z3/src/smt/theory_finite_set_lattice_refutation.cpp

/*++
Copyright (c) 2025 Lorenz Winkler

Module Name:

    theory_finite_lattice_refutation.cpp

--*/

#include "smt/theory_finite_set_lattice_refutation.h"
#include "ast/rewriter/finite_set_axioms.h"
#include "smt/smt_theory.h"
#include "smt/theory_finite_set.h"
#include "smt/smt_context.h"
#include "util/uint_set.h"

// some examples have shown, the introduction of large conflict clauses can severely slow down refutation
const int MAX_DECISION_LITERALS = 10;
const int MAX_VARS = 320;

namespace smt {
    reachability_matrix::reachability_matrix(context &ctx, theory_finite_set_lattice_refutation &t_lattice)
        : reachable(MAX_VARS), links(MAX_VARS * MAX_VARS, {nullptr, nullptr}),
          link_dls(), non_links(MAX_VARS),
          non_link_justifications(MAX_VARS * MAX_VARS, {nullptr, nullptr}), largest_var(0),
          max_size(MAX_VARS), ctx(ctx), t_lattice_refutation(t_lattice) {
        // Initialize the vectors
        link_dls.resize(MAX_VARS * MAX_VARS, 0);
        for (int i = 0; i < MAX_VARS; i++) {
            reachable[i].reset();
            non_links[i].reset();
        }
    }

    int reachability_matrix::get_max_var() {
        return largest_var;
    }

    bool reachability_matrix::is_reachability_forbidden(theory_var source, theory_var dest) {
        return non_links[source].contains(dest);
    }

    bool reachability_matrix::in_bounds(theory_var source, theory_var dest) {
        return source >= 0 && dest >= 0 && source < max_size && dest < max_size;
    }

    bool reachability_matrix::is_reachable(theory_var source, theory_var dest) {
        return reachable[source].contains(dest);
    }

    bool reachability_matrix::is_linked(theory_var source, theory_var dest) {
        return links[source * max_size + dest].first != nullptr;
    }

    bool reachability_matrix::bitwise_or_rows(int source_dest, int source) {
        // Check if there's anything to add
        bool has_new_elements = false;
        for (unsigned dest : reachable[source]) {
            if (!reachable[source_dest].contains(dest)) {
                has_new_elements = true;
                break;
            }
        }
        
        if (!has_new_elements) {
            return false;
        }
        
        // Push trail before modifying (captures current state for undo)
        ctx.push_trail(value_trail(reachable[source_dest]));
        
        // Save elements before modification for conflict checking
        uint_set old_reachable = reachable[source_dest];
        
        // Compute union: reachable[source_dest] |= reachable[source]
        reachable[source_dest] |= reachable[source];
        
        // Check for conflicts with newly added reachabilities
        for (unsigned dest : reachable[source_dest]) {
            if (!old_reachable.contains(dest)) {
                check_reachability_conflict(source_dest, dest);
            }
        }
        
        return true;
    }

    bool reachability_matrix::set_reachability(theory_var source, theory_var dest, enode_pair reachability_witness) {
        if (!in_bounds(source, dest) || is_reachable(source, dest)) {
            return false;
        }
        ctx.push_trail(value_trail(largest_var));
        largest_var = std::max({largest_var, source, dest});

        ctx.push_trail(value_trail(reachable[source]));
        reachable[source].insert(dest);
        ctx.push_trail(value_trail(links[source * max_size + dest]));
        links[source * max_size + dest] = reachability_witness;
        ctx.push_trail(value_trail(link_dls[source * max_size + dest]));
        TRACE(finite_set, tout << "set_reachability(" << source << "," << dest << "), dl: " << ctx.get_scope_level());
        link_dls[source * max_size + dest] = ctx.get_scope_level();

        check_reachability_conflict(source, dest);
        // update reachability of source
        bitwise_or_rows(source, dest);

        for (int i = 0; i <= largest_var; i++) {  // update reachability of i to the nodes reachable from dest
            if (!is_reachable(i, source) || i == source) {
                continue;
            }
            bitwise_or_rows(i, source);
        }
        return true;
    }

