alpha_eq defined and exported

diff --git a/helm/software/components/ng_kernel/nCicReduction.ml b/helm/software/components/ng_kernel/nCicReduction.ml
index 1815ceedfcf5c87e9d387068ffbfb039c76763ff..2e13a5304b23b5adca91ef71dcb9c7d2f4349781 100644 (file)
--- a/helm/software/components/ng_kernel/nCicReduction.ml
+++ b/helm/software/components/ng_kernel/nCicReduction.ml
@@ -190,127 +190,134 @@ let get_relevance = ref (fun ~metasenv:_ ~subst:_ _ _ -> assert false);;
 
 let set_get_relevance f = get_relevance := f;;
 
+let alpha_eq ~test_lambda_source aux test_eq_only metasenv subst context t1 t2 =
+ if t1 === t2 then
+   true
+ else
+   match (t1,t2) with
+   | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only -> 
+       NCicEnvironment.universe_leq a b
+   | (C.Sort (C.Type a), C.Sort (C.Type b)) -> 
+       NCicEnvironment.universe_eq a b
+   | (C.Sort C.Prop,C.Sort (C.Type _)) -> (not test_eq_only)
+   | (C.Sort C.Prop, C.Sort C.Prop) -> true
+
+   | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
+       aux true context s1 s2 &&
+       aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
+   | (C.Lambda (name1,s1,t1), C.Lambda(_,_,t2)) ->
+      if test_lambda_source then
+       aux test_eq_only context t1 t2
+      else
+       (* thanks to inversion of well typedness, the source 
+        * of these lambdas must be already convertible *)
+       aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
+   | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
+      aux test_eq_only context ty1 ty2 &&
+      aux test_eq_only context s1 s2 &&
+      aux test_eq_only ((name1, C.Def (s1,ty1))::context) t1 t2
+
+   | (C.Meta (n1,(s1, C.Irl _)), C.Meta (n2,(s2, C.Irl _))) 
+      when n1 = n2 && s1 = s2 -> true
+   | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 &&
+      let l1 = NCicUtils.expand_local_context l1 in
+      let l2 = NCicUtils.expand_local_context l2 in
+      (try List.for_all2 
+        (fun t1 t2 -> aux test_eq_only context 
+          (NCicSubstitution.lift s1 t1) 
+          (NCicSubstitution.lift s2 t2))  
+        l1 l2
+      with Invalid_argument "List.for_all2" -> 
+        prerr_endline ("Meta " ^ string_of_int n1 ^ 
+          " occurrs with local contexts of different lenght\n"^
+          NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^
+          NCicPp.ppterm ~metasenv ~subst ~context t2);
+        assert false) -> true
+
+   | C.Meta (n1,l1), _ ->
+      (try 
+         let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
+         let term = NCicSubstitution.subst_meta l1 term in
+          aux test_eq_only context term t2
+       with NCicUtils.Subst_not_found _ -> false)
+   | _, C.Meta (n2,l2) ->
+      (try 
+         let _,_,term,_ = NCicUtils.lookup_subst n2 subst in
+         let term = NCicSubstitution.subst_meta l2 term in
+          aux test_eq_only context t1 term
+       with NCicUtils.Subst_not_found _ -> false)
+   
+   | (C.Appl ((C.Const r1) as hd1::tl1), C.Appl (C.Const r2::tl2)) 
+       when (Ref.eq r1 r2 && 
+         List.length (E.get_relevance r1) >= List.length tl1) ->
+     let relevance = E.get_relevance r1 in
+     let relevance = match r1 with
+         | Ref.Ref (_,Ref.Con (_,_,lno)) ->
+             let _,relevance = HExtlib.split_nth lno relevance in
+               HExtlib.mk_list false lno @ relevance
+         | _ -> relevance
+     in
+     (try
+         HExtlib.list_forall_default3_var
+          (fun t1 t2 b -> not b || aux true context t1 t2 )
+          tl1 tl2 true relevance
+        with Invalid_argument _ -> false
+           | HExtlib.FailureAt fail ->
+             let relevance = 
+               !get_relevance ~metasenv ~subst context hd1 tl1 in
+             let _,relevance = HExtlib.split_nth fail relevance in
+             let b,relevance = (match relevance with
+               | [] -> assert false
+               | b::tl -> b,tl) in
