-- (c) The University of Glasgow 2006 -- -- FamInstEnv: Type checked family instance declarations {-# LANGUAGE CPP, GADTs, ScopedTypeVariables #-} module FamInstEnv ( FamInst(..), FamFlavor(..), famInstAxiom, famInstTyCon, famInstRHS, famInstsRepTyCons, famInstRepTyCon_maybe, dataFamInstRepTyCon, pprFamInst, pprFamInsts, mkImportedFamInst, FamInstEnvs, FamInstEnv, emptyFamInstEnv, emptyFamInstEnvs, extendFamInstEnv, deleteFromFamInstEnv, extendFamInstEnvList, identicalFamInstHead, famInstEnvElts, familyInstances, orphNamesOfFamInst, -- * CoAxioms mkCoAxBranch, mkBranchedCoAxiom, mkUnbranchedCoAxiom, mkSingleCoAxiom, computeAxiomIncomps, FamInstMatch(..), lookupFamInstEnv, lookupFamInstEnvConflicts, isDominatedBy, -- Normalisation topNormaliseType, topNormaliseType_maybe, normaliseType, normaliseTcApp, reduceTyFamApp_maybe, chooseBranch, -- Flattening flattenTys ) where #include "HsVersions.h" import InstEnv import Unify import Type import TcType ( orphNamesOfTypes ) import TypeRep import TyCon import Coercion import CoAxiom import VarSet import VarEnv import Name import UniqFM import Outputable import Maybes import TrieMap import Unique import Util import Var import Pair import SrcLoc import NameSet import FastString {- ************************************************************************ * * Type checked family instance heads * * ************************************************************************ Note [FamInsts and CoAxioms] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ * CoAxioms and FamInsts are just like DFunIds and ClsInsts * A CoAxiom is a System-FC thing: it can relate any two types * A FamInst is a Haskell source-language thing, corresponding to a type/data family instance declaration. - The FamInst contains a CoAxiom, which is the evidence for the instance - The LHS of the CoAxiom is always of form F ty1 .. tyn where F is a type family -} data FamInst -- See Note [FamInsts and CoAxioms] = FamInst { fi_axiom :: CoAxiom Unbranched -- The new coercion axiom introduced -- by this family instance , fi_flavor :: FamFlavor -- Everything below here is a redundant, -- cached version of the two things above -- except that the TyVars are freshened , fi_fam :: Name -- Family name -- Used for "rough matching"; same idea as for class instances -- See Note [Rough-match field] in InstEnv , fi_tcs :: [Maybe Name] -- Top of type args -- INVARIANT: fi_tcs = roughMatchTcs fi_tys -- Used for "proper matching"; ditto , fi_tvs :: [TyVar] -- Template tyvars for full match -- Like ClsInsts, these variables are always -- fresh. See Note [Template tyvars are fresh] -- in InstEnv , fi_tys :: [Type] -- and its arg types -- INVARIANT: fi_tvs = coAxiomTyVars fi_axiom , fi_rhs :: Type -- the RHS, with its freshened vars } data FamFlavor = SynFamilyInst -- A synonym family | DataFamilyInst TyCon -- A data family, with its representation TyCon -- Obtain the axiom of a family instance famInstAxiom :: FamInst -> CoAxiom Unbranched famInstAxiom = fi_axiom -- Split the left-hand side of the FamInst famInstSplitLHS :: FamInst -> (TyCon, [Type]) famInstSplitLHS (FamInst { fi_axiom = axiom, fi_tys = lhs }) = (coAxiomTyCon axiom, lhs) -- Get the RHS of the FamInst famInstRHS :: FamInst -> Type famInstRHS = fi_rhs -- Get the family TyCon of the FamInst famInstTyCon :: FamInst -> TyCon famInstTyCon = coAxiomTyCon . famInstAxiom -- Return the representation TyCons introduced by data family instances, if any famInstsRepTyCons :: [FamInst] -> [TyCon] famInstsRepTyCons fis = [tc | FamInst { fi_flavor = DataFamilyInst tc } <- fis] -- Extracts the TyCon for this *data* (or newtype) instance famInstRepTyCon_maybe :: FamInst -> Maybe TyCon famInstRepTyCon_maybe fi = case fi_flavor fi of DataFamilyInst tycon -> Just tycon SynFamilyInst -> Nothing dataFamInstRepTyCon :: FamInst -> TyCon dataFamInstRepTyCon fi = case fi_flavor fi of DataFamilyInst tycon -> tycon SynFamilyInst -> pprPanic "dataFamInstRepTyCon" (ppr fi) {- ************************************************************************ * * Pretty printing * * ************************************************************************ -} instance NamedThing FamInst where getName = coAxiomName . fi_axiom instance Outputable FamInst where ppr = pprFamInst -- Prints the FamInst as a family instance declaration -- NB: FamInstEnv.pprFamInst is used only for internal, debug printing -- See