X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Focaml%2Fcic_proof_checking%2FcicElim.ml;h=c668d1c9be33420a1b9222a8646c8c3408b7a436;hb=4167cea65ca58897d1a3dbb81ff95de5074700cc;hp=93d64a12ced47376d61198db42edefb7fb656257;hpb=cbd78f48f8aa055e2d66922291717842d84383d1;p=helm.git

diff --git a/helm/ocaml/cic_proof_checking/cicElim.ml b/helm/ocaml/cic_proof_checking/cicElim.ml
index 93d64a12c..c668d1c9b 100644
--- a/helm/ocaml/cic_proof_checking/cicElim.ml
+++ b/helm/ocaml/cic_proof_checking/cicElim.ml
@@ -23,125 +23,393 @@
  * http://helm.cs.unibo.it/
  *)
 
-let fresh_binder =
-  let counter = ref ~-1 in
-  fun () ->
-    incr counter;
-    "elim" ^ string_of_int !counter
-
-  (** 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'
+open Printf
+
+exception Elim_failure of string Lazy.t
+exception Can_t_eliminate
+
+let debug_print = fun _ -> ()
+(*let debug_print s = prerr_endline (Lazy.force s) *)
+
+let counter = ref ~-1 ;;
+
+let fresh_binder () =  Cic.Name "matita_dummy"
+(*
+ incr counter;
+ Cic.Name ("e" ^ string_of_int !counter) *)
+
+  (** verifies if a given inductive type occurs in a term in target position *)
+let rec recursive uri typeno = function
+  | Cic.Prod (_, _, target) -> recursive uri typeno target
+  | Cic.MutInd (uri', typeno', [])
+  | Cic.Appl (Cic.MutInd  (uri', typeno', []) :: _) ->
+      UriManager.eq uri uri' && typeno = typeno'
   | _ -> false
 
+  (** given a list of constructor types, return true if at least one of them is
+  * recursive, false otherwise *)
+let recursive_type uri typeno constructors =
+  let rec aux = function
+    | Cic.Prod (_, src, tgt) -> recursive uri typeno src || aux tgt
+    | _ -> false
+  in
+  List.exists (fun (_, ty) -> aux ty) constructors
+
 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 =
-  assert (subst = []);
+  * @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) dependent paramsno consno t p args =
   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
-    UriManager.eq uri uri' && typeno = typeno' && subst = subst' ->
-      Cic.Appl (Cic.Rel p_rel :: args)
-*)
-  | Cic.Prod (binder, src, tgt) when strip = 0 ->
-      if recursive uri src then
+  | Cic.MutInd (uri', typeno', []) when
+    UriManager.eq uri uri' && typeno = typeno' ->
+      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', []) :: tl) when
+    UriManager.eq uri uri' && typeno = typeno' ->
+      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 typeno src then
         let args = List.map (CicSubstitution.lift 2) args in
         let phi =
-          (delta (uri, typeno, subst) strip consno src
-            (CicSubstitution.lift 1 p) [Cic.Rel 1])
+          let src = CicSubstitution.lift 1 src in
+          delta (uri, typeno) dependent paramsno consno src
+            (CicSubstitution.lift 1 p) [Cic.Rel 1]
         in
-        Cic.Prod (Cic.Name (fresh_binder ()), src,
+        let tgt = CicSubstitution.lift 1 tgt in
+        Cic.Prod (fresh_binder (), src,
           Cic.Prod (Cic.Anonymous, phi,
-            delta (uri, typeno, subst) strip consno tgt
+            delta (uri, typeno) 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 (), src,
+          delta (uri, typeno) dependent paramsno consno tgt
+            (CicSubstitution.lift 1 p) (args @ [Cic.Rel 1]))
   | _ -> assert false
 
-let rec add_params indno ty eliminator =
+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) dependent paramsno consno t p args =
+  let t = strip_left_params consno paramsno t in
+  delta (ury, typeno) dependent paramsno consno t p args
+
+let rec add_params binder indno ty eliminator =
   if indno = 0 then
     eliminator
   else
     match ty with
-    | Cic.Prod (binder, src, tgt) ->
-        Cic.Prod (binder, src, add_params (indno - 1) tgt eliminator)
+    | Cic.Prod (name, src, tgt) ->
+       let name =
+        match name with
+           Cic.Name _ -> name
+         | Cic.Anonymous -> fresh_binder ()
+       in
+        binder name src (add_params binder (indno - 1) tgt eliminator)
     | _ -> assert false
 
 let rec mk_rels consno = function
   | 0 -> []
   | n -> Cic.Rel (n+consno) :: mk_rels consno (n-1)
 
