(* 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/
 *)

let fresh_binder =
  let counter = ref ~-1 in
  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', _, _) -> 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 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') ->
      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' ->
      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) dependent paramsno consno src
            (CicSubstitution.lift 1 p) [Cic.Rel 1])
        in
        Cic.Prod (fresh_binder dependent, src,
          Cic.Prod (Cic.Anonymous, phi,
            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 (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
  else
    match ty with
    | Cic.Prod (binder, src, tgt) ->
        Cic.Prod (binder, src, add_params (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 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, 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 leftno = 0 then
          indty
        else
          Cic.Appl (indty :: mk_rels 0 paramsno)
      in
      let mk_constructor consno =
        let constructor = Cic.MutConstruct (uri, typeno, consno, subst) in
        if leftno = 0 then
          constructor
        else
          Cic.Appl (constructor :: mk_rels consno leftno)
      in
      let eliminator =
        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) dependent leftno !consno
                  constructor p [mk_constructor !consno]),
                acc))
            constructors
            final_ty))
      in
      add_params leftno ty eliminator
  | _ -> assert false