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(..), funTyCon
16 import Type ( typeKind, tyVarsOfType, splitAppTy_maybe
19 import Var ( TyVar, tyVarKind )
21 import VarEnv ( TyVarSubstEnv, emptySubstEnv, lookupSubstEnv, extendSubstEnv,
25 import Unique ( Uniquable(..) )
26 import Outputable( panic )
27 import Util ( snocView )
30 %************************************************************************
32 \subsection{Unification wih a explicit substitution}
34 %************************************************************************
36 Unify types with an explicit substitution and no monad.
40 = (TyVarSet, -- Set of template tyvars
41 TyVarSubstEnv) -- Not necessarily idempotent
43 unifyTysX :: TyVarSet -- Template tyvars
46 -> Maybe TyVarSubstEnv
47 unifyTysX tmpl_tyvars ty1 ty2
48 = uTysX ty1 ty2 (\(_,s) -> Just s) (tmpl_tyvars, emptySubstEnv)
50 unifyTyListsX :: TyVarSet -> [Type] -> [Type]
51 -> Maybe TyVarSubstEnv
52 unifyTyListsX tmpl_tyvars tys1 tys2
53 = uTyListsX tys1 tys2 (\(_,s) -> Just s) (tmpl_tyvars, emptySubstEnv)
58 -> (MySubst -> Maybe result)
62 uTysX (NoteTy _ ty1) ty2 k subst = uTysX ty1 ty2 k subst
63 uTysX ty1 (NoteTy _ ty2) k subst = uTysX ty1 ty2 k subst
65 -- Variables; go for uVar
66 uTysX (TyVarTy tyvar1) (TyVarTy tyvar2) k subst
69 uTysX (TyVarTy tyvar1) ty2 k subst@(tmpls,_)
70 | tyvar1 `elemVarSet` tmpls
71 = uVarX tyvar1 ty2 k subst
72 uTysX ty1 (TyVarTy tyvar2) k subst@(tmpls,_)
73 | tyvar2 `elemVarSet` tmpls
74 = uVarX tyvar2 ty1 k subst
76 -- Functions; just check the two parts
77 uTysX (FunTy fun1 arg1) (FunTy fun2 arg2) k subst
78 = uTysX fun1 fun2 (uTysX arg1 arg2 k) subst
80 -- Type constructors must match
81 uTysX (TyConApp con1 tys1) (TyConApp con2 tys2) k subst
82 | (con1 == con2 && length tys1 == length tys2)
83 = uTyListsX tys1 tys2 k subst
85 -- Applications need a bit of care!
86 -- They can match FunTy and TyConApp, so use splitAppTy_maybe
87 -- NB: we've already dealt with type variables and Notes,
88 -- so if one type is an App the other one jolly well better be too
89 uTysX (AppTy s1 t1) ty2 k subst
90 = case splitAppTy_maybe ty2 of
91 Just (s2, t2) -> uTysX s1 s2 (uTysX t1 t2 k) subst
92 Nothing -> Nothing -- Fail
94 uTysX ty1 (AppTy s2 t2) k subst
95 = case splitAppTy_maybe ty1 of
96 Just (s1, t1) -> uTysX s1 s2 (uTysX t1 t2 k) subst
97 Nothing -> Nothing -- Fail
99 -- Not expecting for-alls in unification
101 uTysX (ForAllTy _ _) ty2 k subst = panic "Unify.uTysX subst:ForAllTy (1st arg)"
102 uTysX ty1 (ForAllTy _ _) k subst = panic "Unify.uTysX subst:ForAllTy (2nd arg)"
105 -- Anything else fails
106 uTysX ty1 ty2 k subst = Nothing
109 uTyListsX [] [] k subst = k subst
110 uTyListsX (ty1:tys1) (ty2:tys2) k subst = uTysX ty1 ty2 (uTyListsX tys1 tys2 k) subst
111 uTyListsX tys1 tys2 k subst = Nothing -- Fail if the lists are different lengths
115 -- Invariant: tv1 is a unifiable variable
116 uVarX tv1 ty2 k subst@(tmpls, env)
117 = case lookupSubstEnv env tv1 of
118 Just (DoneTy ty1) -> -- Already bound
119 uTysX ty1 ty2 k subst
121 Nothing -- Not already bound
122 | typeKind ty2 == tyVarKind tv1
123 && occur_check_ok ty2
124 -> -- No kind mismatch nor occur check
125 k (tmpls, extendSubstEnv env tv1 (DoneTy ty2))
127 | otherwise -> Nothing -- Fail if kind mis-match or occur check
129 occur_check_ok ty = all occur_check_ok_tv (varSetElems (tyVarsOfType ty))
130 occur_check_ok_tv tv | tv1 == tv = False
131 | otherwise = case lookupSubstEnv env tv of
133 Just (DoneTy ty) -> occur_check_ok ty
138 %************************************************************************
140 \subsection{Matching on types}
142 %************************************************************************
144 Matching is a {\em unidirectional} process, matching a type against a
145 template (which is just a type with type variables in it). The
146 matcher assumes that there are no repeated type variables in the
147 template, so that it simply returns a mapping of type variables to
148 types. It also fails on nested foralls.
