Add CAD-based solver (#4834)

Based on #4774, this PR adds a new CadSolver class that allows the NonlinearExtension to actually employ the CAD-based method. In more detail:

add --nl-cad option
add CadSolver class that wraps cad::CDCAC with support for checks, model construction and conflict generation
add new Inference types for the NlLemma class
use CadSolver in NonlinearExtension (if --nl-cad is given)

1 files changed, 141 insertions, 0 deletions

diff --git a/src/theory/arith/nl/cad_solver.cpp b/src/theory/arith/nl/cad_solver.cpp
new file mode 100644
index 000000000..783fb0187
--- /dev/null
+++ b/src/theory/arith/nl/cad_solver.cpp
@@ -0,0 +1,141 @@
+/*********************                                                        */
+/*! \file cad_solver.cpp
+ ** \verbatim
+ ** Top contributors (to current version):
+ **   Gereon Kremer
+ ** This file is part of the CVC4 project.
+ ** Copyright (c) 2009-2019 by the authors listed in the file AUTHORS
+ ** in the top-level source directory) and their institutional affiliations.
+ ** All rights reserved.  See the file COPYING in the top-level source
+ ** directory for licensing information.\endverbatim
+ **
+ ** \brief Implementation of new non-linear solver
+ **/
+
+#include "theory/arith/nl/cad_solver.h"
+
+#ifdef CVC4_POLY_IMP
+#include <poly/polyxx.h>
+#endif
+
+#include "inference.h"
+#include "theory/arith/nl/cad/cdcac.h"
+#include "theory/arith/nl/poly_conversion.h"
+#include "util/poly_util.h"
+
+namespace CVC4 {
+namespace theory {
+namespace arith {
+namespace nl {
+
+CadSolver::CadSolver(TheoryArith& containing, NlModel& model)
+    : d_foundSatisfiability(false), d_containing(containing), d_model(model)
+{
+  d_ranVariable =
+      NodeManager::currentNM()->mkSkolem("__z",
+                                         NodeManager::currentNM()->realType(),
+                                         "",
+                                         NodeManager::SKOLEM_EXACT_NAME);
+}
+
+CadSolver::~CadSolver() {}
+
+void CadSolver::initLastCall(const std::vector<Node>& assertions)
+{
+#ifdef CVC4_POLY_IMP
+  if (Trace.isOn("nl-cad"))
+  {
+    Trace("nl-cad") << "CadSolver::initLastCall" << std::endl;
+    Trace("nl-cad") << "* Assertions: " << std::endl;
+    for (const Node& a : assertions)
+    {
+      Trace("nl-cad") << "  " << a << std::endl;
+    }
+  }
+  // store or process assertions
+  d_CAC.reset();
+  for (const Node& a : assertions)
+  {
+    d_CAC.getConstraints().addConstraint(a);
+  }
+  d_CAC.computeVariableOrdering();
+#else
+  Warning() << "Tried to use CadSolver but libpoly is not available. Compile "
+               "with --poly."
+            << std::endl;
+#endif
+}
+
+std::vector<NlLemma> CadSolver::checkFull()
+{
+#ifdef CVC4_POLY_IMP
+  std::vector<NlLemma> lems;
+  auto covering = d_CAC.getUnsatCover();
+  if (covering.empty())
+  {
+    d_foundSatisfiability = true;
+    Trace("nl-cad") << "SAT: " << d_CAC.getModel() << std::endl;
+  }
+  else
+  {
+    d_foundSatisfiability = false;
+    auto mis = collectConstraints(covering);
+    Trace("nl-cad") << "Collected MIS: " << mis << std::endl;
+    auto* nm = NodeManager::currentNM();
+    for (auto& n : mis)
+    {
+      n = n.negate();
+    }
+    Assert(!mis.empty()) << "Infeasible subset can not be empty";
+    if (mis.size() == 1)
+    {
+      lems.emplace_back(mis.front(), Inference::CAD_CONFLICT);
+    }
+    else
+    {
+      lems.emplace_back(nm->mkNode(Kind::OR, mis), Inference::CAD_CONFLICT);
+    }
+    Trace("nl-cad") << "UNSAT with MIS: " << lems.back().d_lemma << std::endl;
+  }
+  return lems;
+#else
+  Warning() << "Tried to use CadSolver but libpoly is not available. Compile "
+               "with --poly."
+            << std::endl;
+#endif
+}
+
+bool CadSolver::constructModelIfAvailable(std::vector<Node>& assertions)
+{
+#ifdef CVC4_POLY_IMP
+  if (!d_foundSatisfiability)
+  {
+    return false;
+  }
+  assertions.clear();
+  for (const auto& v : d_CAC.getVariableOrdering())
+  {
+    Node variable = d_CAC.getConstraints().varMapper()(v);
+    Node value = value_to_node(d_CAC.getModel().get(v), d_ranVariable);
+    if (value.isConst())
+    {
+      d_model.addCheckModelSubstitution(variable, value);
+    }
+    else
+    {
+      d_model.addCheckModelWitness(variable, value);
+    }
+    Trace("nl-cad") << "-> " << v << " = " << value << std::endl;
+  }
+  return true;
+#else
+  Warning() << "Tried to use CadSolver but libpoly is not available. Compile "
+               "with --poly."
+            << std::endl;
+#endif
+}
+
+}  // namespace nl
+}  // namespace arith
+}  // namespace theory
+}  // namespace CVC4