+%************************************************************************
+%* *
+\subsection{Unification with an explicit substitution}
+%* *
+%************************************************************************
+
+Unify types with an explicit substitution and no monad.
+Ignore usage annotations.
+
+\begin{code}
+type MySubst
+ = (TyVarSet, -- Set of template tyvars
+ TyVarSubstEnv) -- Not necessarily idempotent
+
+unifyTysX :: TyVarSet -- Template tyvars
+ -> Type
+ -> Type
+ -> Maybe TyVarSubstEnv
+unifyTysX tmpl_tyvars ty1 ty2
+ = uTysX ty1 ty2 (\(_,s) -> Just s) (tmpl_tyvars, emptySubstEnv)
+
+unifyExtendTysX :: TyVarSet -- Template tyvars
+ -> TyVarSubstEnv -- Substitution to start with
+ -> Type
+ -> Type
+ -> Maybe TyVarSubstEnv -- Extended substitution
+unifyExtendTysX tmpl_tyvars subst ty1 ty2
+ = uTysX ty1 ty2 (\(_,s) -> Just s) (tmpl_tyvars, subst)
+
+unifyTyListsX :: TyVarSet -> [Type] -> [Type]
+ -> Maybe TyVarSubstEnv
+unifyTyListsX tmpl_tyvars tys1 tys2
+ = uTyListsX tys1 tys2 (\(_,s) -> Just s) (tmpl_tyvars, emptySubstEnv)
+
+
+uTysX :: Type
+ -> Type
+ -> (MySubst -> Maybe result)
+ -> MySubst
+ -> Maybe result
+
+uTysX (NoteTy _ ty1) ty2 k subst = uTysX ty1 ty2 k subst
+uTysX ty1 (NoteTy _ ty2) k subst = uTysX ty1 ty2 k subst
+
+ -- Variables; go for uVar
+uTysX (TyVarTy tyvar1) (TyVarTy tyvar2) k subst
+ | tyvar1 == tyvar2
+ = k subst
+uTysX (TyVarTy tyvar1) ty2 k subst@(tmpls,_)
+ | tyvar1 `elemVarSet` tmpls
+ = uVarX tyvar1 ty2 k subst
+uTysX ty1 (TyVarTy tyvar2) k subst@(tmpls,_)
+ | tyvar2 `elemVarSet` tmpls
+ = uVarX tyvar2 ty1 k subst
+
+ -- Predicates
+uTysX (SourceTy (IParam n1 t1)) (SourceTy (IParam n2 t2)) k subst
+ | n1 == n2 = uTysX t1 t2 k subst
+uTysX (SourceTy (ClassP c1 tys1)) (SourceTy (ClassP c2 tys2)) k subst
+ | c1 == c2 = uTyListsX tys1 tys2 k subst
+uTysX (SourceTy (NType tc1 tys1)) (SourceTy (NType tc2 tys2)) k subst
+ | tc1 == tc2 = uTyListsX tys1 tys2 k subst
+
+ -- Functions; just check the two parts
+uTysX (FunTy fun1 arg1) (FunTy fun2 arg2) k subst
+ = uTysX fun1 fun2 (uTysX arg1 arg2 k) subst
+
+ -- Type constructors must match
+uTysX (TyConApp con1 tys1) (TyConApp con2 tys2) k subst
+ | (con1 == con2 && equalLength tys1 tys2)
+ = uTyListsX tys1 tys2 k subst
+
+ -- Applications need a bit of care!
