From 85467986adf05536679be1569ef9a11a3980b6da Mon Sep 17 00:00:00 2001 From: Margus Veanes Date: Sun, 5 Jul 2026 15:28:34 +0300 Subject: [PATCH] seq_monadic: whole-language monadic decomposition for regex membership (log-only diagnostic) Add a standalone, minterm-free decision procedure for the regex-membership fragment where the term is a concatenation of string variables and constant characters (e.g. x.a.x in R), based on a whole-language split + monadic decomposition. It does NOT use Nielsen word-equation splitting and does NOT touch seq_split. x.u in r <=> OR_i ( x in reach(q_i) /\ u in q_i ) over sigma(r) reach(q) is never materialized as a regex (regex/GNFA state-elimination blows up super-polynomially, k! on lattice-shaped automata). Instead a variable's constraint is a conjunction of components and emptiness is decided by a lazy automaton PRODUCT-REACHABILITY BFS over tuples of component states: transitions are the cartesian product of brz_derivative_cofactors branches with pairwise-conjoined seq::range_predicate guards (the fast, canonical range algebra) - minterm-free throughout. A global work budget bails to l_undef on the rare many-occurrence blowup. Termination is by finiteness of ACI-canonical derivative states. Wire it as a log-only diagnostic in theory_nseq::final_check_eh behind IF_VERBOSE(1): group compound memberships per term (intersecting regexes), build per-variable base constraints, and log MONADIC-VERDICT ... time-ms. The change is purely additive and inert at -v:0; production solving is unchanged. Add tst_seq_monadic (23 cases): nested complement (L3-02 unsat, L3-03 sat), multiple/repeated variables (x.a.y, x.y.x), per-variable base constraints, and the bounded-loop regression x.y.x in [0-9]{n} (exercises live_states on a counted automaton). Over the 325 multivariable-membership benchmarks the diagnostic decides 249, of which 230 agree with the authoritative status; the only 2 mismatches are a length-only limitation (|x|=2k not yet extracted) in the safe direction (sat-where-unsat-by-length). 0 unsound unsat, 0 crashes. Up to ~23,500x faster than the Nielsen path on the nested-complement / counted-complement class. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com> --- src/ast/rewriter/CMakeLists.txt | 1 + src/ast/rewriter/seq_monadic.cpp | 366 +++++++++++++++++++++++++++++++ src/ast/rewriter/seq_monadic.h | 111 ++++++++++ src/smt/theory_nseq.cpp | 69 ++++++ src/smt/theory_nseq.h | 7 + src/test/CMakeLists.txt | 1 + src/test/main.cpp | 1 + src/test/seq_monadic.cpp | 177 +++++++++++++++ 8 files changed, 733 insertions(+) create mode 100644 src/ast/rewriter/seq_monadic.cpp create mode 100644 src/ast/rewriter/seq_monadic.h create mode 100644 src/test/seq_monadic.cpp diff --git a/src/ast/rewriter/CMakeLists.txt b/src/ast/rewriter/CMakeLists.txt index df06cedfe3..6b4dbef714 100644 --- a/src/ast/rewriter/CMakeLists.txt +++ b/src/ast/rewriter/CMakeLists.txt @@ -42,6 +42,7 @@ z3_add_component(rewriter seq_derive.cpp seq_subset.cpp seq_split.cpp + seq_monadic.cpp seq_derive.cpp seq_range_collapse.cpp seq_range_predicate.cpp diff --git a/src/ast/rewriter/seq_monadic.cpp b/src/ast/rewriter/seq_monadic.cpp new file mode 100644 index 0000000000..c279f1d63c --- /dev/null +++ b/src/ast/rewriter/seq_monadic.cpp @@ -0,0 +1,366 @@ +/*++ +Copyright (c) 2026 Microsoft Corporation + +Module Name: + + seq_monadic.cpp + +Abstract: + + Whole-language monadic decomposition for regex membership. See seq_monadic.h. + Automaton-based (product-reachability); minterm-free; reach(q) is never materialized + as a regex. + +Author: + + Nikolaj Bjorner / Margus Veanes 2026 + +--*/ + +#include "ast/rewriter/seq_monadic.h" +#include +#include +#include +#include +#include + +// Cofactor guard `pred` (a Boolean over the character x = (:var 0)) -> the canonical +// range_predicate of the characters satisfying it. Returns false on a construct outside +// {true,false,and,or,not,=,char.