pprTyThing.pprFamInst for printing for the user pprFamInst :: FamInst -> SDoc pprFamInst famInst = hang (pprFamInstHdr famInst) 2 (vcat [ ifPprDebug (ptext (sLit "Coercion axiom:") <+> ppr ax) , ifPprDebug (ptext (sLit "RHS:") <+> ppr (famInstRHS famInst)) ]) where ax = fi_axiom famInst pprFamInstHdr :: FamInst -> SDoc pprFamInstHdr fi@(FamInst {fi_flavor = flavor}) = pprTyConSort <+> pp_instance <+> pp_head where -- For *associated* types, say "type T Int = blah" -- For *top level* type instances, say "type instance T Int = blah" pp_instance | isTyConAssoc fam_tc = empty | otherwise = ptext (sLit "instance") (fam_tc, etad_lhs_tys) = famInstSplitLHS fi vanilla_pp_head = pprTypeApp fam_tc etad_lhs_tys pp_head | DataFamilyInst rep_tc <- flavor , isAlgTyCon rep_tc , let extra_tvs = dropList etad_lhs_tys (tyConTyVars rep_tc) , not (null extra_tvs) = getPprStyle $ \ sty -> if debugStyle sty then vanilla_pp_head -- With -dppr-debug just show it as-is else pprTypeApp fam_tc (etad_lhs_tys ++ mkTyVarTys extra_tvs) -- Without -dppr-debug, eta-expand -- See Trac #8674 -- (This is probably over the top now that we use this -- only for internal debug printing; PprTyThing.pprFamInst -- is used for user-level printing.) | otherwise = vanilla_pp_head pprTyConSort = case flavor of SynFamilyInst -> ptext (sLit "type") DataFamilyInst tycon | isDataTyCon tycon -> ptext (sLit "data") | isNewTyCon tycon -> ptext (sLit "newtype") | isAbstractTyCon tycon -> ptext (sLit "data") | otherwise -> ptext (sLit "WEIRD") <+> ppr tycon pprFamInsts :: [FamInst] -> SDoc pprFamInsts finsts = vcat (map pprFamInst finsts) {- Note [Lazy axiom match] ~~~~~~~~~~~~~~~~~~~~~~~ It is Vitally Important that mkImportedFamInst is *lazy* in its axiom parameter. The axiom is loaded lazily, via a forkM, in TcIface. Sometime later, mkImportedFamInst is called using that axiom. However, the axiom may itself depend on entities which are not yet loaded as of the time of the mkImportedFamInst. Thus, if mkImportedFamInst eagerly looks at the axiom, a dependency loop spontaneously appears and GHC hangs. The solution is simply for mkImportedFamInst never, ever to look inside of the axiom until everything else is good and ready to do so. We can assume that this readiness has been achieved when some other code pulls on the axiom in the FamInst. Thus, we pattern match on the axiom lazily (in the where clause, not in the parameter list) and we assert the consistency of names there also. -} -- Make a family instance representation from the information found in an -- interface file. In particular, we get the rough match info from the iface -- (instead of computing it here). mkImportedFamInst :: Name -- Name of the family -> [Maybe Name] -- Rough match info -> CoAxiom Unbranched -- Axiom introduced -> FamInst -- Resulting family instance mkImportedFamInst fam mb_tcs axiom = FamInst { fi_fam = fam, fi_tcs = mb_tcs, fi_tvs = tvs, fi_tys = tys, fi_rhs = rhs, fi_axiom = axiom, fi_flavor = flavor } where -- See Note [Lazy axiom match] ~(CoAxiom { co_ax_branches = ~(FirstBranch ~(CoAxBranch { cab_lhs = tys , cab_tvs = tvs , cab_rhs = rhs })) }) = axiom -- Derive the flavor for an imported FamInst rather disgustingly -- Maybe we should store it in the IfaceFamInst? flavor = case splitTyConApp_maybe rhs of Just (tc, _) | Just ax' <- tyConFamilyCoercion_maybe tc , ax' == axiom -> DataFamilyInst tc _ -> SynFamilyInst {- ************************************************************************ * * FamInstEnv * * ************************************************************************ Note [FamInstEnv] ~~~~~~~~~~~~~~~~~ A FamInstEnv maps a family name to the list of known instances for that family. The same FamInstEnv includes both 'data family' and 'type family' instances. Type families are reduced during type inference, but not data families; the user explains when to use a data family instance by using contructors and pattern matching. Neverthless it is still useful to have data families in the FamInstEnv: - For finding overlaps and conflicts - For finding the representation type...see FamInstEnv.topNormaliseType and its call site in Simplify - In standalone deriving instance Eq (T [Int]) we need to find the representation type for T [Int] Note [Varying number of patterns for data family axioms] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ For data families, the number of