From 721637c98514a77d05d080f53f226cab3a8da1e7 Mon Sep 17 00:00:00 2001
From: Frédéric Besson <frederic.besson@inria.fr>
Date: Tue, 30 Aug 2016 17:12:27 +0200
Subject: plugin micromega : nra also handles non-linear rational arithmetic
 over Q (Fixed #4985)

Lqa.v defines the tactics lra and nra working over Q.
Lra.v defines the tactics lra and nra working over R.
---
 plugins/micromega/Lra.v | 56 +++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 56 insertions(+)
 create mode 100644 plugins/micromega/Lra.v

(limited to 'plugins/micromega/Lra.v')

diff --git a/plugins/micromega/Lra.v b/plugins/micromega/Lra.v
new file mode 100644
index 000000000..7ffe1e4ed
--- /dev/null
+++ b/plugins/micromega/Lra.v
@@ -0,0 +1,56 @@
+(************************************************************************)
+(*  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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