mirror of
https://github.com/Z3Prover/z3
synced 2026-03-07 13:54:53 +00:00
637 lines
21 KiB
C++
637 lines
21 KiB
C++
/*++
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Copyright (c) 2026 Microsoft Corporation
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Module Name:
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euf_sgraph.cpp
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Abstract:
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Sequence/string graph implementation
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Author:
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Nikolaj Bjorner (nbjorner) 2026-03-01
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Clemens Eisenhofer 2026-03-01
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--*/
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#include "ast/euf/euf_sgraph.h"
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#include "ast/euf/euf_seq_plugin.h"
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#include "ast/arith_decl_plugin.h"
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#include "ast/ast_pp.h"
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namespace euf {
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// substitution cache stored on snode for ZIPT-style optimization
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struct snode_subst_cache {
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struct entry {
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unsigned var_id;
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unsigned repl_id;
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snode* result;
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};
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svector<entry> m_entries;
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snode* find(unsigned var_id, unsigned repl_id) const {
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for (auto const& e : m_entries)
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if (e.var_id == var_id && e.repl_id == repl_id)
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return e.result;
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return nullptr;
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}
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void insert(unsigned var_id, unsigned repl_id, snode* result) {
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m_entries.push_back({var_id, repl_id, result});
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}
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};
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sgraph::sgraph(ast_manager& m, egraph& eg, bool add_plugin):
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m(m),
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m_seq(m),
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m_rewriter(m),
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m_egraph(eg),
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m_str_sort(m_seq.str.mk_string_sort(), m),
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m_add_plugin(add_plugin) {
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// create seq_plugin and register it with the egraph
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if (add_plugin)
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m_egraph.add_plugin(alloc(seq_plugin, m_egraph, this));
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// register on_make callback so sgraph creates snodes for new enodes
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std::function<void(enode*)> on_make = [this](enode* n) {
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expr* e = n->get_expr();
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if (m_seq.is_seq(e) || m_seq.is_re(e))
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mk(e);
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};
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m_egraph.set_on_make(on_make);
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}
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sgraph::~sgraph() {
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for (auto* c : m_subst_caches)
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dealloc(c);
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}
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snode_kind sgraph::classify(expr* e) const {
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if (!is_app(e))
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return snode_kind::s_other;
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if (m_seq.str.is_empty(e))
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return snode_kind::s_empty;
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if (m_seq.str.is_string(e)) {
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zstring s;
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if (m_seq.str.is_string(e, s) && s.empty())
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return snode_kind::s_empty;
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return snode_kind::s_other;
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}
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if (m_seq.str.is_concat(e))
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return snode_kind::s_concat;
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if (m_seq.str.is_unit(e)) {
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expr* ch = to_app(e)->get_arg(0);
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if (m_seq.is_const_char(ch))
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return snode_kind::s_char;
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return snode_kind::s_unit;
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}
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if (m_seq.str.is_power(e))
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return snode_kind::s_power;
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if (m_seq.re.is_star(e))
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return snode_kind::s_star;
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if (m_seq.re.is_loop(e))
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return snode_kind::s_loop;
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if (m_seq.re.is_union(e))
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return snode_kind::s_union;
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if (m_seq.re.is_intersection(e))
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return snode_kind::s_intersect;
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if (m_seq.re.is_complement(e))
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return snode_kind::s_complement;
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if (m_seq.re.is_empty(e))
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return snode_kind::s_fail;
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if (m_seq.re.is_full_char(e))
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return snode_kind::s_full_char;
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if (m_seq.re.is_full_seq(e))
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return snode_kind::s_full_seq;
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if (m_seq.re.is_to_re(e))
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return snode_kind::s_to_re;
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if (m_seq.str.is_in_re(e))
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return snode_kind::s_in_re;
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// uninterpreted constants of string sort are variables
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if (is_uninterp_const(e) && m_seq.is_seq(e->get_sort()))
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return snode_kind::s_var;
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return snode_kind::s_other;
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}
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void sgraph::compute_metadata(snode* n) {
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switch (n->m_kind) {
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case snode_kind::s_empty:
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n->m_ground = true;
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n->m_regex_free = true;
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n->m_nullable = true;
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n->m_level = 0;
