+While @lookupFamInstEnv@ uses a one-way match, the next function
+@lookupFamInstEnvConflicts@ uses two-way matching (ie, unification). This is
+needed to check for overlapping instances.
+
+For class instances, these two variants of lookup are combined into one
+function (cf, @InstEnv@). We don't do that for family instances as the
+results of matching and unification are used in two different contexts.
+Moreover, matching is the wildly more frequently used operation in the case of
+indexed synonyms and we don't want to slow that down by needless unification.
+
+\begin{code}
+------------------------------------------------------------
+-- 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
+
+type OneSidedMatch = Bool -- Are optimisations that are only valid for
+ -- one sided matches allowed?
+
+lookup_fam_inst_env -- The worker, local to this module
+ :: MatchFun
+ -> OneSidedMatch
+ -> 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 one_sided (pkg_ie, home_ie) fam tys
+ | not (isFamilyTyCon fam)
+ = []
+ | otherwise
+ = ASSERT2( n_tys >= arity, ppr fam <+> ppr tys ) -- Family type applications must be saturated
+ home_matches ++ pkg_matches
+ where
+ home_matches = lookup home_ie
+ pkg_matches = lookup pkg_ie
+
+ -- See Note [Over-saturated matches]
+ arity = tyConArity fam
+ n_tys = length tys
+ extra_tys = drop arity tys
+ (match_tys, add_extra_tys)
+ | arity > n_tys = (take arity tys, \res_tys -> res_tys ++ extra_tys)
+ | otherwise = (tys, \res_tys -> res_tys)
+ -- The second case is the common one, hence functional representation
+
+ --------------
+ rough_tcs = roughMatchTcs match_tys
+ all_tvs = all isNothing rough_tcs && one_sided
+
+ --------------
+ lookup env = case lookupUFM env fam of
+ Nothing -> [] -- No instances for this class
+ Just (FamIE insts has_tv_insts)
+ -- Short cut for common case:
+ -- The thing we are looking up is of form (C a
+ -- b c), and the FamIE has no instances of
+ -- that form, so don't bother to search
+ | all_tvs && not has_tv_insts -> []
+ | otherwise -> find insts
+
+ --------------
+ find [] = []
+ find (item@(FamInst { fi_tcs = mb_tcs, fi_tvs = tpl_tvs,
+ fi_tys = tpl_tys, fi_tycon = tycon }) : 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 tpl_tvs tpl_tys match_tys
+ = (item, add_extra_tys $ substTyVars subst (tyConTyVars tycon)) : find rest
+
+ -- No match => try next
+ | otherwise
+ = find rest
+\end{code}
+
+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.
+
+
+
+
+%************************************************************************
+%* *
+ Looking up a family instance
+%* *
+%************************************************************************
+
+\begin{code}
+topNormaliseType :: FamInstEnvs
+ -> Type
+ -> Maybe (Coercion, Type)
+
+-- Get rid of *outermost* (or toplevel)
+-- * type functions
+-- * newtypes
+-- using appropriate coercions.
+-- By "outer" we mean that toplevelNormaliseType guarantees to return
+-- a type that does not have a reducible redex (F ty1 .. tyn) as its
+-- outermost form. It *can* return something like (Maybe (F ty)), where
+-- (F ty) is a redex.
