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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
(* \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) 2006-2008 *)
(* *)
(************************************************************************)
Require Import ZMicromega.
Require Import QMicromega.
Require Import RMicromega.
Require Import QArith.
Require Export Ring_normalize.
Require Import ZArith.
Require Import Raxioms.
Require Export RingMicromega.
Require Import VarMap.
Require Tauto.
Ltac micromegac dom d :=
let tac := lazymatch dom with
| Z =>
micromegap d ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| R =>
rmicromegap d ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| _ => fail "Unsupported domain"
end in tac.
Tactic Notation "micromega" constr(dom) int_or_var(n) := micromegac dom n.
Tactic Notation "micromega" constr(dom) := micromegac dom ltac:-1.
Ltac zfarkas := omicronp ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
Ltac omicron dom :=
let tac := lazymatch dom with
| Z =>
zomicronp ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| Q =>
qomicronp ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
apply (QTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| R =>
romicronp ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| _ => fail "Unsupported domain"
end in tac.
Ltac sos dom :=
let tac := lazymatch dom with
| Z =>
sosp ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| _ => fail "Unsupported domain"
end in tac.
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