+             if (not b) then
+               let _,tl1 = HExtlib.split_nth (fail+1) tl1 in
+               let _,tl2 = HExtlib.split_nth (fail+1) tl2 in
+                 try
+                    HExtlib.list_forall_default3
+                    (fun t1 t2 b -> not b || aux true context t1 t2)
+                    tl1 tl2 true relevance
+                 with Invalid_argument _ -> false
+             else false)
+
+   | (C.Appl (hd1::tl1),  C.Appl (hd2::tl2)) ->
+       aux test_eq_only context hd1 hd2 &&
+       let relevance = !get_relevance ~metasenv ~subst context hd1 tl1 in
+        (try
+         HExtlib.list_forall_default3
+          (fun t1 t2 b -> not b || aux true context t1 t2)
+          tl1 tl2 true relevance
+        with Invalid_argument _ -> false)
+
+   | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
+      C.Match (ref2,outtype2,term2,pl2)) ->
+       let _,_,itl,_,_ = E.get_checked_indtys ref1 in
+       let _,_,ty,_ = List.nth itl tyno in
+       let rec remove_prods ~subst context ty = 
+         let ty = whd ~subst context ty in
+         match ty with
+         | C.Sort _ -> ty
+         | C.Prod (name,so,ta) -> remove_prods ~subst ((name,(C.Decl so))::context) ta
+         | _ -> assert false
+       in
+       let is_prop = 
+         match remove_prods ~subst [] ty with
+         | C.Sort C.Prop -> true
+         | _ -> false
+       in
+       Ref.eq ref1 ref2 &&
+       aux test_eq_only context outtype1 outtype2 &&
+       (is_prop || aux test_eq_only context term1 term2) &&
+       (try List.for_all2 (aux test_eq_only context) pl1 pl2
+        with Invalid_argument _ -> false)
+   | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
+   | (_,_) -> false
+;;
+
 (* t1, t2 must be well-typed *)
 let are_convertible ~metasenv ~subst =
  let rec aux test_eq_only context t1 t2 =
-   let alpha_eq test_eq_only t1 t2 =
-     if t1 === t2 then
-       true
-     else
-       match (t1,t2) with
-       | (C.Sort (C.Type a), C.Sort (C.Type b)) when not test_eq_only -> 
-           NCicEnvironment.universe_leq a b
-       | (C.Sort (C.Type a), C.Sort (C.Type b)) -> 
-           NCicEnvironment.universe_eq a b
-       | (C.Sort C.Prop,C.Sort (C.Type _)) -> (not test_eq_only)
-       | (C.Sort C.Prop, C.Sort C.Prop) -> true
-
-       | (C.Prod (name1,s1,t1), C.Prod(_,s2,t2)) ->
-           aux true context s1 s2 &&
-           aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
-       | (C.Lambda (name1,s1,t1), C.Lambda(_,_,t2)) ->
-          (* thanks to inversion of well typedness, the source 
-           * of these lambdas must be already convertible *)
-          aux test_eq_only ((name1, C.Decl s1)::context) t1 t2
-       | (C.LetIn (name1,ty1,s1,t1), C.LetIn(_,ty2,s2,t2)) ->
-          aux test_eq_only context ty1 ty2 &&
-          aux test_eq_only context s1 s2 &&
-          aux test_eq_only ((name1, C.Def (s1,ty1))::context) t1 t2
-
-       | (C.Meta (n1,(s1, C.Irl _)), C.Meta (n2,(s2, C.Irl _))) 
-          when n1 = n2 && s1 = s2 -> true
-       | (C.Meta (n1,(s1, l1)), C.Meta (n2,(s2, l2))) when n1 = n2 &&
-          let l1 = NCicUtils.expand_local_context l1 in
-          let l2 = NCicUtils.expand_local_context l2 in
-          (try List.for_all2 
-            (fun t1 t2 -> aux test_eq_only context 
-              (NCicSubstitution.lift s1 t1) 
-              (NCicSubstitution.lift s2 t2))  
-            l1 l2
-          with Invalid_argument "List.for_all2" -> 
-            prerr_endline ("Meta " ^ string_of_int n1 ^ 
-              " occurrs with local contexts of different lenght\n"^
-              NCicPp.ppterm ~metasenv ~subst ~context t1 ^ " === " ^
-              NCicPp.ppterm ~metasenv ~subst ~context t2);
-            assert false) -> true
-
-       | C.Meta (n1,l1), _ ->
-          (try 
-             let _,_,term,_ = NCicUtils.lookup_subst n1 subst in
