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Diffstat (limited to 'contrib/micromega/Psatz.v')
| -rw-r--r-- | contrib/micromega/Psatz.v | 75 |
1 files changed, 75 insertions, 0 deletions
diff --git a/contrib/micromega/Psatz.v b/contrib/micromega/Psatz.v new file mode 100644 index 00000000..b2dd9910 --- /dev/null +++ b/contrib/micromega/Psatz.v @@ -0,0 +1,75 @@ +(************************************************************************) +(* 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 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) ; + 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) ; + 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 ; + 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 => + psatzl_R ; + 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 lia := + xlia ; + intros __wit __varmap __ff ; + change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; + apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity. |