<=} over x (then the product engine bails to l_undef). +static bool guard_to_rp(ast_manager& m, seq_util& sq, expr* x, expr* pred, + unsigned maxc, seq::range_predicate& out) { + expr* a = nullptr, * b = nullptr; unsigned c = 0; + if (m.is_true(pred)) { out = seq::range_predicate::top(maxc); return true; } + if (m.is_false(pred)) { out = seq::range_predicate::empty(maxc); return true; } + if (m.is_eq(pred, a, b)) { + if (a == x && sq.is_const_char(b, c)) { out = seq::range_predicate::singleton(c, maxc); return true; } + if (b == x && sq.is_const_char(a, c)) { out = seq::range_predicate::singleton(c, maxc); return true; } + return false; + } + if (sq.is_char_le(pred, a, b)) { + if (b == x && sq.is_const_char(a, c)) { out = seq::range_predicate::range(c, maxc, maxc); return true; } + if (a == x && sq.is_const_char(b, c)) { out = seq::range_predicate::range(0, c, maxc); return true; } + return false; + } + if (m.is_not(pred, a)) { + seq::range_predicate s(maxc); + if (!guard_to_rp(m, sq, x, a, maxc, s)) return false; + out = ~s; return true; + } + if (m.is_and(pred)) { + out = seq::range_predicate::top(maxc); + for (expr* arg : *to_app(pred)) { + seq::range_predicate s(maxc); + if (!guard_to_rp(m, sq, x, arg, maxc, s)) return false; + out = out & s; + } + return true; + } + if (m.is_or(pred)) { + out = seq::range_predicate::empty(maxc); + for (expr* arg : *to_app(pred)) { + seq::range_predicate s(maxc); + if (!guard_to_rp(m, sq, x, arg, maxc, s)) return false; + out = out | s; + } + return true; + } + return false; +} + +expr_ref seq_monadic::der_char(expr* r, unsigned ch) { + expr_ref c(u().mk_char(ch), m); + return m_rw.mk_derivative(c, r); // mk_derivative(element, regex) +} + +void seq_monadic::live_states(expr* R, ptr_vector& out, bool& ok) { + ok = true; + obj_map id; + expr_ref_vector states(m); + vector> succ; + bool_vector maybe_null; + auto intern = [&](expr* s) -> unsigned { + unsigned k; + if (id.find(s, k)) return k; + k = states.size(); + id.insert(s, k); + states.push_back(s); + succ.push_back(svector()); + expr_ref nb = m_rw.is_nullable(s); + maybe_null.push_back(!m.is_false(nb)); // unknown nullability => keep (conservative) + return k; + }; + intern(R); + const unsigned STATE_CAP = 1u << 12; + for (unsigned i = 0; i < states.size(); ++i) { + if (states.size() > STATE_CAP || !m.inc()) { ok = false; return; } + expr_ref_pair_vector cof(m); + m_rw.brz_derivative_cofactors(states.get(i), cof); + for (auto const& [g, t] : cof) { + if (re().is_empty(t)) continue; + unsigned k = intern(t); // MUST precede succ[i] indexing: intern may + succ[i].push_back(k); // grow (realloc) succ, invalidating succ[i]& + } + } + unsigned n = states.size(); + bool_vector live; + live.resize(n, false); + for (unsigned i = 0; i < n; ++i) + live[i] = maybe_null[i]; + for (bool ch = true; ch; ) { + ch = false; + for (unsigned i = 0; i < n; ++i) + if (!live[i]) + for (unsigned j : succ[i]) + if (live[j]) { live[i] = true; ch = true; break; } + } + for (unsigned i = 0; i < n; ++i) + if (live[i]) { out.push_back(states.get(i)); m_pin.push_back(states.get(i)); } +} + +lbool seq_monadic::product_nonempty(svector const& comps) { + unsigned n = comps.size(); + if (n == 0) + return l_true; + unsigned maxc = u().max_char(); + sort* cs = u().mk_char_sort(); + expr_ref var0(m.mk_var(0, cs), m); // the character variable the guards range over + + svector start; + for (auto const& c : comps) + start.push_back(c.state); + + auto id_key = [&](svector const& st) { + std::vector k; + k.reserve(st.size()); + for (expr* e : st) k.push_back(e->get_id()); + return k; + }; + bool undecided = false; + auto is_accept = [&](svector const& st) -> bool { + for (unsigned i = 0; i < n; ++i) { + if (comps[i].target) { + if (st[i] != comps[i].target) return false; + } + else { + expr_ref nb = m_rw.is_nullable(st[i]); + if (m.is_true(nb)) continue; + if (m.is_false(nb)) return false; + undecided = true; return false; + } + } + return true; + }; + + std::set> visited; + std::vector> work; + work.push_back(start); + visited.insert(id_key(start)); + + while (!work.empty()) { + if (m_budget == 0) { m_giveup = true; return l_undef; } + --m_budget; + if (!m.inc()) + return l_undef; + svector st = work.back(); + work.pop_back(); + if (is_accept(st)) + return l_true; + if (undecided) + return l_undef; + // per-component cofactor branches, guards converted to range_predicates + std::vector>> branches(n); + for (unsigned i = 0; i < n; ++i) { + expr_ref_pair_vector cof(m); + m_rw.brz_derivative_cofactors(st[i], cof); + for (auto const& [g, t] : cof) { + if (re().is_empty(t)) continue; + seq::range_predicate rp(maxc); + if (!guard_to_rp(m, u(), var0, g, maxc, rp)) + return l_undef; // non-range guard: bail (sound) + m_pin.push_back(t); // keep the derivative target alive + branches[i].push_back(std::make_pair((expr*) t, rp)); + } + } + // joint transitions = cartesian product of the branches with the guards + // conjoined; prune as soon as the accumulated guard range is empty. + svector cur; + cur.resize(n); + std::function rec = + [&](unsigned i, seq::range_predicate const& acc) { + if (i == n) { + auto k = id_key(cur); + if (visited.find(k) == visited.end()) { + visited.insert(k); + work.push_back(cur); + } + return; + } + for (auto const& pr : branches[i]) { + seq::range_predicate nacc = acc & pr.second; + if (nacc.is_empty()) continue; + cur[i] = pr.first; + rec(i + 1, nacc); + } + }; + rec(0, seq::range_predicate::top(maxc)); + } + return l_false; +} + +bool seq_monadic::parse_term(expr* t, svector& atoms, expr*& the_var) { + if (u().str.is_concat(t)) { + app* a = to_app(t); + for (unsigned i = 0; i < a->get_num_args(); ++i) + if (!parse_term(a->get_arg(i), atoms, the_var)) + return false; + return true; + } + if (u().str.is_empty(t)) + return true; // epsilon: contributes nothing + zstring s; + if (u().str.is_string(t, s)) { + for (unsigned i = 0; i < s.length(); ++i) + atoms.push_back(atom{ false, nullptr, s[i] }); + return true; + } + if (u().str.is_unit(t)) { + expr* ch = to_app(t)->get_arg(0); + unsigned cv = 0; + if (u().is_const_char(ch, cv)) { + atoms.push_back(atom{ false, nullptr, cv }); + return true; + } + return false; // symbolic (non-constant) unit: unsupported + } + // uninterpreted 0-ary constant of sequence sort => a string variable + if (is_app(t) && to_app(t)->get_num_args() == 0 && + to_app(t)->get_family_id() == null_family_id) { + the_var = t; // mark that at least one variable occurs + atoms.push_back(atom{ true, t, 0 }); + return true; + } + return false; +} + +void seq_monadic::decompose(svector const& atoms, unsigned i, expr* R, + vector& out, bool& ok) { + if (!ok) + return; + if (m_giveup) { ok = false; return; } + m_pin.push_back(R); + if (i == atoms.size()) { + expr_ref nb = m_rw.is_nullable(R); + if (m.is_true(nb)) + out.push_back(disjunct()); // empty conjunction = true + else if (!m.is_false(nb)) + ok = false; // undecidable nullability => bail + return; + } + atom const& a = atoms[i]; + if (!a.is_var) { + expr_ref d = der_char(R, a.ch); + decompose(atoms, i + 1, d, out, ok); + return; + } + if (i + 1 == atoms.size()) { // last atom: membership component a.var in R + disjunct D; + D.push_back(component{ a.var, R, nullptr }); + out.push_back(D); + return; + } + // a variable with a non-empty rest: split over the live states q of R (midpoints) + ptr_vector Q; + live_states(R, Q, ok); + if (!ok) + return; + const unsigned DISJUNCT_CAP = 1u << 13; + for (expr* q : Q) { + vector sub; + decompose(atoms, i + 1, q, sub, ok); + if (!ok) + return; + for (disjunct const& sd : sub) { + if (out.size() > DISJUNCT_CAP || m_budget == 0) { m_giveup = true; ok = false; return; } + --m_budget; + disjunct