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

 * Top contributors (to current version):

 *   Andrew Reynolds, Mathias Preiner, Abdalrhman Mohamed

 *

 * 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.

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

 *

 * Utilities for skolemization.

 */

#include "cvc5_private.h"

#ifndef CVC5__THEORY__QUANTIFIERS__SKOLEMIZE_H

#define CVC5__THEORY__QUANTIFIERS__SKOLEMIZE_H

#include <unordered_map>

#include <unordered_set>

#include "context/cdhashmap.h"

#include "expr/node.h"

#include "expr/type_node.h"

#include "proof/eager_proof_generator.h"

#include "proof/trust_node.h"

#include "smt/env_obj.h"

namespace cvc5 {

class DTypeConstructor;

namespace theory {

namespace quantifiers {

class QuantifiersState;

class TermRegistry;

/** Skolemization utility

 *

 * This class constructs Skolemization lemmas.

 * Given a quantified formula q = (forall x. P),

 * its skolemization lemma is of the form:

 *   (~ forall x. P ) => ~P * { x -> d_skolem_constants[q] }

 *

 * This class also incorporates techniques for

 * skolemization with "inductive strenghtening", see

 * Section 2 of Reynolds et al., "Induction for SMT

 * Solvers", VMCAI 2015. In the case that x is an inductive

 * datatype or an integer, then we may strengthen the conclusion

 * based on weak well-founded induction. For example, for

 * quantification on lists, a skolemization with inductive

 * strengthening is a lemma of this form:

 *   (~ forall x : List. P( x ) ) =>

 *   ~P( k ) ^ ( is-cons( k ) => P( tail( k ) ) )

 * For the integers it is:

 *   (~ forall x : Int. P( x ) ) =>

 *   ~P( k ) ^ ( x>0 => P( x-1 ) )

 *

 *

 * Inductive strenghtening is not enabled by

 * default and can be enabled by option:

 *   --quant-ind

 */

class Skolemize : protected EnvObj

{

  typedef context::CDHashMap<Node, Node> NodeNodeMap;

 public:

  Skolemize(Env& env, QuantifiersState& qs, TermRegistry& tr);

  /** skolemize quantified formula q

   * If the return value ret of this function is non-null, then ret is a trust

   * node corresponding to a new skolemization lemma we generated for q. These

   * lemmas are constructed once per user-context.

   */

  TrustNode process(Node q);

  /** get skolem constants for quantified formula q */

  bool getSkolemConstants(Node q, std::vector<Node>& skolems);

  /** get the i^th skolem constant for quantified formula q */

  Node getSkolemConstant(Node q, unsigned i);

  /** make skolemized body

   *

   * This returns the skolemized body n of a

   * quantified formula q with inductive strenghtening,

   * where typically n is q[1].

   *

   * The skolem constants/functions we generate by this

   * skolemization are added to sk.

   *

   * The argument fvs are used if we are

   * performing skolemization within a nested quantified

   * formula. In this case, skolem constants we introduce

   * must be parameterized based on the types of fvs and must be

   * applied to fvs.

   *

   * The last two arguments sub and sub_vars are used for

   * to carry the body and indices of other induction

   * variables if a quantified formula to skolemize

   * has multiple induction variables. See page 5

   * of Reynolds et al., VMCAI 2015.

   */

  static Node mkSkolemizedBody(Node q,

                               Node n,

                               std::vector<TNode>& fvs,

                               std::vector<Node>& sk,

                               Node& sub,

                               std::vector<unsigned>& sub_vars);

  /** get the skolemized body for quantified formula q */

  Node getSkolemizedBody(Node q);

  /** is n a variable that we can apply inductive strenghtening to? */

  static bool isInductionTerm(Node n);

  /**

   * Get skolemization vectors, where for each quantified formula that was

   * skolemized, this is the list of skolems that were used to witness the

   * negation of that quantified formula (which is equivalent to an existential

   * one).

   *

   * This is used for the command line option

   *   --dump-instantiations

   * which prints an informal justification of steps taken by the quantifiers

   * module.

   */

  void getSkolemTermVectors(std::map<Node, std::vector<Node> >& sks) const;

 private:

  /** Are proofs enabled? */

  bool isProofEnabled() const;

  /** get self selectors

   * For datatype constructor dtc with type dt,

   * this collects the set of datatype selector applications,

   * applied to term n, whose return type in ntn, and stores

   * them in the vector selfSel.

   */

  static void getSelfSel(const DType& dt,

                         const DTypeConstructor& dc,

                         Node n,

                         TypeNode ntn,

                         std::vector<Node>& selfSel);

  /** Reference to the quantifiers state */

  QuantifiersState& d_qstate;

  /** Reference to the term registry */

  TermRegistry& d_treg;

  /** quantified formulas that have been skolemized */

  NodeNodeMap d_skolemized;

  /** map from quantified formulas to the list of skolem constants */

  std::unordered_map<Node, std::vector<Node>> d_skolem_constants;

  /** map from quantified formulas to their skolemized body */

  std::unordered_map<Node, Node> d_skolem_body;

  /** Eager proof generator for skolemization lemmas */

  std::unique_ptr<EagerProofGenerator> d_epg;

};

}  // namespace quantifiers

}  // namespace theory

}  // namespace cvc5

#endif /* CVC5__THEORY__QUANTIFIERS__SKOLEMIZE_H */