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https://github.com/Z3Prover/z3
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e4cc27810f
Refactor close_with_core to simplify logic and remove unnecessary parameters. Update sibling resolvent computation and try_resolve_upwards for clarity.
318 lines
11 KiB
C++
318 lines
11 KiB
C++
/*++
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Copyright (c) 2025 Microsoft Corporation
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Module Name:
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search_tree.h
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Abstract:
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A binary search tree for managing the search space of a DPLL(T) solver.
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It supports splitting on atoms, backtracking on conflicts, and activating nodes.
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Nodes can be in one of three states: open, closed, or active.
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- Closed nodes are fully explored (both children are closed).
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- Active nodes have no children and are currently being explored.
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- Open nodes either have children that are open or are leaves.
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A node can be split if it is active. After splitting, it becomes open and has two open children.
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Backtracking on a conflict closes all nodes below the last node whose atom is in the conflict set.
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Activation searches an open node closest to a seed node.
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Author:
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Ilana Shapiro 2025-9-06
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--*/
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#include "util/util.h"
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#include "util/vector.h"
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#pragma once
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namespace search_tree {
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enum class status { open, closed, active };
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template<typename Config>
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class node {
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typedef typename Config::literal literal;
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literal m_literal;
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node* m_left = nullptr, * m_right = nullptr, * m_parent = nullptr;
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status m_status;
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vector<literal> m_core;
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public:
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node(literal const& l, node* parent) :
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m_literal(l), m_parent(parent), m_status(status::open) {}
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~node() {
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dealloc(m_left);
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dealloc(m_right);
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}
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status get_status() const { return m_status; }
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void set_status(status s) { m_status = s; }
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literal const& get_literal() const { return m_literal; }
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bool literal_is_null() const { return Config::is_null(m_literal); }
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void split(literal const& a, literal const& b) {
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SASSERT(!Config::literal_is_null(a));
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SASSERT(!Config::literal_is_null(b));
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if (m_status != status::active)
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return;
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SASSERT(!m_left);
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SASSERT(!m_right);
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m_left = alloc(node<Config>, a, this);
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m_right = alloc(node<Config>, b, this);
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m_status = status::open;
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}
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node* left() const { return m_left; }
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node* right() const { return m_right; }
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node* parent() const { return m_parent; }
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node* find_active_node() {
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if (m_status == status::active)
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return this;
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if (m_status != status::open)
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return nullptr;
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node* nodes[2] = { m_left, m_right };
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for (unsigned i = 0; i < 2; ++i) {
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auto res = nodes[i] ? nodes[i]->find_active_node() : nullptr;
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if (res)
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return res;
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}
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if (m_left->get_status() == status::closed && m_right->get_status() == status::closed)
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m_status = status::closed;
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return nullptr;
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}
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void display(std::ostream& out, unsigned indent) const {
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for (unsigned i = 0; i < indent; ++i)
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out << " ";
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Config::display_literal(out, m_literal);
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out << (get_status() == status::open ? " (o)" : get_status() == status::closed ? " (c)" : " (a)");
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out << "\n";
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if (m_left)
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m_left->display(out, indent + 2);
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if (m_right)
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m_right->display(out, indent + 2);
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}
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bool has_core() const { return !m_core.empty(); }
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void set_core(vector<literal> const &core) {
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m_core = core;
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}
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vector<literal> const & get_core() const { return m_core; }
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void clear_core() { m_core.clear(); }
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};
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template<typename Config>
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class tree {
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typedef typename Config::literal literal;
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scoped_ptr<node<Config>> m_root = nullptr;
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literal m_null_literal;
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random_gen m_rand;
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// return an active node in the subtree rooted at n, or nullptr if there is none
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// close nodes that are fully explored (whose children are all closed)
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node<Config>* activate_from_root(node<Config>* n) {
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if (!n)
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return nullptr;
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if (n->get_status() != status::open)
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return nullptr;
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auto left = n->left();
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auto right = n->right();
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if (!left && !right) {
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n->set_status(status::active);
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return n;
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}
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node<Config>* nodes[2] = { left, right };
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unsigned index = m_rand(2);
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auto child = activate_from_root(nodes[index]);
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if (child)
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return child;
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child = activate_from_root(nodes[1 - index]);
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if (child)
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return child;
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if (left && right && left->get_status() == status::closed && right->get_status() == status::closed)
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n->set_status(status::closed);
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return nullptr;
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}
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void close(node<Config>* n) {
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if (!n || n->get_status() == status::closed)
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return;
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n->set_status(status::closed);
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close(n->left);
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close(n->right);
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}
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// Invariants:
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// Cores labeling nodes are subsets of the literals on the path to the node and the (external) assumption literals.
