2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
4 \section{Type subsumption and unification}
8 -- Full-blown subsumption
9 tcSubOff, tcSubExp, tcGen,
10 checkSigTyVars, checkSigTyVarsWrt, sigCtxt, findGlobals,
12 -- Various unifications
13 unifyTauTy, unifyTauTyList, unifyTauTyLists,
14 unifyKind, unifyKinds, unifyOpenTypeKind, unifyFunKind,
16 --------------------------------
18 Expected(..), newHole, readExpectedType,
19 zapExpectedType, zapExpectedTo, zapExpectedBranches,
20 subFunTys, unifyFunTy,
21 zapToListTy, unifyListTy,
22 zapToPArrTy, unifyPArrTy,
23 zapToTupleTy, unifyTupleTy
27 #include "HsVersions.h"
30 import HsSyn ( HsExpr(..) )
31 import TcHsSyn ( mkHsLet,
32 ExprCoFn, idCoercion, isIdCoercion, mkCoercion, (<.>), (<$>) )
33 import TypeRep ( Type(..), SourceType(..), TyNote(..), openKindCon )
35 import TcRnMonad -- TcType, amongst others
36 import TcType ( TcKind, TcType, TcSigmaType, TcRhoType, TcTyVar, TcTauType,
37 TcTyVarSet, TcThetaType, TyVarDetails(SigTv),
38 isTauTy, isSigmaTy, mkFunTys,
39 tcSplitAppTy_maybe, tcSplitTyConApp_maybe,
40 tcGetTyVar_maybe, tcGetTyVar,
41 mkFunTy, tyVarsOfType, mkPhiTy,
42 typeKind, tcSplitFunTy_maybe, mkForAllTys,
43 isSkolemTyVar, isUserTyVar,
44 tidyOpenType, tidyOpenTypes, tidyOpenTyVar, tidyOpenTyVars,
45 eqKind, openTypeKind, liftedTypeKind, isTypeKind, mkArrowKind,
46 hasMoreBoxityInfo, allDistinctTyVars
48 import Inst ( newDicts, instToId, tcInstCall )
49 import TcMType ( getTcTyVar, putTcTyVar, tcInstType, newKindVar,
50 newTyVarTy, newTyVarTys, newOpenTypeKind,
51 zonkTcType, zonkTcTyVars, zonkTcTyVarsAndFV )
52 import TcSimplify ( tcSimplifyCheck )
53 import TysWiredIn ( listTyCon, parrTyCon, mkListTy, mkPArrTy, mkTupleTy )
54 import TcEnv ( tcGetGlobalTyVars, findGlobals )
55 import TyCon ( tyConArity, isTupleTyCon, tupleTyConBoxity )
56 import PprType ( pprType )
57 import Id ( Id, mkSysLocal )
58 import Var ( Var, varName, tyVarKind )
59 import VarSet ( emptyVarSet, unitVarSet, unionVarSet, elemVarSet, varSetElems )
61 import Name ( isSystemName )
62 import ErrUtils ( Message )
63 import BasicTypes ( Boxity, Arity, isBoxed )
64 import Util ( equalLength, lengthExceeds, notNull )
70 * A hole is always filled in with an ordinary type, not another hole.
72 %************************************************************************
74 \subsection{'hole' type variables}
76 %************************************************************************
79 data Expected ty = Infer (TcRef ty) -- The hole to fill in for type inference
80 | Check ty -- The type to check during type checking
82 newHole :: TcM (TcRef ty)
83 newHole = newMutVar (error "Empty hole in typechecker")
85 readExpectedType :: Expected ty -> TcM ty
86 readExpectedType (Infer hole) = readMutVar hole
87 readExpectedType (Check ty) = returnM ty
89 zapExpectedType :: Expected TcType -> TcM TcTauType
90 -- In the inference case, ensure we have a monotype
91 zapExpectedType (Infer hole)
92 = do { ty <- newTyVarTy openTypeKind ;
96 zapExpectedType (Check ty) = return ty
98 zapExpectedTo :: Expected TcType -> TcTauType -> TcM ()
99 zapExpectedTo (Infer hole) ty2 = writeMutVar hole ty2
100 zapExpectedTo (Check ty1) ty2 = unifyTauTy ty1 ty2
102 zapExpectedBranches :: [a] -> Expected TcType -> TcM (Expected TcType)
103 -- Zap the expected type to a monotype if there is more than one branch
104 zapExpectedBranches branches exp_ty
105 | lengthExceeds branches 1 = zapExpectedType exp_ty `thenM` \ exp_ty' ->
106 return (Check exp_ty')
107 | otherwise = returnM exp_ty
109 instance Outputable ty => Outputable (Expected ty) where
110 ppr (Check ty) = ptext SLIT("Expected type") <+> ppr ty
111 ppr (Infer hole) = ptext SLIT("Inferring type")
115 %************************************************************************
117 \subsection[Unify-fun]{@unifyFunTy@}
119 %************************************************************************
121 @subFunTy@ and @unifyFunTy@ is used to avoid the fruitless
122 creation of type variables.
124 * subFunTy is used when we might be faced with a "hole" type variable,
125 in which case we should create two new holes.
