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https://github.com/Z3Prover/z3
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Derive with ranges (#9963)
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com> Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com> Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com> Co-authored-by: Margus Veanes <margus@microsoft.com> Co-authored-by: Margus Veanes <veanes@users.noreply.github.com>
This commit is contained in:
Nikolaj Bjorner
GitHub
parent
0596c7c634
commit
22c2635786
24 changed files with 3462 additions and 1000 deletions
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@ -115,15 +115,18 @@ add_executable(test-z3
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polynomial_factorization.cpp
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polynorm.cpp
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prime_generator.cpp
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seq_regex_bisim.cpp
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proof_checker.cpp
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qe_arith.cpp
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mbp_qel.cpp
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quant_elim.cpp
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quant_solve.cpp
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random.cpp
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range_predicate.cpp
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rational.cpp
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rcf.cpp
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region.cpp
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regex_range_collapse.cpp
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sat_local_search.cpp
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sat_lookahead.cpp
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sat_user_scope.cpp
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@ -113,6 +113,8 @@
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X(api_bug) \
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X(api_special_relations) \
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X(arith_rewriter) \
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X(range_predicate) \
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X(regex_range_collapse) \
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X(seq_rewriter) \
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X(check_assumptions) \
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X(smt_context) \
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@ -195,6 +197,7 @@
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X(finite_set) \
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X(finite_set_rewriter) \
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X(fpa) \
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X(seq_regex_bisim) \
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X(term_enumeration) \
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X(lcube)
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260
src/test/range_predicate.cpp
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260
src/test/range_predicate.cpp
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@ -0,0 +1,260 @@
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/*++
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Copyright (c) 2026 Microsoft Corporation
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Module Name:
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test/range_predicate.cpp
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Abstract:
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Unit tests for the range-algebra value type seq::range_predicate.
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The tests exercise:
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* factory constructors and canonical-form invariants,
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* extensional equality and total ordering,
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* Boolean operations (|, &, ~, -, ^) on hand-picked instances,
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* exhaustive verification of de-Morgan and lattice laws on a
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small character domain, by enumerating every subset.
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Author:
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Margus Veanes (veanes) 2026
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--*/
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#include "ast/rewriter/seq_range_predicate.h"
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#include "util/debug.h"
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#include <cstdint>
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#include <iostream>
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#include <sstream>
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using seq::range_predicate;
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namespace {
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// Build a range_predicate from a bitmask over [0, max_char] for testing.
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range_predicate from_mask(uint64_t mask, unsigned max_char) {
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range_predicate r = range_predicate::empty(max_char);
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for (unsigned c = 0; c <= max_char; ++c)
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if ((mask >> c) & 1u)
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r = r | range_predicate::singleton(c, max_char);
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return r;
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}
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// Convert a range_predicate back to a bitmask for cross-checking.
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uint64_t to_mask(range_predicate const& r) {
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uint64_t mask = 0;
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for (unsigned c = 0; c <= r.max_char(); ++c)
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if (r.contains(c))
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mask |= (uint64_t(1) << c);
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return mask;
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}
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void test_factories() {
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auto e = range_predicate::empty(255);
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ENSURE(e.is_empty());
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ENSURE(!e.is_top());
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ENSURE(e.num_ranges() == 0);
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ENSURE(e.cardinality() == 0);
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auto t = range_predicate::top(255);
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ENSURE(!t.is_empty());
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ENSURE(t.is_top());
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ENSURE(t.num_ranges() == 1);
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ENSURE(t.cardinality() == 256);
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ENSURE(t.contains(0));
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ENSURE(t.contains(255));
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auto s = range_predicate::singleton(42, 255);
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ENSURE(s.num_ranges() == 1);
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ENSURE(s.cardinality() == 1);
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ENSURE(s.contains(42));
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ENSURE(!s.contains(41));
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unsigned c = 0;
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ENSURE(s.is_singleton(c));
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ENSURE(c == 42);
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auto r = range_predicate::range(10, 20, 255);
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ENSURE(r.num_ranges() == 1);
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ENSURE(r.cardinality() == 11);
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ENSURE(r.contains(10));
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ENSURE(r.contains(20));
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ENSURE(!r.contains(9));
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ENSURE(!r.contains(21));
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// Reversed bounds produce empty.
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auto bad = range_predicate::range(20, 10, 255);
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ENSURE(bad.is_empty());
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// Clipping at max_char.
