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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/>.
*/
#include "atp/infer/resolution.h"
#include "atp/core/clause.h"
#include "atp/core/symbol_table.h"
#include "atp/core/term.h"
#include "atp/core/term_bank.h"
#include "atp/core/types.h"
#include "atp/infer/substitution.h"
#include "atp/infer/unification.h"
#include <string>
#include <unordered_map>
#include <vector>
namespace atp {
namespace {
/// Recursively collect all variable TermIds appearing in a term.
void collectVariables(TermId term, const TermBank& bank,
std::unordered_map<TermId, bool>& seen) {
if (bank.isVariable(term)) {
seen[term] = true;
return;
}
// Copy args to avoid dangling ref (bank is const here, but be safe)
const Term& t = bank.getTerm(term);
for (TermId arg : t.args) {
collectVariables(arg, bank, seen);
}
}
} // namespace
Clause renameVariables(const Clause& c, TermBank& bank, SymbolTable& symbols,
uint32_t& next_var_id) {
// 1. Collect all variables in the clause
std::unordered_map<TermId, bool> var_set;
for (const auto& lit : c.literals) {
collectVariables(lit.atom, bank, var_set);
}
if (var_set.empty()) {
return c; // Ground clause — nothing to rename
}
// 2. Create fresh variables and build a substitution
Substitution rename_subst;
for (auto& [old_var_id, _] : var_set) {
std::string fresh_name = "_R" + std::to_string(next_var_id++);
SymbolId fresh_sym = symbols.intern(fresh_name, SymbolKind::kVariable);
TermId fresh_var = bank.makeVar(fresh_sym);
rename_subst.bind(old_var_id, fresh_var);
}
// 3. Apply the renaming substitution to all literals
Clause renamed;
renamed.id = c.id;
renamed.rule = c.rule;
renamed.parent1 = c.parent1;
renamed.parent2 = c.parent2;
renamed.depth = c.depth;
for (const auto& lit : c.literals) {
TermId new_atom = applySubstitution(rename_subst, lit.atom, bank);
renamed.literals.push_back({.atom = new_atom, .is_positive = lit.is_positive});
}
return renamed;
}
std::optional<Clause> resolve(TermBank& bank, const Clause& c1, size_t lit_idx1,
const Clause& c2, size_t lit_idx2) {
// Must have opposite polarity
if (c1.literals[lit_idx1].is_positive == c2.literals[lit_idx2].is_positive) {
return std::nullopt;
}
// Rename c2's variables to avoid clashes with c1
// Use a static counter — safe for single-threaded prover
static uint32_t var_counter = 0;
auto& symbols = const_cast<SymbolTable&>(bank.symbols());
Clause c2r = renameVariables(c2, bank, symbols, var_counter);
// Unify the complementary atoms
Substitution subst;
if (!unify(bank, c1.literals[lit_idx1].atom, c2r.literals[lit_idx2].atom, subst)) {
return std::nullopt;
}
// Build the resolvent: all literals except the resolved pair, with subst applied
Clause resolvent;
resolvent.rule = InferenceRule::kResolution;
resolvent.parent1 = c1.id;
resolvent.parent2 = c2.id;
for (size_t i = 0; i < c1.literals.size(); ++i) {
if (i != lit_idx1) {
TermId new_atom = applySubstitution(subst, c1.literals[i].atom, bank);
resolvent.literals.push_back(
{.atom = new_atom, .is_positive = c1.literals[i].is_positive});
}
}
for (size_t i = 0; i < c2r.literals.size(); ++i) {
if (i != lit_idx2) {
TermId new_atom = applySubstitution(subst, c2r.literals[i].atom, bank);
resolvent.literals.push_back(
{.atom = new_atom, .is_positive = c2r.literals[i].is_positive});
}
}
return resolvent;
}
std::vector<Clause> allResolvents(TermBank& bank, const Clause& c1, const Clause& c2) {
std::vector<Clause> results;
for (size_t i = 0; i < c1.literals.size(); ++i) {
for (size_t j = 0; j < c2.literals.size(); ++j) {
if (c1.literals[i].is_positive != c2.literals[j].is_positive) {
if (auto r = resolve(bank, c1, i, c2, j)) {
results.push_back(std::move(*r));
}
}
}
}
return results;
}
std::vector<Clause> factor(TermBank& bank, const Clause& c) {
std::vector<Clause> results;
for (size_t i = 0; i < c.literals.size(); ++i) {
for (size_t j = i + 1; j < c.literals.size(); ++j) {
if (c.literals[i].is_positive != c.literals[j].is_positive) {
continue; // Must have same polarity
}
Substitution subst;
if (!unify(bank, c.literals[i].atom, c.literals[j].atom, subst)) {
continue;
}
// Build factored clause: drop literal j, apply subst to all
Clause factored;
factored.rule = InferenceRule::kFactoring;
factored.parent1 = c.id;
for (size_t k = 0; k < c.literals.size(); ++k) {
if (k != j) {
TermId new_atom = applySubstitution(subst, c.literals[k].atom, bank);
factored.literals.push_back(
{.atom = new_atom, .is_positive = c.literals[k].is_positive});
}
}
results.push_back(std::move(factored));
}
}
return results;
}
} // namespace atp
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