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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_ltac.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 ist =
if (is_empty_type (List.assoc 1 ist.lmatch)) then
<:tactic<ElimType ?1;Assumption>>
else
failwith "is_empty"
let is_unit ist =
if (is_unit_type (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
failwith "is_unit"
let is_conj ist =
if (is_conjunction (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
failwith "is_conj"
let is_disj ist =
if (is_disjunction (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
failwith "is_disj"
let not_dep_intros ist =
<:tactic<
Repeat
Match Context With
| [|- ?1 -> ?2 ] -> Intro>>
let init_intros =
(tclORELSE (tclTHEN (intros_until_n_wored 1)
(interp (tacticIn not_dep_intros))) intros)
let axioms ist =
let t_is_unit = tacticIn is_unit
and t_is_empty = tacticIn is_empty in
<:tactic<
Match Context With
|[|- ?1] -> $t_is_unit;Constructor
|[_:?1 |- ?] -> $t_is_empty
|[_:?1 |- ?1] -> Assumption>>
let simplif t_reduce ist =
let t_is_unit = tacticIn is_unit
and t_is_conj = tacticIn is_conj
and t_is_disj = tacticIn is_disj
and t_not_dep_intros = tacticIn not_dep_intros in
<:tactic<
$t_not_dep_intros;
Repeat
($t_reduce;
(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|Intros;Apply id;
Try Left;Assumption]|Intros;Apply id;Try Right;Assumption]
| [id0: ?1-> ?2; id1: ?1|- ?] -> Generalize (id0 id1);Intro;Clear id0
| [id: ?1 -> ?2|- ?] ->
$t_is_unit;Cut ?2;[Intro;Clear id|Intros;Apply id;Constructor;Fail]
| [|- (?1 ? ?)] -> $t_is_conj;Split);
$t_not_dep_intros)>>
let rec tauto_main t_reduce ist =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn (simplif t_reduce)
and t_is_disj = tacticIn is_disj
and t_tauto_main = tacticIn (tauto_main t_reduce) 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;Try Intro;
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 t_reduce ist =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn (simplif t_reduce)
and t_intuition_main = tacticIn (intuition_main t_reduce) 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 id in
interp <:tactic<Unfold not iff in $ast_id>>
let reduction_not_iff = Tacticals.onAllClauses (fun ido -> unfold_not_iff ido)
let red = function
| None -> interp <:tactic<Repeat Red>>
| Some id ->
let ast_id = nvar id in
interp <:tactic<Repeat (Red in $ast_id)>>
let reduction = Tacticals.onAllClauses red
(* Trick to coerce a tactic into an ast, since not provided in quotation *)
let _ = hide_atomic_tactic "OnAllClausesRepeatRed" reduction
let _ = hide_atomic_tactic "OnAllClausesUnfoldNotIff" reduction_not_iff
let t_reduction = ope ("OnAllClausesRepeatRed",[])
let t_reduction_not_iff = ope ("OnAllClausesUnfoldNotIff",[])
(* As a simple heuristic, first we try to avoid reduction both in tauto and
intuition *)
let tauto g =
try
(tclTHEN init_intros
(tclORELSE
(interp (tacticIn (tauto_main t_reduction_not_iff)))
(interp (tacticIn (tauto_main t_reduction))))) g
with UserError _ -> errorlabstrm "tauto" [< str "Tauto failed" >]
let intuition =
tclTHEN init_intros
(tclORELSE
(interp (tacticIn (intuition_main t_reduction_not_iff)))
(interp (tacticIn (intuition_main t_reduction))))
let _ = hide_atomic_tactic "Tauto" tauto
let _ = hide_atomic_tactic "Intuition" intuition
|
