever we see
783 them, since we do not need to know anything about their arguments in
784 order to expand them; this is what justifies not having to treat them
785 as specially as type function applications. The thing that causes
786 some subtleties is that we prefer to leave type synonym applications
787 *unexpanded* whenever possible, in order to generate better error
790 If we encounter an equality constraint with type synonym applications
791 on both sides, or a type synonym application on one side and some sort
792 of type application on the other, we simply must expand out the type
793 synonyms in order to continue decomposing the equality constraint into
794 primitive equality constraints. For example, suppose we have
798 and we encounter the equality
802 In order to continue we must expand F a into [Int], giving us the
807 which we can then decompose into the more primitive equality
812 However, if we encounter an equality constraint with a type synonym
813 application on one side and a variable on the other side, we should
814 NOT (necessarily) expand the type synonym, since for the purpose of
815 good error messages we want to leave type synonyms unexpanded as much
818 However, there is a subtle point with type synonyms and the occurs
819 check that takes place for equality constraints of the form tv ~ xi.
820 As an example, suppose we have
824 and we come across the equality constraint
828 This should not actually fail the occurs check, since expanding out
829 the type synonym results in the legitimate equality constraint a ~
830 Int. We must actually do this expansion, because unifying a with F a
831 will lead the type checker into infinite loops later. Put another
832 way, canonical equality constraints should never *syntactically*
833 contain the LHS variable in the RHS type. However, we don't always
834 need to expand type synonyms when doing an occurs check; for example,
839 is obviously fine no matter what F expands to. And in this case we
840 would rather unify a with F b (rather than F b's expansion) in order
841 to get better error messages later.
843 So, when doing an occurs check with a type synonym application on the
844 RHS, we use some heuristics to find an expansion of the RHS which does
845 not contain the variable from the LHS. In particular, given
849 we first try expanding each of the ti to types which no longer contain
850 a. If this turns out to be impossible, we next try expanding F