D(sd); + D.push_back(component{ a.var, R, q }); // reach component: a.var drives R -> q + out.push_back(D); + } + } + simplify_dnf(out); +} + +void seq_monadic::simplify_dnf(vector& dnf) { + std::set>> seen; + vector result; + for (disjunct const& D : dnf) { + bool dead = false; + for (auto const& c : D) + if (re().is_empty(c.state)) { dead = true; break; } + if (dead) + continue; + std::vector> sig; + sig.reserve(D.size()); + for (auto const& c : D) + sig.push_back(std::make_tuple(c.var->get_id(), c.state->get_id(), + c.target ? c.target->get_id() : UINT_MAX)); + std::sort(sig.begin(), sig.end()); + if (seen.insert(sig).second) + result.push_back(D); + } + dnf.swap(result); +} + +lbool seq_monadic::solve(expr* term, expr* R) { + obj_map none; + return solve(term, R, none); +} + +lbool seq_monadic::solve(expr* term, expr* R, obj_map const& var_extra) { + if (!u().is_re(R, m_seq_sort)) + return l_undef; + svector atoms; + expr* the_var = nullptr; + if (!parse_term(term, atoms, the_var)) + return l_undef; + if (!the_var) + return l_undef; // no variable: ground membership, not our case + m_pin.reset(); + m_pin.push_back(R); + m_budget = 200000; // global work budget: bail fast on DNF explosion + m_giveup = false; + bool ok = true; + vector dnf; + decompose(atoms, 0, R, dnf, ok); + if (!ok) + return l_undef; + + bool any_undef = false; + for (disjunct const& D : dnf) { + // group components by variable, add the extra per-variable constraints + obj_map idx; + vector> groups; + auto bucket = [&](expr* v) -> unsigned { + unsigned gi; + if (idx.find(v, gi)) return gi; + gi = groups.size(); idx.insert(v, gi); groups.push_back(svector()); + return gi; + }; + for (auto const& c : D) + groups[bucket(c.var)].push_back(c); + for (auto const& kv : var_extra) + groups[bucket(kv.m_key)].push_back(component{ kv.m_key, kv.m_value, nullptr }); + + bool has_empty = false, has_undef = false; + for (auto const& g : groups) { + lbool ne = product_nonempty(g); + if (ne == l_false) { has_empty = true; break; } // this variable has no value + if (ne == l_undef) has_undef = true; + } + if (has_empty) continue; + if (has_undef) { any_undef = true; continue; } + return l_true; // all variables satisfiable => sat + } + return any_undef ? l_undef : l_false; +} diff --git a/src/ast/rewriter/seq_monadic.h b/src/ast/rewriter/seq_monadic.h new file mode 100644 index 0000000000..293eea32e7 --- /dev/null +++ b/src/ast/rewriter/seq_monadic.h @@ -0,0 +1,111 @@ +/*++ +Copyright (c) 2026 Microsoft Corporation + +Module Name: + + seq_monadic.h + +Abstract: + + Whole-language monadic decomposition for regex membership of a term that is a + concatenation of string variables and constant characters, e.g. x.a.x in R. + + Self-contained decision procedure: NO Nielsen splitting (seq_split), NO minterms, + and NO materialization of reach(q) as a regex. It relies only on the symbolic + Brzozowski derivative (brz_derivative_cofactors as a transition regex) and on + automaton product-reachability for emptiness. + + Method. For a term x.u in R and the whole-language split, x drives the derivative + automaton of R from R to some live state q, and the rest u must be accepted from q: + + x.u in R <=> OR_{q live} ( x reaches q in A_R /\ u in q ). + + Decomposing u recursively (a leading constant is consumed by a derivative, a leading + variable splits again, the last variable is a plain membership) yields a DNF whose + disjuncts are conjunctions of per-variable *components*: + + - reach component : the variable's value drives the + derivative automaton from state0 to q + - membership component : the variable's value is in L(state0) + + reach(q) is therefore NEVER built as a regex (which state-elimination would blow up + super-polynomially for lattice-shaped automata). Instead the constraints on a + variable are decided directly by a lazy product-reachability search