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auto clipped = range_predicate::range(200, 1000, 255);
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ENSURE(clipped.num_ranges() == 1);
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ENSURE(clipped[0] == std::make_pair(200u, 255u));
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}
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void test_equality_and_order() {
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auto a = range_predicate::range(1, 5, 31);
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auto b = range_predicate::range(1, 5, 31);
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auto c = range_predicate::range(1, 6, 31);
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ENSURE(a == b);
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ENSURE(a != c);
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ENSURE(a.hash() == b.hash());
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ENSURE(a < c || c < a);
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ENSURE(!(a < a));
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auto empty = range_predicate::empty(31);
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ENSURE(empty < a);
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// Canonical merging of adjacent ranges.
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auto d = range_predicate::range(0, 4, 31) | range_predicate::range(5, 10, 31);
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auto e = range_predicate::range(0, 10, 31);
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ENSURE(d == e);
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}
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void test_union_intersection_hand() {
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unsigned const M = 31;
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auto a = range_predicate::range(0, 4, M) | range_predicate::range(10, 14, M);
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auto b = range_predicate::range(3, 11, M);
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auto u = a | b; // [0,14]
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ENSURE(u.num_ranges() == 1);
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ENSURE(u[0] == std::make_pair(0u, 14u));
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auto i = a & b; // [3,4] U [10,11]
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ENSURE(i.num_ranges() == 2);
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ENSURE(i[0] == std::make_pair(3u, 4u));
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ENSURE(i[1] == std::make_pair(10u, 11u));
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auto d = a - b; // [0,2] U [12,14]
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ENSURE(d.num_ranges() == 2);
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ENSURE(d[0] == std::make_pair(0u, 2u));
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ENSURE(d[1] == std::make_pair(12u, 14u));
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auto x = a ^ b; // [0,2] U [5,9] U [12,14]
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ENSURE(x.num_ranges() == 3);
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ENSURE(x[0] == std::make_pair(0u, 2u));
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ENSURE(x[1] == std::make_pair(5u, 9u));
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ENSURE(x[2] == std::make_pair(12u, 14u));
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}
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void test_complement_hand() {
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unsigned const M = 10;
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auto e = range_predicate::empty(M);
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ENSURE((~e).is_top());
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auto t = range_predicate::top(M);
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ENSURE((~t).is_empty());
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// ~([2,3] U [7,8]) = [0,1] U [4,6] U [9,10]
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auto a = range_predicate::range(2, 3, M) | range_predicate::range(7, 8, M);
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auto na = ~a;
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ENSURE(na.num_ranges() == 3);
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ENSURE(na[0] == std::make_pair(0u, 1u));
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ENSURE(na[1] == std::make_pair(4u, 6u));
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ENSURE(na[2] == std::make_pair(9u, 10u));
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// ~([0,4]) = [5,10]
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auto b = range_predicate::range(0, 4, M);
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auto nb = ~b;
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ENSURE(nb.num_ranges() == 1);
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ENSURE(nb[0] == std::make_pair(5u, 10u));
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// ~([5,10]) = [0,4]
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auto cnb = ~nb;
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ENSURE(cnb == b);
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}
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// Exhaustively verify the lattice / de-Morgan laws on a small domain
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// by enumerating every possible subset (bitmask).
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void test_exhaustive_laws() {
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unsigned const M = 5; // 6 characters -> 64 subsets
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unsigned const N = 1u << (M + 1);
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for (unsigned i = 0; i < N; ++i) {
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range_predicate A = from_mask(i, M);
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ENSURE(to_mask(A) == i);
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// ~ ~ A == A
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ENSURE(~~A == A);
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// A | ~A == top
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ENSURE((A | ~A).is_top());
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// A & ~A == empty
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ENSURE((A & ~A).is_empty());
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// cardinality matches popcount
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unsigned pop = 0;
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for (unsigned k = 0; k <= M; ++k) if ((i >> k) & 1u) ++pop;
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ENSURE(A.cardinality() == pop);
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}
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for (unsigned i = 0; i < N; ++i) {
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range_predicate A = from_mask(i, M);
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for (unsigned j = 0; j < N; ++j) {
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range_predicate B = from_mask(j, M);
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// Bitmask reference semantics.
