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.

6 files changed, 152 insertions, 33 deletions

diff --git a/plugins/micromega/Lqa.v b/plugins/micromega/Lqa.v
new file mode 100644
index 000000000..0055600a0
--- /dev/null
+++ b/plugins/micromega/Lqa.v
@@ -0,0 +1,55 @@
+(************************************************************************)
+(*  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 QMicromega.
+Require Import QArith.
+Require Import RingMicromega.
+Require Import VarMap.
+Require Coq.micromega.Tauto.
+Declare ML Module "micromega_plugin".
+
+(** Here, lra stands for linear rational arithmetic *)
+Ltac lra := lra_Q ; 
+    (abstract(intros __wit __varmap __ff ;
+               change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
+               apply (QTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true))).
+
+(** Here, nra stands for non-linear rational arithmetic *)
+Ltac nra :=
+  xnqa ;
+  (abstract(intros __wit __varmap __ff ;
+             change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
+             apply (QTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true))).
+
+Ltac xpsatz dom d :=
+  let tac := lazymatch dom with
+  | 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  (abstract(intros __wit __varmap __ff ;
+                      change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
+                      apply (QTautoChecker_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: *)
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: *)
diff --git a/plugins/micromega/Psatz.v b/plugins/micromega/Psatz.v
index fafd8a5f2..b1f242f58 100644
--- a/plugins/micromega/Psatz.v
+++ b/plugins/micromega/Psatz.v
@@ -8,7 +8,7 @@
 (*                                                                      *)
 (* Micromega: A reflexive tactic using the Positivstellensatz           *)
 (*                                                                      *)
-(*  Frédéric Besson (Irisa/Inria) 2006-2008                             *)
+(*  Frédéric Besson (Irisa/Inria) 2006-2016                             *)
 (*                                                                      *)
 (************************************************************************)
 
@@ -75,35 +75,39 @@ Ltac psatzl dom :=
   let tac := lazymatch dom with
   | Z => lia
   | 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 (abstract(intros __wit __varmap __ff ;
-        change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
-        apply (QTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true)))
+    lra_Q ;
+      (abstract(intros __wit __varmap __ff ;
+                 change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
+                 apply (QTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true)))
   | 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 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"
+    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))))
+| _ => fail "Unsupported domain"
   end in tac.
 
 
 Ltac lra := 
   first [ psatzl R | psatzl Q ].
 
-Ltac nra := 
+Ltac nra_R := 
   unfold Rdiv in * ; 
   xnra ;     
   abstract 
     (intros __wit __varmap __ff ;
-     change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
-     apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity).
-                                                                       
+      change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ;
+      apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity).
+
+Ltac nra_Q := 
+  xnqa ;
+  (abstract(intros __wit __varmap __ff ;
+             change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ;
+             apply (QTautoChecker_sound __ff __wit); vm_cast_no_check (eq_refl true))).
+
+Ltac nra := 
+  first [ nra_R | nra_Q ].  
 
 
 (* Local Variables: *)
diff --git a/plugins/micromega/coq_micromega.ml b/plugins/micromega/coq_micromega.ml
index b8e5e66ca..edcb00b90 100644
--- a/plugins/micromega/coq_micromega.ml
+++ b/plugins/micromega/coq_micromega.ml
@@ -2100,11 +2100,7 @@ let tauto_lia ff =
   * solvers
   *)
 
-let psatzl_Z =
- micromega_gen parse_zarith  Mc.negate Mc.normalise Mc.zunsat Mc.zdeduce zz_domain_spec
-  [ linear_Z ] 
-
-let psatzl_Q =
+let lra_Q =
  micromega_gen parse_qarith Mc.qnegate Mc.qnormalise Mc.qunsat Mc.qdeduce qq_domain_spec
   [ linear_prover_Q ] 
 
@@ -2112,7 +2108,7 @@ let psatz_Q i  =
  micromega_gen parse_qarith Mc.qnegate Mc.qnormalise Mc.qunsat Mc.qdeduce qq_domain_spec
   [ non_linear_prover_Q "real_nonlinear_prover" (Some i) ]
 
-let psatzl_R  =
+let lra_R  =
  micromega_genr [ linear_prover_R ]
 
 let psatz_R i  =
@@ -2136,21 +2132,21 @@ let sos_R  =
  micromega_genr  [ non_linear_prover_R "pure_sos" None ] 
 
 
-let xlia  =
-  try 
-    micromega_gen parse_zarith Mc.negate Mc.normalise Mc.zunsat Mc.zdeduce zz_domain_spec
+let xlia  =  micromega_gen parse_zarith Mc.negate Mc.normalise Mc.zunsat Mc.zdeduce zz_domain_spec
       [ linear_Z ] 
-  with reraise -> (*Printexc.print_backtrace stdout ;*) raise reraise
 
 let xnlia  =
-  try 
     micromega_gen parse_zarith Mc.negate Mc.normalise Mc.zunsat Mc.zdeduce zz_domain_spec
       [ nlinear_Z ] 
-  with reraise -> (*Printexc.print_backtrace stdout ;*) raise reraise
 
 let nra  = 
  micromega_genr  [ nlinear_prover_R ] 
 
+let nqa  =
+ micromega_gen parse_qarith Mc.qnegate Mc.qnormalise Mc.qunsat Mc.qdeduce qq_domain_spec
+  [ nlinear_prover_R ]
+
+   
 
 (* Local Variables: *)
 (* coding: utf-8 *)
diff --git a/plugins/micromega/g_micromega.ml4 b/plugins/micromega/g_micromega.ml4
index e6b5cc60d..974dcee87 100644
--- a/plugins/micromega/g_micromega.ml4
+++ b/plugins/micromega/g_micromega.ml4
@@ -37,6 +37,12 @@ TACTIC EXTEND NRA
 [ "xnra"  ] -> [  (Coq_micromega.nra)]
 END
 
+TACTIC EXTEND NQA
+[ "xnqa"  ] -> [  (Coq_micromega.nqa)]
+END
+
+
+  
 TACTIC EXTEND Sos_Z
 | [ "sos_Z" ] -> [ (Coq_micromega.sos_Z) ]
    END
@@ -50,11 +56,11 @@ TACTIC EXTEND Sos_R
 END
 
 TACTIC EXTEND LRA_Q
-[ "psatzl_Q"  ] -> [   (Coq_micromega.psatzl_Q) ]
+[ "lra_Q"  ] -> [   (Coq_micromega.lra_Q) ]
 END
 
 TACTIC EXTEND LRA_R
-[ "psatzl_R"  ] -> [   (Coq_micromega.psatzl_R) ]
+[ "lra_R"  ] -> [   (Coq_micromega.lra_R) ]
 END
 
 TACTIC EXTEND PsatzR
diff --git a/plugins/micromega/vo.itarget b/plugins/micromega/vo.itarget
index bf6a1a7db..cb4b2b8a5 100644
--- a/plugins/micromega/vo.itarget
+++ b/plugins/micromega/vo.itarget
@@ -10,4 +10,6 @@ Tauto.vo
 VarMap.vo
 ZCoeff.vo
 ZMicromega.vo
-Lia.vo
\ No newline at end of file
+Lia.vo
+Lqa.vo
+Lra.vo
\ No newline at end of file