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 | isEmptyVarSet (tyVarsOfTypes xis)
326 = do { let (tyvars, sc_theta, _, _) = classBigSig cls
327 sc_theta1 = substTheta (zipTopTvSubst tyvars xis) sc_theta
328 ; sc_vars <- zipWithM inst_one sc_theta1 [0..]
329 ; mkCanonicals flavor sc_vars }
330 -- NB: Since there is a call to mkCanonicals,
331 -- this will add *recursively* all superclasses
333 inst_one pred n = newGivOrDerEvVar pred (EvSuperClass ev n)
334 flavor = case orig_flavor of
335 Given loc -> Given loc
336 Wanted loc -> Derived loc DerSC
337 Derived {} -> orig_flavor
338 -- NB: the non-immediate superclasses will show up as
339 -- Derived, and we want their superclasses too!
341 canIP :: CtFlavor -> EvVar -> IPName Name -> TcType -> TcS CanonicalCts
342 -- See Note [Canonical implicit parameter constraints] to see why we don't
343 -- immediately canonicalize (flatten) IP constraints.
345 = return $ singleCCan $ CIPCan { cc_id = v
351 canEq :: CtFlavor -> EvVar -> Type -> Type -> TcS CanonicalCts
353 | tcEqType ty1 ty2 -- Dealing with equality here avoids
354 -- later spurious occurs checks for a~a
355 = do { when (isWanted fl) (setWantedCoBind cv ty1)
358 -- If one side is a variable, orient and flatten,
359 -- WITHOUT expanding type synonyms, so that we tend to
360 -- substitute a ~ Age rather than a ~ Int when @type Age = Int@
361 canEq fl cv ty1@(TyVarTy {}) ty2
362 = do { untch <- getUntouchables
363 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
364 canEq fl cv ty1 ty2@(TyVarTy {})
365 = do { untch <- getUntouchables
366 ; canEqLeaf untch fl cv (classify ty1) (classify ty2) }
367 -- NB: don't use VarCls directly because tv1 or tv2 may be scolems!
369 canEq fl cv (TyConApp fn tys) ty2
370 | isSynFamilyTyCon fn, length tys == tyConArity fn
371 = do { untch <- getUntouchables
372 ; canEqLeaf untch fl cv (FunCls fn tys) (classify ty2) }
373 canEq fl cv ty1 (TyConApp fn tys)
374 | isSynFamilyTyCon fn, length tys == tyConArity fn
375 = do { untch <- getUntouchables
376 ; canEqLeaf untch fl cv (classify ty1) (FunCls fn tys) }
379 | Just (t1a,t1b,t1c) <- splitCoPredTy_maybe s1,
380 Just (t2a,t2b,t2c) <- splitCoPredTy_maybe s2
381 = do { (v1,v2,v3) <- if isWanted fl then
382 do { v1 <- newWantedCoVar t1a t2a
383 ; v2 <- newWantedCoVar t1b t2b
384 ; v3 <- newWantedCoVar t1c t2c
385 ; let res_co = mkCoPredCo (mkCoVarCoercion v1)
386 (mkCoVarCoercion v2) (mkCoVarCoercion v3)
387 ; setWantedCoBind cv res_co
388 ; return (v1,v2,v3) }
389 else let co_orig = mkCoVarCoercion cv
390 coa = mkCsel1Coercion co_orig
391 cob = mkCsel2Coercion co_orig
392 coc = mkCselRCoercion co_orig
393 in do { v1 <- newGivOrDerCoVar t1a t2a coa
394 ; v2 <- newGivOrDerCoVar t1b t2b cob
395 ; v3 <- newGivOrDerCoVar t1c t2c coc
396 ; return (v1,v2,v3) }
397 ; cc1 <- canEq fl v1 t1a t2a
398 ; cc2 <- canEq fl v2 t1b t2b
399 ; cc3 <- canEq fl v3 t1c t2c
400 ; return (cc1 `andCCan` cc2 `andCCan` cc3) }
403 -- Split up an equality between function types into two equalities.