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// If a parent is open, then the one of the children is open.
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void close_with_core(node<Config>* n, vector<literal> const &C) {
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if (!n || n->get_status() == status::closed)
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return;
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node<Config>* p = n->parent();
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if (p && any_of(C, [](auto const& l) { return l == n->get_literal(); }})) {
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close_with_core(p, C);
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return;
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}
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close(n->left());
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close(n->right());
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n->set_core(C);
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n->set_status(status::closed);
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if (p)
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try_resolve_upwards(p);
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}
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// Given complementary sibling nodes for literals x and ¬x, sibling resolvent = (core_left ∪ core_right) \ {x, ¬x}
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vector<literal> compute_sibling_resolvent(node<Config>* left, node<Config>* right) {
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vector<literal> res;
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auto &core_l = left->get_core();
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auto &core_r = right->get_core();
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if (core_l.empty() || core_r.empty() || left->parent() != right->parent())
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return res;
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auto lit_l = left->get_literal();
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auto lit_r = right->get_literal();
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for (auto const& lit : core_l)
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if (lit != lit_l && !res.contains(lit))
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res.push_back(lit);
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for (auto const& lit : core_r)
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if (lit != lit_l && !res.contains(lit))
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res.push_back(lit);
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return res;
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}
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void try_resolve_upwards(node<Config>* p) {
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auto left = p->left();
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auto right = p->right();
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if (!left || !right)
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return;
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// only attempt when both children are closed and each has a core
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if (left->get_status() != status::closed || right->get_status() != status::closed)
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return;
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auto resolvent = compute_sibling_resolvent(left, right);
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close_with_core(p, resolvent);
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}
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public:
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tree(literal const& null_literal) : m_null_literal(null_literal) {
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reset();
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}
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void set_seed(unsigned seed) {
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m_rand.set_seed(seed);
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}
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void reset() {
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m_root = alloc(node<Config>, m_null_literal, nullptr);
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m_root->set_status(status::active);
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}
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// Split current node if it is active.
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// After the call, n is open and has two children.
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void split(node<Config>* n, literal const& a, literal const& b) {
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n->split(a, b);
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}
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// conflict is given by a set of literals.
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// they are subsets of the literals on the path from root to n AND the external assumption literals
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void backtrack(node<Config>* n, vector<literal> const& conflict) {
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if (conflict.empty()) {
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close_with_core(m_root.get(), conflict);
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return;
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}
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SASSERT(n != m_root.get());
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// all literals in conflict are on the path from root to n
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// remove assumptions from conflict to ensure this.
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DEBUG_CODE(
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auto on_path = [&](literal const& a) {
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node<Config>* p = n;
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while (p) {
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if (p->get_literal() == a)
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return true;
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p = p->parent();
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}
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return false;
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};
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SASSERT(all_of(conflict, [&](auto const& a) { return on_path(a); }));
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);
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while (n) {
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if (any_of(conflict, [&](auto const& a) { return a == n->get_literal(); })) {
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// close the subtree under n (preserves core attached to n), and attempt to resolve upwards
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close_with_core(n, conflict);
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return;
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}
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n = n->parent();
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}
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UNREACHABLE();
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}
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// return an active node in the tree, or nullptr if there is none
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// first check if there is a node to activate under n,
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// if not, go up the tree and try to activate a sibling subtree
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node<Config>* activate_node(node<Config>* n) {
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if (!n) {
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if (m_root->get_status() == status::active)
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return m_root.get();
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n = m_root.get();
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}
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auto res = activate_from_root(n);
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if (res)
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return res;
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auto p = n->parent();
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while (p) {
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if (p->left() && p->left()->get_status() == status::closed &&
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p->right() && p->right()->get_status() == status::closed) {
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p->set_status(status::closed);
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n = p;
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p = n->parent();
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continue;
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}
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if (n == p->left()) {
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res = activate_from_root(p->right());
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if (res)
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return res;
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}
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else {
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VERIFY(n == p->right());
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res = activate_from_root(p->left());
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if (res)
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return res;
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}
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n = p;
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p = n->parent();
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}
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return nullptr;
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}
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node<Config>* find_active_node() {
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return m_root->find_active_node();
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}
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vector<literal> const& get_core_from_root() const {
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return m_root->get_core();
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}
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bool is_closed() const {
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return m_root->get_status() == status::closed;
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}
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std::ostream& display(std::ostream& out) const {
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m_root->display(out, 0);
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return out;
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}
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};
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}
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