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(***********************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA-Rocquencourt & LRI-CNRS-Orsay *)
(* \VV/ *************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(***********************************************************************)
(*i camlp4deps: "parsing/grammar.cma kernel/names.cmo parsing/ast.cmo parsing/g_tactic.cmo parsing/g_constr.cmo" i*)
(*i $Id$ i*)
open Ast
open Coqast
open Hipattern
open Names
open Pp
open Proof_type
open Tacmach
open Tacinterp
open Tactics
open Util
let is_empty () =
if (is_empty_type (List.assoc 1 !r_lmatch)) then
<:tactic<ElimType ?1;Assumption>>
else
failwith "is_empty"
let is_unit () =
if (is_unit_type (List.assoc 1 !r_lmatch)) then
<:tactic<Constructor>>
else
failwith "is_unit"
let is_conj () =
if (is_conjunction (List.assoc 1 !r_lmatch)) then
<:tactic<Idtac>>
else
failwith "is_conj"
let is_disj () =
if (is_disjunction (List.assoc 1 !r_lmatch)) then
<:tactic<Idtac>>
else
failwith "is_disj"
let not_dep_intros () =
<:tactic<
Repeat
Match Context With
| [|- ?1 -> ?2 ] -> Intro>>
let init_intros () =
(tclORELSE (tclTHEN (intros_until_n_wored 1) (interp (not_dep_intros ())))
intros)
let axioms () =
let t_is_unit = tacticIn is_unit
and t_is_empty = tacticIn is_empty in
<:tactic<
Match Context With
|[ |- ?1] -> $t_is_unit
|[ _:?1 |- ?] -> $t_is_empty
|[ _:?1 |- ?1] -> Assumption>>
let simplif () =
let t_is_conj = tacticIn is_conj
and t_is_disj = tacticIn is_disj
and t_not_dep_intros = tacticIn not_dep_intros in
<:tactic<
$t_not_dep_intros;
Repeat
((Match Context With
| [id: (?1 ? ?) |- ?] -> $t_is_conj;Elim id;Do 2 Intro;Clear id
| [id: (?1 ? ?) |- ?] -> $t_is_disj;Elim id;Intro;Clear id
| [id: (?1 ?2 ?3) -> ?4|- ?] ->
$t_is_conj;Cut ?2-> ?3-> ?4;[Intro;Clear id|Intros;Apply id;
Try Split;Assumption]
| [id: (?1 ?2 ?3) -> ?4|- ?] ->
$t_is_disj;Cut ?3-> ?4;[Cut ?2-> ?4;[Intros;Clear id|Intro;Apply id;
Left;Assumption]|Intro;Apply id;Right;Assumption]
| [id0: ?1-> ?2; id1: ?1|- ?] -> Generalize (id0 id1);Intro;Clear id0
| [|- (?1 ? ?)] -> $t_is_conj;Split);$t_not_dep_intros)>>
let rec tauto_main () =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn simplif
and t_is_disj = tacticIn is_disj
and t_tauto_main = tacticIn tauto_main in
<:tactic<
$t_simplif;$t_axioms
Orelse
(Match Context With
| [id:(?1-> ?2)-> ?3|- ?] ->
Cut ?2-> ?3;[Intro;Cut ?1-> ?2;[Intro;Cut ?3;[Intro;Clear id|
Intros;Apply id;Assumption]|Clear id]|Intros;Apply id;Intros;
Assumption];$t_tauto_main
| [|- (?1 ? ?)] ->
$t_is_disj;(Left;$t_tauto_main) Orelse (Right;$t_tauto_main))
Orelse
(Intro;$t_tauto_main)>>
let rec intuition_main () =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn simplif
and t_intuition_main = tacticIn intuition_main in
<:tactic<
$t_simplif;$t_axioms
Orelse Try (Solve [Auto with *|Intro;$t_intuition_main])>>
let unfold_not_iff = function
| None -> interp <:tactic<Unfold not iff>>
| Some id ->
let ast_id = nvar (string_of_id id) in
interp <:tactic<Unfold not iff in $ast_id>>
let reduction_not_iff = Tacticals.onAllClauses (fun ido -> unfold_not_iff ido)
let compute = function
| None -> interp <:tactic<Compute>>
| Some id ->
let ast_id = nvar (string_of_id id) in
interp <:tactic<Compute in $ast_id>>
let reduction = Tacticals.onAllClauses (fun ido -> compute ido)
(* As a simple heuristic, first we try to avoid reduction both in *)
(* tauto and intuition *)
let tauto g =
try
(tclTHEN (init_intros ())
(tclORELSE
(tclTHEN reduction_not_iff (interp (tauto_main ())))
(tclTHEN reduction (interp (tauto_main ()))))) g
with UserError _ -> errorlabstrm "tauto" [< 'sTR "Tauto failed" >]
let intuition =
tclTHEN (init_intros ())
(tclORELSE
(tclTHEN reduction_not_iff (interp (intuition_main ())))
(tclTHEN reduction (interp (intuition_main ()))))
let _ = hide_atomic_tactic "Tauto" tauto
let _ = hide_atomic_tactic "Intuition" intuition
|
