snapshot

diff --git a/helm/ocaml/cic_proof_checking/cicElim.ml b/helm/ocaml/cic_proof_checking/cicElim.ml
index 93d64a12ced47376d61198db42edefb7fb656257..1de440d56a08dec54196ddf557f3f0925aecc5f1 100644 (file)
--- a/helm/ocaml/cic_proof_checking/cicElim.ml
+++ b/helm/ocaml/cic_proof_checking/cicElim.ml
@@ -25,64 +25,92 @@
 
 let fresh_binder =
   let counter = ref ~-1 in
-  fun () ->
-    incr counter;
-    "elim" ^ string_of_int !counter
+  function
+    | true ->
+        incr counter;
+        Cic.Name ("elim" ^ string_of_int !counter)
+    | _ -> Cic.Anonymous
 
   (** verifies if a given uri occurs in a term in target position *)
 let rec recursive uri = function
   | Cic.Prod (_, _, target) -> recursive uri target
-  | Cic.MutInd (uri', _, _)
-  | Cic.Appl [ Cic.MutInd (uri', _, _); _ ] -> UriManager.eq uri uri'
+  | Cic.MutInd (uri', _, _) -> UriManager.eq uri uri'
+  | Cic.Appl args -> List.exists (recursive uri) args
   | _ -> false
 
 let unfold_appl = function
   | Cic.Appl ((Cic.Appl args) :: tl) -> Cic.Appl (args @ tl)
   | t -> t
 
+let rec split l n =
+ match (l,n) with
+    (l,0) -> ([], l)
+  | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2)
+  | (_,_) -> assert false
+
   (** build elimination principle part related to a single constructor
-  * @param strip number of Prod to ignore in this constructor (i.e. number of
-  * inductive parameters) *)
-let rec delta (uri, typeno, subst) strip consno t p args =
+  * @param paramsno number of Prod to ignore in this constructor (i.e. number of
+  * inductive parameters)
+  * @param dependent true if we are in the dependent case (i.e. sort <> Prop) *)
+let rec delta (uri, typeno, subst) dependent paramsno consno t p args =
   assert (subst = []);
   match t with
-  | Cic.MutInd (uri', typeno', subst')
-  | Cic.Appl (Cic.MutInd (uri', typeno', subst') :: _) when
-    UriManager.eq uri uri' && typeno = typeno' && subst = subst' ->
-      (match args with
-      | [] -> assert false
-      | [arg] -> unfold_appl (Cic.Appl [p; arg])
-      | _ -> unfold_appl (Cic.Appl [p; unfold_appl (Cic.Appl args)]))
-(*
-  | Cic.Appl (Cic.MutInd (uri', typeno', subst') :: _) when
+  | Cic.MutInd (uri', typeno', subst') ->
+      if dependent then
+        (match args with
+        | [] -> assert false
+        | [arg] -> unfold_appl (Cic.Appl [p; arg])
+        | _ -> unfold_appl (Cic.Appl [p; unfold_appl (Cic.Appl args)]))
+      else
+        p
+  | Cic.Appl (Cic.MutInd (uri', typeno', subst') :: tl) when
     UriManager.eq uri uri' && typeno = typeno' && subst = subst' ->
-      Cic.Appl (Cic.Rel p_rel :: args)
-*)
-  | Cic.Prod (binder, src, tgt) when strip = 0 ->
+      let (lparams, rparams) = split tl paramsno in
+      if dependent then
+        (match args with
+        | [] -> assert false
+        | [arg] -> unfold_appl (Cic.Appl (p :: rparams @ [arg]))
+        | _ ->
+            unfold_appl (Cic.Appl (p ::
+              rparams @ [unfold_appl (Cic.Appl args)])))
+      else  (* non dependent *)
+        (match rparams with
+        | [] -> p
+        | _ -> Cic.Appl (p :: rparams))
+  | Cic.Prod (binder, src, tgt) ->
       if recursive uri src then
         let args = List.map (CicSubstitution.lift 2) args in
         let phi =
-          (delta (uri, typeno, subst) strip consno src
+          (delta (uri, typeno, subst) dependent paramsno consno src
             (CicSubstitution.lift 1 p) [Cic.Rel 1])
         in
-        Cic.Prod (Cic.Name (fresh_binder ()), src,
+        Cic.Prod (fresh_binder dependent, src,
           Cic.Prod (Cic.Anonymous, phi,
-            delta (uri, typeno, subst) strip consno tgt
+            delta (uri, typeno, subst) dependent paramsno consno tgt
               (CicSubstitution.lift 2 p) (args @ [Cic.Rel 2])))
       else  (* non recursive *)
         let args = List.map (CicSubstitution.lift 1) args in
-        Cic.Prod (Cic.Name (fresh_binder ()), src,
-          delta (uri, typeno, subst) strip consno tgt (CicSubstitution.lift 1 p)
-            (args @ [Cic.Rel 1]))
-  | Cic.Prod (_, _, tgt) (* when strip > 0 *) ->
-      (* after stripping the parameters we lift of 1 since P has been inserted
-      * in the way *)
-      let tgt =
-        if strip = 1 then CicSubstitution.lift consno tgt else tgt
-      in
-      delta (uri, typeno, subst) (strip - 1) consno tgt p args
+        Cic.Prod (fresh_binder dependent, src,
+          delta (uri, typeno, subst) dependent paramsno consno tgt
+            (CicSubstitution.lift 1 p) (args @ [Cic.Rel 1]))
   | _ -> assert false
 