404 canEq fl cv (FunTy s1 t1) (FunTy s2 t2)
405 = do { (argv, resv) <-
407 do { argv <- newWantedCoVar s1 s2
408 ; resv <- newWantedCoVar t1 t2
409 ; setWantedCoBind cv $
410 mkFunCoercion (mkCoVarCoercion argv) (mkCoVarCoercion resv)
411 ; return (argv,resv) }
412 else let [arg,res] = decomposeCo 2 (mkCoVarCoercion cv)
413 in do { argv <- newGivOrDerCoVar s1 s2 arg
414 ; resv <- newGivOrDerCoVar t1 t2 res
415 ; return (argv,resv) }
416 ; cc1 <- canEq fl argv s1 s2 -- inherit original kinds and locations
417 ; cc2 <- canEq fl resv t1 t2
418 ; return (cc1 `andCCan` cc2) }
420 canEq fl cv (PredTy (IParam n1 t1)) (PredTy (IParam n2 t2))
422 = if isWanted fl then
423 do { v <- newWantedCoVar t1 t2
424 ; setWantedCoBind cv $ mkIParamPredCo n1 (mkCoVarCoercion cv)
426 else return emptyCCan -- DV: How to decompose given IP coercions?
428 canEq fl cv (PredTy (ClassP c1 tys1)) (PredTy (ClassP c2 tys2))
430 = if isWanted fl then
431 do { vs <- zipWithM newWantedCoVar tys1 tys2
432 ; setWantedCoBind cv $ mkClassPPredCo c1 (map mkCoVarCoercion vs)
433 ; andCCans <$> zipWith3M (canEq fl) vs tys1 tys2
435 else return emptyCCan
436 -- How to decompose given dictionary (and implicit parameter) coercions?
437 -- You may think that the following is right:
438 -- let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
439 -- in zipWith3M newGivOrDerCoVar tys1 tys2 cos
440 -- But this assumes that the coercion is a type constructor-based
441 -- coercion, and not a PredTy (ClassP cn cos) coercion. So we chose
442 -- to not decompose these coercions. We have to get back to this
443 -- when we clean up the Coercion API.
445 canEq fl cv (TyConApp tc1 tys1) (TyConApp tc2 tys2)
446 | isAlgTyCon tc1 && isAlgTyCon tc2
448 , length tys1 == length tys2
449 = -- Generate equalities for each of the corresponding arguments
450 do { argsv <- if isWanted fl then
451 do { argsv <- zipWithM newWantedCoVar tys1 tys2
452 ; setWantedCoBind cv $ mkTyConCoercion tc1 (map mkCoVarCoercion argsv)
455 let cos = decomposeCo (length tys1) (mkCoVarCoercion cv)
456 in zipWith3M newGivOrDerCoVar tys1 tys2 cos
457 ; andCCans <$> zipWith3M (canEq fl) argsv tys1 tys2 }
459 -- See Note [Equality between type applications]
460 -- Note [Care with type applications] in TcUnify
462 | Just (s1,t1) <- tcSplitAppTy_maybe ty1
463 , Just (s2,t2) <- tcSplitAppTy_maybe ty2
466 then do { cv1 <- newWantedCoVar s1 s2
467 ; cv2 <- newWantedCoVar t1 t2
468 ; setWantedCoBind cv $
469 mkAppCoercion (mkCoVarCoercion cv1) (mkCoVarCoercion cv2)
471 else let co1 = mkLeftCoercion $ mkCoVarCoercion cv
472 co2 = mkRightCoercion $ mkCoVarCoercion cv
473 in do { cv1 <- newGivOrDerCoVar s1 s2 co1
474 ; cv2 <- newGivOrDerCoVar t1 t2 co2
476 ; cc1 <- canEq fl cv1 s1 s2
477 ; cc2 <- canEq fl cv2 t1 t2
478 ; return (cc1 `andCCan` cc2) }
480 canEq fl _ s1@(ForAllTy {}) s2@(ForAllTy {})
481 | tcIsForAllTy s1, tcIsForAllTy s2,
483 = canEqFailure fl s1 s2
485 = do { traceTcS "Ommitting decomposition of given polytype equality" (pprEq s1 s2)
488 -- Finally expand any type synonym applications.
489 canEq fl cv ty1 ty2 | Just ty1' <- tcView ty1 = canEq fl cv ty1' ty2
490 canEq fl cv ty1 ty2 | Just ty2' <- tcView ty2 = canEq fl cv ty1 ty2'
491 canEq fl _ ty1 ty2 = canEqFailure fl ty1 ty2
493 canEqFailure :: CtFlavor -> Type -> Type -> TcS CanonicalCts
494 canEqFailure fl ty1 ty2
495 = do { addErrorTcS MisMatchError fl ty1 ty2
499 Note [Equality between type applications]
500 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
501 If we see an equality of the form s1 t1 ~ s2 t2 we can always split
502 it up into s1 ~ s2 /\ t1 ~ t2, since s1 and s2 can't be type
503 functions (type functions use the TyConApp constructor, which never
504 shows up as the LHS of an AppTy). Other than type functions, types
505 in Haskell are always
507 (1) generative: a b ~ c d implies a ~ c, since different type
508 constructors always generate distinct types
510 (2) injective: a b ~ a d implies b ~ d; we never generate the
511 same type from different type arguments.