patterns may vary between instances. For example data family T a b data instance T Int a = T1 a | T2 data instance T Bool [a] = T3 a Then we get a data type for each instance, and an axiom: data TInt a = T1 a | T2 data TBoolList a = T3 a axiom ax7 :: T Int ~ TInt -- Eta-reduced axiom ax8 a :: T Bool [a] ~ TBoolList a These two axioms for T, one with one pattern, one with two. The reason for this eta-reduction is decribed in TcInstDcls Note [Eta reduction for data family axioms] -} type FamInstEnv = UniqFM FamilyInstEnv -- Maps a family to its instances -- See Note [FamInstEnv] type FamInstEnvs = (FamInstEnv, FamInstEnv) -- External package inst-env, Home-package inst-env newtype FamilyInstEnv = FamIE [FamInst] -- The instances for a particular family, in any order instance Outputable FamilyInstEnv where ppr (FamIE fs) = ptext (sLit "FamIE") <+> vcat (map ppr fs) -- INVARIANTS: -- * The fs_tvs are distinct in each FamInst -- of a range value of the map (so we can safely unify them) emptyFamInstEnvs :: (FamInstEnv, FamInstEnv) emptyFamInstEnvs = (emptyFamInstEnv, emptyFamInstEnv) emptyFamInstEnv :: FamInstEnv emptyFamInstEnv = emptyUFM famInstEnvElts :: FamInstEnv -> [FamInst] famInstEnvElts fi = [elt | FamIE elts <- eltsUFM fi, elt <- elts] familyInstances :: (FamInstEnv, FamInstEnv) -> TyCon -> [FamInst] familyInstances (pkg_fie, home_fie) fam = get home_fie ++ get pkg_fie where get env = case lookupUFM env fam of Just (FamIE insts) -> insts Nothing -> [] -- | Collects the names of the concrete types and type constructors that -- make up the LHS of a type family instance, including the family -- name itself. -- -- For instance, given `type family Foo a b`: -- `type instance Foo (F (G (H a))) b = ...` would yield [Foo,F,G,H] -- -- Used in the implementation of ":info" in GHCi. orphNamesOfFamInst :: FamInst -> NameSet orphNamesOfFamInst fam_inst = orphNamesOfTypes (concat (brListMap cab_lhs (coAxiomBranches axiom))) `extendNameSet` getName (coAxiomTyCon axiom) where axiom = fi_axiom fam_inst extendFamInstEnvList :: FamInstEnv -> [FamInst] -> FamInstEnv extendFamInstEnvList inst_env fis = foldl extendFamInstEnv inst_env fis extendFamInstEnv :: FamInstEnv -> FamInst -> FamInstEnv extendFamInstEnv inst_env ins_item@(FamInst {fi_fam = cls_nm}) = addToUFM_C add inst_env cls_nm (FamIE [ins_item]) where add (FamIE items) _ = FamIE (ins_item:items) deleteFromFamInstEnv :: FamInstEnv -> FamInst -> FamInstEnv -- Used only for overriding in GHCi deleteFromFamInstEnv inst_env fam_inst@(FamInst {fi_fam = fam_nm}) = adjustUFM adjust inst_env fam_nm where adjust :: FamilyInstEnv -> FamilyInstEnv adjust (FamIE items) = FamIE (filterOut (identicalFamInstHead fam_inst) items) identicalFamInstHead :: FamInst -> FamInst -> Bool -- ^ True when the LHSs are identical -- Used for overriding in GHCi identicalFamInstHead (FamInst { fi_axiom = ax1 }) (FamInst { fi_axiom = ax2 }) = coAxiomTyCon ax1 == coAxiomTyCon ax2 && brListLength brs1 == brListLength brs2 && and (brListZipWith identical_branch brs1 brs2) where brs1 = coAxiomBranches ax1 brs2 = coAxiomBranches ax2 identical_branch br1 br2 = isJust (tcMatchTys tvs1 lhs1 lhs2) && isJust (tcMatchTys tvs2 lhs2 lhs1) where tvs1 = mkVarSet (coAxBranchTyVars br1) tvs2 = mkVarSet (coAxBranchTyVars br2) lhs1 = coAxBranchLHS br1 lhs2 = coAxBranchLHS br2 {- ************************************************************************ * * Compatibility * * ************************************************************************ Note [Apartness] ~~~~~~~~~~~~~~~~ In dealing with closed type families, we must be able to check that one type will never reduce to another. This check is called /apartness/. The check is always between a target (which may be an arbitrary type) and a pattern. Here is how we do it: apart(target, pattern) = not (unify(flatten(target), pattern)) where flatten (implemented in flattenTys, below) converts all type-family applications into fresh variables. (See Note [Flattening].) Note [Compatibility] ~~~~~~~~~~~~~~~~~~~~ Two patterns are /compatible/ if either of the following conditions hold: 1) The patterns are apart. 