(*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