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ENSURE(to_mask(A | B) == (i | j));
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ENSURE(to_mask(A & B) == (i & j));
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ENSURE(to_mask(A - B) == (i & ~j & ((1u << (M + 1)) - 1u)));
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ENSURE(to_mask(A ^ B) == (i ^ j));
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// de-Morgan
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ENSURE(~(A | B) == (~A & ~B));
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ENSURE(~(A & B) == (~A | ~B));
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// Commutativity
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ENSURE((A | B) == (B | A));
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ENSURE((A & B) == (B & A));
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// (A - B) == A & ~B
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ENSURE((A - B) == (A & ~B));
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// (A ^ B) == (A | B) - (A & B)
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ENSURE((A ^ B) == ((A | B) - (A & B)));
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// Extensional equality is reflexive on equal masks.
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if (i == j) {
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ENSURE(A == B);
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ENSURE(A.hash() == B.hash());
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}
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}
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}
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}
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void test_total_order_strict() {
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unsigned const M = 5;
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unsigned const N = 1u << (M + 1);
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// Strict total order: for any distinct A, B exactly one of A<B, B<A holds.
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for (unsigned i = 0; i < N; ++i) {
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range_predicate A = from_mask(i, M);
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ENSURE(!(A < A));
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for (unsigned j = i + 1; j < N; ++j) {
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range_predicate B = from_mask(j, M);
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bool lt = A < B;
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bool gt = B < A;
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ENSURE(lt != gt);
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ENSURE(lt || gt);
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}
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}
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}
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void test_display() {
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std::ostringstream oss;
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oss << range_predicate::empty(31);
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ENSURE(oss.str() == "[]");
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oss.str("");
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oss << range_predicate::range(3, 7, 31);
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ENSURE(oss.str() == "[3-7]");
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oss.str("");
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oss << range_predicate::singleton(9, 31);
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ENSURE(oss.str() == "[9]");
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oss.str("");
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auto p = range_predicate::range(0, 2, 31) | range_predicate::singleton(5, 31);
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oss << p;
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ENSURE(oss.str() == "[0-2,5]");
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}
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}
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void tst_range_predicate() {
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test_factories();
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test_equality_and_order();
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test_union_intersection_hand();
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test_complement_hand();
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test_exhaustive_laws();
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test_total_order_strict();
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test_display();
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std::cout << "range_predicate unit tests passed\n";
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}
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244
src/test/regex_range_collapse.cpp
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244
src/test/regex_range_collapse.cpp
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@ -0,0 +1,244 @@
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/*++
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Copyright (c) 2026 Microsoft Corporation
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Module Name:
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regex_range_collapse.cpp - unit tests
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--*/
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#include "ast/rewriter/seq_range_collapse.h"
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#include "ast/reg_decl_plugins.h"
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#include "ast/ast_pp.h"
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#include "ast/arith_decl_plugin.h"
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#include "util/util.h"
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#include <iostream>
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namespace {
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using seq::range_predicate;
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using seq::regex_to_range_predicate;
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using seq::range_predicate_to_regex;
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static void check(bool ok, char const* what) {
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if (!ok) {
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std::cerr << "regex_range_collapse FAILED: " << what << "\n";
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ENSURE(false);
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}
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}
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static expr_ref mk_singleton_str(seq_util& u, unsigned c) {
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return expr_ref(u.str.mk_string(zstring(c)), u.get_manager());
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}
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static bool extract_range_chars(seq_util& u, expr* e, unsigned& lo, unsigned& hi) {
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expr* lo_e = nullptr; expr* hi_e = nullptr;
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if (!u.re.is_range(e, lo_e, hi_e))
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return false;
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// Accept either string-constant or (seq.unit (Char N)) bound form.