2) The patterns unify with a substitution S, and their right hand sides equal under that substitution. For open type families, only compatible instances are allowed. For closed type families, the story is slightly more complicated. Consider the following: type family F a where F Int = Bool F a = Int g :: Show a => a -> F a g x = length (show x) Should that type-check? No. We need to allow for the possibility that 'a' might be Int and therefore 'F a' should be Bool. We can simplify 'F a' to Int only when we can be sure that 'a' is not Int. To achieve this, after finding a possible match within the equations, we have to go back to all previous equations and check that, under the substitution induced by the match, other branches are surely apart. (See Note [Apartness].) This is similar to what happens with class instance selection, when we need to guarantee that there is only a match and no unifiers. The exact algorithm is different here because the the potentially-overlapping group is closed. As another example, consider this: type family G x type instance where G Int = Bool G a = Double type family H y -- no instances Now, we want to simplify (G (H Char)). We can't, because (H Char) might later simplify to be Int. So, (G (H Char)) is stuck, for now. While everything above is quite sound, it isn't as expressive as we'd like. Consider this: type family J a where J Int = Int J a = a Can we simplify (J b) to b? Sure we can. Yes, the first equation matches if b is instantiated with Int, but the RHSs coincide there, so it's all OK. So, the rule is this: when looking up a branch in a closed type family, we find a branch that matches the target, but then we make sure that the target is apart from every previous *incompatible* branch. We don't check the branches that are compatible with the matching branch, because they are either irrelevant (clause 1 of compatible) or benign (clause 2 of compatible). -} -- See Note [Compatibility] compatibleBranches :: CoAxBranch -> CoAxBranch -> Bool compatibleBranches (CoAxBranch { cab_lhs = lhs1, cab_rhs = rhs1 }) (CoAxBranch { cab_lhs = lhs2, cab_rhs = rhs2 }) = case tcUnifyTysFG instanceBindFun lhs1 lhs2 of SurelyApart -> True Unifiable subst | Type.substTy subst rhs1 `eqType` Type.substTy subst rhs2 -> True _ -> False -- takes a CoAxiom with unknown branch incompatibilities and computes -- the compatibilities -- See Note [Storing compatibility] in CoAxiom computeAxiomIncomps :: CoAxiom br -> CoAxiom br computeAxiomIncomps ax@(CoAxiom { co_ax_branches = branches }) = ax { co_ax_branches = go [] branches } where go :: [CoAxBranch] -> BranchList CoAxBranch br -> BranchList CoAxBranch br go prev_branches (FirstBranch br) = FirstBranch (br { cab_incomps = mk_incomps br prev_branches }) go prev_branches (NextBranch br tail) = let br' = br { cab_incomps = mk_incomps br prev_branches } in NextBranch br' (go (br' : prev_branches) tail) mk_incomps :: CoAxBranch -> [CoAxBranch] -> [CoAxBranch] mk_incomps br = filter (not . compatibleBranches br) {- ************************************************************************ * * Constructing axioms These functions are here because tidyType / tcUnifyTysFG are not available in CoAxiom * * ************************************************************************ Note [Tidy axioms when we build them] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We print out axioms and don't want to print stuff like F k k a b = ... Instead we must tidy those kind variables. See Trac #7524. -} -- all axiom roles are Nominal, as this is only used with type families mkCoAxBranch :: [TyVar] -- original, possibly stale, tyvars -> [Type] -- LHS patterns -> Type -- RHS -> SrcSpan -> CoAxBranch mkCoAxBranch tvs lhs rhs loc = CoAxBranch { cab_tvs = tvs1 , cab_lhs = tidyTypes env lhs , cab_roles = map (const Nominal) tvs1 , cab_rhs = tidyType env rhs , cab_loc = loc , cab_incomps = placeHolderIncomps } where (env, tvs1) = tidyTyVarBndrs emptyTidyEnv tvs -- See Note [Tidy axioms when we build them] -- all of the following code is here to avoid mutual dependencies with -- Coercion mkBranchedCoAxiom :: Name -> TyCon -> [CoAxBranch] -> CoAxiom Branched mkBranchedCoAxiom ax_name fam_tc branches = computeAxiomIncomps $ CoAxiom { co_ax_unique = nameUnique ax_name , co_ax_name = ax_name , co_ax_tc = fam_tc , co_ax_role = Nominal , co_ax_implicit = False , co_ax_branches = toBranchList branches } mkUnbranchedCoAxiom :: Name -> TyCon -> CoAxBranch -> CoAxiom Unbranched mkUnbranchedCoAxiom ax_name fam_tc branch = CoAxiom { co_ax_unique = nameUnique ax_name , co_ax_name = ax_name , co_ax_tc = fam_tc , co_ax_role = Nominal , co_ax_implicit = False , co_ax_branches = FirstBranch (branch { cab_incomps = [] }) } mkSingleCoAxiom :: Name -> [TyVar] -> TyCon -> [Type] -> Type -> CoAxiom Unbranched mkSingleCoAxiom ax_name tvs fam_tc lhs_tys rhs_ty = CoAxiom { co_ax_unique = nameUnique ax_name , co_ax_name = ax_name , co_ax_tc = fam_tc , co_ax_role = Nominal , co_ax_implicit = False , co_ax_branches = FirstBranch (branch { cab_incomps = [] }) } where branch = mkCoAxBranch tvs lhs_tys rhs_ty (getSrcSpan ax_name) {- ************************************************************************ * * Looking up a family instance * * ************************************************************************ @lookupFamInstEnv@ looks up in a @FamInstEnv@, using a one-way match. Multiple matches are only possible in case of type families (not data families), and then, it doesn't matter which match we choose (as the instances are guaranteed confluent). We return the matching family instances and the type instance at which it matches. For example, if we lookup 'T [Int]' and have a family instance data instance T [a] = .. desugared to data :R42T a = .. coe :Co:R42T a :: T [a] ~ :R42T a we return the matching instance '(FamInst{.., fi_tycon = :R42T}, Int)'. -} -- when matching a type family application, we get a FamInst, -- and the list of types the axiom should be applied to data FamInstMatch = FamInstMatch { fim_instance :: FamInst , fim_tys :: [Type] } -- See Note [Over-saturated matches] instance Outputable FamInstMatch where ppr (FamInstMatch { fim_instance = inst , fim_tys = tys }) = ptext (sLit "match with") <+> parens (ppr inst) <+> ppr tys lookupFamInstEnv :: FamInstEnvs -> TyCon -> [Type] -- What we are looking for -> [FamInstMatch] -- Successful matches -- Precondition: the tycon is saturated (or over-saturated) lookupFamInstEnv = lookup_fam_inst_env match where match _ tpl_tvs tpl_tys tys = tcMatchTys tpl_tvs tpl_tys tys lookupFamInstEnvConflicts :: FamInstEnvs -> FamInst -- Putative new instance -> [FamInstMatch] -- Conflicting matches (don't look at the fim_tys field) -- E.g. when we are about to add -- f : type instance F [a] = a->a -- we do (lookupFamInstConflicts f [b]) -- to find conflicting matches -- -- Precondition: the tycon is saturated (or over-saturated) lookupFamInstEnvConflicts envs fam_inst@(FamInst { fi_axiom = new_axiom }) = lookup_fam_inst_env my_unify envs fam tys where (fam, tys) = famInstSplitLHS fam_inst -- In example above, fam tys' = F [b] my_unify (FamInst { fi_axiom = old_axiom }) tpl_tvs tpl_tys _ = ASSERT2( tyVarsOfTypes tys `disjointVarSet` tpl_tvs, (ppr fam <+> ppr tys) $$ (ppr tpl_tvs <+> ppr tpl_tys) ) -- Unification will break badly if the variables overlap -- They shouldn't because we allocate separate uniques for them if compatibleBranches (coAxiomSingleBranch old_axiom) new_branch then Nothing else Just noSubst -- Note [Family instance overlap conflicts] noSubst = panic "lookupFamInstEnvConflicts noSubst" new_branch = coAxiomSingleBranch new_axiom {- Note [Family instance overlap conflicts] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - In the case of data family instances, any overlap is fundamentally a conflict (as these instances imply injective type mappings). - In the case of type family instances, overlap is admitted as long as the right-hand sides of the overlapping rules coincide under the overlap substitution. eg type instance F a Int = a type instance F Int b = b These two overlap on (F Int Int) but then both RHSs are Int, so all is well. We require that they are syntactically equal; anything else would be difficult to test for at this stage. -} ------------------------------------------------------------ -- Might be a one-way match or a unifier type MatchFun = FamInst -- The FamInst template -> TyVarSet -> [Type] -- fi_tvs, fi_tys of that FamInst -> [Type] -- Target to match against -> Maybe TvSubst lookup_fam_inst_env' -- The worker, local to this module :: MatchFun -> FamInstEnv -> TyCon -> [Type] -- What we are looking for -> [FamInstMatch] lookup_fam_inst_env' match_fun ie fam match_tys | isOpenFamilyTyCon fam , Just (FamIE insts) <- lookupUFM ie fam = find insts -- The common case | otherwise = [] where find [] = [] find (item@(FamInst { fi_tcs = mb_tcs, fi_tvs = tpl_tvs, fi_tys = tpl_tys }) : rest) -- Fast check for no match, uses the "rough match" fields | instanceCantMatch rough_tcs mb_tcs = find