127 * unifyFunTy is used when we expect to encounter only "ordinary"
128 type variables, so we should create new ordinary type variables
132 -> Expected TcRhoType -- Fail if ty isn't a function type
133 -> ([(pat, Expected TcRhoType)] -> Expected TcRhoType -> TcM a)
136 subFunTys pats (Infer hole) thing_inside
137 = -- This is the interesting case
138 mapM new_pat_hole pats `thenM` \ pats_w_holes ->
139 newHole `thenM` \ res_hole ->
142 thing_inside pats_w_holes (Infer res_hole) `thenM` \ answer ->
144 -- Extract the answers
145 mapM read_pat_hole pats_w_holes `thenM` \ arg_tys ->
146 readMutVar res_hole `thenM` \ res_ty ->
148 -- Write the answer into the incoming hole
149 writeMutVar hole (mkFunTys arg_tys res_ty) `thenM_`
151 -- And return the answer
154 new_pat_hole pat = newHole `thenM` \ hole -> return (pat, Infer hole)
155 read_pat_hole (pat, Infer hole) = readMutVar hole
157 subFunTys pats (Check ty) thing_inside
158 = go pats ty `thenM` \ (pats_w_tys, res_ty) ->
159 thing_inside pats_w_tys res_ty
161 go [] ty = return ([], Check ty)
162 go (pat:pats) ty = unifyFunTy ty `thenM` \ (arg,res) ->
163 go pats res `thenM` \ (pats_w_tys, final_res) ->
164 return ((pat, Check arg) : pats_w_tys, final_res)
166 unifyFunTy :: TcRhoType -- Fail if ty isn't a function type
167 -> TcM (TcType, TcType) -- otherwise return arg and result types
169 unifyFunTy ty@(TyVarTy tyvar)
170 = getTcTyVar tyvar `thenM` \ maybe_ty ->
172 Just ty' -> unifyFunTy ty'
173 Nothing -> unify_fun_ty_help ty
176 = case tcSplitFunTy_maybe ty of
177 Just arg_and_res -> returnM arg_and_res
178 Nothing -> unify_fun_ty_help ty
180 unify_fun_ty_help ty -- Special cases failed, so revert to ordinary unification
181 = newTyVarTy openTypeKind `thenM` \ arg ->
182 newTyVarTy openTypeKind `thenM` \ res ->
183 unifyTauTy ty (mkFunTy arg res) `thenM_`
188 zapToListTy :: Expected TcType -- expected list type
189 -> TcM TcType -- list element type
191 zapToListTy (Check ty) = unifyListTy ty
192 zapToListTy (Infer hole) = do { elt_ty <- newTyVarTy liftedTypeKind ;
193 writeMutVar hole (mkListTy elt_ty) ;
196 unifyListTy :: TcType -> TcM TcType
197 unifyListTy ty@(TyVarTy tyvar)
198 = getTcTyVar tyvar `thenM` \ maybe_ty ->
200 Just ty' -> unifyListTy ty'
201 other -> unify_list_ty_help ty
204 = case tcSplitTyConApp_maybe ty of
205 Just (tycon, [arg_ty]) | tycon == listTyCon -> returnM arg_ty
206 other -> unify_list_ty_help ty
208 unify_list_ty_help ty -- Revert to ordinary unification
209 = newTyVarTy liftedTypeKind `thenM` \ elt_ty ->
210 unifyTauTy ty (mkListTy elt_ty) `thenM_`
213 -- variant for parallel arrays
215 zapToPArrTy :: Expected TcType -- Expected list type
216 -> TcM TcType -- List element type
218 zapToPArrTy (Check ty) = unifyPArrTy ty
219 zapToPArrTy (Infer hole) = do { elt_ty <- newTyVarTy liftedTypeKind ;
220 writeMutVar hole (mkPArrTy elt_ty) ;
223 unifyPArrTy :: TcType -> TcM TcType
225 unifyPArrTy ty@(TyVarTy tyvar)
226 = getTcTyVar tyvar `thenM` \ maybe_ty ->
228 Just ty' -> unifyPArrTy ty'
229 _ -> unify_parr_ty_help ty
231 = case tcSplitTyConApp_maybe ty of
232 Just (tycon, [arg_ty]) | tycon == parrTyCon -> returnM arg_ty
233 _ -> unify_parr_ty_help ty
235 unify_parr_ty_help ty -- Revert to ordinary unification
236 = newTyVarTy liftedTypeKind `thenM` \ elt_ty ->
237 unifyTauTy ty (mkPArrTy elt_ty) `thenM_`
242 zapToTupleTy :: Boxity -> Arity -> Expected TcType -> TcM [TcType]
243 zapToTupleTy boxity arity (Check ty) = unifyTupleTy boxity arity ty
244 zapToTupleTy boxity arity (Infer hole) = do { (tup_ty, arg_tys) <- new_tuple_ty boxity arity ;
245 writeMutVar hole tup_ty ;
248 unifyTupleTy boxity arity ty@(TyVarTy tyvar)
249 = getTcTyVar tyvar `thenM` \ maybe_ty ->
251 Just ty' -> unifyTupleTy boxity arity ty'
252 other -> unify_tuple_ty_help boxity arity ty
254 unifyTupleTy boxity arity ty
255 = case tcSplitTyConApp_maybe ty of
256 Just (tycon, arg_tys)
258 && tyConArity tycon == arity
259 && tupleTyConBoxity tycon == boxity
261 other -> unify_tuple_ty_help boxity arity ty
263 unify_tuple_ty_help boxity arity ty
264 = new_tuple_ty boxity arity `thenM` \ (tup_ty, arg_tys) ->
265 unifyTauTy ty tup_ty `thenM_`
268 new_tuple_ty boxity arity
269 = newTyVarTys arity kind `thenM` \ arg_tys ->
270 return (mkTupleTy boxity arity arg_tys, arg_tys)
272 kind | isBoxed boxity = liftedTypeKind
273 | otherwise = openTypeKind
277 %************************************************************************
279 \subsection{Subsumption}
281 %************************************************************************
283 All the tcSub calls have the form
285 tcSub expected_ty offered_ty
287 offered_ty <= expected_ty
289 That is, that a value of type offered_ty is acceptable in
290 a place expecting a value of type expected_ty.
