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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" i*)
(*i $Id$ i*)
open Ast
open Coqast
open Hipattern
open Names
open Libnames
open Pp
open Proof_type
open Tacticals
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
<:tactic<Fail>>
let is_unit ist =
if (is_unit_type (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let is_conj ist =
let ind=(List.assoc 1 ist.lmatch) in
if (is_conjunction ind) && (is_nodep_ind ind) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let is_disj ist =
if (is_disjunction (List.assoc 1 ist.lmatch)) then
<:tactic<Idtac>>
else
<:tactic<Fail>>
let not_dep_intros ist =
<:tactic<
Repeat
Match Context With
| [|- ?1 -> ?2 ] -> Intro>>
let axioms ist =
let t_is_unit = tacticIn is_unit
and t_is_empty = tacticIn is_empty in
<:tactic<
Match Reverse Context With
|[|- ?1] -> $t_is_unit;Constructor 1
|[_:?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
((Match Reverse Context With
| [id: (?1 ? ?) |- ?] ->
$t_is_conj;Elim id;Do 2 Intro;Clear id;$t_reduce
| [id: (?1 ? ?) |- ?] -> $t_is_disj;Elim id;Intro;Clear id;$t_reduce
| [id0: ?1-> ?2; id1: ?1|- ?] -> Generalize (id0 id1);Intro;Clear id0
| [id: ?1 -> ?2|- ?] ->
$t_is_unit;Cut ?2;
[Intro;Clear id
| (* id : ?1 -> ?2 |- ?2 *)
Cut ?1;[Exact id|Constructor 1;Fail]
]
| [id: (?1 ?2 ?3) -> ?4|- ?] ->
$t_is_conj;Cut ?2-> ?3-> ?4;
[Intro;Clear id;$t_reduce
| (* id: (?1 ?2 ?3) -> ?4 |- ?2 -> ?3 -> ?4 *)
Intro;Intro; Cut (?1 ?2 ?3);[Exact id|Split;Assumption]
]
| [id: (?1 ?2 ?3) -> ?4|- ?] ->
$t_is_disj;
Cut ?3-> ?4;
[Cut ?2-> ?4;
[Intro;Intro;Clear id;$t_reduce
| (* id: (?1 ?2 ?3) -> ?4 |- ?2 -> ?4 *)
Intro; Cut (?1 ?2 ?3);[Exact id|Left;Assumption]
]
| (* id: (?1 ?2 ?3) -> ?4 |- ?3 -> ?4 *)
Intro; Cut (?1 ?2 ?3);[Exact id|Right;Assumption]
]
| [|- (?1 ? ?)] -> $t_is_conj;Split;$t_reduce);
$t_not_dep_intros)>>
let rec tauto_intuit t_reduce t_solver ist =
let t_axioms = tacticIn axioms
and t_simplif = tacticIn (simplif t_reduce)
and t_is_disj = tacticIn is_disj
and t_tauto_intuit = tacticIn (tauto_intuit t_reduce t_solver) in
<:tactic<
$t_reduce;
($t_simplif;$t_axioms
Orelse
(Match Reverse Context With
| [id:(?1-> ?2)-> ?3|- ?] ->
Cut ?3;
[Intro;Clear id
| Cut ?1 -> ?2;
[Exact id|Generalize [y:?2](id [x:?1]y);Intro;Clear id]
]; Solve [ $t_tauto_intuit ]
| [|- (?1 ? ?)] ->
$t_is_disj;Solve [Left;$t_tauto_intuit | Right;$t_tauto_intuit]
)
Orelse
(* NB: [|- ? -> ?] matches any product *)
(Match Context With |[ |- ? -> ? ] -> Intro;$t_tauto_intuit)
Orelse
$t_solver
) >>
let unfold_not_iff = function
| None -> interp <:tactic<Unfold not iff>>
| Some id -> let id = (dummy_loc,id) in interp <:tactic<Unfold not iff in $id>>
let reduction_not_iff =
Tacticals.onAllClauses (fun ido -> unfold_not_iff ido)
let t_reduction_not_iff = Tacexpr.TacArg (valueIn (VTactic reduction_not_iff))
let intuition_gen tac =
interp (tacticIn (tauto_intuit t_reduction_not_iff tac))
let simplif_gen = interp (tacticIn (simplif t_reduction_not_iff))
let tauto g =
try intuition_gen <:tactic<Fail>> g
with
Refiner.FailError _ | UserError _ ->
errorlabstrm "tauto" [< str "Tauto failed" >]
let default_intuition_tac = <:tactic< Auto with * >>
TACTIC EXTEND Tauto
| [ "Tauto" ] -> [ tauto ]
END
TACTIC EXTEND TSimplif
| [ "Simplif" ] -> [ simplif_gen ]
END
TACTIC EXTEND Intuition
| [ "Intuition" ] -> [ intuition_gen default_intuition_tac ]
| [ "Intuition" tactic(t) ] -> [ intuition_gen t ]
END
|