rest -- Proper check | Just subst <- match_fun item (mkVarSet tpl_tvs) tpl_tys match_tys1 = (FamInstMatch { fim_instance = item , fim_tys = substTyVars subst tpl_tvs `chkAppend` match_tys2 }) : find rest -- No match => try next | otherwise = find rest where (rough_tcs, match_tys1, match_tys2) = split_tys tpl_tys -- Precondition: the tycon is saturated (or over-saturated) -- Deal with over-saturation -- See Note [Over-saturated matches] split_tys tpl_tys | isTypeFamilyTyCon fam = pre_rough_split_tys | otherwise = let (match_tys1, match_tys2) = splitAtList tpl_tys match_tys rough_tcs = roughMatchTcs match_tys1 in (rough_tcs, match_tys1, match_tys2) (pre_match_tys1, pre_match_tys2) = splitAt (tyConArity fam) match_tys pre_rough_split_tys = (roughMatchTcs pre_match_tys1, pre_match_tys1, pre_match_tys2) lookup_fam_inst_env -- The worker, local to this module :: MatchFun -> FamInstEnvs -> TyCon -> [Type] -- What we are looking for -> [FamInstMatch] -- Successful matches -- Precondition: the tycon is saturated (or over-saturated) lookup_fam_inst_env match_fun (pkg_ie, home_ie) fam tys = lookup_fam_inst_env' match_fun home_ie fam tys ++ lookup_fam_inst_env' match_fun pkg_ie fam tys {- Note [Over-saturated matches] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It's ok to look up an over-saturated type constructor. E.g. type family F a :: * -> * type instance F (a,b) = Either (a->b) The type instance gives rise to a newtype TyCon (at a higher kind which you can't do in Haskell!): newtype FPair a b = FP (Either (a->b)) Then looking up (F (Int,Bool) Char) will return a FamInstMatch (FPair, [Int,Bool,Char]) The "extra" type argument [Char] just stays on the end. We handle data families and type families separately here: * For type families, all instances of a type family must have the same arity, so we can precompute the split between the match_tys and the overflow tys. This is done in pre_rough_split_tys. * For data family instances, though, we need to re-split for each instance, because the breakdown might be different for each instance. Why? Because of eta reduction; see Note [Eta reduction for data family axioms] in TcInstDcls. -} -- checks if one LHS is dominated by a list of other branches -- in other words, if an application would match the first LHS, it is guaranteed -- to match at least one of the others. The RHSs are ignored. -- This algorithm is conservative: -- True -> the LHS is definitely covered by the others -- False -> no information -- It is currently (Oct 2012) used only for generating errors for -- inaccessible branches. If these errors go unreported, no harm done. -- This is defined here to avoid a dependency from CoAxiom to Unify isDominatedBy :: CoAxBranch -> [CoAxBranch] -> Bool isDominatedBy branch branches = or $ map match branches where lhs = coAxBranchLHS branch match (CoAxBranch { cab_tvs = tvs, cab_lhs = tys }) = isJust $ tcMatchTys (mkVarSet tvs) tys lhs {- ************************************************************************ * * Choosing an axiom application * * ************************************************************************ The lookupFamInstEnv function does a nice job for *open* type families, but we also need to handle closed ones when normalising a type: -} reduceTyFamApp_maybe :: FamInstEnvs -> Role -- Desired role of result coercion -> TyCon -> [Type] -> Maybe (Coercion, Type) -- Attempt to do a *one-step* reduction of a type-family application -- but *not* newtypes -- Works on type-synonym families always; data-families only if -- the role we seek is representational -- It does *not* normlise the type arguments first, so this may not -- go as far as you want. If you want normalised type arguments, -- use normaliseTcArgs first. -- -- The TyCon can be oversaturated. -- Works on both open and closed families reduceTyFamApp_maybe envs role tc tys | Phantom <- role = Nothing | case role of Representational -> isOpenFamilyTyCon tc _ -> isOpenTypeFamilyTyCon tc -- If we seek a representational coercion -- (e.g. the call in topNormaliseType_maybe) then we can -- unwrap data families as well as type-synonym families; -- otherwise only type-synonym families , FamInstMatch { fim_instance = fam_inst , fim_tys = inst_tys } : _ <- lookupFamInstEnv envs tc tys -- NB: Allow multiple matches because of compatible overlap = let ax = famInstAxiom fam_inst co = mkUnbranchedAxInstCo