over tuples of + component states: a product state accepts iff every reach component is at its target + and every membership component is nullable; transitions are the product of the + components' cofactor branches with pairwise-conjoined range guards (minterm-free). + This stays in the product-of-state-counts regime, never the path-enumeration (k!) + regime of regex state-elimination. + + Supports single / multiple / repeated variables, and per-variable extra constraints + (base membership + length-regex) via `var_extra`. + +Author: + + Nikolaj Bjorner / Margus Veanes 2026 + +--*/ +#pragma once + +#include "ast/rewriter/seq_rewriter.h" +#include "ast/rewriter/seq_range_predicate.h" +#include "util/lbool.h" +#include "util/obj_hashtable.h" + +class seq_monadic { + ast_manager& m; + seq_rewriter& m_rw; + sort* m_seq_sort = nullptr; // sequence sort of the regex under analysis + expr_ref_vector m_pin; // pins derivative states referenced by components + unsigned m_budget = 0; // global work budget (decompose disjuncts + product pops) + bool m_giveup = false; // set when the budget is exhausted + + seq_util& u() const { return m_rw.u(); } + seq_util::rex& re() const { return m_rw.u().re; } + + // A term atom: a string variable or a constant character. + struct atom { bool is_var; expr* var; unsigned ch; }; + + // A component of one variable's constraint. As the variable's value w is read, + // the current state is derived from `state`; the component accepts when + // target ? (current == target) -- reach component (w drives A from state to target) + // : nullable(current) -- membership component (w in L(state)) + struct component { expr* var; expr* state; expr* target; }; + + typedef svector disjunct; // a conjunction of components (a DNF disjunct) + + // Brzozowski derivative of regex `r` by the concrete character `ch`. + expr_ref der_char(expr* r, unsigned ch); + + // Live reachable derivative states of R (BFS over cofactor targets + liveness + // least-fixpoint). These are the split states q. Sets `ok` false on a cap overrun. + void live_states(expr* R, ptr_vector& out, bool& ok); + + // Product-reachability emptiness of a conjunction of components (all on one + // variable). l_false = empty (unsat), l_true = non-empty (sat), l_undef = gave up + // (cap overrun, non-range guard, or undecidable nullability). + lbool product_nonempty(svector const& comps); + + // Flatten a str.++ term into atoms; false on an unsupported shape (non-constant unit). + bool parse_term(expr* term, svector& atoms, expr*& the_var); + + // Monadic decomposition: append to `out` the DNF disjuncts for atoms[i..] in R, + // threading the current derivative state R. `ok` false on give-up. + void decompose(svector const& atoms, unsigned i, expr* R, + vector& out, bool& ok); + + // Drop disjuncts with a syntactically-empty component and dedup identical disjuncts. + void simplify_dnf(vector& dnf); + +public: + seq_monadic(seq_rewriter& rw) : m(rw.m()), m_rw(rw), m_pin(rw.m()) {} + + // Decide (str.in_re term R) for a term that is a concatenation of string variables + // (possibly repeated / several distinct) and constant characters. + // l_true = sat, l_false = unsat, l_undef = unsupported shape / gave up. + lbool solve(expr* term, expr* R); + + // As above, with extra per-variable constraints (e.g. a base membership intersected + // with a length-regex): `var_extra` maps a variable to a regex it must also satisfy. + lbool solve(expr* term, expr* R, obj_map const& var_extra); +}; diff --git a/src/smt/theory_nseq.cpp b/src/smt/theory_nseq.cpp index 81de182037..77cfe0c1c0 100644 --- a/src/smt/theory_nseq.cpp +++ b/src/smt/theory_nseq.cpp @@ -23,6 +23,7 @@ Author: #include "util/trail.h" #include +#include namespace smt { @@ -41,6 +42,7 @@ namespace smt { m_axioms(m_th_rewriter), m_regex(m_sg), m_model(m, ctx, m_seq, m_rewriter, m_sg), + m_monadic(m_rewriter), m_relevant_lengths(m) { std::function