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/******************************************************************************
* Top contributors (to current version):
* Andrew Reynolds, Tim King, Mathias Preiner
*
* 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.
* ****************************************************************************
*
* Arithmetic instantiator.
*/
#include "cvc5_private.h"
#ifndef CVC5__THEORY__QUANTIFIERS__CEG_ARITH_INSTANTIATOR_H
#define CVC5__THEORY__QUANTIFIERS__CEG_ARITH_INSTANTIATOR_H
#include <vector>
#include "expr/node.h"
#include "theory/quantifiers/cegqi/ceg_instantiator.h"
#include "theory/quantifiers/cegqi/vts_term_cache.h"
namespace cvc5 {
namespace theory {
namespace quantifiers {
/** Arithmetic instantiator
*
* This implements a selection function for arithmetic, which is based on
* variants of:
* - Loos/Weispfenning's method (virtual term substitution) for linear real
* arithmetic,
* - Ferrante/Rackoff's method (interior points) for linear real arithmetic,
* - Cooper's method for linear arithmetic.
* For details, see Reynolds et al, "Solving Linear Arithmetic Using
* Counterexample-Guided Instantiation", FMSD 2017.
*
* This class contains all necessary information for instantiating a single
* real or integer typed variable of a single quantified formula.
*/
class ArithInstantiator : public Instantiator
{
public:
ArithInstantiator(Env& env, TypeNode tn, VtsTermCache* vtc);
virtual ~ArithInstantiator() {}
/** reset */
void reset(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
CegInstEffort effort) override;
/** this instantiator processes equalities */
bool hasProcessEquality(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
CegInstEffort effort) override;
/**
* Process the equality term[0]=term[1]. If this equality is equivalent to one
* of the form c * pv = t, then we add the substitution c * pv -> t to sf and
* recurse.
*/
bool processEquality(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
std::vector<TermProperties>& term_props,
std::vector<Node>& terms,
CegInstEffort effort) override;
/** this instantiator processes assertions */
bool hasProcessAssertion(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
CegInstEffort effort) override;
/** this instantiator processes literals lit of kinds EQUAL and GEQ */
Node hasProcessAssertion(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
Node lit,
CegInstEffort effort) override;
/** process assertion lit
*
* If lit can be turned into a bound of the form c * pv <> t, then we store
* information about this bound (see d_mbp_bounds).
*
* If cbqiModel is false (not the default), we recursively try adding the
* substitution { c * pv -> t } to sf and recursing.
*/
bool processAssertion(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
Node lit,
Node alit,
CegInstEffort effort) override;
/** process assertions
*
* This is called after processAssertion has been called on all current bounds
* for pv. This method selects the "best" bound of those we have seen, which
* can be one of the following:
* - Maximal lower bound,
* - Minimal upper bound,
* - Midpoint of maximal lower and minimal upper bounds, [if pv is not Int,
* and --cbqi-midpoint]
* - (+-) Infinity, [if no upper (resp. lower) bounds, and --cbqi-use-vts-inf]
* - Zero, [if no bounds]
* - Non-optimal bounds. [if the above bounds fail, and --cbqi-nopt]
*/
bool processAssertions(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
CegInstEffort effort) override;
/**
* This instantiator needs to postprocess variables that have substitutions
* with coefficients, i.e. c*x -> t.
*/
bool needsPostProcessInstantiationForVariable(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
CegInstEffort effort) override;
/** post-process instantiation for variable
*
* If the solved form for integer variable pv is a substitution with
* coefficients c*x -> t, this turns its solved form into x -> div(t,c), where
* div is integer division.
*/
bool postProcessInstantiationForVariable(CegInstantiator* ci,
SolvedForm& sf,
Node pv,
CegInstEffort effort) override;
std::string identify() const override { return "Arith"; }
private:
/** pointer to the virtual term substitution term cache class */
VtsTermCache* d_vtc;
/** zero/one */
Node d_zero;
Node d_one;
//--------------------------------------current bounds
/** Virtual term symbols (vts), where 0: infinity, 1: delta. */
Node d_vts_sym[2];
/** Current 0:lower, 1:upper bounds for the variable to instantiate */
std::vector<Node> d_mbp_bounds[2];
/** Coefficients for the lower/upper bounds for the variable to instantiate */
std::vector<Node> d_mbp_coeff[2];
/** Coefficients for virtual terms for each bound. */
std::vector<Node> d_mbp_vts_coeff[2][2];
/** The source literal (explanation) for each bound. */
std::vector<Node> d_mbp_lit[2];
//--------------------------------------end current bounds
/** solve arith
*
* Given variable to instantiate pv, this isolates the atom into solved form:
* veq_c * pv <> val + vts_coeff_delta * delta + vts_coeff_inf * inf
* where we ensure val has Int type if pv has Int type, and val does not
* contain vts symbols.
*
* It returns a CegTermType:
* CEG_TT_INVALID if it was not possible to put atom into a solved form,
* CEG_TT_LOWER if <> in the above equation is >=,
* CEG_TT_UPPER if <> in the above equation is <=, or
* CEG_TT_EQUAL if <> in the above equation is =.
*/
CegTermType solve_arith(CegInstantiator* ci,
Node v,
Node atom,
Node& veq_c,
Node& val,
Node& vts_coeff_inf,
Node& vts_coeff_delta);
/** get model based projection value
*
* Given a implied (non-strict) bound:
* c*e <=/>= t + inf_coeff*INF + delta_coeff*DELTA
* this method returns ret, the minimal (resp. maximal) term such that:
* c*ret <> t + inf_coeff*INF + delta_coeff*DELTA
* is satisfied in the current model M, and such that the divisibilty
* constraint is also satisfied:
* ret^M mod c*theta = (c*e)^M mod c*theta
* where the input theta is a constant (which is assumed to be 1 if null). The
* values of me and mt are the current model values of e and t respectively.
*
* For example, if e has Real type and:
* isLower = false, e^M = 0, t^M = 2, inf_coeff = 0, delta_coeff = 2
* Then, this function returns t+2*delta.
*
* For example, if e has Int type and:
* isLower = true, e^M = 4, t^M = 2, theta = 3
* Then, this function returns t+2, noting that (t+2)^M mod 3 = e^M mod 3 = 2.
*
* For example, if e has Int type and:
* isLower = false, e^M = 1, t^M = 5, theta = 3
* Then, this function returns t-1, noting that (t-1)^M mod 3 = e^M mod 3 = 1.
*
* The value that is added or substracted from t in the return value when e
* is an integer is the value of "rho" from Figure 6 of Reynolds et al,
* "Solving Linear Arithmetic Using Counterexample-Guided Instantiation",
* FMSD 2017.
*/
Node getModelBasedProjectionValue(CegInstantiator* ci,
Node e,
Node t,
bool isLower,
Node c,
Node me,
Node mt,
Node theta,
Node inf_coeff,
Node delta_coeff);
/** Return the rewritten form of the negation of t */
Node negate(const Node& t) const;
};
} // namespace quantifiers
} // namespace theory
} // namespace cvc5
#endif /* CVC5__THEORY__QUANTIFIERS__CEG_ARITH_INSTANTIATOR_H */
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