514 Note [Canonical ordering for equality constraints]
515 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
516 Implemented as (<+=) below:
518 - Type function applications always come before anything else.
519 - Variables always come before non-variables (other than type
520 function applications).
522 Note that we don't need to unfold type synonyms on the RHS to check
523 the ordering; that is, in the rules above it's OK to consider only
524 whether something is *syntactically* a type function application or
525 not. To illustrate why this is OK, suppose we have an equality of the
526 form 'tv ~ S a b c', where S is a type synonym which expands to a
527 top-level application of the type function F, something like
531 Then to canonicalize 'tv ~ S a b c' we flatten the RHS, and since S's
532 expansion contains type function applications the flattener will do
533 the expansion and then generate a skolem variable for the type
534 function application, so we end up with something like this:
539 where x is the skolem variable. This is one extra equation than
540 absolutely necessary (we could have gotten away with just 'F d e ~ tv'
541 if we had noticed that S expanded to a top-level type function
542 application and flipped it around in the first place) but this way
543 keeps the code simpler.
545 Unlike the OutsideIn(X) draft of May 7, 2010, we do not care about the
546 ordering of tv ~ tv constraints. There are several reasons why we
549 (1) In order to be able to extract a substitution that doesn't
550 mention untouchable variables after we are done solving, we might
551 prefer to put touchable variables on the left. However, in and
552 of itself this isn't necessary; we can always re-orient equality
553 constraints at the end if necessary when extracting a substitution.
555 (2) To ensure termination we might think it necessary to put
556 variables in lexicographic order. However, this isn't actually
557 necessary as outlined below.
559 While building up an inert set of canonical constraints, we maintain
560 the invariant that the equality constraints in the inert set form an
561 acyclic rewrite system when viewed as L-R rewrite rules. Moreover,
562 the given constraints form an idempotent substitution (i.e. none of
563 the variables on the LHS occur in any of the RHS's, and type functions
564 never show up in the RHS at all), the wanted constraints also form an
565 idempotent substitution, and finally the LHS of a given constraint
566 never shows up on the RHS of a wanted constraint. There may, however,
567 be a wanted LHS that shows up in a given RHS, since we do not rewrite
568 given constraints with wanted constraints.
570 Suppose we have an inert constraint set
573 tg_1 ~ xig_1 -- givens
576 tw_1 ~ xiw_1 -- wanteds
580 where each t_i can be either a type variable or a type function
581 application. Now suppose we take a new canonical equality constraint,
582 t' ~ xi' (note among other things this means t' does not occur in xi')
583 and try to react it with the existing inert set. We show by induction
584 on the number of t_i which occur in t' ~ xi' that this process will
587 There are several ways t' ~ xi' could react with an existing constraint:
589 TODO: finish this proof. The below was for the case where the entire
590 inert set is an idempotent subustitution...
592 (b) We could have t' = t_j for some j. Then we obtain the new
593 equality xi_j ~ xi'; note that neither xi_j or xi' contain t_j. We
594 now canonicalize the new equality, which may involve decomposing it
595 into several canonical equalities, and recurse on these. However,
596 none of the new equalities will contain t_j, so they have fewer
597 occurrences of the t_i than the original equation.
599 (a) We could have t_j occurring in xi' for some j, with t' /=
600 t_j. Then we substitute xi_j for t_j in xi' and continue. However,
601 since none of the t_i occur in xi_j, we have decreased the
602 number of t_i that occur in xi', since we eliminated t_j and did not
603 introduce any new ones.
