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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 *)
(************************************************************************)
(*i camlp4deps: "parsing/grammar.cma" i*)
(*i $Id: tauto.ml4 10731 2008-03-30 22:30:44Z herbelin $ i*)
open Hipattern
open Names
open Libnames
open Pp
open Proof_type
open Tacticals
open Tacinterp
open Tactics
open Util
let assoc_last ist =
match List.assoc (Names.id_of_string "X1") ist.lfun with
| VConstr c -> c
| _ -> failwith "tauto: anomaly"
let is_empty ist =
if is_empty_type (assoc_last ist) then
<:tactic<idtac>>
else
<:tactic<fail>>
let is_unit ist =
if is_unit_type (assoc_last ist) then
<:tactic<idtac>>
else
<:tactic<fail>>
let is_conj ist =
let ind = assoc_last ist in
if (is_conjunction ind) && (is_nodep_ind ind) then
<:tactic<idtac>>
else
<:tactic<fail>>
let is_disj ist =
if is_disjunction (assoc_last ist) then
<:tactic<idtac>>
else
<:tactic<fail>>
let not_dep_intros ist =
<:tactic<
repeat match goal with
| |- (?X1 -> ?X2) => intro
| |- (Coq.Init.Logic.iff _ _) => unfold Coq.Init.Logic.iff
| |- (Coq.Init.Logic.not _) => unfold Coq.Init.Logic.not
| H:(Coq.Init.Logic.iff _ _)|- _ => unfold Coq.Init.Logic.iff in H
| H:(Coq.Init.Logic.not _)|-_ => unfold Coq.Init.Logic.not in H
| H:(Coq.Init.Logic.iff _ _)->_|- _ => unfold Coq.Init.Logic.iff in H
| H:(Coq.Init.Logic.not _)->_|-_ => unfold Coq.Init.Logic.not in H
end >>
let axioms ist =
let t_is_unit = tacticIn is_unit
and t_is_empty = tacticIn is_empty in
<:tactic<
match reverse goal with
| |- ?X1 => $t_is_unit; constructor 1
| _:?X1 |- _ => $t_is_empty; elimtype X1; assumption
| _:?X1 |- ?X1 => assumption
end >>
let simplif 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
(match reverse goal with
| id: (?X1 _ _) |- _ =>
$t_is_conj; elim id; do 2 intro; clear id
| id: (?X1 _ _) |- _ => $t_is_disj; elim id; intro; clear id
| id0: ?X1-> ?X2, id1: ?X1|- _ =>
(* generalize (id0 id1); intro; clear id0 does not work
(see Marco Maggiesi's bug PR#301)
so we instead use Assert and exact. *)
assert X2; [exact (id0 id1) | clear id0]
| id: ?X1 -> ?X2|- _ =>
$t_is_unit; cut X2;
[ intro; clear id
| (* id : ?X1 -> ?X2 |- ?X2 *)
cut X1; [exact id| constructor 1; fail]
]
| id: (?X1 ?X2 ?X3) -> ?X4|- _ =>
$t_is_conj; cut (X2-> X3-> X4);
[ intro; clear id
| (* id: (?X1 ?X2 ?X3) -> ?X4 |- ?X2 -> ?X3 -> ?X4 *)
intro; intro; cut (X1 X2 X3); [exact id| split; assumption]
]
| id: (?X1 ?X2 ?X3) -> ?X4|- _ =>
$t_is_disj;
cut (X3-> X4);
[cut (X2-> X4);
[intro; intro; clear id
| (* id: (?X1 ?X2 ?X3) -> ?X4 |- ?X2 -> ?X4 *)
intro; cut (X1 X2 X3); [exact id| left; assumption]
]
| (* id: (?X1 ?X2 ?X3) -> ?X4 |- ?X3 -> ?X4 *)
intro; cut (X1 X2 X3); [exact id| right; assumption]
]
| |- (?X1 _ _) => $t_is_conj; split
end;
$t_not_dep_intros) >>
let rec tauto_intuit t_reduce solver ist =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn simplif
and t_is_disj = tacticIn is_disj
and t_tauto_intuit = tacticIn (tauto_intuit t_reduce solver) in
let t_solver = Tacexpr.TacArg (valueIn (VTactic (dummy_loc,solver))) in
<:tactic<
($t_simplif;$t_axioms
|| match reverse goal with
| id:(?X1-> ?X2)-> ?X3|- _ =>
cut X3;
[ intro; clear id; $t_tauto_intuit
| cut (X1 -> X2);
[ exact id
| generalize (fun y:X2 => id (fun x:X1 => y)); intro; clear id;
solve [ $t_tauto_intuit ]]]
| |- (?X1 _ _) =>
$t_is_disj; solve [left;$t_tauto_intuit | right;$t_tauto_intuit]
end
||
(* NB: [|- _ -> _] matches any product *)
match goal with | |- _ -> _ => intro; $t_tauto_intuit
| |- _ => $t_reduce;$t_solver
end
||
$t_solver
) >>
let reduction_not_iff=interp
<:tactic<repeat
match goal with
| |- _ => progress unfold Coq.Init.Logic.not, Coq.Init.Logic.iff
| H:_ |- _ => progress unfold Coq.Init.Logic.not, Coq.Init.Logic.iff in H
end >>
let t_reduction_not_iff =
Tacexpr.TacArg (valueIn (VTactic (dummy_loc,reduction_not_iff)))
let intuition_gen tac =
interp (tacticIn (tauto_intuit t_reduction_not_iff tac))
let simplif_gen = interp (tacticIn simplif)
let tauto g =
try intuition_gen (interp <:tactic<fail>>) g
with
Refiner.FailError _ | UserError _ ->
errorlabstrm "tauto" [< str "tauto failed" >]
let default_intuition_tac = interp <:tactic< auto with * >>
TACTIC EXTEND tauto
| [ "tauto" ] -> [ tauto ]
END
TACTIC EXTEND intuition
| [ "intuition" ] -> [ intuition_gen default_intuition_tac ]
| [ "intuition" tactic(t) ] -> [ intuition_gen (snd t) ]
END
|
