(************************************************************************)
(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2010     *)
(*   \VV/  **************************************************************)
(*    //   *      This file is distributed under the terms of the       *)
(*         *       GNU Lesser General Public License Version 2.1        *)
(************************************************************************)

(* $Id: elim.ml 13323 2010-07-24 15:57:30Z herbelin $ *)

open Pp
open Util
open Names
open Term
open Termops
open Environ
open Libnames
open Reduction
open Inductiveops
open Proof_type
open Clenv
open Hipattern
open Tacmach
open Tacticals
open Tactics
open Hiddentac
open Genarg
open Tacexpr

let introElimAssumsThen tac ba =
  let nassums =
    List.fold_left
      (fun acc b -> if b then acc+2 else acc+1)
      0 ba.branchsign
  in
  let introElimAssums = tclDO nassums intro in
  (tclTHEN introElimAssums (elim_on_ba tac ba))

let introCaseAssumsThen tac ba =
  let case_thin_sign =
    List.flatten
      (List.map (function b -> if b then [false;true] else [false])
	ba.branchsign)
  in
  let n1 = List.length case_thin_sign in
  let n2 = List.length ba.branchnames in
  let (l1,l2),l3 =
    if n1 < n2 then list_chop n1 ba.branchnames, []
    else
      (ba.branchnames, []),
       if n1 > n2 then snd (list_chop n2 case_thin_sign) else [] in
  let introCaseAssums =
    tclTHEN (intros_pattern no_move l1) (intros_clearing l3) in
  (tclTHEN introCaseAssums (case_on_ba (tac l2) ba))

(* The following tactic Decompose repeatedly applies the
   elimination(s) rule(s) of the types satisfying the predicate
   ``recognizer'' onto a certain hypothesis. For example :

Require Elim.
Require Le.
   Goal (y:nat){x:nat | (le O x)/\(le x y)}->{x:nat | (le O x)}.
   Intros y H.
   Decompose [sig and] H;EAuto.
   Qed.

Another example :

   Goal (A,B,C:Prop)(A/\B/\C \/ B/\C \/ C/\A) -> C.
   Intros A B C H; Decompose [and or] H; Assumption.
   Qed.
*)

let elimHypThen tac id gl =
  elimination_then tac ([],[]) (mkVar id) gl

let rec general_decompose_on_hyp recognizer =
  ifOnHyp recognizer (general_decompose_aux recognizer) (fun _ -> tclIDTAC)

and general_decompose_aux recognizer id =
  elimHypThen
    (introElimAssumsThen
       (fun bas ->
	  tclTHEN (clear [id])
	    (tclMAP (general_decompose_on_hyp recognizer)
               (ids_of_named_context bas.assums))))
    id

(* Faudrait ajouter un COMPLETE pour que l'hypothèse créée ne reste
   pas si aucune élimination n'est possible *)

(* Meilleures stratégies mais perte de compatibilité *)
let tmphyp_name = id_of_string "_TmpHyp"
let up_to_delta = ref false (* true *)

let general_decompose recognizer c gl =
  let typc = pf_type_of gl c in
  tclTHENSV (cut typc)
    [| tclTHEN (intro_using tmphyp_name)
         (onLastHypId
	    (ifOnHyp recognizer (general_decompose_aux recognizer)
	      (fun id -> clear [id])));
       exact_no_check c |] gl

let head_in gls indl t =
  try
    let ity,_ =
      if !up_to_delta
      then find_mrectype (pf_env gls) (project gls) t
      else extract_mrectype t
    in List.mem ity indl
  with Not_found -> false

let inductive_of = function
  | IndRef ity -> ity
  | r ->
      errorlabstrm "Decompose"
        (Printer.pr_global r ++ str " is not an inductive type.")

let decompose_these c l gls =
  let indl = (*List.map inductive_of*) l in
  general_decompose (fun (_,t) -> head_in gls indl t) c gls

let decompose_nonrec c gls =
  general_decompose
    (fun (_,t) -> is_non_recursive_type t)
    c gls

let decompose_and c gls =
  general_decompose
    (fun (_,t) -> is_record t)
    c gls

let decompose_or c gls =
  general_decompose
    (fun (_,t) -> is_disjunction t)
    c gls

let inj_open c = (Evd.empty,c)

let h_decompose l c =
  Refiner.abstract_tactic (TacDecompose (l,c)) (decompose_these c l)

let h_decompose_or c =
  Refiner.abstract_tactic (TacDecomposeOr c) (decompose_or c)

let h_decompose_and c =
  Refiner.abstract_tactic (TacDecomposeAnd c) (decompose_and c)

(* The tactic Double performs a double induction *)

let simple_elimination c gls =
  simple_elimination_then (fun _ -> tclIDTAC) c gls

let induction_trailer abs_i abs_j bargs =
  tclTHEN
    (tclDO (abs_j - abs_i) intro)
    (onLastHypId
       (fun id gls ->
	  let idty = pf_type_of gls (mkVar id) in
	  let fvty = global_vars (pf_env gls) idty in
	  let possible_bring_hyps =
	    (List.tl (nLastDecls (abs_j - abs_i) gls)) @ bargs.assums
          in
	  let (hyps,_) =
            List.fold_left
	      (fun (bring_ids,leave_ids) (cid,_,cidty as d) ->
                 if not (List.mem cid leave_ids)
                 then (d::bring_ids,leave_ids)
                 else (bring_ids,cid::leave_ids))
	      ([],fvty) possible_bring_hyps
	  in
          let ids = List.rev (ids_of_named_context hyps) in
	  (tclTHENSEQ
            [bring_hyps hyps; tclTRY (clear ids);
	     simple_elimination (mkVar id)])
          gls))

let double_ind h1 h2 gls =
  let abs_i = depth_of_quantified_hypothesis true h1 gls in
  let abs_j = depth_of_quantified_hypothesis true h2 gls in
  let (abs_i,abs_j) =
    if abs_i < abs_j then (abs_i,abs_j) else
    if abs_i > abs_j then (abs_j,abs_i) else
      error "Both hypotheses are the same." in
  (tclTHEN (tclDO abs_i intro)
     (onLastHypId
       	(fun id ->
           elimination_then
             (introElimAssumsThen (induction_trailer abs_i abs_j))
             ([],[]) (mkVar id)))) gls

let h_double_induction h1 h2 =
  Refiner.abstract_tactic (TacDoubleInduction (h1,h2)) (double_ind h1 h2)