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/********************* */
/*! \file skolemize.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 skolemization
**/
#include "cvc4_private.h"
#ifndef CVC4__THEORY__QUANTIFIERS__SKOLEMIZE_H
#define CVC4__THEORY__QUANTIFIERS__SKOLEMIZE_H
#include <unordered_map>
#include <unordered_set>
#include "context/cdhashmap.h"
#include "expr/datatype.h"
#include "expr/node.h"
#include "expr/type_node.h"
#include "theory/quantifiers/quant_util.h"
namespace CVC4 {
namespace theory {
namespace quantifiers {
/** 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
{
typedef context::CDHashMap<Node, Node, NodeHashFunction> NodeNodeMap;
public:
Skolemize(QuantifiersEngine* qe, context::UserContext* u);
~Skolemize() {}
/** skolemize quantified formula q
* If the return value ret of this function
* is non-null, then ret is a new skolemization lemma
* we generated for q. These lemmas are constructed
* once per user-context.
*/
Node 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 arguments fvTypes and 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 fvTypes 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<TypeNode>& fvTypes,
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);
/** print all skolemizations
* This is used for the command line option
* --dump-instantiations
* which prints an informal justification
* of steps taken by the quantifiers module.
* Returns true if we printed at least one
* skolemization.
*/
bool printSkolemization(std::ostream& out);
private:
/** 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);
/** quantifiers engine that owns this module */
QuantifiersEngine* d_quantEngine;
/** 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>, NodeHashFunction>
d_skolem_constants;
/** map from quantified formulas to their skolemized body */
std::unordered_map<Node, Node, NodeHashFunction> d_skolem_body;
};
} /* CVC4::theory::quantifiers namespace */
} /* CVC4::theory namespace */
} /* CVC4 namespace */
#endif /* CVC4__THEORY__QUANTIFIERS__SKOLEMIZE_H */
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