(* 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 T    = ProceduralTypes
module Cl   = ProceduralClassify

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

let cic = D.deannotate_term

let get_ind_type uri tyno =
   match E.get_obj Un.empty_ugraph uri with
      | C.InductiveDefinition (tys, _, lpsno, _), _ -> lpsno, List.nth tys tyno
      | _                                           -> assert false

let get_default_eliminator context uri tyno ty =
   let _, (name, _, _, _) = get_ind_type uri tyno in
   let sort, _ = TC.type_of_aux' [] context ty Un.empty_ugraph in
   let ext = match sort with
      | C.Sort C.Prop     -> "_ind"
      | C.Sort C.Set      -> "_rec"
      | C.Sort C.CProp    -> "_rec"
      | C.Sort (C.Type _) -> "_rect" 
      | C.Meta (_,_)      -> assert false
      | _                 -> assert false
   in
   let buri = UM.buri_of_uri uri in
   let uri = UM.uri_of_string (buri ^ "/" ^ name ^ ext ^ ".con") in
   C.Const (uri, [])

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 rec need_whd i = function
   | C.ACast (_, t, _)               -> need_whd i t
   | C.AProd (_, _, _, t) when i > 0 -> need_whd (pred i) t
   | _                    when i > 0 -> true
   | _                               -> false

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 C.ARel (id, rid, m + n, b)
      | 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 fake_annotate c =
   let get_binder c m =
      try match List.nth c (pred m) with
	 | Some (C.Name s, _) -> s
	 | _                  -> assert false
      with
         | Invalid_argument _ -> assert false 
   in
   let mk_decl n v = Some (n, C.Decl v) in
   let mk_def n v = Some (n, C.Def (v, None)) in
   let mk_fix (name, _, _, bo) = mk_def (C.Name name) bo in
   let mk_cofix (name, _, bo) = mk_def (C.Name name) bo in
   let rec ann_xns c (uri, t) = uri, ann_term c t
   and ann_ms c = function
      | None   -> None
      | Some t -> Some (ann_term c t)
   and ann_fix newc c (name, i, ty, bo) =
      "", name, i, ann_term c ty, ann_term (List.rev_append newc c) bo
   and ann_cofix newc c (name, ty, bo) =
      "", name, ann_term c ty, ann_term (List.rev_append newc c) bo
   and ann_term c = function
      | C.Sort sort -> C.ASort ("", sort)
      | C.Implicit ann -> C.AImplicit ("", ann)
      | C.Rel m -> C.ARel ("", "", m, get_binder c m)
      | C.Const (uri, xnss) -> C.AConst ("", uri, List.map (ann_xns c) xnss)
      | C.Var (uri, xnss) -> C.AVar ("", uri, List.map (ann_xns c) xnss)
      | C.MutInd (uri, tyno, xnss) -> C.AMutInd ("", uri, tyno, List.map (ann_xns c) xnss)
      | C.MutConstruct (uri, tyno, consno, xnss) -> C.AMutConstruct ("", uri,tyno,consno, List.map (ann_xns c) xnss)
      | C.Meta (i, mss) -> C.AMeta("", i, List.map (ann_ms c) mss)
      | C.Appl ts -> C.AAppl ("", List.map (ann_term c) ts)
      | C.Cast (te, ty) -> C.ACast ("", ann_term c te, ann_term c ty)
      | C.MutCase (sp, i, outty, t, pl) -> C.AMutCase ("", sp, i, ann_term c outty, ann_term c t, List.map (ann_term c) pl)      
      | C.Prod (n, s, t) -> C.AProd ("", n, ann_term c s, ann_term (mk_decl n s :: c) t)
      | C.Lambda (n, s, t) -> C.ALambda ("", n, ann_term c s, ann_term (mk_decl n s :: c) t)
      | C.LetIn (n, s, t) -> C.ALetIn ("", n, ann_term c s, ann_term (mk_def n s :: c) t)
      | C.Fix (i, fl) -> C.AFix ("", i, List.map (ann_fix (List.rev_map mk_fix fl) c) fl)
      | C.CoFix (i, fl) -> C.ACoFix ("", i, List.map (ann_cofix (List.rev_map mk_cofix fl) c) fl)
   in
   ann_term c

let rec add_abst n t =
   if n <= 0 then t else
   let t = C.ALambda ("", C.Name "foo", C.AImplicit ("", None), lift 0 1 t) in  
   add_abst (pred n) t

let mk_ind context id uri tyno outty arg cases =
try   
   let is_recursive = function
      | C.MutInd (u, no, _) -> UM.eq u uri && no = tyno
      | _                   -> false
   in
   let lpsno, (_, _, _, constructors) = get_ind_type uri tyno in
   let inty, _ = TC.type_of_aux' [] context (cic arg) Un.empty_ugraph in
   let ps = match inty with
      | C.MutInd _                  -> []
      | C.Appl (C.MutInd _ :: args) -> List.map (fake_annotate context) args
      | _                           -> assert false
   in
   let lps, rps = T.list_split lpsno ps in
   let eliminator = get_default_eliminator context uri tyno inty in
   let eliminator = fake_annotate context eliminator in
   let arg_ref = T.mk_arel 0 "foo" in
   let body = C.AMutCase (id, uri, tyno, outty, arg_ref, cases) in
   let predicate = add_abst (succ (List.length rps)) body in   
   let map2 case (_, cty) = 
      let map (h, case, k) premise = 
         if h > 0 then pred h, lift k 1 case, k else
	 if is_recursive premise then 0, lift (succ k) 1 case, succ k else
	 0, case, succ k
      in
      let premises, _ = Cl.split context cty in
      let _, lifted_case, _ =
         List.fold_left map (lpsno, case, 1) (List.rev (List.tl premises))
      in
      lifted_case
   in
   let lifted_cases = List.map2 map2 cases constructors in
   let args = eliminator :: lps @ predicate :: lifted_cases @ rps @ [arg] in
   Some (C.AAppl (id, args))
with Invalid_argument _ -> failwith "PCn.mk_ind"