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n->m_length = 0;
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break;
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case snode_kind::s_char:
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n->m_ground = true;
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n->m_regex_free = true;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_var:
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n->m_ground = false;
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n->m_regex_free = true;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_unit:
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n->m_ground = n->num_args() > 0 ? n->arg(0)->is_ground() : true;
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n->m_regex_free = true;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_concat: {
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SASSERT(n->num_args() == 2);
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snode* l = n->arg(0);
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snode* r = n->arg(1);
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n->m_ground = l->is_ground() && r->is_ground();
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n->m_regex_free = l->is_regex_free() && r->is_regex_free();
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n->m_nullable = l->is_nullable() && r->is_nullable();
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n->m_level = std::max(l->level(), r->level()) + 1;
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n->m_length = l->length() + r->length();
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++m_stats.m_num_concat;
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break;
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}
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case snode_kind::s_power: {
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// s^n: nullable follows base, consistent with ZIPT's PowerToken
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// the exponent n is assumed to be a symbolic integer, may or may not be zero
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SASSERT(n->num_args() >= 1);
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snode* base = n->arg(0);
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n->m_ground = base->is_ground();
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n->m_regex_free = base->is_regex_free();
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n->m_nullable = base->is_nullable();
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n->m_level = 1;
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n->m_length = 1;
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++m_stats.m_num_power;
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break;
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}
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case snode_kind::s_star:
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SASSERT(n->num_args() == 1);
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n->m_ground = n->arg(0)->is_ground();
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n->m_regex_free = false;
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n->m_nullable = true;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_loop: {
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bool base_nullable = n->num_args() > 0 && n->arg(0)->is_nullable();
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unsigned lo = 0, hi = 0;
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expr* body = nullptr;
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bool lo_zero = n->get_expr() && m_seq.re.is_loop(n->get_expr(), body, lo, hi) && lo == 0;
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n->m_ground = n->num_args() > 0 ? n->arg(0)->is_ground() : true;
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n->m_regex_free = false;
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n->m_nullable = lo_zero || base_nullable;
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n->m_level = 1;
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n->m_length = 1;
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break;
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}
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case snode_kind::s_union:
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SASSERT(n->num_args() == 2);
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n->m_ground = n->arg(0)->is_ground() && n->arg(1)->is_ground();
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n->m_regex_free = false;
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n->m_nullable = n->arg(0)->is_nullable() || n->arg(1)->is_nullable();
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_intersect:
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SASSERT(n->num_args() == 2);
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n->m_ground = n->arg(0)->is_ground() && n->arg(1)->is_ground();
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n->m_regex_free = false;
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n->m_nullable = n->arg(0)->is_nullable() && n->arg(1)->is_nullable();
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_complement:
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SASSERT(n->num_args() == 1);
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n->m_ground = n->arg(0)->is_ground();
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n->m_regex_free = false;
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n->m_nullable = !n->arg(0)->is_nullable();
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_fail:
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n->m_ground = true;
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n->m_regex_free = false;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_full_char:
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n->m_ground = true;
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n->m_regex_free = false;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_full_seq:
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n->m_ground = true;
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n->m_regex_free = false;
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n->m_nullable = true;
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_to_re:
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SASSERT(n->num_args() == 1);
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n->m_ground = n->arg(0)->is_ground();
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n->m_regex_free = false;
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n->m_nullable = n->arg(0)->is_nullable();
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n->m_level = 1;
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n->m_length = 1;
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break;
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case snode_kind::s_in_re:
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SASSERT(n->num_args() == 2);
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n->m_ground = n->arg(0)->is_ground() && n->arg(1)->is_ground();
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n->m_regex_free = false;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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default:
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n->m_ground = true;
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n->m_regex_free = true;
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n->m_nullable = false;
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n->m_level = 1;
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n->m_length = 1;
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break;
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}
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}
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static const unsigned HASH_BASE = 31;
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// Compute a 2x2 polynomial hash matrix for associativity-respecting hashing.
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// Unsigned overflow is intentional and well-defined (mod 2^32).
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// M[0][0] tracks HASH_BASE^(num_leaves), which is always nonzero since
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// HASH_BASE is odd. M[0][1] is the actual hash value.