607 = FskCls TcTyVar -- ^ Flatten skolem
608 | VarCls TcTyVar -- ^ Non-flatten-skolem variable
609 | FunCls TyCon [Type] -- ^ Type function, exactly saturated
610 | OtherCls TcType -- ^ Neither of the above
612 unClassify :: TypeClassifier -> TcType
613 unClassify (VarCls tv) = TyVarTy tv
614 unClassify (FskCls tv) = TyVarTy tv
615 unClassify (FunCls fn tys) = TyConApp fn tys
616 unClassify (OtherCls ty) = ty
618 classify :: TcType -> TypeClassifier
620 classify (TyVarTy tv)
622 FlatSkol {} <- tcTyVarDetails tv = FskCls tv
623 | otherwise = VarCls tv
624 classify (TyConApp tc tys) | isSynFamilyTyCon tc
625 , tyConArity tc == length tys
627 classify ty | Just ty' <- tcView ty
628 = case classify ty' of
629 OtherCls {} -> OtherCls ty
630 var_or_fn -> var_or_fn
634 -- See note [Canonical ordering for equality constraints].
635 reOrient :: TcsUntouchables -> TypeClassifier -> TypeClassifier -> Bool
636 -- (t1 `reOrient` t2) responds True
637 -- iff we should flip to (t2~t1)
638 -- We try to say False if possible, to minimise evidence generation
640 -- Postcondition: After re-orienting, first arg is not OTherCls
641 reOrient _untch (OtherCls {}) (FunCls {}) = True
642 reOrient _untch (OtherCls {}) (FskCls {}) = True
643 reOrient _untch (OtherCls {}) (VarCls {}) = True
644 reOrient _untch (OtherCls {}) (OtherCls {}) = panic "reOrient" -- One must be Var/Fun
646 reOrient _untch (FunCls {}) (VarCls {}) = False
647 -- See Note [No touchables as FunEq RHS] in TcSMonad
648 reOrient _untch (FunCls {}) _ = False -- Fun/Other on rhs
650 reOrient _untch (VarCls {}) (FunCls {}) = True
652 reOrient _untch (VarCls {}) (FskCls {}) = False
654 reOrient _untch (VarCls {}) (OtherCls {}) = False
655 reOrient _untch (VarCls tv1) (VarCls tv2)
656 | isMetaTyVar tv2 && not (isMetaTyVar tv1) = True
658 -- Just for efficiency, see CTyEqCan invariants
660 reOrient _untch (FskCls {}) (VarCls tv2) = isMetaTyVar tv2
661 -- Just for efficiency, see CTyEqCan invariants
663 reOrient _untch (FskCls {}) (FskCls {}) = False
664 reOrient _untch (FskCls {}) (FunCls {}) = True
665 reOrient _untch (FskCls {}) (OtherCls {}) = False
668 canEqLeaf :: TcsUntouchables
670 -> TypeClassifier -> TypeClassifier -> TcS CanonicalCts
671 -- Canonicalizing "leaf" equality constraints which cannot be
672 -- decomposed further (ie one of the types is a variable or
673 -- saturated type function application).
676 -- * one of the two arguments is not OtherCls
677 -- * the two types are not equal (looking through synonyms)
678 canEqLeaf untch fl cv cls1 cls2
679 | cls1 `re_orient` cls2
680 = do { cv' <- if isWanted fl
681 then do { cv' <- newWantedCoVar s2 s1
682 ; setWantedCoBind cv $ mkSymCoercion (mkCoVarCoercion cv')
684 else newGivOrDerCoVar s2 s1 (mkSymCoercion (mkCoVarCoercion cv))
685 ; canEqLeafOriented fl cv' cls2 s1 }
688 = canEqLeafOriented fl cv cls1 s2
690 re_orient = reOrient untch
695 canEqLeafOriented :: CtFlavor -> CoVar
696 -> TypeClassifier -> TcType -> TcS CanonicalCts
697 -- First argument is not OtherCls
698 canEqLeafOriented fl cv cls1@(FunCls fn tys1) s2 -- cv : F tys1
699 | let k1 = kindAppResult (tyConKind fn) tys1,
700 let k2 = typeKind s2,
701 isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CFunEqCan
702 = addErrorTcS KindError fl (unClassify cls1) s2 >> return emptyCCan
703 -- Eagerly fails, see Note [Kind errors] in TcInteract
706 = ASSERT2( isSynFamilyTyCon fn, ppr (unClassify cls1) )
707 do { (xis1,cos1,ccs1) <- flattenMany fl tys1 -- Flatten type function arguments
708 -- cos1 :: xis1 ~ tys1
