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/********************* */
/*! \file proof_rule.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 Proof rule enumeration
**/
#include "cvc4_private.h"
#ifndef CVC4__EXPR__PROOF_RULE_H
#define CVC4__EXPR__PROOF_RULE_H
#include <iosfwd>
namespace CVC4 {
/**
* An enumeration for proof rules. This enumeration is analogous to Kind for
* Node objects. In the documentation below, P:F denotes a ProofNode that
* proves formula F.
*
* Conceptually, the following proof rules form a calculus whose target
* user is the Node-level theory solvers. This means that the rules below
* are designed to reason about, among other things, common operations on Node
* objects like Rewriter::rewrite or Node::substitute. It is intended to be
* translated or printed in other formats.
*
* The following PfRule values include core rules and those categorized by
* theory, including the theory of equality.
*
* The "core rules" include two distinguished rules which have special status:
* (1) ASSUME, which represents an open leaf in a proof.
* (2) SCOPE, which closes the scope of assumptions.
* The core rules additionally correspond to generic operations that are done
* internally on nodes, e.g. calling Rewriter::rewrite.
*/
enum class PfRule : uint32_t
{
//================================================= Core rules
//======================== Assume and Scope
// ======== Assumption (a leaf)
// Children: none
// Arguments: (F)
// --------------
// Conclusion: F
//
// This rule has special status, in that an application of assume is an
// open leaf in a proof that is not (yet) justified. An assume leaf is
// analogous to a free variable in a term, where we say "F is a free
// assumption in proof P" if it contains an application of F that is not
// bound by SCOPE (see below).
ASSUME,
// ======== Scope (a binder for assumptions)
// Children: (P:F)
// Arguments: (F1, ..., Fn)
// --------------
// Conclusion: (=> (and F1 ... Fn) F) or (not (and F1 ... Fn)) if F is false
//
// This rule has a dual purpose with ASSUME. It is a way to close
// assumptions in a proof. We require that F1 ... Fn are free assumptions in
// P and say that F1, ..., Fn are not free in (SCOPE P). In other words, they
// are bound by this application. For example, the proof node:
// (SCOPE (ASSUME F) :args F)
// has the conclusion (=> F F) and has no free assumptions. More generally, a
// proof with no free assumptions always concludes a valid formula.
SCOPE,
//================================================= Unknown rule
UNKNOWN,
};
/**
* Converts a proof rule to a string. Note: This function is also used in
* `safe_print()`. Changing this function name or signature will result in
* `safe_print()` printing "<unsupported>" instead of the proper strings for
* the enum values.
*
* @param id The proof rule
* @return The name of the proof rule
*/
const char* toString(PfRule id);
/**
* Writes a proof rule name to a stream.
*
* @param out The stream to write to
* @param id The proof rule to write to the stream
* @return The stream
*/
std::ostream& operator<<(std::ostream& out, PfRule id);
} // namespace CVC4
#endif /* CVC4__EXPR__PROOF_RULE_H */
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