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void sgraph::compute_hash_matrix(snode* n) {
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if (n->is_empty()) {
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// identity matrix: concat with empty is identity
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n->m_hash_matrix[0][0] = 1;
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n->m_hash_matrix[0][1] = 0;
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n->m_hash_matrix[1][0] = 0;
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n->m_hash_matrix[1][1] = 1;
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}
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else if (n->is_concat()) {
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snode* l = n->arg(0);
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snode* r = n->arg(1);
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if (l->has_cached_hash() && r->has_cached_hash()) {
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// 2x2 matrix multiplication: M(L) * M(R)
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n->m_hash_matrix[0][0] = l->m_hash_matrix[0][0] * r->m_hash_matrix[0][0] + l->m_hash_matrix[0][1] * r->m_hash_matrix[1][0];
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n->m_hash_matrix[0][1] = l->m_hash_matrix[0][0] * r->m_hash_matrix[0][1] + l->m_hash_matrix[0][1] * r->m_hash_matrix[1][1];
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n->m_hash_matrix[1][0] = l->m_hash_matrix[1][0] * r->m_hash_matrix[0][0] + l->m_hash_matrix[1][1] * r->m_hash_matrix[1][0];
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n->m_hash_matrix[1][1] = l->m_hash_matrix[1][0] * r->m_hash_matrix[0][1] + l->m_hash_matrix[1][1] * r->m_hash_matrix[1][1];
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}
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}
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else {
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// leaf/token: [[HASH_BASE, value], [0, 1]]
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// +1 avoids zero hash values; wraps safely on unsigned overflow
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unsigned v = n->get_expr() ? n->get_expr()->get_id() + 1 : n->id() + 1;
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n->m_hash_matrix[0][0] = HASH_BASE;
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n->m_hash_matrix[0][1] = v;
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n->m_hash_matrix[1][0] = 0;
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n->m_hash_matrix[1][1] = 1;
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}
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}
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snode* sgraph::mk_snode(expr* e, snode_kind k, unsigned num_args, snode* const* args) {
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unsigned id = m_nodes.size();
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snode* n = snode::mk(m_region, e, k, id, num_args, args);
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compute_metadata(n);
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compute_hash_matrix(n);
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m_nodes.push_back(n);
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if (e) {
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unsigned eid = e->get_id();
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m_expr2snode.reserve(eid + 1, nullptr);
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m_expr2snode[eid] = n;
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// pin expression via egraph (the egraph has an expr trail)
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mk_enode(e);
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}
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++m_stats.m_num_nodes;
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return n;
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}
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snode* sgraph::mk(expr* e) {
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SASSERT(e);
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snode* n = find(e);
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if (n)
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return n;
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snode_kind k = classify(e);
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if (!is_app(e))
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return mk_snode(e, k, 0, nullptr);
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app* a = to_app(e);
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unsigned arity = a->get_num_args();
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// recursively register children
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// for seq/re children, create classified snodes
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// for other children (e.g. integer exponents), create s_other snodes
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snode_vector child_nodes;
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for (unsigned i = 0; i < arity; ++i) {
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expr* ch = a->get_arg(i);
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snode* cn = mk(ch);
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child_nodes.push_back(cn);
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}
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return mk_snode(e, k, child_nodes.size(), child_nodes.data());
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}
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snode* sgraph::find(expr* e) const {
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if (!e)
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return nullptr;
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unsigned eid = e->get_id();