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if (u.re.is_range(e, lo, hi))
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return true;
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expr* lc = nullptr; expr* hc = nullptr;
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if (u.str.is_unit(lo_e, lc) && u.is_const_char(lc, lo) &&
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u.str.is_unit(hi_e, hc) && u.is_const_char(hc, hi))
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return true;
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return false;
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}
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static void run() {
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ast_manager m;
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reg_decl_plugins(m);
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seq_util u(m);
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unsigned const M = u.max_char();
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sort* str_sort = u.str.mk_string_sort();
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sort* re_sort = u.re.mk_re(str_sort);
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// primitives
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{
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range_predicate p(M);
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check(regex_to_range_predicate(u, u.re.mk_empty(re_sort), p) && p.is_empty(),
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"re.empty -> empty");
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check(regex_to_range_predicate(u, u.re.mk_full_char(re_sort), p) && p.is_top(),
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"re.full_char -> top");
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}
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// re.range "a" "z"
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{
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range_predicate p(M);
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expr_ref a = mk_singleton_str(u, 'a');
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expr_ref z = mk_singleton_str(u, 'z');
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expr_ref r(u.re.mk_range(a, z), m);
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check(regex_to_range_predicate(u, r, p) && p.num_ranges() == 1 &&
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p[0].first == 'a' && p[0].second == 'z',
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"re.range a z -> [a,z]");
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}
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// Disjoint union: (a..z) | (0..9)
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{
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range_predicate p(M);
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expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'z')), m);
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expr_ref r2(u.re.mk_range(mk_singleton_str(u, '0'), mk_singleton_str(u, '9')), m);
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expr_ref un(u.re.mk_union(r1, r2), m);
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check(regex_to_range_predicate(u, un, p) && p.num_ranges() == 2,
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"(a-z)|(0-9) -> 2 ranges");
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// canonical order: lower lo first
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check(p[0].first == '0' && p[0].second == '9' && p[1].first == 'a' && p[1].second == 'z',
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"(a-z)|(0-9) ranges in canonical order");
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}
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// Overlapping union: (a..c) | (b..f) -> (a..f)
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{
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range_predicate p(M);
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expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'c')), m);
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expr_ref r2(u.re.mk_range(mk_singleton_str(u, 'b'), mk_singleton_str(u, 'f')), m);
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expr_ref un(u.re.mk_union(r1, r2), m);
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check(regex_to_range_predicate(u, un, p) && p.num_ranges() == 1 &&
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p[0].first == 'a' && p[0].second == 'f',
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"(a-c)|(b-f) -> (a-f)");
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}
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// Adjacent union: (a..c) | (d..f) -> (a..f) (canonical predicate merges adjacent)
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{
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range_predicate p(M);
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expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'c')), m);
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expr_ref r2(u.re.mk_range(mk_singleton_str(u, 'd'), mk_singleton_str(u, 'f')), m);
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expr_ref un(u.re.mk_union(r1, r2), m);
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check(regex_to_range_predicate(u, un, p) && p.num_ranges() == 1 &&
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p[0].first == 'a' && p[0].second == 'f',
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"(a-c)|(d-f) -> (a-f) via adjacency");
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}
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// Disjoint intersection: (a..z) & (0..9) -> empty
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{
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range_predicate p(M);
|
||||
expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'z')), m);
|
||||
expr_ref r2(u.re.mk_range(mk_singleton_str(u, '0'), mk_singleton_str(u, '9')), m);
|
||||
expr_ref ix(u.re.mk_inter(r1, r2), m);
|
||||
check(regex_to_range_predicate(u, ix, p) && p.is_empty(),
|
||||
"(a-z)&(0-9) -> empty");
|
||||
}
|
||||
// Overlapping intersection: (a..f) & (c..z) -> (c..f)
|
||||
{
|
||||
range_predicate p(M);
|
||||
expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'f')), m);
|
||||
expr_ref r2(u.re.mk_range(mk_singleton_str(u, 'c'), mk_singleton_str(u, 'z')), m);
|
||||
expr_ref ix(u.re.mk_inter(r1, r2), m);
|
||||
check(regex_to_range_predicate(u, ix, p) && p.num_ranges() == 1 &&
|
||||
p[0].first == 'c' && p[0].second == 'f',
|
||||
"(a-f)&(c-z) -> (c-f)");
|
||||
}
|
||||
// Complement: re.complement is intentionally NOT a char-class op
|
||||
// (it operates over Σ*), so it must NOT be translated.
|
||||
{
|
||||
range_predicate p(M);
|
||||
expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'z')), m);
|
||||
expr_ref cmp(u.re.mk_complement(r1), m);
|
||||
check(!regex_to_range_predicate(u, cmp, p),
|
||||
"re.comp of range is NOT translatable (sequence-level complement)");
|
||||
}
|
||||
// Diff: (a..f) \ (c..z) -> (a..b)
|
||||
{
|
||||
range_predicate p(M);
|
||||
expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'f')), m);
|
||||
expr_ref r2(u.re.mk_range(mk_singleton_str(u, 'c'), mk_singleton_str(u, 'z')), m);
|
||||
expr_ref df(u.re.mk_diff(r1, r2), m);
|
||||
check(regex_to_range_predicate(u, df, p) && p.num_ranges() == 1 &&
|
||||
p[0].first == 'a' && p[0].second == 'b',
|
||||
"(a-f) \\ (c-z) -> (a-b)");
|
||||
}
|
||||
// Negative: re.* of a range is NOT a char class
|
||||
{
|
||||
range_predicate p(M);
|
||||
expr_ref r1(u.re.mk_range(mk_singleton_str(u, 'a'), mk_singleton_str(u, 'z')), m);
|
||||
expr_ref star(u.re.mk_star(r1), m);
|
||||
check(!regex_to_range_predicate(u, star, p),
|
||||
"re.* of range not translatable");
|
||||
}
|
||||
|
||||
// Negative: a regex whose element type is NOT a sequence of
|
||||
// characters (here (Seq Int)) must be rejected outright, even for
|
||||
// shapes that structurally resemble char-class operators.