292 It returns a coercion function
293 co_fn :: offered_ty -> expected_ty
294 which takes an HsExpr of type offered_ty into one of type
298 tcSubExp :: Expected TcRhoType -> TcRhoType -> TcM ExprCoFn
299 tcSubOff :: TcSigmaType -> Expected TcSigmaType -> TcM ExprCoFn
302 These two check for holes
305 tcSubExp expected_ty offered_ty
306 = traceTc (text "tcSubExp" <+> (ppr expected_ty $$ ppr offered_ty)) `thenM_`
307 checkHole expected_ty offered_ty tcSub
309 tcSubOff expected_ty offered_ty
310 = checkHole offered_ty expected_ty (\ off exp -> tcSub exp off)
312 -- checkHole looks for a hole in its first arg;
313 -- If so, and it is uninstantiated, it fills in the hole
314 -- with its second arg
315 -- Otherwise it calls thing_inside, passing the two args, looking
316 -- through any instantiated hole
318 checkHole (Infer hole) other_ty thing_inside
319 = do { writeMutVar hole other_ty; return idCoercion }
321 checkHole (Check ty) other_ty thing_inside
322 = thing_inside ty other_ty
325 No holes expected now. Add some error-check context info.
328 tcSub :: TcSigmaType -> TcSigmaType -> TcM ExprCoFn -- Locally used only
329 tcSub expected_ty actual_ty
330 = traceTc (text "tcSub" <+> details) `thenM_`
331 addErrCtxtM (unifyCtxt "type" expected_ty actual_ty)
332 (tc_sub expected_ty expected_ty actual_ty actual_ty)
334 details = vcat [text "Expected:" <+> ppr expected_ty,
335 text "Actual: " <+> ppr actual_ty]
338 tc_sub carries the types before and after expanding type synonyms
341 tc_sub :: TcSigmaType -- expected_ty, before expanding synonyms
342 -> TcSigmaType -- ..and after
343 -> TcSigmaType -- actual_ty, before
344 -> TcSigmaType -- ..and after
347 -----------------------------------
349 tc_sub exp_sty (NoteTy _ exp_ty) act_sty act_ty = tc_sub exp_sty exp_ty act_sty act_ty
350 tc_sub exp_sty exp_ty act_sty (NoteTy _ act_ty) = tc_sub exp_sty exp_ty act_sty act_ty
352 -----------------------------------
353 -- Generalisation case
354 -- actual_ty: d:Eq b => b->b
355 -- expected_ty: forall a. Ord a => a->a
356 -- co_fn e /\a. \d2:Ord a. let d = eqFromOrd d2 in e
358 -- It is essential to do this *before* the specialisation case
359 -- Example: f :: (Eq a => a->a) -> ...
360 -- g :: Ord b => b->b
363 tc_sub exp_sty expected_ty act_sty actual_ty
364 | isSigmaTy expected_ty
365 = tcGen expected_ty (tyVarsOfType actual_ty) (
366 -- It's really important to check for escape wrt the free vars of
367 -- both expected_ty *and* actual_ty
368 \ body_exp_ty -> tc_sub body_exp_ty body_exp_ty act_sty actual_ty
369 ) `thenM` \ (gen_fn, co_fn) ->
370 returnM (gen_fn <.> co_fn)
372 -----------------------------------
373 -- Specialisation case:
374 -- actual_ty: forall a. Ord a => a->a
375 -- expected_ty: Int -> Int
376 -- co_fn e = e Int dOrdInt
378 tc_sub exp_sty expected_ty act_sty actual_ty
379 | isSigmaTy actual_ty
380 = tcInstCall Rank2Origin actual_ty `thenM` \ (inst_fn, body_ty) ->
381 tc_sub exp_sty expected_ty body_ty body_ty `thenM` \ co_fn ->
382 returnM (co_fn <.> inst_fn)
384 -----------------------------------
387 tc_sub _ (FunTy exp_arg exp_res) _ (FunTy act_arg act_res)
388 = tcSub_fun exp_arg exp_res act_arg act_res
390 -----------------------------------
391 -- Type variable meets function: imitate
393 -- NB 1: we can't just unify the type variable with the type
394 -- because the type might not be a tau-type, and we aren't
395 -- allowed to instantiate an ordinary type variable with
398 -- NB 2: can we short-cut to an error case?
399 -- when the arg/res is not a tau-type?
400 -- NO! e.g. f :: ((forall a. a->a) -> Int) -> Int
402 -- is perfectly fine, because we can instantiat f's type to a monotype
404 -- However, we get can get jolly unhelpful error messages.
405 -- e.g. foo = id runST
407 -- Inferred type is less polymorphic than expected
408 -- Quantified type variable `s' escapes
409 -- Expected type: ST s a -> t
410 -- Inferred type: (forall s1. ST s1 a) -> a
411 -- In the first argument of `id', namely `runST'
412 -- In a right-hand side of function `foo': id runST
414 -- I'm not quite sure what to do about this!
416 tc_sub exp_sty exp_ty@(FunTy exp_arg exp_res) _ (TyVarTy tv)
417 = getTcTyVar tv `thenM` \ maybe_ty ->
419 Just ty -> tc_sub exp_sty exp_ty ty ty
420 Nothing -> imitateFun tv exp_sty `thenM` \ (act_arg, act_res) ->
421 tcSub_fun exp_arg exp_res act_arg act_res
423 tc_sub _ (TyVarTy tv) act_sty act_ty@(FunTy act_arg act_res)
424 = getTcTyVar tv `thenM` \ maybe_ty ->
426 Just ty -> tc_sub ty ty act_sty act_ty
427 Nothing -> imitateFun tv act_sty `thenM` \ (exp_arg, exp_res) ->
428 tcSub_fun exp_arg exp_res act_arg act_res
430 -----------------------------------
432 -- If none of the above match, we revert to the plain unifier
433 tc_sub exp_sty expected_ty act_sty actual_ty
434 = uTys exp_sty expected_ty act_sty actual_ty `thenM_`
438 %************************************************************************
440 \subsection{Functions}
442 %************************************************************************
445 tcSub_fun exp_arg exp_res act_arg act_res
446 = tc_sub act_arg act_arg exp_arg exp_arg `thenM` \ co_fn_arg ->
447 tc_sub exp_res exp_res act_res act_res `thenM` \ co_fn_res ->
448 newUnique `thenM` \ uniq ->
450 -- co_fn_arg :: HsExpr exp_arg -> HsExpr act_arg
451 -- co_fn_res :: HsExpr act_res -> HsExpr exp_res
452 -- co_fn :: HsExpr (act_arg -> act_res) -> HsExpr (exp_arg -> exp_res)
453 arg_id = mkSysLocal FSLIT("sub") uniq exp_arg
454 coercion | isIdCoercion co_fn_arg,
455 isIdCoercion co_fn_res = idCoercion
456 | otherwise = mkCoercion co_fn
458 co_fn e = DictLam [arg_id]
459 (co_fn_res <$> (HsApp e (co_fn_arg <$> (HsVar arg_id))))
460 -- Slight hack; using a "DictLam" to get an ordinary simple lambda
461 -- HsVar arg_id :: HsExpr exp_arg
462 -- co_fn_arg $it :: HsExpr act_arg
463 -- HsApp e $it :: HsExpr act_res
464 -- co_fn_res $it :: HsExpr exp_res
468 imitateFun :: TcTyVar -> TcType -> TcM (TcType, TcType)
470 = -- NB: tv is an *ordinary* tyvar and so are the new ones
472 -- Check that tv isn't a type-signature type variable
473 -- (This would be found later in checkSigTyVars, but
474 -- we get a better error message if we do it here.)