role ax inst_tys ty = pSnd (coercionKind co) in Just (co, ty) | Just ax <- isClosedSynFamilyTyCon_maybe tc , Just (ind, inst_tys) <- chooseBranch ax tys = let co = mkAxInstCo role ax ind inst_tys ty = pSnd (coercionKind co) in Just (co, ty) | Just ax <- isBuiltInSynFamTyCon_maybe tc , Just (coax,ts,ty) <- sfMatchFam ax tys = let co = mkAxiomRuleCo coax ts [] in Just (co, ty) | otherwise = Nothing -- The axiom can be oversaturated. (Closed families only.) chooseBranch :: CoAxiom Branched -> [Type] -> Maybe (BranchIndex, [Type]) chooseBranch axiom tys = do { let num_pats = coAxiomNumPats axiom (target_tys, extra_tys) = splitAt num_pats tys branches = coAxiomBranches axiom ; (ind, inst_tys) <- findBranch (fromBranchList branches) 0 target_tys ; return (ind, inst_tys ++ extra_tys) } -- The axiom must *not* be oversaturated findBranch :: [CoAxBranch] -- branches to check -> BranchIndex -- index of current branch -> [Type] -- target types -> Maybe (BranchIndex, [Type]) findBranch (CoAxBranch { cab_tvs = tpl_tvs, cab_lhs = tpl_lhs, cab_incomps = incomps } : rest) ind target_tys = case tcMatchTys (mkVarSet tpl_tvs) tpl_lhs target_tys of Just subst -- matching worked. now, check for apartness. | all (isSurelyApart . tcUnifyTysFG instanceBindFun flattened_target . coAxBranchLHS) incomps -> -- matching worked & we're apart from all incompatible branches. success Just (ind, substTyVars subst tpl_tvs) -- failure. keep looking _ -> findBranch rest (ind+1) target_tys where isSurelyApart SurelyApart = True isSurelyApart _ = False flattened_target = flattenTys in_scope target_tys in_scope = mkInScopeSet (unionVarSets $ map (tyVarsOfTypes . coAxBranchLHS) incomps) -- fail if no branches left findBranch [] _ _ = Nothing {- ************************************************************************ * * Looking up a family instance * * ************************************************************************ -} topNormaliseType :: FamInstEnvs -> Type -> Type topNormaliseType env ty = case topNormaliseType_maybe env ty of Just (_co, ty') -> ty' Nothing -> ty topNormaliseType_maybe :: FamInstEnvs -> Type -> Maybe (Coercion, Type) -- ^ Get rid of *outermost* (or toplevel) -- * type function redex -- * newtypes -- using appropriate coercions. Specifically, if -- topNormaliseType_maybe env ty = Maybe (co, ty') -- then -- (a) co :: ty ~ ty' -- (b) ty' is not a newtype, and is not a type-family redex -- -- However, ty' can be something like (Maybe (F ty)), where -- (F ty) is a redex. -- -- Its a bit like Type.repType, but handles type families too -- The coercion returned is always an R coercion topNormaliseType_maybe env ty = topNormaliseTypeX_maybe stepper ty where stepper = unwrapNewTypeStepper `composeSteppers` \ rec_nts tc tys -> let (args_co, ntys) = normaliseTcArgs env Representational tc tys in case reduceTyFamApp_maybe env Representational tc ntys of Just (co, rhs) -> NS_Step rec_nts rhs (args_co `mkTransCo` co) Nothing -> NS_Done --------------- normaliseTcApp :: FamInstEnvs -> Role -> TyCon -> [Type] -> (Coercion, Type) -- See comments on normaliseType for the arguments of this function normaliseTcApp env role tc tys | isTypeSynonymTyCon tc , Just (tenv, rhs, ntys') <- tcExpandTyCon_maybe tc ntys , (co2, ninst_rhs) <- normaliseType env role (Type.substTy (mkTopTvSubst tenv) rhs) = if isReflCo co2 then (args_co, mkTyConApp tc ntys) else (args_co `mkTransCo` co2, mkAppTys ninst_rhs ntys') | Just (first_co, ty') <- reduceTyFamApp_maybe env role tc ntys , (rest_co,nty) <- normaliseType env role ty' = (args_co `mkTransCo` first_co `mkTransCo` rest_co, nty) | otherwise -- No unique matching family instance exists; -- we do not do anything = (args_co, mkTyConApp tc ntys) where (args_co, ntys) = normaliseTcArgs env role tc tys --------------- normaliseTcArgs :: FamInstEnvs -- environment with family instances -> Role -- desired role of output coercion -> TyCon -> [Type] -- tc tys -> (Coercion, [Type]) -- (co, new_tys), where -- co :: tc tys ~ tc new_tys normaliseTcArgs env role tc tys = (mkTyConAppCo role tc cois, ntys) where (cois, ntys) = zipWithAndUnzip (normaliseType env) (tyConRolesX role tc) tys --------------- normaliseType :: FamInstEnvs -- environment with family instances -> Role -- desired role of output coercion -> Type -- old type -> (Coercion, Type) -- (coercion,new type), where -- co :: old-type ~ new_type -- Normalise the