--- /dev/null
+(* Copyright (C) 2004, HELM Team.
+ *
+ * This file is part of HELM, an Hypertextual, Electronic
+ * Library of Mathematics, developed at the Computer Science
+ * Department, University of Bologna, Italy.
+ *
+ * HELM is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU General Public License
+ * as published by the Free Software Foundation; either version 2
+ * of the License, or (at your option) any later version.
+ *
+ * HELM is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with HELM; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+ * MA 02111-1307, USA.
+ *
+ * For details, see the HELM World-Wide-Web page,
+ * http://helm.cs.unibo.it/
+ *)
+
+(* $Id$ *)
+
+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 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', []) 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 =
+ let src = CicSubstitution.lift 1 src in
+ delta (uri, typeno) dependent paramsno consno src
+ (CicSubstitution.lift 1 p) [Cic.Rel 1]
+ in
+ let tgt = CicSubstitution.lift 1 tgt in
+ Cic.Prod (fresh_binder (), src,
+ Cic.Prod (Cic.Anonymous, phi,
+ 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 (fresh_binder (), src,
+ delta (uri, typeno) 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) 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 (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 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 (fix :: [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, leftno, _) ->
+ let (name, inductive, ty, constructors) =
+ try
+ List.nth indTypes typeno
+ with Failure _ -> assert false
+ in
+ let ty = Unshare.unshare ~fresh_univs:true ty in
+ let constructors =
+ List.map (fun (name,c)-> name,Unshare.unshare ~fresh_univs:true c) constructors
+ 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
+ | _ -> assert false
+ 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, []) in
+ if paramsno = 0 then
+ indty
+ else
+ Cic.Appl (indty :: mk_rels 0 paramsno)
+ in
+ let mk_constructor consno =
+ let constructor = Cic.MutConstruct (uri, typeno, consno, []) in
+ if leftno = 0 then
+ constructor
+ else
+ Cic.Appl (constructor :: mk_rels consno leftno)
+ in
+ 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
+ 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, ["aux", 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 name = name ^ 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))
+
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