    bool reachability_matrix::set_non_reachability(theory_var source, theory_var dest,
                                                   enode_pair non_reachability_witness) {
        if (is_reachability_forbidden(source, dest)) {
            return false;
        }
        ctx.push_trail(value_trail(largest_var));
        largest_var = std::max({largest_var, source, dest});
        ctx.push_trail(value_trail(non_links[source]));
        non_links[source].insert(dest);
        ctx.push_trail(value_trail(non_link_justifications[source * max_size + dest]));
        non_link_justifications[source * max_size + dest] = non_reachability_witness;
        check_reachability_conflict(source, dest);
        return true;
    }

    theory_finite_set_lattice_refutation::theory_finite_set_lattice_refutation(theory_finite_set &th)
        : m(th.m), ctx(th.ctx), th(th), u(m), bs(m), m_assumption(m), reachability(th.ctx, *this) {}

    // determines if the two enodes capture a subset relation:
    // checks, whether intersect_expr = intersect(subset, return_value) for some return value
    // otherwise return null
    enode *theory_finite_set_lattice_refutation::get_superset(enode *subset, enode *intersect_expr) {
        expr *arg1 = nullptr, *arg2 = nullptr;
        if (u.is_intersect(intersect_expr->get_expr(), arg1, arg2)) {
            if (arg1 == subset->get_expr()) {
                return ctx.get_enode(arg2);
            }
            if (arg2 == subset->get_expr()) {
                return ctx.get_enode(arg1);
            }
        }
        return nullptr;
    }

    void theory_finite_set_lattice_refutation::add_equality(theory_var v1, theory_var v2) {
        auto n1 = th.get_enode(v1);
        auto n2 = th.get_enode(v2);

        enode *subset = n1;
        enode *superset = get_superset(n1, n2);
        if (superset == nullptr) {
            subset = n2;
            superset = get_superset(n2, n1);
        }
        if (superset == nullptr) {
            add_set_equality(n1, n2);
            return;
        }
        TRACE(finite_set, tout << "new_eq_intersection: " << enode_pp(subset, ctx) << "(" << th.get_th_var(subset)
                               << ")" << "\\subseteq " << enode_pp(superset, ctx) << "(" << th.get_th_var(superset)
                               << ")");
        add_subset(subset->get_th_var(th.get_id()), superset->get_th_var(th.get_id()), {n1, n2});
    };

    void reachability_matrix::get_path(theory_var source, theory_var dest, vector<enode_pair> &path,
                                       int &num_decisions) {
        SASSERT(is_reachable(source, dest));
        bool_vector visited(max_size, false);
        if (source != dest) {
            visited[source] = true;
        }
        num_decisions = 0;
        do {
            bool success = false;
            // TRACE(finite_set, tout << "get_path:source: "<<source);
            for (int i = 0; i <= largest_var; i++) {
                if (!visited[i] && is_linked(source, i) && ((is_reachable(i, dest)) || i == dest)) {
                    path.push_back(links[source * max_size + i]);
                    if (link_dls[source * max_size + i] != 0) {
                        num_decisions += 1;
                    }

                    source = i;
                    visited[source] = true;
                    success = true;
                    break;
                }
            }
            SASSERT(success);
        } while (source != dest);
        TRACE(finite_set, tout << "get_path_num_decisions: " << num_decisions);
    }

    bool reachability_matrix::check_reachability_conflict(theory_var source, theory_var dest) {
        if (is_reachable(source, dest) && is_reachability_forbidden(source, dest)) {
            TRACE(finite_set, tout << "found_conflict1: " << source << " -> " << dest);
            vector<enode_pair> path;
            int num_decisions;
            get_path(source, dest, path, num_decisions);
            // TRACE(finite_set, tout << "found path: "<<source<<" -> "<<dest<<" length: "<<path.size());
            if (num_decisions <= MAX_DECISION_LITERALS) {
                TRACE(finite_set, tout << "num_decisions: " << num_decisions << " path_length: " << path.size());

                enode_pair diseq = non_link_justifications[source * max_size + dest];
                t_lattice_refutation.trigger_conflict(path, diseq);
            }

            return true;
        }
        return false;
    }

    void reachability_matrix::print_relations() {
        TRACE(finite_set, tout << "largest_var: " << largest_var);
        for (size_t i = 0; i < max_size; i++) {
            for (size_t j = 0; j < max_size; j++) {
                if (is_reachable(i, j)) {
                    TRACE(finite_set, tout << "reachable: " << i << "->" << j);
                }
            }
        }
    }

