2 % (c) The GRASP/AQUA Project, Glasgow University, 1992-1998
6 This module contains a unifier and a matcher, both of which
7 use an explicit substitution
10 module Unify ( unifyTysX, unifyTyListsX,
11 match, matchTy, matchTys
14 import TypeRep ( Type(..) ) -- friend
15 import Type ( typeKind, tyVarsOfType, splitAppTy_maybe )
17 import PprType () -- Instances
18 -- This import isn't strictly necessary, but it makes sure that
19 -- PprType is below Unify in the hierarchy, which in turn makes
20 -- fewer modules boot-import PprType
22 import Var ( tyVarKind )
24 import VarEnv ( TyVarSubstEnv, emptySubstEnv, lookupSubstEnv, extendSubstEnv,
28 import Outputable( panic )
31 %************************************************************************
33 \subsection{Unification wih a explicit substitution}
35 %************************************************************************
37 Unify types with an explicit substitution and no monad.
41 = (TyVarSet, -- Set of template tyvars
42 TyVarSubstEnv) -- Not necessarily idempotent
44 unifyTysX :: TyVarSet -- Template tyvars
47 -> Maybe TyVarSubstEnv
48 unifyTysX tmpl_tyvars ty1 ty2
49 = uTysX ty1 ty2 (\(_,s) -> Just s) (tmpl_tyvars, emptySubstEnv)
51 unifyTyListsX :: TyVarSet -> [Type] -> [Type]
52 -> Maybe TyVarSubstEnv
53 unifyTyListsX tmpl_tyvars tys1 tys2
54 = uTyListsX tys1 tys2 (\(_,s) -> Just s) (tmpl_tyvars, emptySubstEnv)
59 -> (MySubst -> Maybe result)
63 uTysX (NoteTy _ ty1) ty2 k subst = uTysX ty1 ty2 k subst
64 uTysX ty1 (NoteTy _ ty2) k subst = uTysX ty1 ty2 k subst
66 -- Variables; go for uVar
67 uTysX (TyVarTy tyvar1) (TyVarTy tyvar2) k subst
70 uTysX (TyVarTy tyvar1) ty2 k subst@(tmpls,_)
71 | tyvar1 `elemVarSet` tmpls
72 = uVarX tyvar1 ty2 k subst
73 uTysX ty1 (TyVarTy tyvar2) k subst@(tmpls,_)
74 | tyvar2 `elemVarSet` tmpls
75 = uVarX tyvar2 ty1 k subst
77 -- Functions; just check the two parts
78 uTysX (FunTy fun1 arg1) (FunTy fun2 arg2) k subst
79 = uTysX fun1 fun2 (uTysX arg1 arg2 k) subst
81 -- Type constructors must match
82 uTysX (TyConApp con1 tys1) (TyConApp con2 tys2) k subst
83 | (con1 == con2 && length tys1 == length tys2)
84 = uTyListsX tys1 tys2 k subst
86 -- Applications need a bit of care!
87 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
88 -- NB: we've already dealt with type variables and Notes,
89 -- so if one type is an App the other one jolly well better be too
90 uTysX (AppTy s1 t1) ty2 k subst
91 = case splitAppTy_maybe ty2 of
92 Just (s2, t2) -> uTysX s1 s2 (uTysX t1 t2 k) subst
93 Nothing -> Nothing -- Fail
95 uTysX ty1 (AppTy s2 t2) k subst
96 = case splitAppTy_maybe ty1 of
97 Just (s1, t1) -> uTysX s1 s2 (uTysX t1 t2 k) subst
98 Nothing -> Nothing -- Fail
100 -- Not expecting for-alls in unification
102 uTysX (ForAllTy _ _) ty2 k subst = panic "Unify.uTysX subst:ForAllTy (1st arg)"
103 uTysX ty1 (ForAllTy _ _) k subst = panic "Unify.uTysX subst:ForAllTy (2nd arg)"
106 -- Anything else fails
107 uTysX ty1 ty2 k subst = Nothing
110 uTyListsX [] [] k subst = k subst
111 uTyListsX (ty1:tys1) (ty2:tys2) k subst = uTysX ty1 ty2 (uTyListsX tys1 tys2 k) subst
112 uTyListsX tys1 tys2 k subst = Nothing -- Fail if the lists are different lengths
116 -- Invariant: tv1 is a unifiable variable
117 uVarX tv1 ty2 k subst@(tmpls, env)
118 = case lookupSubstEnv env tv1 of
119 Just (DoneTy ty1) -> -- Already bound
120 uTysX ty1 ty2 k subst
122 Nothing -- Not already bound
123 | typeKind ty2 == tyVarKind tv1
124 && occur_check_ok ty2
125 -> -- No kind mismatch nor occur check
126 k (tmpls, extendSubstEnv env tv1 (DoneTy ty2))
128 | otherwise -> Nothing -- Fail if kind mis-match or occur check
130 occur_check_ok ty = all occur_check_ok_tv (varSetElems (tyVarsOfType ty))
131 occur_check_ok_tv tv | tv1 == tv = False
132 | otherwise = case lookupSubstEnv env tv of
134 Just (DoneTy ty) -> occur_check_ok ty
139 %************************************************************************
141 \subsection{Matching on types}
143 %************************************************************************
145 Matching is a {\em unidirectional} process, matching a type against a
146 template (which is just a type with type variables in it). The
147 matcher assumes that there are no repeated type variables in the
148 template, so that it simply returns a mapping of type variables to
149 types. It also fails on nested foralls.
