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/*
* richard-atp-engine: A saturation-based automated theorem prover for first-order logic.
* Copyright (C) 2026 Richard Qin
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*/
#pragma once
/// @file ordering.h
/// @brief Term orderings for equality reasoning (KBO, LPO).
///
/// Term orderings are the foundation of equality-based theorem proving.
/// They ensure that rewriting always terminates by enforcing a well-founded
/// ordering on terms. Required by paramodulation, demodulation, and
/// ordered resolution.
#include "atp/core/term_bank.h"
#include "atp/core/types.h"
namespace atp {
/// Ordering comparison result.
enum class OrderResult : uint8_t {
kLessThan, ///< t1 < t2
kEqual, ///< t1 = t2
kGreaterThan, ///< t1 > t2
kIncomparable, ///< t1 and t2 are incomparable
};
/// Abstract base for term orderings.
/// Concrete implementations: KBO (Knuth-Bendix), LPO (Lexicographic Path).
class TermOrdering {
public:
virtual ~TermOrdering() = default;
/// Compare two terms under the ordering.
[[nodiscard]] virtual OrderResult compare(const TermBank& bank, TermId t1,
TermId t2) const = 0;
};
} // namespace atp
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