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if (eid < m_expr2snode.size())
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return m_expr2snode[eid];
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return nullptr;
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}
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enode* sgraph::mk_enode(expr* e) {
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enode* n = m_egraph.find(e);
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if (n) return n;
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enode_vector args;
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if (is_app(e)) {
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for (expr* arg : *to_app(e)) {
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enode* a = mk_enode(arg);
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args.push_back(a);
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}
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}
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return m_egraph.mk(e, 0, args.size(), args.data());
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}
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void sgraph::push() {
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m_scopes.push_back(m_nodes.size());
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++m_num_scopes;
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m_egraph.push();
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}
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void sgraph::pop(unsigned num_scopes) {
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if (num_scopes == 0)
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return;
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SASSERT(num_scopes <= m_num_scopes);
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unsigned new_lvl = m_num_scopes - num_scopes;
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unsigned old_sz = m_scopes[new_lvl];
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for (unsigned i = m_nodes.size(); i-- > old_sz; ) {
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snode* n = m_nodes[i];
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if (n->get_expr()) {
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unsigned eid = n->get_expr()->get_id();
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if (eid < m_expr2snode.size())
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m_expr2snode[eid] = nullptr;
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}
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}
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m_nodes.shrink(old_sz);
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m_scopes.shrink(new_lvl);
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m_num_scopes = new_lvl;
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m_egraph.pop(num_scopes);
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}
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snode* sgraph::mk_var(symbol const& name) {
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expr_ref e(m.mk_const(name, m_str_sort), m);
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return mk(e);
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}
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snode* sgraph::mk_char(unsigned ch) {
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expr_ref c(m_seq.str.mk_char(ch), m);
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expr_ref u(m_seq.str.mk_unit(c), m);
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return mk(u);
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}
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snode* sgraph::mk_empty() {
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expr_ref e(m_seq.str.mk_empty(m_str_sort), m);
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return mk(e);
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}
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snode* sgraph::mk_concat(snode* a, snode* b) {
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if (a->is_empty()) return b;
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if (b->is_empty()) return a;
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expr_ref e(m_seq.str.mk_concat(a->get_expr(), b->get_expr()), m);
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return mk(e);
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}
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snode* sgraph::drop_first(snode* n) {
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if (n->is_empty() || n->is_token())
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return mk_empty();
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SASSERT(n->is_concat());
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snode* l = n->arg(0);
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snode* r = n->arg(1);
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if (l->is_token() || l->is_empty())
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return r;
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return mk_concat(drop_first(l), r);
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}
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snode* sgraph::drop_last(snode* n) {
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if (n->is_empty() || n->is_token())
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return mk_empty();
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SASSERT(n->is_concat());
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snode* l = n->arg(0);
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snode* r = n->arg(1);
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if (r->is_token() || r->is_empty())
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return l;