150 @matchTys@ matches corresponding elements of a list of templates and
154 matchTy :: TyVarSet -- Template tyvars
156 -> Type -- Proposed instance of template
157 -> Maybe TyVarSubstEnv -- Matching substitution
160 matchTys :: TyVarSet -- Template tyvars
161 -> [Type] -- Templates
162 -> [Type] -- Proposed instance of template
163 -> Maybe (TyVarSubstEnv, -- Matching substitution
164 [Type]) -- Left over instance types
166 matchTy tmpls ty1 ty2 = match ty1 ty2 tmpls (\ senv -> Just senv) emptySubstEnv
168 matchTys tmpls tys1 tys2 = match_list tys1 tys2 tmpls
169 (\ (senv,tys) -> Just (senv,tys))
173 @match@ is the main function.
176 match :: Type -> Type -- Current match pair
177 -> TyVarSet -- Template vars
178 -> (TyVarSubstEnv -> Maybe result) -- Continuation
179 -> TyVarSubstEnv -- Current subst
182 -- When matching against a type variable, see if the variable
183 -- has already been bound. If so, check that what it's bound to
184 -- is the same as ty; if not, bind it and carry on.
186 match (TyVarTy v) ty tmpls k senv
187 | v `elemVarSet` tmpls
188 = -- v is a template variable
189 case lookupSubstEnv senv v of
190 Nothing -> k (extendSubstEnv senv v (DoneTy ty))
191 Just (DoneTy ty') | ty' == ty -> k senv -- Succeeds
192 | otherwise -> Nothing -- Fails
195 = -- v is not a template variable; ty had better match
196 -- Can't use (==) because types differ
198 TyVarTy v' | v == v' -> k senv -- Success
199 other -> Nothing -- Failure
201 match (FunTy arg1 res1) (FunTy arg2 res2) tmpls k senv
202 = match arg1 arg2 tmpls (match res1 res2 tmpls k) senv
204 match (AppTy fun1 arg1) ty2 tmpls k senv
205 = case splitAppTy_maybe ty2 of
206 Just (fun2,arg2) -> match fun1 fun2 tmpls (match arg1 arg2 tmpls k) senv
207 Nothing -> Nothing -- Fail
209 match (TyConApp tc1 tys1) (TyConApp tc2 tys2) tmpls k senv
211 = match_list tys1 tys2 tmpls k' senv
213 k' (senv', tys2') | null tys2' = k senv' -- Succeed
214 | otherwise = Nothing -- Fail
216 -- With type synonyms, we have to be careful for the exact
217 -- same reasons as in the unifier. Please see the
218 -- considerable commentary there before changing anything
220 match (NoteTy _ ty1) ty2 tmpls k senv = match ty1 ty2 tmpls k senv
221 match ty1 (NoteTy _ ty2) tmpls k senv = match ty1 ty2 tmpls k senv
224 match _ _ _ _ _ = Nothing
226 match_list [] tys2 tmpls k senv = k (senv, tys2)
227 match_list (ty1:tys1) [] tmpls k senv = Nothing -- Not enough arg tys => failure
228 match_list (ty1:tys1) (ty2:tys2) tmpls k senv = match ty1 ty2 tmpls (match_list tys1 tys2 tmpls k) senv