475 checkM (not (isSkolemTyVar tv))
476 (failWithTcM (unifyWithSigErr tv ty)) `thenM_`
478 newTyVarTy openTypeKind `thenM` \ arg ->
479 newTyVarTy openTypeKind `thenM` \ res ->
480 putTcTyVar tv (mkFunTy arg res) `thenM_`
485 %************************************************************************
487 \subsection{Generalisation}
489 %************************************************************************
492 tcGen :: TcSigmaType -- expected_ty
493 -> TcTyVarSet -- Extra tyvars that the universally
494 -- quantified tyvars of expected_ty
495 -- must not be unified
496 -> (TcRhoType -> TcM result) -- spec_ty
497 -> TcM (ExprCoFn, result)
498 -- The expression has type: spec_ty -> expected_ty
500 tcGen expected_ty extra_tvs thing_inside -- We expect expected_ty to be a forall-type
501 -- If not, the call is a no-op
502 = tcInstType SigTv expected_ty `thenM` \ (forall_tvs, theta, phi_ty) ->
504 -- Type-check the arg and unify with poly type
505 getLIE (thing_inside phi_ty) `thenM` \ (result, lie) ->
507 -- Check that the "forall_tvs" havn't been constrained
508 -- The interesting bit here is that we must include the free variables
509 -- of the expected_ty. Here's an example:
510 -- runST (newVar True)
511 -- Here, if we don't make a check, we'll get a type (ST s (MutVar s Bool))
512 -- for (newVar True), with s fresh. Then we unify with the runST's arg type
513 -- forall s'. ST s' a. That unifies s' with s, and a with MutVar s Bool.
514 -- So now s' isn't unconstrained because it's linked to a.
515 -- Conclusion: include the free vars of the expected_ty in the
516 -- list of "free vars" for the signature check.
518 newDicts SignatureOrigin theta `thenM` \ dicts ->
519 tcSimplifyCheck sig_msg forall_tvs dicts lie `thenM` \ inst_binds ->
522 zonkTcTyVars forall_tvs `thenM` \ forall_tys ->
523 traceTc (text "tcGen" <+> vcat [text "extra_tvs" <+> ppr extra_tvs,
524 text "expected_ty" <+> ppr expected_ty,
525 text "inst ty" <+> ppr forall_tvs <+> ppr theta <+> ppr phi_ty,
526 text "free_tvs" <+> ppr free_tvs,
527 text "forall_tys" <+> ppr forall_tys]) `thenM_`
530 checkSigTyVarsWrt free_tvs forall_tvs `thenM` \ zonked_tvs ->
532 traceTc (text "tcGen:done") `thenM_`
535 -- This HsLet binds any Insts which came out of the simplification.
536 -- It's a bit out of place here, but using AbsBind involves inventing
537 -- a couple of new names which seems worse.
538 dict_ids = map instToId dicts
539 co_fn e = TyLam zonked_tvs (DictLam dict_ids (mkHsLet inst_binds e))
541 returnM (mkCoercion co_fn, result)
543 free_tvs = tyVarsOfType expected_ty `unionVarSet` extra_tvs
544 sig_msg = ptext SLIT("expected type of an expression")
549 %************************************************************************
551 \subsection[Unify-exported]{Exported unification functions}
553 %************************************************************************
555 The exported functions are all defined as versions of some
556 non-exported generic functions.
558 Unify two @TauType@s. Dead straightforward.
561 unifyTauTy :: TcTauType -> TcTauType -> TcM ()
562 unifyTauTy ty1 ty2 -- ty1 expected, ty2 inferred
563 = -- The unifier should only ever see tau-types
564 -- (no quantification whatsoever)
565 ASSERT2( isTauTy ty1, ppr ty1 )
566 ASSERT2( isTauTy ty2, ppr ty2 )
567 addErrCtxtM (unifyCtxt "type" ty1 ty2) $
571 @unifyTauTyList@ unifies corresponding elements of two lists of
572 @TauType@s. It uses @uTys@ to do the real work. The lists should be
573 of equal length. We charge down the list explicitly so that we can
574 complain if their lengths differ.
577 unifyTauTyLists :: [TcTauType] -> [TcTauType] -> TcM ()
578 unifyTauTyLists [] [] = returnM ()
579 unifyTauTyLists (ty1:tys1) (ty2:tys2) = uTys ty1 ty1 ty2 ty2 `thenM_`
580 unifyTauTyLists tys1 tys2
581 unifyTauTyLists ty1s ty2s = panic "Unify.unifyTauTyLists: mismatched type lists!"
584 @unifyTauTyList@ takes a single list of @TauType@s and unifies them
585 all together. It is used, for example, when typechecking explicit
586 lists, when all the elts should be of the same type.
589 unifyTauTyList :: [TcTauType] -> TcM ()
590 unifyTauTyList [] = returnM ()
591 unifyTauTyList [ty] = returnM ()
592 unifyTauTyList (ty1:tys@(ty2:_)) = unifyTauTy ty1 ty2 `thenM_`
596 %************************************************************************
598 \subsection[Unify-uTys]{@uTys@: getting down to business}
600 %************************************************************************
602 @uTys@ is the heart of the unifier. Each arg happens twice, because
603 we want to report errors in terms of synomyms if poss. The first of
604 the pair is used in error messages only; it is always the same as the
605 second, except that if the first is a synonym then the second may be a
606 de-synonym'd version. This way we get better error messages.
