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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2012 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Errors
open Term
open Hipattern
open Tacmach
open Tacticals
open Tactics
open Coqlib
open Reductionops
open Misctypes
open Proofview.Notations
(* Absurd *)
let absurd c gls =
let env = pf_env gls and sigma = project gls in
let j = Retyping.get_judgment_of env sigma c in
let sigma, j = Coercion.inh_coerce_to_sort Loc.ghost env sigma j in
let c = j.Environ.utj_val in
(tclTHENS
(tclTHEN (elim_type (build_coq_False ())) (cut c))
([(tclTHENS
(cut (mkApp(build_coq_not (),[|c|])))
([(tclTHEN (Proofview.V82.of_tactic intros)
((fun gl ->
let ida = pf_nth_hyp_id gl 1
and idna = pf_nth_hyp_id gl 2 in
exact_no_check (mkApp(mkVar idna,[|mkVar ida|])) gl)));
tclIDTAC]));
tclIDTAC])) { gls with Evd.sigma; }
let absurd c = Proofview.V82.tactic (absurd c)
(* Contradiction *)
let filter_hyp f tac =
let rec seek = function
| [] -> raise Not_found
| (id,_,t)::rest when f t -> tac id
| _::rest -> seek rest in
Goal.hyps >>- fun hyps ->
seek (Environ.named_context_of_val hyps)
let contradiction_context =
Goal.env >>- fun env ->
Goal.defs >>- fun sigma ->
let rec seek_neg l = match l with
| [] -> Proofview.tclZERO (UserError ("" , Pp.str"No such contradiction"))
| (id,_,typ)::rest ->
let typ = whd_betadeltaiota env sigma typ in
if is_empty_type typ then
simplest_elim (mkVar id)
else match kind_of_term typ with
| Prod (na,t,u) when is_empty_type u ->
(Proofview.tclORELSE
begin
Tacmach.New.pf_apply is_conv_leq >>- fun is_conv_leq ->
filter_hyp (fun typ -> is_conv_leq typ t)
(fun id' -> simplest_elim (mkApp (mkVar id,[|mkVar id'|])))
end
begin function
| Not_found -> seek_neg rest
| e -> Proofview.tclZERO e
end)
| _ -> seek_neg rest in
Goal.hyps >>- fun hyps ->
let hyps = Environ.named_context_of_val hyps in
seek_neg hyps
let is_negation_of env sigma typ t =
match kind_of_term (whd_betadeltaiota env sigma t) with
| Prod (na,t,u) -> is_empty_type u && is_conv_leq env sigma typ t
| _ -> false
let contradiction_term (c,lbind as cl) =
Goal.env >>- fun env ->
Goal.defs >>- fun sigma ->
Tacmach.New.pf_apply Typing.type_of >>- fun type_of ->
let typ = type_of c in
let _, ccl = splay_prod env sigma typ in
if is_empty_type ccl then
Tacticals.New.tclTHEN (elim false cl None) (Proofview.V82.tactic (tclTRY assumption))
else
Proofview.tclORELSE
begin
if lbind = NoBindings then
filter_hyp (is_negation_of env sigma typ)
(fun id -> simplest_elim (mkApp (mkVar id,[|c|])))
else
Proofview.tclZERO Not_found
end
begin function
| Not_found -> Proofview.tclZERO (Errors.UserError ("",Pp.str"Not a contradiction."))
| e -> Proofview.tclZERO e
end
let contradiction = function
| None -> Tacticals.New.tclTHEN intros contradiction_context
| Some c -> contradiction_term c
|