+
+-- Its a bit like Type.repType, but handles type families too
+
+topNormaliseType env ty
+ = go [] ty
+ where
+ go :: [TyCon] -> Type -> Maybe (Coercion, Type)
+ go rec_nts ty | Just ty' <- coreView ty -- Expand synonyms
+ = go rec_nts ty'
+
+ go rec_nts (TyConApp tc tys)
+ | isNewTyCon tc -- Expand newtypes
+ = if tc `elem` rec_nts -- See Note [Expanding newtypes] in Type.lhs
+ then Nothing
+ else let nt_co = mkAxInstCo (newTyConCo tc) tys
+ in add_co nt_co rec_nts' nt_rhs
+
+ | isFamilyTyCon tc -- Expand open tycons
+ , (co, ty) <- normaliseTcApp env tc tys
+ -- Note that normaliseType fully normalises,
+ -- but it has do to so to be sure that
+ , not (isReflCo co)
+ = add_co co rec_nts ty
+ where
+ nt_rhs = newTyConInstRhs tc tys
+ rec_nts' | isRecursiveTyCon tc = tc:rec_nts
+ | otherwise = rec_nts
+
+ go _ _ = Nothing
+
+ add_co co rec_nts ty
+ = case go rec_nts ty of
+ Nothing -> Just (co, ty)
+ Just (co', ty') -> Just (mkTransCo co co', ty')
+
+
+---------------
+normaliseTcApp :: FamInstEnvs -> TyCon -> [Type] -> (Coercion, Type)
+normaliseTcApp env tc tys
+ | isFamilyTyCon tc
+ , tyConArity tc <= length tys -- Unsaturated data families are possible
+ , [(fam_inst, inst_tys)] <- lookupFamInstEnv env tc ntys
+ = let -- A matching family instance exists
+ rep_tc = famInstTyCon fam_inst
+ co_tycon = expectJust "lookupFamInst" (tyConFamilyCoercion_maybe rep_tc)
+ co = mkAxInstCo co_tycon inst_tys
+ first_coi = mkTransCo tycon_coi co
+ (rest_coi,nty) = normaliseType env (mkTyConApp rep_tc inst_tys)
+ fix_coi = mkTransCo first_coi rest_coi
+ in
+ (fix_coi, nty)
+
+ | otherwise -- No unique matching family instance exists;
+ -- we do not do anything
+ = (tycon_coi, TyConApp tc ntys)
+
+ where
+ -- Normalise the arg types so that they'll match
+ -- when we lookup in in the instance envt
+ (cois, ntys) = mapAndUnzip (normaliseType env) tys
+ tycon_coi = mkTyConAppCo tc cois
+
+---------------
+normaliseType :: FamInstEnvs -- environment with family instances
+ -> Type -- old type
+ -> (Coercion, Type) -- (coercion,new type), where
+ -- co :: old-type ~ new_type
+-- Normalise the input type, by eliminating *all* type-function redexes
+-- Returns with Refl if nothing happens
+
+normaliseType env ty
+ | Just ty' <- coreView ty = normaliseType env ty'
+normaliseType env (TyConApp tc tys)
+ = normaliseTcApp env tc tys
+normaliseType env (AppTy ty1 ty2)
+ = let (coi1,nty1) = normaliseType env ty1
+ (coi2,nty2) = normaliseType env ty2
+ in (mkAppCo coi1 coi2, mkAppTy nty1 nty2)
+normaliseType env (FunTy ty1 ty2)
+ = let (coi1,nty1) = normaliseType env ty1
+ (coi2,nty2) = normaliseType env ty2
+ in (mkFunCo coi1 coi2, mkFunTy nty1 nty2)
+normaliseType env (ForAllTy tyvar ty1)
+ = let (coi,nty1) = normaliseType env ty1
+ in (mkForAllCo tyvar coi, ForAllTy tyvar nty1)
+normaliseType _ ty@(TyVarTy _)
+ = (Refl ty,ty)
+normaliseType env (PredTy predty)
+ = normalisePred env predty
+
+---------------
+normalisePred :: FamInstEnvs -> PredType -> (Coercion,Type)
+normalisePred env (ClassP cls tys)
+ = let (cos,tys') = mapAndUnzip (normaliseType env) tys
+ in (mkPredCo $ ClassP cls cos, PredTy $ ClassP cls tys')
+normalisePred env (IParam ipn ty)
+ = let (co,ty') = normaliseType env ty
+ in (mkPredCo $ (IParam ipn co), PredTy $ IParam ipn ty')
+normalisePred env (EqPred ty1 ty2)
+ = let (co1,ty1') = normaliseType env ty1
+ (co2,ty2') = normaliseType env ty2
+ in (mkPredCo $ (EqPred co1 co2), PredTy $ EqPred ty1' ty2')
+\end{code}