/******************************************************************************

 * Top contributors (to current version):

 *   Andrew Reynolds, Martin Brain, Gereon Kremer

 *

 * This file is part of the cvc5 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.

 * ****************************************************************************

 *

 * Operator elimination for arithmetic.

 */

#pragma once

#include <map>

#include "expr/node.h"

#include "expr/skolem_manager.h"

#include "proof/eager_proof_generator.h"

#include "smt/env_obj.h"

#include "theory/logic_info.h"

#include "theory/skolem_lemma.h"

namespace cvc5 {

class TConvProofGenerator;

namespace theory {

namespace arith {

class OperatorElim : protected EnvObj, public EagerProofGenerator

{

 public:

  OperatorElim(Env& env);

  /** Eliminate operators in this term.

   *

   * Eliminate operators in term n. If n has top symbol that is not a core

   * one (including division, int division, mod, to_int, is_int, syntactic sugar

   * transcendental functions), then we replace it by a form that eliminates

   * that operator. This may involve the introduction of witness terms.

   *

   * @param n The node to eliminate

   * @param lems The lemmas that we wish to add concerning n. It is the

   * responsbility of the caller to process these lemmas.

   * @param partialOnly Whether we only want to eliminate partial operators.

   * @return the trust node of kind REWRITE encapsulating the eliminated form

   * of n and a proof generator for proving this equivalence.

   */

  TrustNode eliminate(Node n,

                      std::vector<SkolemLemma>& lems,

                      bool partialOnly = false);

  /**

   * Get axiom for term n. This returns the axiom that this class uses to

   * eliminate the term n, which is determined by its top-most symbol.

   */

  static Node getAxiomFor(Node n);

 private:

  /**

   * Function symbols used to implement:

   * (1) Uninterpreted division-by-zero semantics.  Needed to deal with partial

   * division function ("/"),

   * (2) Uninterpreted int-division-by-zero semantics.  Needed to deal with

   * partial function "div",

   * (3) Uninterpreted mod-zero semantics.  Needed to deal with partial

   * function "mod".

   *

   * If the option arithNoPartialFun() is enabled, then the range of this map

   * stores Skolem constants instead of Skolem functions, meaning that the

   * function-ness of e.g. division by zero is ignored.

   *

   * Note that this cache is used only for performance reasons. Conceptually,

   * these skolem functions actually live in SkolemManager.

   */

  std::map<SkolemFunId, Node> d_arithSkolem;

  /**

   * Eliminate operators in term n. If n has top symbol that is not a core

   * one (including division, int division, mod, to_int, is_int, syntactic sugar

   * transcendental functions), then we replace it by a form that eliminates

   * that operator. This may involve the introduction of witness terms.

   *

   * One exception to the above rule is that we may leave certain applications

   * like (/ 4 1) unchanged, since replacing this by 4 changes its type from

   * real to int. This is important for some subtyping issues during

   * expandDefinition. Moreover, applications like this can be eliminated

   * trivially later by rewriting.

   *

   * This method is called both during expandDefinition and during ppRewrite.

   *

   * @param n The node to eliminate operators from.

   * @return The (single step) eliminated form of n.

   */

  Node eliminateOperators(Node n,

                          std::vector<SkolemLemma>& lems,

                          TConvProofGenerator* tg,

                          bool partialOnly);

  /** get arithmetic skolem

   *

   * Returns the Skolem in the above map for the given id, creating it if it

   * does not already exist.

   */

  Node getArithSkolem(SkolemFunId asi);

  /**

   * Make the witness term, which creates a witness term based on the skolem

   * manager with this class as a proof generator.

   */

  Node mkWitnessTerm(Node v,

                     Node pred,

                     const std::string& prefix,

                     const std::string& comment,

                     std::vector<SkolemLemma>& lems);

  /** get arithmetic skolem application

   *

   * By default, this returns the term f( n ), where f is the Skolem function

   * for the identifier asi.

   *

   * If the option arithNoPartialFun is enabled, this returns f, where f is

   * the Skolem constant for the identifier asi.

   */

  Node getArithSkolemApp(Node n, SkolemFunId asi);

  /**

   * Called when a non-linear term n is given to this class. Throw an exception

   * if the logic is linear.

   */

  void checkNonLinearLogic(Node term);

};

}  // namespace arith

}  // namespace theory

}  // namespace cvc5