(* 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
module PEH  = ProofEngineHelpers
module PT   = PrimitiveTactics

module DTI  = DoubleTypeInference

(* 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, ty, s, t) -> C.ALetIn (id, n, lift_term k s, lift_term k ty, 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 id 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 ty = Some (n, C.Def (v, ty)) in
      let mk_fix (name, _, ty, bo) = mk_def (C.Name name) bo ty in
      let mk_cofix (name, ty, bo) = mk_def (C.Name name) bo ty 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) =
         id, name, i, ann_term c ty, ann_term (List.rev_append newc c) bo
      and ann_cofix newc c (name, ty, bo) =
         id, name, ann_term c ty, ann_term (List.rev_append newc c) bo
      and ann_term c = function
         | C.Sort sort -> C.ASort (id, sort)
         | C.Implicit ann -> C.AImplicit (id, ann)
         | C.Rel m -> C.ARel (id, id, m, get_binder c m)
         | C.Const (uri, xnss) -> C.AConst (id, uri, List.map (ann_xns c) xnss)
         | C.Var (uri, xnss) -> C.AVar (id, uri, List.map (ann_xns c) xnss)
         | C.MutInd (uri, tyno, xnss) -> C.AMutInd (id, uri, tyno, List.map (ann_xns c) xnss)
         | C.MutConstruct (uri, tyno, consno, xnss) -> C.AMutConstruct (id, uri,tyno,consno, List.map (ann_xns c) xnss)
         | C.Meta (i, mss) -> C.AMeta(id, i, List.map (ann_ms c) mss)
         | C.Appl ts -> C.AAppl (id, List.map (ann_term c) ts)
         | C.Cast (te, ty) -> C.ACast (id, ann_term c te, ann_term c ty)
         | C.MutCase (sp, i, outty, t, pl) -> C.AMutCase (id, sp, i, ann_term c outty, ann_term c t, List.map (ann_term c) pl)
         | C.Prod (n, s, t) -> C.AProd (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
         | C.Lambda (n, s, t) -> C.ALambda (id, n, ann_term c s, ann_term (mk_decl n s :: c) t)
         | C.LetIn (n, s, ty, t) -> C.ALetIn (id, n, ann_term c s, ann_term c ty, ann_term (mk_def n s ty :: c) t)
         | C.Fix (i, fl) -> C.AFix (id, i, List.map (ann_fix (List.rev_map mk_fix fl) c) fl)
         | C.CoFix (i, fl) -> C.ACoFix (id, i, List.map (ann_cofix (List.rev_map mk_cofix fl) c) fl)
      in
      ann_term c

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 succ (k - n) <= m && m <= k 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, ty, t) -> 
         let s, ty, t = gen_term k s, gen_term k ty, gen_term (succ k) t in
         if is_meta [s; t] then meta id else C.ALetIn (id, anon, s, ty, 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 psno predicate =
   let body = generalize psno predicate in
   clear_absts 0 psno body

let get_clears c p xtypes = 
   let meta = C.Implicit None in
   let rec aux c names p it et = function
      | []                                                -> 
         List.rev c, List.rev names         
      | Some (C.Name name as n, C.Decl v) as hd :: tl     ->
         let hd, names, v = 
	    if DTI.does_not_occur 1 p && DTI.does_not_occur 1 it && DTI.does_not_occur 1 et then 
	       Some (C.Anonymous, C.Decl v), name :: names, meta 
	    else 
	       hd, names, v
	 in
	 let p = C.Lambda (n, v, p) in
	 let it = C.Prod (n, v, it) in
	 let et = C.Prod (n, v, et) in
	 aux (hd :: c) names p it et tl
      | Some (C.Name name as n, C.Def (v, x)) as hd :: tl ->
         let hd, names, v = 
	    if DTI.does_not_occur 1 p && DTI.does_not_occur 1 it && DTI.does_not_occur 1 et then 
	       Some (C.Anonymous, C.Def (v, x)), name :: names, meta
	    else 
	       hd, names, v
	 in
	 let p = C.LetIn (n, v, x, p) in
	 let it = C.LetIn (n, v, x, it) in
	 let et = C.LetIn (n, v, x, et) in
	 aux (hd :: c) names p it et tl
      | Some (C.Anonymous as n, C.Decl v) as hd :: tl     ->
	 let p = C.Lambda (n, meta, p) in
	 let it = C.Lambda (n, meta, it) in
	 let et = C.Lambda (n, meta, et) in
	 aux (hd :: c) names p it et tl
      | Some (C.Anonymous as n, C.Def (v, _)) as hd :: tl ->
	 let p = C.LetIn (n, meta, meta, p) in
	 let it = C.LetIn (n, meta, meta, it) in
	 let et = C.LetIn (n, meta, meta, et) in
	 aux (hd :: c) names p it et tl
      | None :: tl                                        -> assert false
   in
   match xtypes with 
      | Some (it, et) -> aux [] [] p it et c
      | None          -> c, []

let clear c hyp =
   let rec aux c = function
      | []            -> List.rev c
      | Some (C.Name name, entry) :: tail when name = hyp ->
	 aux (Some (C.Anonymous, entry) :: c) tail
      | entry :: tail -> aux (entry :: c) tail
   in
   aux [] c

let elim_inferred_type context goal arg using cpattern =
   let metasenv, ugraph = [], Un.oblivion_ugraph in 
   let ety, _ugraph = TC.type_of_aux' metasenv context using ugraph in
   let _splits, args_no = PEH.split_with_whd (context, ety) in
   let _metasenv, predicate, _arg, actual_args = PT.mk_predicate_for_elim 
      ~context ~metasenv ~ugraph ~goal ~arg ~using ~cpattern ~args_no
   in
   let ty = C.Appl (predicate :: actual_args) in
   let upto = List.length actual_args in
   Rd.head_beta_reduce ~delta:false ~upto ty