(* Copyright (C) 2003-2005, 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://cs.unibo.it/helm/.
 *)

module C    = Cic
module E    = CicEnvironment
module Un   = CicUniv
module TC   = CicTypeChecker 
module D    = Deannotate
module UM   = UriManager
module Rd   = CicReduction

(* helpers ******************************************************************)

let cic = D.deannotate_term

let rec list_sub start length = function
   | _  :: tl when start  > 0 -> list_sub (pred start) length tl
   | hd :: tl when length > 0 -> hd :: list_sub start (pred length) tl
   | _                        -> []
    
(* proof construction *******************************************************)

let lift k n =
   let rec lift_xns k (uri, t) = uri, lift_term k t
   and lift_ms k = function
      | None   -> None
      | Some t -> Some (lift_term k t)
   and lift_fix len k (id, name, i, ty, bo) =
      id, name, i, lift_term k ty, lift_term (k + len) bo
   and lift_cofix len k (id, name, ty, bo) =
      id, name, lift_term k ty, lift_term (k + len) bo
   and lift_term k = function
      | C.ASort _ as t -> t
      | C.AImplicit _ as t -> t
      | C.ARel (id, rid, m, b) as t -> 
         if m < k then t else 
	 if m + n > 0 then C.ARel (id, rid, m + n, b) else
	 assert false
      | C.AConst (id, uri, xnss) -> C.AConst (id, uri, List.map (lift_xns k) xnss)
      | C.AVar (id, uri, xnss) -> C.AVar (id, uri, List.map (lift_xns k) xnss)
      | C.AMutInd (id, uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (lift_xns k) xnss)
      | C.AMutConstruct (id, uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (lift_xns k) xnss)
      | C.AMeta (id, i, mss) -> C.AMeta(id, i, List.map (lift_ms k) mss)
      | C.AAppl (id, ts) -> C.AAppl (id, List.map (lift_term k) ts)
      | C.ACast (id, te, ty) -> C.ACast (id, lift_term k te, lift_term k ty)
      | C.AMutCase (id, sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, lift_term k outty, lift_term k t, List.map (lift_term k) pl)
      | C.AProd (id, n, s, t) -> C.AProd (id, n, lift_term k s, lift_term (succ k) t)
      | C.ALambda (id, n, s, t) -> C.ALambda (id, n, lift_term k s, lift_term (succ k) t)
      | C.ALetIn (id, n, s, t) -> C.ALetIn (id, n, lift_term k s, lift_term (succ k) t)
      | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (lift_fix (List.length fl) k) fl)
      | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (lift_cofix (List.length fl) k) fl)
   in
   lift_term k

let clear_absts m =
   let rec aux k n = function
      | C.AImplicit (_, None) as t         -> t
      | C.ALambda (id, s, v, t) when k > 0 -> 
         C.ALambda (id, s, v, aux (pred k) n t)
      | C.ALambda (_, _, _, t) when n > 0  -> 
         aux 0 (pred n) (lift 1 (-1) t)
      | t                      when n > 0  ->
	    Printf.eprintf "CLEAR: %u %s\n" n (CicPp.ppterm (cic t));
	    assert false 
      | t                                  -> t
   in 
   aux m

let hole id = C.AImplicit (id, Some `Hole)

let meta id = C.AImplicit (id, None)

let anon = C.Anonymous

let generalize n =
   let is_meta =
      let map b = function
         | C.AImplicit (_, None) when b -> b
	 | _                            -> false
      in
      List.fold_left map true
   in
   let rec gen_fix len k (id, name, i, ty, bo) =
      id, name, i, gen_term k ty, gen_term (k + len) bo
   and gen_cofix len k (id, name, ty, bo) =
      id, name, gen_term k ty, gen_term (k + len) bo
   and gen_term k = function
      | C.ASort (id, _) 
      | C.AImplicit (id, _)
      | C.AConst (id, _, _)
      | C.AVar (id, _, _)
      | C.AMutInd (id, _, _, _)
      | C.AMutConstruct (id, _, _, _, _)
      | C.AMeta (id, _, _) -> meta id
      | C.ARel (id, _, m, _) -> 
         if m = succ (k - n) then hole id else meta id
      | C.AAppl (id, ts) -> 
         let ts = List.map (gen_term k) ts in
         if is_meta ts then meta id else C.AAppl (id, ts)
      | C.ACast (id, te, ty) -> 
         let te, ty = gen_term k te, gen_term k ty in
	 if is_meta [te; ty] then meta id else C.ACast (id, te, ty)
      | C.AMutCase (id, sp, i, outty, t, pl) ->         
	 let outty, t, pl = gen_term k outty, gen_term k t, List.map (gen_term k) pl in
	 if is_meta (outty :: t :: pl) then meta id else hole id (* C.AMutCase (id, sp, i, outty, t, pl) *)
      | C.AProd (id, _, s, t) -> 
         let s, t = gen_term k s, gen_term (succ k) t in
         if is_meta [s; t] then meta id else C.AProd (id, anon, s, t)
      | C.ALambda (id, _, s, t) ->
         let s, t = gen_term k s, gen_term (succ k) t in
         if is_meta [s; t] then meta id else C.ALambda (id, anon, s, t)
      | C.ALetIn (id, _, s, t) -> 
         let s, t = gen_term k s, gen_term (succ k) t in
         if is_meta [s; t] then meta id else C.ALetIn (id, anon, s, t)
      | C.AFix (id, i, fl) -> C.AFix (id, i, List.map (gen_fix (List.length fl) k) fl)
      | C.ACoFix (id, i, fl) -> C.ACoFix (id, i, List.map (gen_cofix (List.length fl) k) fl)
   in
   gen_term 0

let mk_pattern rpsno predicate =
   let body = generalize rpsno predicate in
   clear_absts 0 rpsno body