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return mk_concat(l, drop_last(r));
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}
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snode* sgraph::drop_left(snode* n, unsigned count) {
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if (count == 0 || n->is_empty()) return n;
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if (count >= n->length()) return mk_empty();
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for (unsigned i = 0; i < count; ++i)
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n = drop_first(n);
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return n;
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}
|
|
|
|
snode* sgraph::drop_right(snode* n, unsigned count) {
|
|
if (count == 0 || n->is_empty()) return n;
|
|
if (count >= n->length()) return mk_empty();
|
|
for (unsigned i = 0; i < count; ++i)
|
|
n = drop_last(n);
|
|
return n;
|
|
}
|
|
|
|
snode* sgraph::subst(snode* n, snode* var, snode* replacement) {
|
|
if (n == var)
|
|
return replacement;
|
|
if (n->is_empty() || n->is_char())
|
|
return n;
|
|
if (n->is_concat()) {
|
|
// check substitution cache (ZIPT-style optimization)
|
|
if (n->m_subst_cache) {
|
|
snode* cached = n->m_subst_cache->find(var->id(), replacement->id());
|
|
if (cached)
|
|
return cached;
|
|
}
|
|
snode* result = mk_concat(subst(n->arg(0), var, replacement),
|
|
subst(n->arg(1), var, replacement));
|
|
// cache the result
|
|
if (!n->m_subst_cache) {
|
|
n->m_subst_cache = alloc(snode_subst_cache);
|
|
m_subst_caches.push_back(n->m_subst_cache);
|
|
}
|
|
n->m_subst_cache->insert(var->id(), replacement->id(), result);
|
|
return result;
|
|
}
|
|
// for non-concat compound nodes (power, star, etc.), no substitution into children
|
|
return n;
|
|
}
|
|
|
|
snode* sgraph::brzozowski_deriv(snode* re, snode* elem) {
|
|
expr* re_expr = re->get_expr();
|
|
expr* elem_expr = elem->get_expr();
|
|
if (!re_expr || !elem_expr)
|
|
return nullptr;
|
|
// unwrap str.unit to get the character expression
|
|
expr* ch = nullptr;
|
|
if (m_seq.str.is_unit(elem_expr, ch))
|
|
elem_expr = ch;
|
|
expr_ref result = m_rewriter.mk_derivative(elem_expr, re_expr);
|
|
if (!result)
|
|
return nullptr;
|
|
return mk(result);
|
|
}
|
|
|
|
void sgraph::collect_re_predicates(snode* re, expr_ref_vector& preds) {
|
|
if (!re || !re->get_expr())
|
|
return;
|
|
expr* e = re->get_expr();
|
|
expr* ch = nullptr, *lo = nullptr, *hi = nullptr;
|
|
// leaf regex predicates: character ranges and single characters
|
|
if (m_seq.re.is_range(e, lo, hi)) {
|
|
preds.push_back(e);
|
|
return;
|
|
}
|
|
if (m_seq.re.is_to_re(e))
|
|
return;
|
|
if (m_seq.re.is_full_char(e))
|
|
return;
|
|
if (m_seq.re.is_full_seq(e))
|
|
return;
|
|
if (m_seq.re.is_empty(e))
|
|
return;
|
|
// recurse into compound regex operators
|
|
for (unsigned i = 0; i < re->num_args(); ++i)
|
|
collect_re_predicates(re->arg(i), preds);
|
|
}
|
|
|
|
void sgraph::compute_minterms(snode* re, snode_vector& minterms) {
|
|
// extract character predicates from the regex
|
|
expr_ref_vector preds(m);
|
|
collect_re_predicates(re, preds);
|
|
if (preds.empty()) {
|
|
// no predicates means the whole alphabet is one minterm
|
|
// represented by full_char
|
|
expr_ref fc(m_seq.re.mk_full_char(m_str_sort), m);
|
|
minterms.push_back(mk(fc));
|
|
return;
|
|
}
|
|
// generate minterms as conjunctions/negations of predicates
|
|
// for n predicates, there are up to 2^n minterms
|
|
unsigned n = preds.size();
|
|
// cap at reasonable size to prevent exponential blowup
|
|
if (n > 20)
|
|
n = 20;
|
|
for (unsigned mask = 0; mask < (1u << n); ++mask) {
|
|
expr_ref_vector conj(m);
|
|
for (unsigned i = 0; i < n; ++i) {
|
|
if (mask & (1u << i))
|
|
conj.push_back(preds.get(i));
|
|
else
|
|
conj.push_back(m_seq.re.mk_complement(preds.get(i)));
|
|
}
|
|
SASSERT(!conj.empty());
|
|
// intersect all terms
|
|
expr_ref mt(conj.get(0), m);
|
|
for (unsigned i = 1; i < conj.size(); ++i)
|
|
mt = m_seq.re.mk_inter(mt, conj.get(i));
|
|
minterms.push_back(mk(mt));
|
|
}
|
|
}
|
|
|
|
std::ostream& sgraph::display(std::ostream& out) const {
|
|
auto kind_str = [](snode_kind k) -> char const* {
|
|
switch (k) {
|
|
case snode_kind::s_empty: return "empty";
|
|
case snode_kind::s_char: return "char";
|
|
case snode_kind::s_var: return "var";
|
|
case snode_kind::s_unit: return "unit";
|
|
case snode_kind::s_concat: return "concat";
|
|
case snode_kind::s_power: return "power";
|
|
case snode_kind::s_star: return "star";
|
|
case snode_kind::s_loop: return "loop";
|
|
case snode_kind::s_union: return "union";
|
|
case snode_kind::s_intersect: return "intersect";
|
|
case snode_kind::s_complement: return "complement";
|
|
case snode_kind::s_fail: return "fail";
|
|
case snode_kind::s_full_char: return "full_char";
|
|
case snode_kind::s_full_seq: return "full_seq";
|
|
case snode_kind::s_to_re: return "to_re";
|
|
case snode_kind::s_in_re: return "in_re";
|
|
case snode_kind::s_other: return "other";
|
|
}
|
|
return "?";
|
|
};
|
|
for (snode* n : m_nodes) {
|
|
out << "snode[" << n->id() << "] "
|
|
<< kind_str(n->kind())
|
|
<< " level=" << n->level()
|
|
<< " len=" << n->length()
|
|
<< " ground=" << n->is_ground()
|
|
<< " rfree=" << n->is_regex_free()
|
|
<< " nullable=" << n->is_nullable();
|
|
if (n->num_args() > 0) {
|
|
out << " args=(";
|
|
for (unsigned i = 0; i < n->num_args(); ++i) {
|
|
if (i > 0) out << ", ";
|
|
out << n->arg(i)->id();
|
|
}
|
|
out << ")";
|
|
}
|
|
if (n->get_expr())
|
|
out << " expr=" << mk_pp(n->get_expr(), m);
|
|
out << "\n";
|
|
}
|
|
return out;
|
|
}
|
|
|
|
void sgraph::collect_statistics(statistics& st) const {
|
|
st.update("seq-graph-nodes", m_stats.m_num_nodes);
|
|
st.update("seq-graph-concat", m_stats.m_num_concat);
|
|
st.update("seq-graph-power", m_stats.m_num_power);
|
|
st.update("seq-graph-hash-hits", m_stats.m_num_hash_hits);
|
|
m_egraph.collect_statistics(st);
|
|
}
|
|
|
|
}
|
|
|