709 ; (xi2, co2, ccs2) <- flatten fl s2 -- Flatten entire RHS
711 ; let ccs = ccs1 `andCCan` ccs2
712 no_flattening_happened = isEmptyCCan ccs
713 ; cv_new <- if no_flattening_happened then return cv
714 else if isGiven fl then return cv
715 else do { cv' <- newWantedCoVar (unClassify (FunCls fn xis1)) xi2
717 ; let -- fun_co :: F xis1 ~ F tys1
718 fun_co = mkTyConCoercion fn cos1
719 -- want_co :: F tys1 ~ s2
720 want_co = mkSymCoercion fun_co
721 `mkTransCoercion` mkCoVarCoercion cv'
722 `mkTransCoercion` co2
723 -- der_co :: F xis1 ~ xi2
725 `mkTransCoercion` mkCoVarCoercion cv
726 `mkTransCoercion` mkSymCoercion co2
728 then setWantedCoBind cv want_co
729 else setWantedCoBind cv' der_co
732 ; let final_cc = CFunEqCan { cc_id = cv_new
737 ; return $ ccs `extendCCans` final_cc }
739 -- Otherwise, we have a variable on the left, so call canEqLeafTyVarLeft
740 canEqLeafOriented fl cv (FskCls tv) s2
741 = canEqLeafTyVarLeft fl cv tv s2
742 canEqLeafOriented fl cv (VarCls tv) s2
743 = canEqLeafTyVarLeft fl cv tv s2
744 canEqLeafOriented _ cv (OtherCls ty1) ty2
745 = pprPanic "canEqLeaf" (ppr cv $$ ppr ty1 $$ ppr ty2)
747 canEqLeafTyVarLeft :: CtFlavor -> CoVar -> TcTyVar -> TcType -> TcS CanonicalCts
748 -- Establish invariants of CTyEqCans
749 canEqLeafTyVarLeft fl cv tv s2 -- cv : tv ~ s2
750 | isGiven fl && not (k1 `compatKind` k2) -- Establish the kind invariant for CTyEqCan
751 = addErrorTcS KindError fl (mkTyVarTy tv) s2 >> return emptyCCan
752 -- Eagerly fails, see Note [Kind errors] in TcInteract
754 = do { (xi2, co, ccs2) <- flatten fl s2 -- Flatten RHS co : xi2 ~ s2
755 ; mxi2' <- canOccursCheck fl tv xi2 -- Do an occurs check, and return a possibly
756 -- unfolded version of the RHS, if we had to
757 -- unfold any type synonyms to get rid of tv.
759 Nothing -> addErrorTcS OccCheckError fl (mkTyVarTy tv) xi2 >> return emptyCCan ;
761 do { let no_flattening_happened = isEmptyCCan ccs2
762 ; cv_new <- if no_flattening_happened then return cv
763 else if isGiven fl then return cv
764 else do { cv' <- newWantedCoVar (mkTyVarTy tv) xi2' -- cv' : tv ~ xi2
766 then setWantedCoBind cv (mkCoVarCoercion cv' `mkTransCoercion` co)
767 else setWantedCoBind cv' (mkCoVarCoercion cv `mkTransCoercion`
771 ; return $ ccs2 `extendCCans` CTyEqCan { cc_id = cv_new
774 , cc_rhs = xi2' } } } }
779 -- See Note [Type synonyms and canonicalization].
780 -- Check whether the given variable occurs in the given type. We may
781 -- have needed to do some type synonym unfolding in order to get rid
782 -- of the variable, so we also return the unfolded version of the
783 -- type, which is guaranteed to be syntactically free of the given
784 -- type variable. If the type is already syntactically free of the
785 -- variable, then the same type is returned.
787 -- Precondition: the two types are not equal (looking though synonyms)
788 canOccursCheck :: CtFlavor -> TcTyVar -> Xi -> TcS (Maybe Xi)
789 canOccursCheck _gw tv xi = return (expandAway tv xi)
792 @expandAway tv xi@ expands synonyms in xi just enough to get rid of
793 occurrences of tv, if that is possible; otherwise, it returns Nothing.
794 For example, suppose we have
797 expandAway b (F Int b) = Just [Int]
799 expandAway a (F a Int) = Nothing
801 We don't promise to do the absolute minimum amount of expanding
802 necessary, but we try not to do expansions we don't need to. We
803 prefer doing inner expansions first. For example,
804 type F a b = (a, Int, a, [a])
807 expandAway b (F (G b)) = F Char
808 even though we could also expand F to get rid of b.
