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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(* $Id: contradiction.ml,v 1.3.2.1 2004/07/16 19:30:52 herbelin Exp $ *)
+
+open Util
+open Term
+open Proof_type
+open Hipattern
+open Tacmach
+open Tacticals
+open Tactics
+open Coqlib
+open Reductionops
+open Rawterm
+
+(* Absurd *)
+
+let absurd c gls =
+  (tclTHENS
+     (tclTHEN (elim_type (build_coq_False ())) (cut c)) 
+     ([(tclTHENS
+          (cut (applist(build_coq_not (),[c]))) 
+	  ([(tclTHEN intros
+	       ((fun gl ->
+		   let ida = pf_nth_hyp_id gl 1
+                   and idna = pf_nth_hyp_id gl 2 in
+                   exact_no_check (applist(mkVar idna,[mkVar ida])) gl)));
+            tclIDTAC]));
+       tclIDTAC])) gls
+
+(* Contradiction *)
+
+let filter_hyp f tac gl =
+  let rec seek = function
+    | [] -> raise Not_found
+    | (id,_,t)::rest when f t -> tac id gl
+    | _::rest -> seek rest in
+  seek (pf_hyps gl)
+
+let contradiction_context gl =
+  let env = pf_env gl in
+  let sigma = project gl in
+  let rec seek_neg l gl = match l with
+    | [] ->  error "No such contradiction"
+    | (id,_,typ)::rest ->
+	let typ = whd_betadeltaiota env sigma typ in
+	if is_empty_type typ then
+	  simplest_elim (mkVar id) gl
+	else match kind_of_term typ with
+	  | Prod (na,t,u) when is_empty_type u ->
+	      (try
+		filter_hyp (fun typ -> pf_conv_x_leq gl typ t) 
+		  (fun id' -> simplest_elim (mkApp (mkVar id,[|mkVar id'|])))
+		  gl
+	      with Not_found -> seek_neg rest gl)
+	  | _ -> seek_neg rest gl in
+  seek_neg (pf_hyps gl) gl
+
+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) gl =
+  let env = pf_env gl in
+  let sigma = project gl in
+  let typ = pf_type_of gl c in
+  let _, ccl = splay_prod env sigma typ in
+  if is_empty_type ccl then
+    tclTHEN (elim cl None) (tclTRY assumption) gl
+  else
+    try
+      if lbind = NoBindings then
+	filter_hyp (is_negation_of env sigma typ)
+	  (fun id -> simplest_elim (mkApp (mkVar id,[|c|]))) gl
+      else
+	raise Not_found
+    with Not_found -> error "Not a contradiction"
+
+let contradiction = function
+  | None -> tclTHEN intros contradiction_context
+  | Some c -> contradiction_term c