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(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *)
(* \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 Rdefinitions.
Require Export RingMicromega.
Require Import VarMap.
Require Tauto.
Declare ML Module "micromega_plugin".
Ltac xpsatz dom d :=
let tac := lazymatch dom with
| Z =>
(sos_Z || psatz_Z 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 =>
(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 (intros __wit __varmap __ff ;
change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity)
| Q =>
(sos_Q || psatz_Q 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 (intros __wit __varmap __ff ;
change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
apply (QTautoChecker_sound __ff __wit); vm_compute ; reflexivity)
| _ => 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.
Ltac psatzl dom :=
let tac := lazymatch dom with
| Z =>
psatzl_Z ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
| Q =>
psatzl_Q ;
(* 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 (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 =>
unfold Rdiv in * ;
psatzl_R ;
(* 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 (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 lra :=
first [ psatzl R | psatzl Q ].
Ltac lia :=
zify ; unfold Z.succ in * ;
(*cbv delta - [Z.add Z.sub Z.opp Z.mul Z.pow Z.gt Z.ge Z.le Z.lt iff not] ;*) xlia ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
Ltac nia :=
zify ; unfold Z.succ in * ;
xnlia ;
intros __wit __varmap __ff ;
change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ;
apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
(* Local Variables: *)
(* coding: utf-8 *)
(* End: *)
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