811 expandAway :: TcTyVar -> Xi -> Maybe Xi
812 expandAway tv t@(TyVarTy tv')
813 | tv == tv' = Nothing
816 | not (tv `elemVarSet` tyVarsOfType xi) = Just xi
817 expandAway tv (AppTy ty1 ty2)
818 = do { ty1' <- expandAway tv ty1
819 ; ty2' <- expandAway tv ty2
820 ; return (mkAppTy ty1' ty2') }
821 -- mkAppTy <$> expandAway tv ty1 <*> expandAway tv ty2
822 expandAway tv (FunTy ty1 ty2)
823 = do { ty1' <- expandAway tv ty1
824 ; ty2' <- expandAway tv ty2
825 ; return (mkFunTy ty1' ty2') }
826 -- mkFunTy <$> expandAway tv ty1 <*> expandAway tv ty2
827 expandAway tv ty@(ForAllTy {})
828 = let (tvs,rho) = splitForAllTys ty
829 tvs_knds = map tyVarKind tvs
830 in if tv `elemVarSet` tyVarsOfTypes tvs_knds then
831 -- Can't expand away the kinds unless we create
832 -- fresh variables which we don't want to do at this point.
834 else do { rho' <- expandAway tv rho
835 ; return (mkForAllTys tvs rho') }
836 expandAway tv (PredTy pred)
837 = do { pred' <- expandAwayPred tv pred
838 ; return (PredTy pred') }
839 -- For a type constructor application, first try expanding away the
840 -- offending variable from the arguments. If that doesn't work, next
841 -- see if the type constructor is a type synonym, and if so, expand
843 expandAway tv ty@(TyConApp tc tys)
844 = (mkTyConApp tc <$> mapM (expandAway tv) tys) <|> (tcView ty >>= expandAway tv)
846 expandAwayPred :: TcTyVar -> TcPredType -> Maybe TcPredType
847 expandAwayPred tv (ClassP cls tys)
848 = do { tys' <- mapM (expandAway tv) tys; return (ClassP cls tys') }
849 expandAwayPred tv (EqPred ty1 ty2)
850 = do { ty1' <- expandAway tv ty1
851 ; ty2' <- expandAway tv ty2
852 ; return (EqPred ty1' ty2') }
853 expandAwayPred tv (IParam nm ty)
854 = do { ty' <- expandAway tv ty
855 ; return (IParam nm ty') }
861 Note [Type synonyms and canonicalization]
862 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
864 We treat type synonym applications as xi types, that is, they do not
865 count as type function applications. However, we do need to be a bit
866 careful with type synonyms: like type functions they may not be
867 generative or injective. However, unlike type functions, they are
868 parametric, so there is no problem in expanding them whenever we see
869 them, since we do not need to know anything about their arguments in
870 order to expand them; this is what justifies not having to treat them
871 as specially as type function applications. The thing that causes
872 some subtleties is that we prefer to leave type synonym applications
873 *unexpanded* whenever possible, in order to generate better error
876 If we encounter an equality constraint with type synonym applications
877 on both sides, or a type synonym application on one side and some sort
878 of type application on the other, we simply must expand out the type
879 synonyms in order to continue decomposing the equality constraint into
880 primitive equality constraints. For example, suppose we have
884 and we encounter the equality
888 In order to continue we must expand F a into [Int], giving us the
893 which we can then decompose into the more primitive equality
898 However, if we encounter an equality constraint with a type synonym
899 application on one side and a variable on the other side, we should
900 NOT (necessarily) expand the type synonym, since for the purpose of
901 good error messages we want to leave type synonyms unexpanded as much
904 However, there is a subtle point with type synonyms and the occurs
905 check that takes place for equality constraints of the form tv ~ xi.
906 As an example, suppose we have
910 and we come across the equality constraint
914 This should not actually fail the occurs check, since expanding out
915 the type synonym results in the legitimate equality constraint a ~
916 Int. We must actually do this expansion, because unifying a with F a
917 will lead the type checker into infinite loops later. Put another
918 way, canonical equality constraints should never *syntactically*
919 contain the LHS variable in the RHS type. However, we don't always
920 need to expand type synonyms when doing an occurs check; for example,
925 is obviously fine no matter what F expands to. And in this case we
926 would rather unify a with F b (rather than F b's expansion) in order
927 to get better error messages later.
929 So, when doing an occurs check with a type synonym application on the
930 RHS, we use some heuristics to find an expansion of the RHS which does
931 not contain the variable from the LHS. In particular, given
935 we first try expanding each of the ti to types which no longer contain
936 a. If this turns out to be impossible, we next try expanding F