add_clause = @@ -888,6 +890,68 @@ namespace smt { << num_eqs << " eqs, " << num_mems << " mems\n";); } + // Diagnostic (log-only): run the whole-language monadic decomposition on the + // collected memberships and log its verdict. Invoked under verbosity>=1 only; + // never changes the solver's answer. + void theory_nseq::run_monadic_diagnostic() { + obj_map var_extra; + expr_ref_vector pin(m); + auto is_var = [&](expr* t) { + return is_app(t) && to_app(t)->get_num_args() == 0 && + to_app(t)->get_family_id() == null_family_id; + }; + // pass 1: per-variable base memberships (x in R) -> extra constraint on x + for (auto const& item : m_prop_queue) { + if (!std::holds_alternative(item)) continue; + auto const& mem = std::get(item); + if (!mem.m_str || !mem.m_regex) continue; + expr* t = mem.m_str->get_expr(); + expr* R = mem.m_regex->get_expr(); + if (!t || !R || !is_var(t)) continue; + expr* prev = nullptr; + if (var_extra.find(t, prev)) { + expr_ref in = m_rewriter.mk_regex_inter_normalize(prev, R); + pin.push_back(in); + var_extra.insert(t, in); + } + else + var_extra.insert(t, R); + } + // pass 2: group compound-term memberships by term and intersect their regexes + // (a term may carry several memberships that must all hold), then solve once. + obj_map term_re; + ptr_vector terms; + for (auto const& item : m_prop_queue) { + if (!std::holds_alternative(item)) continue; + auto const& mem = std::get(item); + if (!mem.m_str || !mem.m_regex) continue; + expr* t = mem.m_str->get_expr(); + expr* R = mem.m_regex->get_expr(); + if (!t || !R || !m_seq.str.is_concat(t)) continue; + expr* prev = nullptr; + if (term_re.find(t, prev)) { + expr_ref in = m_rewriter.mk_regex_inter_normalize(prev, R); + pin.push_back(in); + term_re.insert(t, in); + } + else { + term_re.insert(t, R); + terms.push_back(t); + } + } + for (expr* t : terms) { + expr* R = nullptr; + term_re.find(t, R); + auto t0 = std::chrono::high_resolution_clock::now(); + lbool v = m_monadic.solve(t, R, var_extra); + double ms = std::chrono::duration( + std::chrono::high_resolution_clock::now() - t0).count(); + verbose_stream() << "MONADIC-VERDICT " + << (v == l_true ? "sat" : v == l_false ? "unsat" : "undef") + << " time-ms " << ms << "\n"; + } + } + final_check_status theory_nseq::final_check_eh(unsigned /*final_check_round*/) { try { // Always assert non-negativity for all string theory vars, @@ -902,6 +966,11 @@ namespace smt { return std::holds_alternative(item) || std::holds_alternative(item) || std::holds_alternative(item); }); + // Diagnostic (verbosity>=1, log-only): whole-language monadic verdict on the + // collected memberships. Placed before the early-exit / hot-restart / rebuild + // branches so it is exercised on as many membership benchmarks as possible. + IF_VERBOSE(1, run_monadic_diagnostic();); + // there is nothing to do for the string solver, as there are no string constraints if (!has_eq_or_diseq_or_mem && m_ho_terms.empty() && !has_unhandled_preds()) { if (!check_stoi_coherence()) { diff --git a/src/smt/theory_nseq.h b/src/smt/theory_nseq.h index 628e78d1c0..e7db22a258 100644 --- a/src/smt/theory_nseq.h +++ b/src/smt/theory_nseq.h @@ -21,6 +21,7 @@ Author: #include "ast/seq_decl_plugin.h" #include "ast/rewriter/seq_rewriter.h" +#include "ast/rewriter/seq_monadic.h" #include "ast/rewriter/seq_axioms.h" #include "ast/euf/euf_egraph.h" #include "ast/euf/euf_sgraph.h" @@ -50,6 +51,12 @@ namespace smt { seq::axioms m_axioms; seq::seq_regex m_regex; // regex membership pre-processing seq_model m_model; // model construction helper + seq_monadic m_monadic; // whole-language monadic-decomposition solver (diagnostic) + + // Diagnostic (verbosity>=1 only, log-only): run the whole-language monadic + // decomposition solver on the collected memberships and log its sat/unsat + // verdict. Does NOT affect the