input type, by eliminating *all* type-function redexes -- but *not* newtypes (which are visible to the programmer) -- Returns with Refl if nothing happens -- Try to not to disturb type syonyms if possible normaliseType env role (TyConApp tc tys) = normaliseTcApp env role tc tys normaliseType _env role ty@(LitTy {}) = (mkReflCo role ty, ty) normaliseType env role (AppTy ty1 ty2) = let (coi1,nty1) = normaliseType env role ty1 (coi2,nty2) = normaliseType env Nominal ty2 in (mkAppCo coi1 coi2, mkAppTy nty1 nty2) normaliseType env role (FunTy ty1 ty2) = let (coi1,nty1) = normaliseType env role ty1 (coi2,nty2) = normaliseType env role ty2 in (mkFunCo role coi1 coi2, mkFunTy nty1 nty2) normaliseType env role (ForAllTy tyvar ty1) = let (coi,nty1) = normaliseType env role ty1 in (mkForAllCo tyvar coi, ForAllTy tyvar nty1) normaliseType _ role ty@(TyVarTy _) = (mkReflCo role ty,ty) {- ************************************************************************ * * Flattening * * ************************************************************************ Note [Flattening] ~~~~~~~~~~~~~~~~~ As described in http://research.microsoft.com/en-us/um/people/simonpj/papers/ext-f/axioms-extended.pdf we sometimes need to flatten core types before unifying them. Flattening means replacing all top-level uses of type functions with fresh variables, taking care to preserve sharing. That is, the type (Either (F a b) (F a b)) should flatten to (Either c c), never (Either c d). Defined here because of module dependencies. -} type FlattenMap = TypeMap TyVar -- See Note [Flattening] flattenTys :: InScopeSet -> [Type] -> [Type] flattenTys in_scope tys = snd $ coreFlattenTys all_in_scope emptyTypeMap tys where -- when we hit a type function, we replace it with a fresh variable -- but, we need to make sure that this fresh variable isn't mentioned -- *anywhere* in the types we're flattening, even if locally-bound in -- a forall. That way, we can ensure consistency both within and outside -- of that forall. all_in_scope = in_scope `extendInScopeSetSet` allTyVarsInTys tys coreFlattenTys :: InScopeSet -> FlattenMap -> [Type] -> (FlattenMap, [Type]) coreFlattenTys in_scope = go [] where go rtys m [] = (m, reverse rtys) go rtys m (ty : tys) = let (m', ty') = coreFlattenTy in_scope m ty in go (ty' : rtys) m' tys coreFlattenTy :: InScopeSet -> FlattenMap -> Type -> (FlattenMap, Type) coreFlattenTy in_scope = go where go m ty | Just ty' <- coreView ty = go m ty' go m ty@(TyVarTy {}) = (m, ty) go m (AppTy ty1 ty2) = let (m1, ty1') = go m ty1 (m2, ty2') = go m1 ty2 in (m2, AppTy ty1' ty2') go m (TyConApp tc tys) -- NB: Don't just check if isFamilyTyCon: this catches *data* families, -- which are generative and thus can be preserved during flattening | not (isGenerativeTyCon tc Nominal) = let (m', tv) = coreFlattenTyFamApp in_scope m tc tys in (m', mkTyVarTy tv) | otherwise = let (m', tys') = coreFlattenTys in_scope m tys in (m', mkTyConApp tc tys') go m (FunTy ty1 ty2) = let (m1, ty1') = go m ty1 (m2, ty2') = go m1 ty2 in (m2, FunTy ty1' ty2') -- Note to RAE: this will have to be changed with kind families go m (ForAllTy tv ty) = let (m', ty') = go m ty in (m', ForAllTy tv ty') go m ty@(LitTy {}) = (m, ty) coreFlattenTyFamApp :: InScopeSet -> FlattenMap -> TyCon -- type family tycon -> [Type] -- args -> (FlattenMap, TyVar) coreFlattenTyFamApp in_scope m fam_tc fam_args = case lookupTypeMap m fam_ty of Just tv -> (m, tv) -- we need fresh variables here, but this is called far from -- any good source of uniques. So, we generate one from thin -- air, using the arbitrary prime number 71 as a seed Nothing -> let tyvar_unique = deriveUnique (getUnique fam_tc) 71 tyvar_name = mkSysTvName tyvar_unique (fsLit "fl") tv = uniqAway in_scope $ mkTyVar tyvar_name (typeKind fam_ty) m' = extendTypeMap m fam_ty tv in (m', tv) where fam_ty = TyConApp fam_tc fam_args allTyVarsInTys :: [Type] -> VarSet allTyVarsInTys [] = emptyVarSet allTyVarsInTys (ty:tys) = allTyVarsInTy ty `unionVarSet` allTyVarsInTys tys allTyVarsInTy :: Type -> VarSet allTyVarsInTy = go where go (TyVarTy tv) = unitVarSet tv go (AppTy ty1 ty2) = (go ty1) `unionVarSet` (go ty2) go (TyConApp _ tys) = allTyVarsInTys tys go (FunTy ty1 ty2) = (go ty1) `unionVarSet` (go ty2) go (ForAllTy tv ty) = (go (tyVarKind tv)) `unionVarSet` unitVarSet tv `unionVarSet` (go ty) -- don't remove tv go (LitTy {}) = emptyVarSet