|
||||
{
|
||||
range_predicate p(M);
|
||||
arith_util a(m);
|
||||
sort* int_seq = u.str.mk_seq(a.mk_int());
|
||||
sort* int_re = u.re.mk_re(int_seq);
|
||||
check(!regex_to_range_predicate(u, u.re.mk_empty(int_re), p),
|
||||
"re.empty over (Seq Int) is NOT a char class");
|
||||
check(!regex_to_range_predicate(u, u.re.mk_full_char(int_re), p),
|
||||
"re.full_char over (Seq Int) is NOT a char class");
|
||||
}
|
||||
|
||||
// ---- materialization round-trip ----
|
||||
|
||||
// empty -> re.empty
|
||||
{
|
||||
range_predicate p = range_predicate::empty(M);
|
||||
expr_ref e = range_predicate_to_regex(u, p, str_sort);
|
||||
check(u.re.is_empty(e), "empty -> re.empty");
|
||||
}
|
||||
// top -> re.full_char
|
||||
{
|
||||
range_predicate p = range_predicate::top(M);
|
||||
expr_ref e = range_predicate_to_regex(u, p, str_sort);
|
||||
check(u.re.is_full_char(e), "top -> re.full_char");
|
||||
}
|
||||
// single range -> re.range
|
||||
{
|
||||
range_predicate p = range_predicate::range('a', 'z', M);
|
||||
expr_ref e = range_predicate_to_regex(u, p, str_sort);
|
||||
unsigned lo = 0, hi = 0;
|
||||
check(extract_range_chars(u, e, lo, hi) && lo == 'a' && hi == 'z',
|
||||
"[a-z] -> re.range a z");
|
||||
}
|
||||
// singleton -> re.range c c
|
||||
{
|
||||
range_predicate p = range_predicate::singleton('A', M);
|
||||
expr_ref e = range_predicate_to_regex(u, p, str_sort);
|
||||
unsigned lo = 0, hi = 0;
|
||||
check(extract_range_chars(u, e, lo, hi) && lo == 'A' && hi == 'A',
|
||||
"{A} -> re.range A A");
|
||||
}
|
||||
// 2 ranges -> re.union(range_0, range_1) in canonical order
|
||||
{
|
||||
range_predicate p = range_predicate::range('0', '9', M)
|
||||
| range_predicate::range('a', 'z', M);
|
||||
expr_ref e = range_predicate_to_regex(u, p, str_sort);
|
||||
expr* a = nullptr; expr* b = nullptr;
|
||||
check(u.re.is_union(e, a, b), "2-range -> union");
|
||||
unsigned lo0 = 0, hi0 = 0, lo1 = 0, hi1 = 0;
|
||||
check(extract_range_chars(u, a, lo0, hi0) && lo0 == '0' && hi0 == '9',
|
||||
"union arg0 = (0-9) (canonical: lower lo first)");
|
||||
check(extract_range_chars(u, b, lo1, hi1) && lo1 == 'a' && hi1 == 'z',
|
||||
"union arg1 = (a-z)");
|
||||
}
|
||||
// 3 ranges -> right-associated union
|
||||
{
|
||||
range_predicate p = range_predicate::range(0, 5, M)
|
||||
| range_predicate::range(10, 15, M)
|
||||
| range_predicate::range(20, 25, M);
|
||||
expr_ref e = range_predicate_to_regex(u, p, str_sort);
|
||||
expr* a = nullptr; expr* rest = nullptr;
|
||||
check(u.re.is_union(e, a, rest), "3-range -> union(...)");
|
||||
unsigned lo = 0, hi = 0;
|
||||
check(extract_range_chars(u, a, lo, hi) && lo == 0 && hi == 5, "first arg = (0-5)");
|
||||
expr* b = nullptr; expr* c = nullptr;
|
||||
check(u.re.is_union(rest, b, c), "rest is union(...,...)");
|
||||
check(extract_range_chars(u, b, lo, hi) && lo == 10 && hi == 15, "second range");
|
||||
check(extract_range_chars(u, c, lo, hi) && lo == 20 && hi == 25, "third range");
|
||||
}
|
||||
// Round-trip identity for an arbitrary range-set
|
||||
{
|
||||
range_predicate p_in = range_predicate::range('a', 'c', M)
|
||||
| range_predicate::range('m', 'p', M)
|
||||
| range_predicate::range('x', 'z', M);
|
||||
expr_ref e = range_predicate_to_regex(u, p_in, str_sort);
|
||||
range_predicate p_out(M);
|
||||
check(regex_to_range_predicate(u, e, p_out), "round-trip translatable");
|
||||
check(p_in == p_out, "round-trip equal");
|
||||
}
|
||||
|
||||
std::cerr << "regex_range_collapse tests passed\n";
|
||||
}
|
||||
}
|
||||
|
||||
void tst_regex_range_collapse() {
|
||||
run();
|
||||
}
|
||||
127
src/test/seq_regex_bisim.cpp
Normal file
127
src/test/seq_regex_bisim.cpp
Normal file
|
|
@ -0,0 +1,127 @@
|
|||
// Regression test for the seq::derive::intersect_intervals bug.
