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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 substitution.h
/// @brief Variable binding map: Var -> Term.
///
/// Short-lived object created during unification, applied to build resolvents,
/// then discarded. Never stored long-term.
#include "atp/core/term_bank.h"
#include "atp/core/types.h"
#include <unordered_map>
namespace atp {
/// A substitution σ maps variable TermIds to their bound TermIds.
///
/// Example: σ = { X → f(a), Y → Z }
/// lookup(X) = f(a) (direct binding)
/// resolve(X) = f(a) (same — f(a) is not a variable)
/// resolve(Y) = Z (if Z is unbound, stops at Z)
/// resolve(Y) = f(b) (if Z → f(b) also in σ, walks the chain)
class Substitution {
public:
Substitution() = default;
/// Bind a variable to a term. Returns false if already bound to a different term.
bool bind(TermId var, TermId term);
/// Look up what a variable is directly bound to. Returns kInvalidId if unbound.
[[nodiscard]] TermId lookup(TermId var) const;
/// Walk the binding chain to the final value.
/// If var → Y → f(a), returns f(a).
/// Requires TermBank to check whether intermediate values are variables.
[[nodiscard]] TermId resolve(TermId id, const TermBank& bank) const;
/// Apply this substitution to a term recursively, creating new terms in the bank.
/// Free (unbound) variables are left as-is.
[[nodiscard]] TermId apply(TermId term, TermBank& bank) const;
/// Check if a variable occurs anywhere inside a term (for occurs check).
[[nodiscard]] bool occursIn(TermId var, TermId term, const TermBank& bank) const;
/// Clear all bindings.
void clear();
/// Number of bindings.
[[nodiscard]] size_t size() const { return bindings_.size(); }
/// Check if empty.
[[nodiscard]] bool empty() const { return bindings_.empty(); }
private:
std::unordered_map<TermId, TermId> bindings_;
};
} // namespace atp
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