151 @matchTys@ matches corresponding elements of a list of templates and
155 matchTy :: TyVarSet -- Template tyvars
157 -> Type -- Proposed instance of template
158 -> Maybe TyVarSubstEnv -- Matching substitution
161 matchTys :: TyVarSet -- Template tyvars
162 -> [Type] -- Templates
163 -> [Type] -- Proposed instance of template
164 -> Maybe (TyVarSubstEnv, -- Matching substitution
165 [Type]) -- Left over instance types
167 matchTy tmpls ty1 ty2 = match ty1 ty2 tmpls (\ senv -> Just senv) emptySubstEnv
169 matchTys tmpls tys1 tys2 = match_list tys1 tys2 tmpls
170 (\ (senv,tys) -> Just (senv,tys))
174 @match@ is the main function.
177 match :: Type -> Type -- Current match pair
178 -> TyVarSet -- Template vars
179 -> (TyVarSubstEnv -> Maybe result) -- Continuation
180 -> TyVarSubstEnv -- Current subst
183 -- When matching against a type variable, see if the variable
184 -- has already been bound. If so, check that what it's bound to
185 -- is the same as ty; if not, bind it and carry on.
187 match (TyVarTy v) ty tmpls k senv
188 | v `elemVarSet` tmpls
189 = -- v is a template variable
190 case lookupSubstEnv senv v of
191 Nothing -> k (extendSubstEnv senv v (DoneTy ty))
192 Just (DoneTy ty') | ty' == ty -> k senv -- Succeeds
193 | otherwise -> Nothing -- Fails
196 = -- v is not a template variable; ty had better match
197 -- Can't use (==) because types differ
199 TyVarTy v' | v == v' -> k senv -- Success
200 other -> Nothing -- Failure
202 match (FunTy arg1 res1) (FunTy arg2 res2) tmpls k senv
203 = match arg1 arg2 tmpls (match res1 res2 tmpls k) senv
205 match (AppTy fun1 arg1) ty2 tmpls k senv
206 = case splitAppTy_maybe ty2 of
207 Just (fun2,arg2) -> match fun1 fun2 tmpls (match arg1 arg2 tmpls k) senv
208 Nothing -> Nothing -- Fail
210 match (TyConApp tc1 tys1) (TyConApp tc2 tys2) tmpls k senv
212 = match_list tys1 tys2 tmpls k' senv
214 k' (senv', tys2') | null tys2' = k senv' -- Succeed
215 | otherwise = Nothing -- Fail
217 -- With type synonyms, we have to be careful for the exact
218 -- same reasons as in the unifier. Please see the
219 -- considerable commentary there before changing anything
221 match (NoteTy _ ty1) ty2 tmpls k senv = match ty1 ty2 tmpls k senv
222 match ty1 (NoteTy _ ty2) tmpls k senv = match ty1 ty2 tmpls k senv
225 match _ _ _ _ _ = Nothing
227 match_list [] tys2 tmpls k senv = k (senv, tys2)
228 match_list (ty1:tys1) [] tmpls k senv = Nothing -- Not enough arg tys => failure
229 match_list (ty1:tys1) (ty2:tys2) tmpls k senv = match ty1 ty2 tmpls (match_list tys1 tys2 tmpls k) senv