+++ /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 (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, 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
- | _ -> 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, ["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))
-
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