608 We call the first one \tr{ps_ty1}, \tr{ps_ty2} for ``possible synomym''.
611 uTys :: TcTauType -> TcTauType -- Error reporting ty1 and real ty1
612 -- ty1 is the *expected* type
614 -> TcTauType -> TcTauType -- Error reporting ty2 and real ty2
615 -- ty2 is the *actual* type
618 -- Always expand synonyms (see notes at end)
619 -- (this also throws away FTVs)
620 uTys ps_ty1 (NoteTy n1 ty1) ps_ty2 ty2 = uTys ps_ty1 ty1 ps_ty2 ty2
621 uTys ps_ty1 ty1 ps_ty2 (NoteTy n2 ty2) = uTys ps_ty1 ty1 ps_ty2 ty2
623 -- Variables; go for uVar
624 uTys ps_ty1 (TyVarTy tyvar1) ps_ty2 ty2 = uVar False tyvar1 ps_ty2 ty2
625 uTys ps_ty1 ty1 ps_ty2 (TyVarTy tyvar2) = uVar True tyvar2 ps_ty1 ty1
626 -- "True" means args swapped
629 uTys _ (SourceTy (IParam n1 t1)) _ (SourceTy (IParam n2 t2))
630 | n1 == n2 = uTys t1 t1 t2 t2
631 uTys _ (SourceTy (ClassP c1 tys1)) _ (SourceTy (ClassP c2 tys2))
632 | c1 == c2 = unifyTauTyLists tys1 tys2
633 uTys _ (SourceTy (NType tc1 tys1)) _ (SourceTy (NType tc2 tys2))
634 | tc1 == tc2 = unifyTauTyLists tys1 tys2
636 -- Functions; just check the two parts
637 uTys _ (FunTy fun1 arg1) _ (FunTy fun2 arg2)
638 = uTys fun1 fun1 fun2 fun2 `thenM_` uTys arg1 arg1 arg2 arg2
640 -- Type constructors must match
641 uTys ps_ty1 (TyConApp con1 tys1) ps_ty2 (TyConApp con2 tys2)
642 | con1 == con2 && equalLength tys1 tys2
643 = unifyTauTyLists tys1 tys2
645 | con1 == openKindCon
646 -- When we are doing kind checking, we might match a kind '?'
647 -- against a kind '*' or '#'. Notably, CCallable :: ? -> *, and
648 -- (CCallable Int) and (CCallable Int#) are both OK
649 = unifyOpenTypeKind ps_ty2
651 -- Applications need a bit of care!
652 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
653 -- NB: we've already dealt with type variables and Notes,
654 -- so if one type is an App the other one jolly well better be too
655 uTys ps_ty1 (AppTy s1 t1) ps_ty2 ty2
656 = case tcSplitAppTy_maybe ty2 of
657 Just (s2,t2) -> uTys s1 s1 s2 s2 `thenM_` uTys t1 t1 t2 t2
658 Nothing -> unifyMisMatch ps_ty1 ps_ty2
660 -- Now the same, but the other way round
661 -- Don't swap the types, because the error messages get worse
662 uTys ps_ty1 ty1 ps_ty2 (AppTy s2 t2)
663 = case tcSplitAppTy_maybe ty1 of
664 Just (s1,t1) -> uTys s1 s1 s2 s2 `thenM_` uTys t1 t1 t2 t2
665 Nothing -> unifyMisMatch ps_ty1 ps_ty2
667 -- Not expecting for-alls in unification
668 -- ... but the error message from the unifyMisMatch more informative
669 -- than a panic message!
671 -- Anything else fails
672 uTys ps_ty1 ty1 ps_ty2 ty2 = unifyMisMatch ps_ty1 ps_ty2
678 If you are tempted to make a short cut on synonyms, as in this
682 -- NO uTys (SynTy con1 args1 ty1) (SynTy con2 args2 ty2)
683 -- NO = if (con1 == con2) then
684 -- NO -- Good news! Same synonym constructors, so we can shortcut
685 -- NO -- by unifying their arguments and ignoring their expansions.
686 -- NO unifyTauTypeLists args1 args2
688 -- NO -- Never mind. Just expand them and try again
692 then THINK AGAIN. Here is the whole story, as detected and reported
693 by Chris Okasaki \tr{<Chris_Okasaki@loch.mess.cs.cmu.edu>}:
695 Here's a test program that should detect the problem:
699 x = (1 :: Bogus Char) :: Bogus Bool
702 The problem with [the attempted shortcut code] is that
706 is not a sufficient condition to be able to use the shortcut!
707 You also need to know that the type synonym actually USES all
708 its arguments. For example, consider the following type synonym
709 which does not use all its arguments.
714 If you ever tried unifying, say, \tr{Bogus Char} with \tr{Bogus Bool},
715 the unifier would blithely try to unify \tr{Char} with \tr{Bool} and
716 would fail, even though the expanded forms (both \tr{Int}) should
719 Similarly, unifying \tr{Bogus Char} with \tr{Bogus t} would
720 unnecessarily bind \tr{t} to \tr{Char}.
722 ... You could explicitly test for the problem synonyms and mark them
723 somehow as needing expansion, perhaps also issuing a warning to the
728 %************************************************************************
730 \subsection[Unify-uVar]{@uVar@: unifying with a type variable}
732 %************************************************************************
734 @uVar@ is called when at least one of the types being unified is a
735 variable. It does {\em not} assume that the variable is a fixed point
736 of the substitution; rather, notice that @uVar@ (defined below) nips
737 back into @uTys@ if it turns out that the variable is already bound.