+ -- They can match FunTy and TyConApp, so use splitAppTy_maybe
+ -- NB: we've already dealt with type variables and Notes,
+ -- so if one type is an App the other one jolly well better be too
+uTysX (AppTy s1 t1) ty2 k subst
+ = case tcSplitAppTy_maybe ty2 of
+ Just (s2, t2) -> uTysX s1 s2 (uTysX t1 t2 k) subst
+ Nothing -> Nothing -- Fail
+
+uTysX ty1 (AppTy s2 t2) k subst
+ = case tcSplitAppTy_maybe ty1 of
+ Just (s1, t1) -> uTysX s1 s2 (uTysX t1 t2 k) subst
+ Nothing -> Nothing -- Fail
+
+ -- Not expecting for-alls in unification
+#ifdef DEBUG
+uTysX (ForAllTy _ _) ty2 k subst = panic "Unify.uTysX subst:ForAllTy (1st arg)"
+uTysX ty1 (ForAllTy _ _) k subst = panic "Unify.uTysX subst:ForAllTy (2nd arg)"
+#endif
+
+ -- Ignore usages
+uTysX (UsageTy _ t1) t2 k subst = uTysX t1 t2 k subst
+uTysX t1 (UsageTy _ t2) k subst = uTysX t1 t2 k subst
+
+ -- Anything else fails
+uTysX ty1 ty2 k subst = Nothing
+
+
+uTyListsX [] [] k subst = k subst
+uTyListsX (ty1:tys1) (ty2:tys2) k subst = uTysX ty1 ty2 (uTyListsX tys1 tys2 k) subst
+uTyListsX tys1 tys2 k subst = Nothing -- Fail if the lists are different lengths
+\end{code}
+
+\begin{code}
+-- Invariant: tv1 is a unifiable variable
+uVarX tv1 ty2 k subst@(tmpls, env)
+ = case lookupSubstEnv env tv1 of
+ Just (DoneTy ty1) -> -- Already bound
+ uTysX ty1 ty2 k subst
+
+ Nothing -- Not already bound
+ | typeKind ty2 `eqKind` tyVarKind tv1
+ && occur_check_ok ty2
+ -> -- No kind mismatch nor occur check
+ UASSERT( not (isUTy ty2) )
+ k (tmpls, extendSubstEnv env tv1 (DoneTy ty2))
+
+ | otherwise -> Nothing -- Fail if kind mis-match or occur check
+ where
+ occur_check_ok ty = all occur_check_ok_tv (varSetElems (tyVarsOfType ty))
+ occur_check_ok_tv tv | tv1 == tv = False
+ | otherwise = case lookupSubstEnv env tv of
+ Nothing -> True
+ Just (DoneTy ty) -> occur_check_ok ty
+\end{code}
+
+
+
+%************************************************************************
+%* *
+\subsection{Matching on types}
+%* *
+%************************************************************************
+
+Matching is a {\em unidirectional} process, matching a type against a
+template (which is just a type with type variables in it). The
+matcher assumes that there are no repeated type variables in the
+template, so that it simply returns a mapping of type variables to
+types. It also fails on nested foralls.
+
+@matchTys@ matches corresponding elements of a list of templates and
+types. It and @matchTy@ both ignore usage annotations, unlike the
+main function @match@.
+
+\begin{code}
+matchTy :: TyVarSet -- Template tyvars
+ -> Type -- Template
+ -> Type -- Proposed instance of template
+ -> Maybe TyVarSubstEnv -- Matching substitution
+
+
+matchTys :: TyVarSet -- Template tyvars
+ -> [Type] -- Templates
+ -> [Type] -- Proposed instance of template
+ -> Maybe (TyVarSubstEnv, -- Matching substitution
+ [Type]) -- Left over instance types
+
+matchTy tmpls ty1 ty2 = match ty1 ty2 tmpls (\ senv -> Just senv) emptySubstEnv
+
+matchTys tmpls tys1 tys2 = match_list tys1 tys2 tmpls
+ (\ (senv,tys) -> Just (senv,tys))
+ emptySubstEnv
+\end{code}
+
+@match@ is the main function. It takes a flag indicating whether
+usage annotations are to be respected.