    void theory_finite_set_lattice_refutation::trigger_conflict(vector<enode_pair> equalities,
                                                                enode_pair clashing_disequality) {
        auto eq_expr =
            m.mk_not(m.mk_eq(clashing_disequality.first->get_expr(), clashing_disequality.second->get_expr()));
        auto disequality_literal = ctx.get_literal(eq_expr);
        auto j1 = ext_theory_conflict_justification(th.get_id(), ctx, 1, &disequality_literal, equalities.size(),
                                                    equalities.data());
        auto justification = ctx.mk_justification(j1);
        TRACE(finite_set, tout << "conflict_literal: " << disequality_literal);

        TRACE(finite_set, tout << "setting_partial_order_conflict");
        ctx.set_conflict(justification);
    }

    void theory_finite_set_lattice_refutation::add_disequality(theory_var v1, theory_var v2) {
        auto n1 = th.get_enode(v1);
        auto n2 = th.get_enode(v2);

        enode *subset = n1;
        enode *superset = get_superset(n1, n2);
        if (superset == nullptr) {
            subset = n2;
            superset = get_superset(n2, n1);
        }
        if (superset == nullptr) {
            return;
        }
        TRACE(finite_set, tout << "new_diseq_intersection: " << enode_pp(subset, ctx) << "(" << th.get_th_var(subset)
                               << ")" << "\\not\\subseteq " << enode_pp(superset, ctx) << "(" << th.get_th_var(superset)
                               << ")");
        add_not_subset(subset->get_th_var(th.get_id()), superset->get_th_var(th.get_id()), {n1, n2});
    };

    void theory_finite_set_lattice_refutation::add_subset(theory_var subset_th, theory_var superset_th,
                                                          enode_pair justifying_equality) {
        if (!reachability.in_bounds(subset_th, superset_th)) {
            return;
        }
        if (subset_th == null_theory_var || superset_th == null_theory_var) {
            return;
        }
        reachability.set_reachability(subset_th, superset_th, justifying_equality);
        SASSERT(reachability.is_reachable(subset_th, superset_th));
        if (reachability.is_reachable(superset_th, subset_th)) {
            TRACE(finite_set, tout << "cycle_detected: " << subset_th << " <--> " << superset_th);
            vector<enode_pair> path;
            int num_decisions;
            reachability.get_path(subset_th, subset_th, path, num_decisions);
            // we propagate the equality
            // build justification to be used by all propagated equalities
            auto j1 = ctx.mk_justification(
                ext_theory_conflict_justification(th.get_id(), ctx, 0, nullptr, path.size(), path.data()));

            for (size_t i = 0; i < path.size() - 1; i++) {
                auto set1 = path[i].first;
                auto set2 = path[i + 1].first;
                ctx.add_eq(set1, set2, eq_justification(j1));
                TRACE(finite_set, tout << "added_equality: " << set1 << " == " << set2);
            }
        }
    };

    void theory_finite_set_lattice_refutation::add_not_subset(theory_var subset_th, theory_var superset_th,
                                                              enode_pair justifying_disequality) {
        if (!reachability.in_bounds(subset_th, superset_th)) {
            return;
        }
        if (subset_th == null_theory_var || superset_th == null_theory_var) {
            return;
        }
        reachability.set_non_reachability(subset_th, superset_th, justifying_disequality);
        SASSERT(reachability.is_reachability_forbidden(subset_th, superset_th));
    }

    void theory_finite_set_lattice_refutation::add_set_equality(enode *set1, enode *set2) {
        theory_var set1_th = set1->get_th_var(th.get_id());
        theory_var set2_th = set2->get_th_var(th.get_id());
        if (!reachability.in_bounds(set1_th, set2_th)) {
            return;
        }
        reachability.set_reachability(set1_th, set2_th, {set1, set2});
        SASSERT(reachability.is_reachable(set1_th, set2_th));

        reachability.set_reachability(set2_th, set1_th, {set2, set1});
        SASSERT(reachability.is_reachable(set2_th, set1_th));
    }
}  // namespace smt