740 uVar :: Bool -- False => tyvar is the "expected"
741 -- True => ty is the "expected" thing
743 -> TcTauType -> TcTauType -- printing and real versions
746 uVar swapped tv1 ps_ty2 ty2
747 = traceTc (text "uVar" <+> ppr swapped <+> ppr tv1 <+> (ppr ps_ty2 $$ ppr ty2)) `thenM_`
748 getTcTyVar tv1 `thenM` \ maybe_ty1 ->
750 Just ty1 | swapped -> uTys ps_ty2 ty2 ty1 ty1 -- Swap back
751 | otherwise -> uTys ty1 ty1 ps_ty2 ty2 -- Same order
752 other -> uUnboundVar swapped tv1 maybe_ty1 ps_ty2 ty2
754 -- Expand synonyms; ignore FTVs
755 uUnboundVar swapped tv1 maybe_ty1 ps_ty2 (NoteTy n2 ty2)
756 = uUnboundVar swapped tv1 maybe_ty1 ps_ty2 ty2
759 -- The both-type-variable case
760 uUnboundVar swapped tv1 maybe_ty1 ps_ty2 ty2@(TyVarTy tv2)
762 -- Same type variable => no-op
766 -- Distinct type variables
767 -- ASSERT maybe_ty1 /= Just
769 = getTcTyVar tv2 `thenM` \ maybe_ty2 ->
771 Just ty2' -> uUnboundVar swapped tv1 maybe_ty1 ty2' ty2'
775 -> WARN( not (k1 `hasMoreBoxityInfo` k2), (ppr tv1 <+> ppr k1) $$ (ppr tv2 <+> ppr k2) )
776 putTcTyVar tv2 (TyVarTy tv1) `thenM_`
780 -> WARN( not (k2 `hasMoreBoxityInfo` k1), (ppr tv2 <+> ppr k2) $$ (ppr tv1 <+> ppr k1) )
781 putTcTyVar tv1 ps_ty2 `thenM_`
786 update_tv2 = (k2 `eqKind` openTypeKind) || (not (k1 `eqKind` openTypeKind) && nicer_to_update_tv2)
787 -- Try to get rid of open type variables as soon as poss
789 nicer_to_update_tv2 = isUserTyVar tv1
790 -- Don't unify a signature type variable if poss
791 || isSystemName (varName tv2)
792 -- Try to update sys-y type variables in preference to sig-y ones
794 -- Second one isn't a type variable
795 uUnboundVar swapped tv1 maybe_ty1 ps_ty2 non_var_ty2
796 = -- Check that tv1 isn't a type-signature type variable
797 checkM (not (isSkolemTyVar tv1))
798 (failWithTcM (unifyWithSigErr tv1 ps_ty2)) `thenM_`
800 -- Do the occurs check, and check that we are not
801 -- unifying a type variable with a polytype
802 -- Returns a zonked type ready for the update
803 checkValue tv1 ps_ty2 non_var_ty2 `thenM` \ ty2 ->
805 -- Check that the kinds match
806 checkKinds swapped tv1 ty2 `thenM_`
808 -- Perform the update
809 putTcTyVar tv1 ty2 `thenM_`
814 checkKinds swapped tv1 ty2
815 -- We're about to unify a type variable tv1 with a non-tyvar-type ty2.
816 -- ty2 has been zonked at this stage, which ensures that
817 -- its kind has as much boxity information visible as possible.
818 | tk2 `hasMoreBoxityInfo` tk1 = returnM ()
821 -- Either the kinds aren't compatible
822 -- (can happen if we unify (a b) with (c d))
823 -- or we are unifying a lifted type variable with an
824 -- unlifted type: e.g. (id 3#) is illegal
825 = addErrCtxtM (unifyKindCtxt swapped tv1 ty2) $
829 (k1,k2) | swapped = (tk2,tk1)
830 | otherwise = (tk1,tk2)
836 checkValue tv1 ps_ty2 non_var_ty2
837 -- Do the occurs check, and check that we are not
838 -- unifying a type variable with a polytype
839 -- Return the type to update the type variable with, or fail
841 -- Basically we want to update tv1 := ps_ty2
842 -- because ps_ty2 has type-synonym info, which improves later error messages
847 -- f :: (A a -> a -> ()) -> ()
851 -- x = f (\ x p -> p x)
853 -- In the application (p x), we try to match "t" with "A t". If we go
854 -- ahead and bind t to A t (= ps_ty2), we'll lead the type checker into
855 -- an infinite loop later.
856 -- But we should not reject the program, because A t = ().
857 -- Rather, we should bind t to () (= non_var_ty2).
859 -- That's why we have this two-state occurs-check
860 = zonkTcType ps_ty2 `thenM` \ ps_ty2' ->
861 case okToUnifyWith tv1 ps_ty2' of {
862 Nothing -> returnM ps_ty2' ; -- Success
865 zonkTcType non_var_ty2 `thenM` \ non_var_ty2' ->
866 case okToUnifyWith tv1 non_var_ty2' of
867 Nothing -> -- This branch rarely succeeds, except in strange cases
868 -- like that in the example above
871 Just problem -> failWithTcM (unifyCheck problem tv1 ps_ty2')
874 data Problem = OccurCheck | NotMonoType
876 okToUnifyWith :: TcTyVar -> TcType -> Maybe Problem
877 -- (okToUnifyWith tv ty) checks whether it's ok to unify
880 -- Just p => not ok, problem p
885 ok (TyVarTy tv') | tv == tv' = Just OccurCheck
886 | otherwise = Nothing
887 ok (AppTy t1 t2) = ok t1 `and` ok t2
888 ok (FunTy t1 t2) = ok t1 `and` ok t2
889 ok (TyConApp _ ts) = oks ts
890 ok (ForAllTy _ _) = Just NotMonoType
891 ok (SourceTy st) = ok_st st
892 ok (NoteTy (FTVNote _) t) = ok t
893 ok (NoteTy (SynNote t1) t2) = ok t1 `and` ok t2
894 -- Type variables may be free in t1 but not t2
895 -- A forall may be in t2 but not t1
897 oks ts = foldr (and . ok) Nothing ts
899 ok_st (ClassP _ ts) = oks ts
900 ok_st (IParam _ t) = ok t
901 ok_st (NType _ ts) = oks ts
904 Just p `and` m = Just p
907 %************************************************************************
909 \subsection{Kind unification}
911 %************************************************************************
914 unifyKind :: TcKind -- Expected