+let rec strip_left_params consno leftno = function
+  | t when leftno = 0 -> t (* no need to lift, the term is (hopefully) closed *)
+  | Cic.Prod (_, _, tgt) (* when leftno > 0 *) ->
+      (* after stripping the parameters we lift of consno. consno is 1 based so,
+      * the first constructor will be lifted by 1 (for P), the second by 2 (1
+      * for P and 1 for the 1st constructor), and so on *)
+      if leftno = 1 then
+        CicSubstitution.lift consno tgt
+      else
+        strip_left_params consno (leftno - 1) tgt
+  | _ -> assert false
+
+let delta (ury, typeno, subst) dependent paramsno consno t p args =
+  let t = strip_left_params consno paramsno t in
+  delta (ury, typeno, subst) dependent paramsno consno t p args
+
 let rec add_params indno ty eliminator =
   if indno = 0 then
     eliminator
@@ -96,52 +124,91 @@ let rec mk_rels consno = function
   | 0 -> []
   | n -> Cic.Rel (n+consno) :: mk_rels consno (n-1)
 
+let rec strip_pi = function
+  | Cic.Prod (_, _, tgt) -> strip_pi tgt
+  | t -> t
+
+let rec count_pi = function
+  | Cic.Prod (_, _, tgt) -> count_pi tgt + 1
+  | t -> 0
+
+let rec type_of_p dependent leftno indty = function
+  | Cic.Prod (n, src, tgt) when leftno = 0 ->
+      Cic.Prod (n, src, type_of_p dependent leftno indty tgt)
+  | Cic.Prod (_, _, tgt) -> type_of_p dependent (leftno - 1) indty tgt
+  | t ->
+      if dependent then
+        Cic.Prod (Cic.Anonymous, indty,
+          Cic.Sort (Cic.Type (CicUniv.fresh ())))
+      else
+        Cic.Sort (Cic.Type (CicUniv.fresh ()))
+
+let rec add_right_pi dependent strip liftno rightno indty = function
+  | Cic.Prod (_, src, tgt) when strip = 0 ->
+      Cic.Prod (fresh_binder true,
+        CicSubstitution.lift liftno src,
+        add_right_pi dependent strip liftno rightno indty tgt)
+  | Cic.Prod (_, _, tgt) ->
+      add_right_pi dependent (strip - 1) liftno rightno indty tgt
+  | t ->
+      if dependent then
+        Cic.Prod (fresh_binder dependent,
+          CicSubstitution.lift_from (rightno + 1) liftno indty,
+          Cic.Appl (Cic.Rel (1 + liftno + rightno) :: mk_rels 0 (rightno + 1)))
+      else
+        Cic.Prod (Cic.Anonymous,
+          CicSubstitution.lift_from (rightno + 1) liftno indty,
+          if rightno = 0 then
+            Cic.Rel (1 + liftno + rightno)
+          else
+            Cic.Appl (Cic.Rel (1 + liftno + rightno) :: mk_rels 1 rightno))
+
 let elim_of uri typeno =
   let (obj, univ) = (CicEnvironment.get_obj uri CicUniv.empty_ugraph) in
   let subst = [] in
   match obj with
-  | Cic.InductiveDefinition (indTypes, params, indno) ->
+  | Cic.InductiveDefinition (indTypes, params, leftno) ->
       let (name, inductive, ty, constructors) =
         try
           List.nth indTypes typeno
         with Failure _ -> assert false
       in
+      let paramsno = count_pi ty in (* number of (left or right) parameters *)
+      let dependent = (strip_pi ty <> Cic.Sort Cic.Prop) in
       let conslen = List.length constructors in
       let consno = ref (conslen + 1) in
       let indty =
         let indty = Cic.MutInd (uri, typeno, subst) in
-        if indno = 0 then
+        if leftno = 0 then
           indty
         else
-          Cic.Appl (indty :: mk_rels 0 indno)
+          Cic.Appl (indty :: mk_rels 0 paramsno)
       in
       let mk_constructor consno =
         let constructor = Cic.MutConstruct (uri, typeno, consno, subst) in
-        if indno = 0 then
+        if leftno = 0 then
           constructor
         else
-          Cic.Appl (constructor :: mk_rels consno indno)
+          Cic.Appl (constructor :: mk_rels consno leftno)
       in
       let eliminator =
-        Cic.Prod (Cic.Name "P",
-          (Cic.Prod (Cic.Anonymous,
-            indty,
-            (* Cic.MutInd (uri, typeno, subst), *)
-            Cic.Sort (Cic.Type (CicUniv.fresh ())))),
+        let p_ty = type_of_p dependent leftno indty ty in
+        let final_ty =
+          add_right_pi dependent leftno (conslen + 1) (paramsno - leftno)
+            indty ty
+        in
+        Cic.Prod (Cic.Name "P", p_ty,
           (List.fold_right
             (fun (_, constructor) acc ->
               decr consno;
               let p = Cic.Rel !consno in
               Cic.Prod (Cic.Anonymous,
-                (delta (uri, typeno, subst) indno !consno constructor p
-                  [mk_constructor !consno]),
-                acc)) (* lift acc? see assumption above on delta *)
+                (delta (uri, typeno, subst) dependent leftno !consno
+                  constructor p [mk_constructor !consno]),
+                acc))
             constructors
-            (Cic.Prod (Cic.Name (fresh_binder ()),
-              CicSubstitution.lift (conslen + 1) indty
-              (* Cic.MutInd (uri, typeno, subst) *),
-              Cic.Appl [Cic.Rel (2 + conslen); Cic.Rel 1]))))
+            final_ty))
       in
-      add_params indno ty eliminator
+      add_params leftno ty eliminator
   | _ -> assert false