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/********************* */
/*! \file exponential_solver.h
** \verbatim
** Top contributors (to current version):
** Gereon Kremer, Andrew Reynolds
** This file is part of the CVC4 project.
** Copyright (c) 2009-2021 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 Solving for handling exponential function.
**/
#ifndef CVC4__THEORY__ARITH__NL__TRANSCENDENTAL__EXPONENTIAL_SOLVER_H
#define CVC4__THEORY__ARITH__NL__TRANSCENDENTAL__EXPONENTIAL_SOLVER_H
#include <map>
#include "expr/node.h"
namespace CVC5 {
namespace theory {
namespace arith {
namespace nl {
namespace transcendental {
struct TranscendentalState;
/** Transcendental solver class
*
* This class implements model-based refinement schemes
* for transcendental functions, described in:
*
* - "Satisfiability Modulo Transcendental
* Functions via Incremental Linearization" by Cimatti
* et al., CADE 2017.
*
* It's main functionality are methods that implement lemma schemas below,
* which return a set of lemmas that should be sent on the output channel.
*/
class ExponentialSolver
{
public:
ExponentialSolver(TranscendentalState* tstate);
~ExponentialSolver();
/**
* Ensures that new_a is properly registered as a term where new_a is the
* purified version of a, y being the new skolem used for purification.
*/
void doPurification(TNode a, TNode new_a, TNode y);
/**
* check initial refine
*
* Constructs a set of valid theory lemmas, based on
* simple facts about the exponential function.
* This mostly follows the initial axioms described in
* Section 4 of "Satisfiability
* Modulo Transcendental Functions via Incremental
* Linearization" by Cimatti et al., CADE 2017.
*
* Examples:
*
* exp( x )>0
* x<0 => exp( x )<1
*/
void checkInitialRefine();
/**
* check monotonicity
*
* Constructs a set of valid theory lemmas, based on a
* lemma scheme that ensures that applications
* of the exponential function respect monotonicity.
*
* Examples:
*
* x > y => exp( x ) > exp( y )
*/
void checkMonotonic();
/** Send tangent lemma around c for e */
void doTangentLemma(TNode e, TNode c, TNode poly_approx, std::uint64_t d);
/** Send secant lemmas around c for e */
void doSecantLemmas(TNode e,
TNode poly_approx,
TNode center,
TNode cval,
unsigned d,
unsigned actual_d);
private:
/** Generate bounds for secant lemmas */
std::pair<Node, Node> getSecantBounds(TNode e, TNode center, unsigned d);
/** Holds common state for transcendental solvers */
TranscendentalState* d_data;
/** The transcendental functions we have done initial refinements on */
std::map<Node, bool> d_tf_initial_refine;
}; /* class ExponentialSolver */
} // namespace transcendental
} // namespace nl
} // namespace arith
} // namespace theory
} // namespace CVC5
#endif /* CVC4__THEORY__ARITH__TRANSCENDENTAL_SOLVER_H */
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