-let elim_of uri typeno =
-  let (obj, univ) = (CicEnvironment.get_obj uri CicUniv.empty_ugraph) in
-  let subst = [] in
+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 sort dependent leftno indty = function
+  | Cic.Prod (n, src, tgt) when leftno = 0 ->
+      let n =
+       if dependent then 
+        match n with
+           Cic.Name _ -> n
+         | Cic.Anonymous -> fresh_binder ()
+       else
+        n
+      in
+       Cic.Prod (n, src, type_of_p sort dependent leftno indty tgt)
+  | Cic.Prod (_, _, tgt) -> type_of_p sort dependent (leftno - 1) indty tgt
+  | t ->
+      if dependent then
+        Cic.Prod (Cic.Anonymous, indty, Cic.Sort sort)
+      else
+        Cic.Sort sort
+
+let rec add_right_pi dependent strip liftno liftfrom rightno indty = function
+  | Cic.Prod (_, src, tgt) when strip = 0 ->
+      Cic.Prod (fresh_binder (),
+        CicSubstitution.lift_from liftfrom liftno src,
+        add_right_pi dependent strip liftno (liftfrom + 1) rightno indty tgt)
+  | Cic.Prod (_, _, tgt) ->
+      add_right_pi dependent (strip - 1) liftno liftfrom rightno indty tgt
+  | t ->
+      if dependent then
+        Cic.Prod (fresh_binder (),
+          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 rec add_right_lambda dependent strip liftno liftfrom rightno indty case =
+function
+  | Cic.Prod (_, src, tgt) when strip = 0 ->
+      Cic.Lambda (fresh_binder (),
+        CicSubstitution.lift_from liftfrom liftno src,
+        add_right_lambda dependent strip liftno (liftfrom + 1) rightno indty
+          case tgt)
+  | Cic.Prod (_, _, tgt) ->
+      add_right_lambda true (strip - 1) liftno liftfrom rightno indty
+        case tgt
+  | t ->
+      Cic.Lambda (fresh_binder (),
+        CicSubstitution.lift_from (rightno + 1) liftno indty, case)
+
+let rec branch (uri, typeno) insource paramsno t fix head args =
+  match t with
+  | Cic.MutInd (uri', typeno', []) when
+    UriManager.eq uri uri' && typeno = typeno' ->
+      if insource then
+        (match args with
+        | [arg] -> Cic.Appl (fix :: args)
+        | _ -> Cic.Appl (head :: [Cic.Appl args]))
+      else
+        (match args with
+        | [] -> head
+        | _ -> Cic.Appl (head :: args))
+  | Cic.Appl (Cic.MutInd (uri', typeno', []) :: tl) when
+    UriManager.eq uri uri' && typeno = typeno' ->
+      if insource then
+        let (lparams, rparams) = split tl paramsno in
+        match args with
+        | [arg] -> Cic.Appl (fix :: rparams @ args)
+        | _ -> Cic.Appl (fix :: rparams @ [Cic.Appl args])
+      else
+        (match args with
+        | [] -> head
+        | _ -> Cic.Appl (head :: args))
+  | Cic.Prod (binder, src, tgt) ->
+      if recursive uri typeno src then
+        let args = List.map (CicSubstitution.lift 1) args in
+        let phi =
+          let fix = CicSubstitution.lift 1 fix in
+          let src = CicSubstitution.lift 1 src in
+          branch (uri, typeno) true paramsno src fix head [Cic.Rel 1]
+        in
+        Cic.Lambda (fresh_binder (), src,
+          branch (uri, typeno) insource paramsno tgt
+            (CicSubstitution.lift 1 fix) (CicSubstitution.lift 1 head)
+            (args @ [Cic.Rel 1; phi]))
+      else  (* non recursive *)
+        let args = List.map (CicSubstitution.lift 1) args in
+        Cic.Lambda (fresh_binder (), src,
+          branch (uri, typeno) insource paramsno tgt
+          (CicSubstitution.lift 1 fix) (CicSubstitution.lift 1 head)
+            (args @ [Cic.Rel 1]))
+  | _ -> assert false
+
+let branch (uri, typeno) insource liftno paramsno t fix head args =
+  let t = strip_left_params liftno paramsno t in
+  branch (uri, typeno) insource paramsno t fix head args
+
+let elim_of ~sort uri typeno =
+  counter := ~-1;
+  let (obj, univ) = (CicEnvironment.get_obj CicUniv.empty_ugraph uri) 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 rightno = paramsno - leftno in
+      let dependent = (strip_pi ty <> Cic.Sort Cic.Prop) in
+let head = match strip_pi ty with Cic.Sort s -> s in
       let conslen = List.length constructors in
       let consno = ref (conslen + 1) in
+      if
+       not
+        (CicTypeChecker.check_allowed_sort_elimination uri typeno head sort)
+      then
+       raise Can_t_eliminate;
       let indty =
-        let indty = Cic.MutInd (uri, typeno, subst) in
-        if indno = 0 then
+        let indty = Cic.MutInd (uri, typeno, []) in
+        if paramsno = 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
+        let constructor = Cic.MutConstruct (uri, typeno, consno, []) in
+        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 ())))),
-          (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 *)