-             let term = NCicSubstitution.subst_meta l1 term in
-              aux test_eq_only context term t2
-           with NCicUtils.Subst_not_found _ -> false)
-       | _, C.Meta (n2,l2) ->
-          (try 
-             let _,_,term,_ = NCicUtils.lookup_subst n2 subst in
-             let term = NCicSubstitution.subst_meta l2 term in
-              aux test_eq_only context t1 term
-           with NCicUtils.Subst_not_found _ -> false)
-       
-       | (C.Appl ((C.Const r1) as hd1::tl1), C.Appl (C.Const r2::tl2)) 
-           when (Ref.eq r1 r2 && 
-             List.length (E.get_relevance r1) >= List.length tl1) ->
-         let relevance = E.get_relevance r1 in
-         let relevance = match r1 with
-             | Ref.Ref (_,Ref.Con (_,_,lno)) ->
-                 let _,relevance = HExtlib.split_nth lno relevance in
-                   HExtlib.mk_list false lno @ relevance
-             | _ -> relevance
-         in
-         (try
-             HExtlib.list_forall_default3_var
-              (fun t1 t2 b -> not b || aux true context t1 t2 )
-              tl1 tl2 true relevance
-            with Invalid_argument _ -> false
-              | HExtlib.FailureAt fail ->
-                let relevance = 
-                   !get_relevance ~metasenv ~subst context hd1 tl1 in
-                let _,relevance = HExtlib.split_nth fail relevance in
-                let b,relevance = (match relevance with
-                  | [] -> assert false
-                  | b::tl -> b,tl) in
-                if (not b) then
-                  let _,tl1 = HExtlib.split_nth (fail+1) tl1 in
-                  let _,tl2 = HExtlib.split_nth (fail+1) tl2 in
-                    try
-                        HExtlib.list_forall_default3
-                        (fun t1 t2 b -> not b || aux true context t1 t2)
-                        tl1 tl2 true relevance
-                     with Invalid_argument _ -> false
-                else false)
-
-       | (C.Appl (hd1::tl1),  C.Appl (hd2::tl2)) ->
-           aux test_eq_only context hd1 hd2 &&
-          let relevance = !get_relevance ~metasenv ~subst context hd1 tl1 in
-            (try
-             HExtlib.list_forall_default3
-              (fun t1 t2 b -> not b || aux true context t1 t2)
-              tl1 tl2 true relevance
-            with Invalid_argument _ -> false)
-
-       | (C.Match (Ref.Ref (_,Ref.Ind (_,tyno,_)) as ref1,outtype1,term1,pl1),
-          C.Match (ref2,outtype2,term2,pl2)) ->
-          let _,_,itl,_,_ = E.get_checked_indtys ref1 in
-          let _,_,ty,_ = List.nth itl tyno in
-          let rec remove_prods ~subst context ty = 
-             let ty = whd ~subst context ty in
-             match ty with
-             | C.Sort _ -> ty
-            | C.Prod (name,so,ta) -> remove_prods ~subst ((name,(C.Decl so))::context) ta
-             | _ -> assert false
-           in
-           let is_prop = 
-             match remove_prods ~subst [] ty with
-             | C.Sort C.Prop -> true
-             | _ -> false
-           in
-           Ref.eq ref1 ref2 &&
-           aux test_eq_only context outtype1 outtype2 &&
-           (is_prop || aux test_eq_only context term1 term2) &&
-           (try List.for_all2 (aux test_eq_only context) pl1 pl2
-            with Invalid_argument _ -> false)
-       | (C.Implicit _, _) | (_, C.Implicit _) -> assert false
-       | (_,_) -> false
+  let alpha_eq test_eq_only =
+   alpha_eq ~test_lambda_source:false aux test_eq_only metasenv subst context
   in
    if alpha_eq test_eq_only t1 t2 then 
      true
@@ -365,6 +372,13 @@ let are_convertible ~metasenv ~subst =
   aux false 
 ;;
 
+let alpha_eq metasenv subst =
+ let rec aux test_lambda_source context t1 t2 =
+  alpha_eq ~test_lambda_source aux true metasenv subst context t1 t2
+ in
+  aux true
+;;
+
 let rec head_beta_reduce ~delta ~upto ~subst t l =
  match upto, t, l with
   | 0, C.Appl l1, _ -> C.Appl (l1 @ l)