917 unifyKind k1 k2 = uTys k1 k1 k2 k2
919 unifyKinds :: [TcKind] -> [TcKind] -> TcM ()
920 unifyKinds [] [] = returnM ()
921 unifyKinds (k1:ks1) (k2:ks2) = unifyKind k1 k2 `thenM_`
923 unifyKinds _ _ = panic "unifyKinds: length mis-match"
927 unifyOpenTypeKind :: TcKind -> TcM ()
928 -- Ensures that the argument kind is of the form (Type bx)
929 -- for some boxity bx
931 unifyOpenTypeKind ty@(TyVarTy tyvar)
932 = getTcTyVar tyvar `thenM` \ maybe_ty ->
934 Just ty' -> unifyOpenTypeKind ty'
935 other -> unify_open_kind_help ty
938 | isTypeKind ty = returnM ()
939 | otherwise = unify_open_kind_help ty
941 unify_open_kind_help ty -- Revert to ordinary unification
942 = newOpenTypeKind `thenM` \ open_kind ->
943 unifyKind ty open_kind
947 unifyFunKind :: TcKind -> TcM (Maybe (TcKind, TcKind))
948 -- Like unifyFunTy, but does not fail; instead just returns Nothing
950 unifyFunKind (TyVarTy tyvar)
951 = getTcTyVar tyvar `thenM` \ maybe_ty ->
953 Just fun_kind -> unifyFunKind fun_kind
954 Nothing -> newKindVar `thenM` \ arg_kind ->
955 newKindVar `thenM` \ res_kind ->
956 putTcTyVar tyvar (mkArrowKind arg_kind res_kind) `thenM_`
957 returnM (Just (arg_kind,res_kind))
959 unifyFunKind (FunTy arg_kind res_kind) = returnM (Just (arg_kind,res_kind))
960 unifyFunKind (NoteTy _ ty) = unifyFunKind ty
961 unifyFunKind other = returnM Nothing
964 %************************************************************************
966 \subsection[Unify-context]{Errors and contexts}
968 %************************************************************************
974 unifyCtxt s ty1 ty2 tidy_env -- ty1 expected, ty2 inferred
975 = zonkTcType ty1 `thenM` \ ty1' ->
976 zonkTcType ty2 `thenM` \ ty2' ->
977 returnM (err ty1' ty2')
982 text "Expected" <+> text s <> colon <+> ppr tidy_ty1,
983 text "Inferred" <+> text s <> colon <+> ppr tidy_ty2
986 (env1, [tidy_ty1,tidy_ty2]) = tidyOpenTypes tidy_env [ty1,ty2]
988 unifyKindCtxt swapped tv1 ty2 tidy_env -- not swapped => tv1 expected, ty2 inferred
989 -- tv1 is zonked already
990 = zonkTcType ty2 `thenM` \ ty2' ->
993 err ty2 = (env2, ptext SLIT("When matching types") <+>
994 sep [quotes pp_expected, ptext SLIT("and"), quotes pp_actual])
996 (pp_expected, pp_actual) | swapped = (pp2, pp1)
997 | otherwise = (pp1, pp2)
998 (env1, tv1') = tidyOpenTyVar tidy_env tv1
999 (env2, ty2') = tidyOpenType env1 ty2
1003 unifyMisMatch ty1 ty2
1004 = zonkTcType ty1 `thenM` \ ty1' ->
1005 zonkTcType ty2 `thenM` \ ty2' ->
1007 (env, [tidy_ty1, tidy_ty2]) = tidyOpenTypes emptyTidyEnv [ty1',ty2']
1008 msg = hang (ptext SLIT("Couldn't match"))
1009 4 (sep [quotes (ppr tidy_ty1),
1010 ptext SLIT("against"),
1011 quotes (ppr tidy_ty2)])
1013 failWithTcM (env, msg)
1015 unifyWithSigErr tyvar ty
1016 = (env2, hang (ptext SLIT("Cannot unify the type-signature variable") <+> quotes (ppr tidy_tyvar))
1017 4 (ptext SLIT("with the type") <+> quotes (ppr tidy_ty)))
1019 (env1, tidy_tyvar) = tidyOpenTyVar emptyTidyEnv tyvar
1020 (env2, tidy_ty) = tidyOpenType env1 ty
1022 unifyCheck problem tyvar ty
1024 4 (sep [ppr tidy_tyvar, char '=', ppr tidy_ty]))
1026 (env1, tidy_tyvar) = tidyOpenTyVar emptyTidyEnv tyvar
1027 (env2, tidy_ty) = tidyOpenType env1 ty
1029 msg = case problem of
1030 OccurCheck -> ptext SLIT("Occurs check: cannot construct the infinite type:")
1031 NotMonoType -> ptext SLIT("Cannot unify a type variable with a type scheme:")
1036 %************************************************************************
1038 \subsection{Checking signature type variables}
1040 %************************************************************************
1042 @checkSigTyVars@ is used after the type in a type signature has been unified with
1043 the actual type found. It then checks that the type variables of the type signature
1045 (a) Still all type variables
1046 eg matching signature [a] against inferred type [(p,q)]
1047 [then a will be unified to a non-type variable]
1049 (b) Still all distinct
1050 eg matching signature [(a,b)] against inferred type [(p,p)]
1051 [then a and b will be unified together]
1053 (c) Not mentioned in the environment
1054 eg the signature for f in this:
1060 Here, f is forced to be monorphic by the free occurence of x.
1062 (d) Not (unified with another type variable that is) in scope.
1063 eg f x :: (r->r) = (\y->y) :: forall a. a->r
1064 when checking the expression type signature, we find that
1065 even though there is nothing in scope whose type mentions r,
1066 nevertheless the type signature for the expression isn't right.
1068 Another example is in a class or instance declaration:
1070 op :: forall b. a -> b
1072 Here, b gets unified with a
1074 Before doing this, the substitution is applied to the signature type variable.
1076 We used to have the notion of a "DontBind" type variable, which would
1077 only be bound to itself or nothing. Then points (a) and (b) were
1078 self-checking. But it gave rise to bogus consequential error messages.