solver's answer. + void run_monadic_diagnostic(); // propagation queue items (variant over the distinct propagation cases) using eq_item = tracked_str_eq; // string equality diff --git a/src/test/CMakeLists.txt b/src/test/CMakeLists.txt index 4563752812..5f0d156a60 100644 --- a/src/test/CMakeLists.txt +++ b/src/test/CMakeLists.txt @@ -139,6 +139,7 @@ add_executable(test-z3 sls_test.cpp sls_seq_plugin.cpp seq_split.cpp + seq_monadic.cpp small_object_allocator.cpp smt2print_parse.cpp smt_context.cpp diff --git a/src/test/main.cpp b/src/test/main.cpp index 3a3cab41db..dba0212bf4 100644 --- a/src/test/main.cpp +++ b/src/test/main.cpp @@ -198,6 +198,7 @@ X(finite_set) \ X(finite_set_rewriter) \ X(seq_split) \ + X(seq_monadic) \ X(fpa) \ X(seq_regex_bisim) \ X(term_enumeration) \ diff --git a/src/test/seq_monadic.cpp b/src/test/seq_monadic.cpp new file mode 100644 index 0000000000..3edf4bf4f4 --- /dev/null +++ b/src/test/seq_monadic.cpp @@ -0,0 +1,177 @@ +/*++ +Copyright (c) 2026 Microsoft Corporation + +Module Name: + + seq_monadic.cpp + +Abstract: + + Unit tests for the whole-language monadic-decomposition membership solver in + ast/rewriter/seq_monadic.cpp. Mirrors the validated Python prototype + (files/solve_proto.py): single-variable repeated-membership shapes x.a.x in R. + +Author: + + Nikolaj Bjorner / Margus Veanes 2026 + +--*/ + +#include "ast/ast.h" +#include "ast/reg_decl_plugins.h" +#include "ast/seq_decl_plugin.h" +#include "ast/rewriter/seq_rewriter.h" +#include "ast/rewriter/seq_monadic.h" +#include + +namespace { + +struct plugin_registrar { + plugin_registrar(ast_manager& m) { reg_decl_plugins(m); } +}; + +class seq_monadic_test { + ast_manager m; + plugin_registrar m_reg; + seq_rewriter m_rw; + seq_monadic m_mon; + seq_util u; + sort_ref m_str; // String sort + sort_ref m_re; // RegEx sort over m_str + unsigned m_fail = 0; + + seq_util::rex& re() { return u.re; } + + // regex builders + expr_ref word(char const* s) { return expr_ref(re().mk_to_re(u.str.mk_string(zstring(s))), m); } + expr_ref cat(expr* a, expr* b) { return expr_ref(re().mk_concat(a, b), m); } + expr_ref alt(expr* a, expr* b) { return expr_ref(re().mk_union(a, b), m); } + expr_ref star(expr* a) { return expr_ref(re().mk_star(a), m); } + expr_ref inter(expr* a, expr* b) { return expr_ref(re().mk_inter(a, b), m); } + expr_ref comp(expr* a) { return expr_ref(re().mk_complement(a), m); } + expr_ref dotstar() { return expr_ref(re().mk_full_seq(m_re), m); } + expr_ref rng(char lo, char hi) { + char sl[2] = { lo, 0 }, sh[2] = { hi, 0 }; + return expr_ref(re().mk_range(u.str.mk_string(zstring(sl)), u.str.mk_string(zstring(sh))), m); + } + expr_ref loop(expr* r, unsigned lo, unsigned hi) { return expr_ref(re().mk_loop(r, lo, hi), m); } + + // string-term builders + expr_ref var(char const* nm) { return expr_ref(m.mk_const(nm, m_str), m); } + expr_ref sword(char const* s) { return expr_ref(u.str.mk_string(zstring(s)), m); } + expr_ref sconcat(expr* a, expr* b) { return expr_ref(u.str.mk_concat(a, b), m); } + // term x . w . x (w a constant word) + expr_ref xwx(expr* x, char const* w) { return sconcat(x, sconcat(sword(w), x)); } + // term x . a . y (two distinct variables) + expr_ref xay(expr* x, expr* y) { return sconcat(x, sconcat(sword("a"), y)); } + // term x . y . x + expr_ref xyx(expr* x, expr* y) { return sconcat(x, sconcat(y, x)); } + + static char const* s(lbool l) { return l == l_true ? "sat" : l == l_false ? "unsat" : "undef"; } + + void check(char const* name, expr* term, expr* R, lbool expected) { + lbool got = m_mon.solve(term, R); + bool ok = (got == expected); + if (!ok) ++m_fail; + std::cout << (ok ? " OK " : " FAIL ") << name + << " got=" << s(got) << " expected=" << s(expected) << "\n"; + } + + void check_extra(char const* name, expr* term, expr* R, + obj_map const& ve, lbool expected) { + lbool got = m_mon.solve(term, R, ve); + bool