-            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]))))
+      let p_ty = type_of_p sort dependent leftno indty ty in
+      let final_ty =
+        add_right_pi dependent leftno (conslen + 1) 1 rightno indty ty
       in
-      add_params indno ty eliminator
-  | _ -> assert false
+      let eliminator_type =
+        let cic =
+          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) dependent leftno !consno
+                    constructor p [mk_constructor !consno]),
+                  acc))
+              constructors final_ty))
+        in
+        add_params (fun b s t -> Cic.Prod (b, s, t)) leftno ty cic
+      in
+      let consno = ref (conslen + 1) in
+      let eliminator_body =
+        let fix = Cic.Rel (rightno + 2) in
+        let is_recursive = recursive_type uri typeno constructors in
+        let recshift = if is_recursive then 1 else 0 in
+        let (_, branches) =
+          List.fold_right
+            (fun (_, ty) (shift, branches) ->
+              let head = Cic.Rel (rightno + shift + 1 + recshift) in
+              let b =
+                branch (uri, typeno) false
+                  (rightno + conslen + 2 + recshift) leftno ty fix head []
+              in
+              (shift + 1,  b :: branches))
+            constructors (1, [])
+        in
+        let shiftno  = conslen + rightno + 2 + recshift in
+        let outtype =
+         if dependent then
+          Cic.Rel shiftno
+         else
+          let head =
+           if rightno = 0 then
+            CicSubstitution.lift 1 (Cic.Rel shiftno)
+           else
+            Cic.Appl
+             ((CicSubstitution.lift (rightno + 1) (Cic.Rel shiftno)) ::
+              mk_rels 1 rightno)
+          in
+           add_right_lambda true leftno shiftno 1 rightno indty head ty
+        in
+        let mutcase =
+          Cic.MutCase (uri, typeno, outtype, Cic.Rel 1, branches)
+        in
+        let body =
+          if is_recursive then
+            let fixfun =
+              add_right_lambda dependent leftno (conslen + 2) 1 rightno
+                indty mutcase ty
+            in
+            (* rightno is the decreasing argument, i.e. the argument of
+             * inductive type *)
+            Cic.Fix (0, ["f", rightno, final_ty, fixfun])
+          else
+            add_right_lambda dependent leftno (conslen + 1) 1 rightno indty
+              mutcase ty
+        in
+        let cic =
+          Cic.Lambda (Cic.Name "P", p_ty,
+            (List.fold_right
+              (fun (_, constructor) acc ->
+                decr consno;
+                let p = Cic.Rel !consno in
+                Cic.Lambda (fresh_binder (),
+                  (delta (uri, typeno) dependent leftno !consno
+                    constructor p [mk_constructor !consno]),
+                  acc))
+              constructors body))
+        in
+        add_params (fun b s t -> Cic.Lambda (b, s, t)) leftno ty cic
+      in
+(*
+debug_print (lazy (CicPp.ppterm eliminator_type));
+debug_print (lazy (CicPp.ppterm eliminator_body));
+*)
+      let eliminator_type = 
+	FreshNamesGenerator.mk_fresh_names [] [] [] eliminator_type in
+      let eliminator_body = 
+	FreshNamesGenerator.mk_fresh_names [] [] [] eliminator_body in
+(*
+debug_print (lazy (CicPp.ppterm eliminator_type));
+debug_print (lazy (CicPp.ppterm eliminator_body));
+*)
+      let (computed_type, ugraph) =
+        try
+          CicTypeChecker.type_of_aux' [] [] eliminator_body CicUniv.empty_ugraph
+        with CicTypeChecker.TypeCheckerFailure msg ->
+          raise (Elim_failure (lazy (sprintf 
+            "type checker failure while type checking:\n%s\nerror:\n%s"
+            (CicPp.ppterm eliminator_body) (Lazy.force msg))))
+      in
+      if not (fst (CicReduction.are_convertible []
+        eliminator_type computed_type ugraph))
+      then
+        raise (Failure (sprintf
+          "internal error: type mismatch on eliminator type\n%s\n%s"
+          (CicPp.ppterm eliminator_type) (CicPp.ppterm computed_type)));
+      let suffix =
+        match sort with
+        | Cic.Prop -> "_ind"
+        | Cic.Set -> "_rec"
+        | Cic.Type _ -> "_rect"
+        | _ -> assert false
+      in
+      let name = UriManager.name_of_uri uri ^ suffix in
+      let buri = UriManager.buri_of_uri uri in
+      let uri = UriManager.uri_of_string (buri ^ "/" ^ name ^ ".con") in
+      let obj_attrs = [`Class (`Elim sort); `Generated] in
+       uri,
+       Cic.Constant (name, Some eliminator_body, eliminator_type, [], obj_attrs)
+  | _ ->
+      failwith (sprintf "not an inductive definition (%s)"
+        (UriManager.string_of_uri uri))