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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
(* *)
(* Micromega: A reflexive tactic using the Positivstellensatz *)
(* *)
(* Frédéric Besson (Irisa/Inria) 2016 *)
(* *)
(************************************************************************)
Require Import RMicromega.
Require Import QMicromega.
Require Import Rdefinitions.
Require Import RingMicromega.
Require Import VarMap.
Require Coq.micromega.Tauto.
Declare ML Module "micromega_plugin".
(** Here, lra stands for linear real arithmetic *)
Ltac lra :=
unfold Rdiv in * ;
lra_R ;
(abstract((intros __wit __varmap __ff ;
change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
apply (RTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true)))).
(** Here, nra stands for non-linear real arithmetic *)
Ltac nra :=
xnra ;
(abstract((intros __wit __varmap __ff ;
change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
apply (RTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true)))).
Ltac xpsatz dom d :=
let tac := lazymatch dom with
| R =>
(sos_R || psatz_R d) ;
(* If csdp is not installed, the previous step might not produce any
progress: the rest of the tactical will then fail. Hence the 'try'. *)
try (abstract(intros __wit __varmap __ff ;
change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
apply (RTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true)))
| _ => 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).
(* Local Variables: *)
(* coding: utf-8 *)
(* End: *)
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