+
+\begin{code}
+match :: Type -> Type -- Current match pair
+ -> TyVarSet -- Template vars
+ -> (TyVarSubstEnv -> Maybe result) -- Continuation
+ -> TyVarSubstEnv -- Current subst
+ -> Maybe result
+
+-- When matching against a type variable, see if the variable
+-- has already been bound. If so, check that what it's bound to
+-- is the same as ty; if not, bind it and carry on.
+
+match (TyVarTy v) ty tmpls k senv
+ | v `elemVarSet` tmpls
+ = -- v is a template variable
+ case lookupSubstEnv senv v of
+ Nothing -> UASSERT( not (isUTy ty) )
+ k (extendSubstEnv senv v (DoneTy ty))
+ Just (DoneTy ty') | ty' `tcEqType` ty -> k senv -- Succeeds
+ | otherwise -> Nothing -- Fails
+
+ | otherwise
+ = -- v is not a template variable; ty had better match
+ -- Can't use (==) because types differ
+ case tcGetTyVar_maybe ty of
+ Just v' | v == v' -> k senv -- Success
+ other -> Nothing -- Failure
+ -- This tcGetTyVar_maybe is *required* because it must strip Notes.
+ -- I guess the reason the Note-stripping case is *last* rather than first
+ -- is to preserve type synonyms etc., so I'm not moving it to the
+ -- top; but this means that (without the deNotetype) a type
+ -- variable may not match the pattern (TyVarTy v') as one would
+ -- expect, due to an intervening Note. KSW 2000-06.
+
+ -- Predicates
+match (SourceTy (IParam n1 t1)) (SourceTy (IParam n2 t2)) tmpls k senv
+ | n1 == n2 = match t1 t2 tmpls k senv
+match (SourceTy (ClassP c1 tys1)) (SourceTy (ClassP c2 tys2)) tmpls k senv
+ | c1 == c2 = match_list_exactly tys1 tys2 tmpls k senv
+match (SourceTy (NType tc1 tys1)) (SourceTy (NType tc2 tys2)) tmpls k senv
+ | tc1 == tc2 = match_list_exactly tys1 tys2 tmpls k senv
+
+ -- Functions; just check the two parts
+match (FunTy arg1 res1) (FunTy arg2 res2) tmpls k senv
+ = match arg1 arg2 tmpls (match res1 res2 tmpls k) senv
+
+match (AppTy fun1 arg1) ty2 tmpls k senv
+ = case tcSplitAppTy_maybe ty2 of
+ Just (fun2,arg2) -> match fun1 fun2 tmpls (match arg1 arg2 tmpls k) senv
+ Nothing -> Nothing -- Fail
+
+match (TyConApp tc1 tys1) (TyConApp tc2 tys2) tmpls k senv
+ | tc1 == tc2 = match_list_exactly tys1 tys2 tmpls k senv
+
+-- Newtypes are opaque; other source types should not happen
+match (SourceTy (NType tc1 tys1)) (SourceTy (NType tc2 tys2)) tmpls k senv
+ | tc1 == tc2 = match_list_exactly tys1 tys2 tmpls k senv
+
+match (UsageTy _ ty1) ty2 tmpls k senv = match ty1 ty2 tmpls k senv
+match ty1 (UsageTy _ ty2) tmpls k senv = match ty1 ty2 tmpls k senv
+
+ -- With type synonyms, we have to be careful for the exact
+ -- same reasons as in the unifier. Please see the
+ -- considerable commentary there before changing anything
+ -- here! (WDP 95/05)
+match (NoteTy n1 ty1) ty2 tmpls k senv = match ty1 ty2 tmpls k senv
+match ty1 (NoteTy n2 ty2) tmpls k senv = match ty1 ty2 tmpls k senv
+
+-- Catch-all fails
+match _ _ _ _ _ = Nothing
+
+match_list_exactly tys1 tys2 tmpls k senv
+ = match_list tys1 tys2 tmpls k' senv
+ where
+ k' (senv', tys2') | null tys2' = k senv' -- Succeed
+ | otherwise = Nothing -- Fail