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+/*********************                                                        */
+/*! \file nl_lemma_utils.h
+ ** \verbatim
+ ** Top contributors (to current version):
+ **   Andrew Reynolds
+ ** 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 Utilities for processing lemmas from the non-linear solver
+ **/
+
+#ifndef CVC4__THEORY__ARITH__NL__NL_LEMMA_UTILS_H
+#define CVC4__THEORY__ARITH__NL__NL_LEMMA_UTILS_H
+
+#include <tuple>
+#include <vector>
+#include "expr/node.h"
+
+namespace CVC4 {
+namespace theory {
+namespace arith {
+namespace nl {
+
+class NlModel;
+
+/**
+ * A side effect of adding a lemma in the non-linear solver. This is used
+ * to specify how the state of the non-linear solver should update. This
+ * includes:
+ * - A set of secant points to record (for transcendental secant plane
+ * inferences).
+ */
+struct NlLemmaSideEffect
+{
+  NlLemmaSideEffect() {}
+  ~NlLemmaSideEffect() {}
+  /** secant points to add
+   *
+   * A member (tf, d, c) in this vector indicates that point c should be added
+   * to the list of secant points for an application of a transcendental
+   * function tf for Taylor degree d. This is used for incremental linearization
+   * for underapproximation (resp. overapproximations) of convex (resp.
+   * concave) regions of transcendental functions. For details, see
+   * Cimatti et al., CADE 2017.
+   */
+  std::vector<std::tuple<Node, unsigned, Node> > d_secantPoint;
+};
+
+struct SortNlModel
+{
+  SortNlModel()
+      : d_nlm(nullptr),
+        d_isConcrete(true),
+        d_isAbsolute(false),
+        d_reverse_order(false)
+  {
+  }
+  /** pointer to the model */
+  NlModel* d_nlm;
+  /** are we comparing concrete model values? */
+  bool d_isConcrete;
+  /** are we comparing absolute values? */
+  bool d_isAbsolute;
+  /** are we in reverse order? */
+  bool d_reverse_order;
+  /** the comparison */
+  bool operator()(Node i, Node j);
+};
+
+struct SortNonlinearDegree
+{
+  SortNonlinearDegree(const std::map<Node, unsigned>& m) : d_mdegree(m) {}
+  /** pointer to the non-linear extension */
+  const std::map<Node, unsigned>& d_mdegree;
+  /** Get the degree of n in d_mdegree */
+  unsigned getDegree(Node n) const;
+  /**
+   * Sorts by degree of the monomials, where lower degree monomials come
+   * first.
+   */
+  bool operator()(Node i, Node j);
+};
+
+/** An argument trie, for computing congruent terms */
+class ArgTrie
+{
+ public:
+  /** children of this node */
+  std::map<Node, ArgTrie> d_children;
+  /** the data of this node */
+  Node d_data;
+  /**
+   * Set d as the data on the node whose path is [args], return either d if
+   * that node has no data, or the data that already occurs there.
+   */
+  Node add(Node d, const std::vector<Node>& args);
+};
+
+}  // namespace nl
+}  // namespace arith
+}  // namespace theory
+}  // namespace CVC4
+
+#endif /* CVC4__THEORY__ARITH__NL_LEMMA_UTILS_H */