1081 f = (*) -- Monomorphic
1083 g :: Num a => a -> a
1086 Here, we get a complaint when checking the type signature for g,
1087 that g isn't polymorphic enough; but then we get another one when
1088 dealing with the (Num x) context arising from f's definition;
1089 we try to unify x with Int (to default it), but find that x has already
1090 been unified with the DontBind variable "a" from g's signature.
1091 This is really a problem with side-effecting unification; we'd like to
1092 undo g's effects when its type signature fails, but unification is done
1093 by side effect, so we can't (easily).
1095 So we revert to ordinary type variables for signatures, and try to
1096 give a helpful message in checkSigTyVars.
1099 checkSigTyVars :: [TcTyVar] -> TcM [TcTyVar]
1100 checkSigTyVars sig_tvs = check_sig_tyvars emptyVarSet sig_tvs
1102 checkSigTyVarsWrt :: TcTyVarSet -> [TcTyVar] -> TcM [TcTyVar]
1103 checkSigTyVarsWrt extra_tvs sig_tvs
1104 = zonkTcTyVarsAndFV (varSetElems extra_tvs) `thenM` \ extra_tvs' ->
1105 check_sig_tyvars extra_tvs' sig_tvs
1108 :: TcTyVarSet -- Global type variables. The universally quantified
1109 -- tyvars should not mention any of these
1110 -- Guaranteed already zonked.
1111 -> [TcTyVar] -- Universally-quantified type variables in the signature
1112 -- Not guaranteed zonked.
1113 -> TcM [TcTyVar] -- Zonked signature type variables
1115 check_sig_tyvars extra_tvs []
1117 check_sig_tyvars extra_tvs sig_tvs
1118 = zonkTcTyVars sig_tvs `thenM` \ sig_tys ->
1119 tcGetGlobalTyVars `thenM` \ gbl_tvs ->
1121 env_tvs = gbl_tvs `unionVarSet` extra_tvs
1123 traceTc (text "check_sig_tyvars" <+> (vcat [text "sig_tys" <+> ppr sig_tys,
1124 text "gbl_tvs" <+> ppr gbl_tvs,
1125 text "extra_tvs" <+> ppr extra_tvs])) `thenM_`
1127 checkM (allDistinctTyVars sig_tys env_tvs)
1128 (complain sig_tys env_tvs) `thenM_`
1130 returnM (map (tcGetTyVar "checkSigTyVars") sig_tys)
1133 complain sig_tys globals
1134 = -- "check" checks each sig tyvar in turn
1136 (env2, emptyVarEnv, [])
1137 (tidy_tvs `zip` tidy_tys) `thenM` \ (env3, _, msgs) ->
1139 failWithTcM (env3, main_msg $$ nest 4 (vcat msgs))
1141 (env1, tidy_tvs) = tidyOpenTyVars emptyTidyEnv sig_tvs
1142 (env2, tidy_tys) = tidyOpenTypes env1 sig_tys
1144 main_msg = ptext SLIT("Inferred type is less polymorphic than expected")
1146 check (tidy_env, acc, msgs) (sig_tyvar,ty)
1147 -- sig_tyvar is from the signature;
1148 -- ty is what you get if you zonk sig_tyvar and then tidy it
1150 -- acc maps a zonked type variable back to a signature type variable
1151 = case tcGetTyVar_maybe ty of {
1152 Nothing -> -- Error (a)!
1153 returnM (tidy_env, acc, unify_msg sig_tyvar (quotes (ppr ty)) : msgs) ;
1157 case lookupVarEnv acc tv of {
1158 Just sig_tyvar' -> -- Error (b)!
1159 returnM (tidy_env, acc, unify_msg sig_tyvar thing : msgs)
1161 thing = ptext SLIT("another quantified type variable") <+> quotes (ppr sig_tyvar')
1165 if tv `elemVarSet` globals -- Error (c) or (d)! Type variable escapes
1166 -- The least comprehensible, so put it last
1168 -- get the local TcIds and TyVars from the environment,
1169 -- and pass them to find_globals (they might have tv free)
1170 then findGlobals (unitVarSet tv) tidy_env `thenM` \ (tidy_env1, globs) ->
1171 returnM (tidy_env1, acc, escape_msg sig_tyvar tv globs : msgs)
1174 returnM (tidy_env, extendVarEnv acc tv sig_tyvar, msgs)
1180 -----------------------
1181 escape_msg sig_tv tv globs
1182 = mk_msg sig_tv <+> ptext SLIT("escapes") $$
1183 if notNull globs then
1184 vcat [pp_it <+> ptext SLIT("is mentioned in the environment:"),
1185 nest 2 (vcat globs)]
1187 empty -- Sigh. It's really hard to give a good error message
1188 -- all the time. One bad case is an existential pattern match.
1189 -- We rely on the "When..." context to help.
1191 pp_it | sig_tv /= tv = ptext SLIT("It unifies with") <+> quotes (ppr tv) <> comma <+> ptext SLIT("which")
1192 | otherwise = ptext SLIT("It")
1195 unify_msg tv thing = mk_msg tv <+> ptext SLIT("is unified with") <+> thing
1196 mk_msg tv = ptext SLIT("Quantified type variable") <+> quotes (ppr tv)
1199 These two context are used with checkSigTyVars
1202 sigCtxt :: Id -> [TcTyVar] -> TcThetaType -> TcTauType
1203 -> TidyEnv -> TcM (TidyEnv, Message)
1204 sigCtxt id sig_tvs sig_theta sig_tau tidy_env
1205 = zonkTcType sig_tau `thenM` \ actual_tau ->
1207 (env1, tidy_sig_tvs) = tidyOpenTyVars tidy_env sig_tvs
1208 (env2, tidy_sig_rho) = tidyOpenType env1 (mkPhiTy sig_theta sig_tau)
1209 (env3, tidy_actual_tau) = tidyOpenType env2 actual_tau
1210 sub_msg = vcat [ptext SLIT("Signature type: ") <+> pprType (mkForAllTys tidy_sig_tvs tidy_sig_rho),
1211 ptext SLIT("Type to generalise:") <+> pprType tidy_actual_tau
1213 msg = vcat [ptext SLIT("When trying to generalise the type inferred for") <+> quotes (ppr id),