+
+--------------------------------------
+-- Normalisation
+
+\begin{code}
+ -- get rid of TOPLEVEL type functions by rewriting them
+ -- i.e. treating their equations as a TRS
+toplevelNormaliseFamInst :: FamInstEnvs ->
+ Type ->
+ (CoercionI,Type)
+toplevelNormaliseFamInst env ty
+ | Just ty' <- tcView ty = normaliseFamInst env ty'
+toplevelNormaliseFamInst env ty@(TyConApp tyCon tys)
+ | isOpenTyCon tyCon
+ = normaliseFamInst env ty
+toplevelNormaliseFamInst env ty
+ = (IdCo,ty)
+
+
+ -- get rid of ALL type functions by rewriting them
+ -- i.e. treating their equations as a TRS
+normaliseFamInst :: FamInstEnvs -> -- environment with family instances
+ Type -> -- old type
+ (CoercionI,Type) -- (coercion,new type)
+normaliseFamInst env ty
+ | Just ty' <- tcView ty = normaliseFamInst env ty'
+normaliseFamInst env ty@(TyConApp tyCon tys) =
+ let (cois,ntys) = mapAndUnzip (normaliseFamInst env) tys
+ tycon_coi = mkTyConAppCoI tyCon ntys cois
+ maybe_ty_co = lookupFamInst env tyCon ntys
+ in case maybe_ty_co of
+ -- a matching family instance exists
+ Just (ty',co) ->
+ let first_coi = mkTransCoI tycon_coi (ACo co)
+ (rest_coi,nty) = normaliseFamInst env ty'
+ fix_coi = mkTransCoI first_coi rest_coi
+ in (fix_coi,nty)
+ -- no matching family instance exists
+ -- we do not do anything
+ Nothing ->
+ (tycon_coi,TyConApp tyCon ntys)
+normaliseFamInst env ty@(AppTy ty1 ty2) =
+ let (coi1,nty1) = normaliseFamInst env ty1
+ (coi2,nty2) = normaliseFamInst env ty2
+ in (mkAppTyCoI nty1 coi1 nty2 coi2, AppTy nty1 nty2)
+normaliseFamInst env ty@(FunTy ty1 ty2) =
+ let (coi1,nty1) = normaliseFamInst env ty1
+ (coi2,nty2) = normaliseFamInst env ty2
+ in (mkFunTyCoI nty1 coi1 nty2 coi2, FunTy nty1 nty2)
+normaliseFamInst env ty@(ForAllTy tyvar ty1) =
+ let (coi,nty1) = normaliseFamInst env ty1
+ in (mkForAllTyCoI tyvar coi,ForAllTy tyvar nty1)
+normaliseFamInst env ty@(NoteTy note ty1) =
+ let (coi,nty1) = normaliseFamInst env ty1
+ in (mkNoteTyCoI note coi,NoteTy note nty1)
+normaliseFamInst env ty@(TyVarTy _) =
+ (IdCo,ty)
+normaliseFamInst env (PredTy predty) =
+ normaliseFamInstPred env predty
+
+normaliseFamInstPred :: FamInstEnvs -> PredType -> (CoercionI,Type)
+normaliseFamInstPred env (ClassP cls tys) =
+ let (cois,tys') = mapAndUnzip (normaliseFamInst env) tys
+ in (mkClassPPredCoI cls tys' cois, PredTy $ ClassP cls tys')
+normaliseFamInstPred env (IParam ipn ty) =
+ let (coi,ty') = normaliseFamInst env ty
+ in (mkIParamPredCoI ipn coi, PredTy $ IParam ipn ty')
+normaliseFamInstPred env (EqPred ty1 ty2) =
+ let (coi1,ty1') = normaliseFamInst env ty1
+ (coi2,ty2') = normaliseFamInst env ty2
+ in (mkEqPredCoI ty1' coi1 ty2' coi2, PredTy $ EqPred ty1' ty2')
+
+lookupFamInst :: FamInstEnvs -> TyCon -> [Type] -> Maybe (Type,Coercion)
+
+-- (lookupFamInst F tys) looks for a top-level instance
+-- co : forall a. F tys' = G a
+-- (The rhs is always of form G a; see Note [The FamInst structure]
+-- in FamInst.)
+-- where we can instantiate 'a' with t to make tys'[t/a] = tys
+-- Hence (co t) : F tys ~ G t
+-- Then we return (Just (G t, co t))
+
+lookupFamInst env tycon tys
+ | not (isOpenTyCon tycon) -- Dead code; fix.
+ = Nothing
+ | otherwise
+ = case lookupFamInstEnv env tycon tys of
+ [(subst, fam_inst)] ->
+ Just (mkTyConApp rep_tc substituted_vars, mkTyConApp coercion_tycon substituted_vars)
+ where -- NB: invariant of lookupFamInstEnv is that (tyConTyVars rep_tc)
+ -- is in the domain of the substitution
+ rep_tc = famInstTyCon fam_inst
+ coercion_tycon = expectJust "lookupFamInst" (tyConFamilyCoercion_maybe rep_tc)
+ substituted_vars = substTyVars subst (tyConTyVars rep_tc)
+ other -> Nothing
+\end{code}