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(*                                                                      *)
(* Micromega: A reflexive tactic using the Positivstellensatz           *)
(*                                                                      *)
(*  Frédéric Besson (Irisa/Inria)      2016                             *)
(*                                                                      *)
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Require Import QMicromega.
Require Import QArith.
Require Import RingMicromega.
Require Import VarMap.
Require Coq.micromega.Tauto.
Declare ML Module "micromega_plugin".

Ltac rchange := 
  intros __wit __varmap __ff ;
  change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
  apply (QTautoChecker_sound __ff __wit).

Ltac rchecker_no_abstract := rchange ; vm_compute ; reflexivity.
Ltac rchecker_abstract   := rchange ; vm_cast_no_check (eq_refl true).

Ltac rchecker := rchecker_no_abstract.

(** Here, lra stands for linear rational arithmetic *)
Ltac lra := lra_Q  rchecker.

(** Here, nra stands for non-linear rational arithmetic *)
Ltac nra := xnqa  rchecker.

Ltac xpsatz dom d :=
  let tac := lazymatch dom with
  | Q =>
    ((sos_Q rchecker) || (psatz_Q d rchecker))
  | _ => fail "Unsupported domain"
  end in tac.

Tactic Notation "psatz" constr(dom) int_or_var(n) := xpsatz dom n.
Tactic Notation "psatz" constr(dom) := xpsatz dom ltac:(-1).


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