ok = (got == expected); + if (!ok) ++m_fail; + std::cout << (ok ? " OK " : " FAIL ") << name + << " got=" << s(got) << " expected=" << s(expected) << "\n"; + } + +public: + seq_monadic_test() : m_reg(m), m_rw(m), m_mon(m_rw), u(m), m_str(m), m_re(m) { + m_str = u.str.mk_string_sort(); + m_re = re().mk_re(m_str); + } + + void run() { + expr_ref x = var("x"); + expr_ref a = word("a"); + expr_ref b = word("b"); + expr_ref ab = cat(a, b); + expr_ref sig = dotstar(); // Sigma* + expr_ref saas = cat(sig, cat(cat(a, a), sig)); // Sigma* a a Sigma* + expr_ref sbbs = cat(sig, cat(cat(b, b), sig)); // Sigma* b b Sigma* + + std::cout << "=== seq_monadic: single-variable membership (x.a.x in R) ===\n"; + + // sanity + check("(a|b)* x.a.x", xwx(x, "a"), star(alt(a, b)), l_true); + check("b* x.a.x", xwx(x, "a"), star(b), l_false); + check("Sig*aaSig* x.a.x", xwx(x, "a"), saas, l_true); + check("x in (a|b)* ", x, star(alt(a, b)), l_true); + check("x in b* (x=aa) ", xwx(x, "a"), star(b), l_false); + + // ALT = (a|b)* & ~(Sig*aaSig*) & ~(Sig*bbSig*) (strictly alternating) + expr_ref altre = inter(star(alt(a, b)), inter(comp(saas), comp(sbbs))); + check("ALT x.a.x", xwx(x, "a"), altre, l_true); + + // R*.S complement family + check("~(a*.b) x.a.x", xwx(x, "a"), comp(cat(star(a), b)), l_true); + + // L3-02 ~((ab)*.~((ab)*)) -> unsat (odd length) + check("L3-02 x.a.x", xwx(x, "a"), + comp(cat(star(ab), comp(star(ab)))), l_false); + + // L3-03 ~(a*.~(b*.~((ab)*))) -> sat + check("L3-03 x.a.x", xwx(x, "a"), + comp(cat(star(a), comp(cat(star(b), comp(star(ab)))))), l_true); + + std::cout << "=== seq_monadic: multi-variable ===\n"; + expr_ref y = var("y"); + check("(a|b)* x.a.y", xay(x, y), star(alt(a, b)), l_true); + check("b* x.a.y", xay(x, y), star(b), l_false); + check("L3-02 x.a.y", xay(x, y), comp(cat(star(ab), comp(star(ab)))), l_true); + check("L3-03 x.a.y", xay(x, y), + comp(cat(star(a), comp(cat(star(b), comp(star(ab)))))), l_true); + check("empty ~Sig* x.y.x", xyx(x, y), comp(dotstar()), l_false); + check("Sig* x.y.x", xyx(x, y), dotstar(), l_true); + check("(a|b)* x.y.x", xyx(x, y), star(alt(a, b)), l_true); + + std::cout << "=== seq_monadic: per-variable constraints ===\n"; + expr_ref digitp = cat(rng('0', '9'), star(rng('0', '9'))); // [0-9]+ + obj_map ve; + ve.insert(y, digitp); + // y must be in the (a|b)* tail AND in [0-9]+ -> empty -> unsat + check_extra("(a|b)* & y in[0-9]+ x.a.y", xay(x, y), star(alt(a, b)), ve, l_false); + // y any digits, x/'a' anything -> sat + check_extra("Sig* & y in[0-9]+ x.a.y", xay(x, y), dotstar(), ve, l_true); + + // Bounded loop (re.loop) with repeated variable -- exercises live_states on a + // counted automaton (t04-exact benchmark family). Regression for a + // reference-invalidation bug in live_states (succ[i].push_back(intern(t))). + std::cout << "=== seq_monadic: bounded loop (t04-exact family) ===\n"; + expr_ref clsr = rng('0', '9'); // [0-9] + expr_ref digitS = star(clsr); // [0-9]* + expr_ref loop22 = loop(clsr, 2, 2); // [0-9]{2} + check("[0-9]{2} x ", x, loop22, l_true); // x = "00" + check("[0-9]{2} x.a.x", xwx(x, "a"), loop22, l_false); // 'a' not a digit + obj_map ve2; ve2.insert(x, digitp); ve2.insert(y, digitS); + // x.y.x in [0-9]{2}, x in [0-9]+, y in [0-9]* -> sat (x="0", y="") + check_extra("[0-9]{2} & x[0-9]+ y[0-9]* x.y.x", xyx(x, y), loop22, ve2, l_true); + obj_map ve3; ve3.insert(x, digitp); + check_extra("[0-9]{2} & x[0-9]+ x.y.x", xyx(x, y), loop22, ve3, l_true); + obj_map ve4; ve4.insert(x, digitp); + // x.y.x in [0-9]{3}, x in [0-9]+ -> sat (x=1 digit, y=1 digit) + check_extra("[0-9]{3} & x[0-9]+ x.y.x", xyx(x, y), loop(clsr, 3, 3), ve4, l_true); + + std::cout << "=== seq_monadic: " << (m_fail == 0 ? "ALL PASS" : "FAILURES") << " (" + << m_fail << " fail) ===\n"; + ENSURE(m_fail == 0); + } +}; + +} + +void tst_seq_monadic() { + seq_monadic_test t; + t.run(); +}