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/********************* */
/*! \file arith_proof.h
** \verbatim
** Top contributors (to current version):
** Alex Ozdemir, Guy Katz, Mathias Preiner
** 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 Arith proof
**
** Arith proof
**/
#include "cvc4_private.h"
#ifndef CVC4__ARITH__PROOF_H
#define CVC4__ARITH__PROOF_H
#include <memory>
#include <unordered_set>
#include "expr/expr.h"
#include "proof/arith_proof_recorder.h"
#include "proof/proof_manager.h"
#include "proof/theory_proof.h"
#include "theory/uf/equality_engine.h"
namespace CVC4 {
//proof object outputted by TheoryArith
class ProofArith : public Proof {
public:
ProofArith(std::shared_ptr<theory::eq::EqProof> pf) : d_proof(pf) {}
void toStream(std::ostream& out) const override;
private:
static void toStreamLFSC(std::ostream& out, TheoryProof* tp,
const theory::eq::EqProof& pf,
const ProofLetMap& map);
static Node toStreamRecLFSC(std::ostream& out, TheoryProof* tp,
const theory::eq::EqProof& pf,
unsigned tb, const ProofLetMap& map);
// it is simply an equality engine proof
std::shared_ptr<theory::eq::EqProof> d_proof;
};
namespace theory {
namespace arith {
class TheoryArith;
}
}
typedef std::unordered_set<Type, TypeHashFunction > TypeSet;
class ArithProof : public TheoryProof {
protected:
// std::map<Expr, std::string> d_constRationalString; // all the variable/function declarations
// TypeSet d_sorts; // all the uninterpreted sorts in this theory
ExprSet d_declarations; // all the variable/function declarations
/**
* Where farkas proofs of lemmas are stored.
*/
proof::ArithProofRecorder d_recorder;
theory::TheoryId getTheoryId() override;
public:
ArithProof(theory::arith::TheoryArith* arith, TheoryProofEngine* proofEngine);
void registerTerm(Expr term) override;
};
class LFSCArithProof : public ArithProof {
public:
LFSCArithProof(theory::arith::TheoryArith* arith, TheoryProofEngine* proofEngine)
: ArithProof(arith, proofEngine)
{}
void printOwnedTermAsType(Expr term,
std::ostream& os,
const ProofLetMap& map,
TypeNode expectedType) override;
void printOwnedSort(Type type, std::ostream& os) override;
/**
* Returns the LFSC identifier for the operator of this node.
*
* e.g. "+_Real".
*
* Does not include any parens.
*
* Even if the operator is a comparison (e.g. >=) on integers, will not
* return a purely `Int` predicate like ">=_Int". Instead this treats the
* right hand side as a real.
*/
static std::string getLfscFunction(const Node& n);
/**
* Print a rational number in LFSC format.
* e.g. 5/8 or (~ 1/1)
*
* @param o ostream to print to.
* @param r the rational to print
*/
static void printRational(std::ostream& o, const Rational& r);
/**
* Print an integer in LFSC format.
* e.g. 5 or (~ 1)
*
* @param o ostream to print to.
* @param i the integer to print
*/
static void printInteger(std::ostream& o, const Integer& i);
/**
* Print a value of type poly_formula_norm
*
* @param o ostream to print to
* @param n node (asserted to be of the form [linear polynomial >= constant])
*/
static void printLinearPolynomialPredicateNormalizer(std::ostream& o,
const Node& n);
/**
* Print a value of type poly_norm
*
* @param o ostream to print to
* @param n node (asserted to be a linear polynomial)
*/
static void printLinearPolynomialNormalizer(std::ostream& o, const Node& n);
/**
* Print a value of type poly_norm
*
* @param o ostream to print to
* @param n node (asserted to be a linear monomial)
*/
static void printLinearMonomialNormalizer(std::ostream& o, const Node& n);
/**
* Print a LFSC rational
*
* @param o ostream to print to
* @param n node (asserted to be a const rational)
*/
static void printConstRational(std::ostream& o, const Node& n);
/**
* print the pn_var normalizer for n (type poly_norm)
*
* @param o the ostream to print to
* @param n the node to print (asserted to be a variable)
*/
static void printVariableNormalizer(std::ostream& o, const Node& n);
/**
* print a proof of the lemma
*
* First, we print linearity witnesses, i.e. witnesses that each literal has
* the form:
* [linear polynomial] >= 0 OR
* [linear polynomial] > 0
*
* Then we use those witnesses to prove that the above linearized constraints
* hold.
*
* Then we use the farkas coefficients to combine the literals into a
* variable-free contradiction. The literals may be a mix of strict and
* relaxed inequalities.
*
* @param lemma the set of literals disjoined in the lemma
* @param os stream to print the proof to
* @param paren global closing stream (unused)
* @param map let map (unused)
*/
void printTheoryLemmaProof(std::vector<Expr>& lemma,
std::ostream& os,
std::ostream& paren,
const ProofLetMap& map) override;
void printSortDeclarations(std::ostream& os, std::ostream& paren) override;
void printTermDeclarations(std::ostream& os, std::ostream& paren) override;
void printDeferredDeclarations(std::ostream& os,
std::ostream& paren) override;
void printAliasingDeclarations(std::ostream& os,
std::ostream& paren,
const ProofLetMap& globalLetMap) override;
/**
* Given a node that is an arith literal (an arith comparison or negation
* thereof), prints a proof of that literal.
*
* If the node represents a tightenable bound (e.g. [Int] < 3) then it prints
* a proof of the tightening instead. (e.g. [Int] <= 2).
*
* @return a pair comprising:
* * the new node (after tightening) and
* * a string proving it.
*/
std::pair<Node, std::string> printProofAndMaybeTighten(const Node& bound);
/**
* Return whether this node, when serialized to LFSC, has sort `Bool`. Otherwise, the sort is `formula`.
*/
bool printsAsBool(const Node& n) override;
TypeNode equalityType(const Expr& left, const Expr& right) override;
};
}/* CVC4 namespace */
#endif /* CVC4__ARITH__PROOF_H */
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