|
||||
//
|
||||
// Background: derive uses a path-tracking interval set to compute symbolic
|
||||
// derivatives. The intersect_intervals routine used to react to a single
|
||||
// disjoint interval by dropping the entire kept suffix and skipping the rest
|
||||
// of the list, which silently killed valid branches in derivatives such as
|
||||
// D(a|b). That made the bisimulation procedure conclude bogus equalities
|
||||
// like a* == (a|b)*.
|
||||
//
|
||||
// This file also covers the seq::derive top-level-cache poisoning bug.
|
||||
// `m_top_cache` is keyed only by the regex; the routine used to populate it
|
||||
// while `m_ele` was set to a *concrete* character, baking that character
|
||||
// into the cached "symbolic" derivative. Subsequent calls with the same
|
||||
// regex but a different ele then returned a stale concrete answer instead
|
||||
// of the true symbolic derivative. The simplest victim is
|
||||
// (str.in_re "aP" (re.++ (re.* "a") "P"))
|
||||
// which used to return false because the derivative wrt 'a' was cached and
|
||||
// re-used as the derivative wrt 'P'.
|
||||
#include "ast/ast.h"
|
||||
#include "ast/ast_pp.h"
|
||||
#include "ast/reg_decl_plugins.h"
|
||||
#include "ast/seq_decl_plugin.h"
|
||||
#include "ast/rewriter/seq_rewriter.h"
|
||||
#include "ast/rewriter/seq_regex_bisim.h"
|
||||
#include "ast/rewriter/th_rewriter.h"
|
||||
#include <iostream>
|
||||
|
||||
static void test_a_star_neq_ab_star() {
|
||||
ast_manager m;
|
||||
reg_decl_plugins(m);
|
||||
seq_util u(m);
|
||||
seq_rewriter rw(m);
|
||||
|
||||
sort_ref str_sort(u.str.mk_string_sort(), m);
|
||||
|
||||
zstring sa("a"), sb("b");
|
||||
expr_ref re_a(u.re.mk_to_re(u.str.mk_string(sa)), m);
|
||||
expr_ref re_b(u.re.mk_to_re(u.str.mk_string(sb)), m);
|
||||
expr_ref a_star(u.re.mk_star(re_a), m);
|
||||
expr_ref ab(u.re.mk_union(re_a, re_b), m);
|
||||
expr_ref ab_star(u.re.mk_star(ab), m);
|
||||
|
||||
expr_ref d_ab = rw.mk_brz_derivative(ab);
|
||||
std::cout << "D(a|b) = " << mk_pp(d_ab, m) << "\n";
|
||||
|
||||
// Both the 'a' branch and the 'b' branch of D(a|b) must reach epsilon.
|
||||
// Collect the regex leaves of the symbolic derivative and require at
|
||||
// least two distinct accepting leaves (one for 'a' and one for 'b').
|
||||
expr_ref_vector leaves(m);
|
||||
auto collect = [&](expr* e, auto&& self) -> void {
|
||||
expr* c, *t, *f;
|
||||
if (m.is_ite(e, c, t, f) || u.re.is_union(e, t, f) || u.re.is_antimirov_union(e, t, f)) {
|
||||
self(t, self);
|
||||
self(f, self);
|
||||
return;
|
||||
}
|
||||
if (u.re.is_empty(e)) return;
|
||||
leaves.push_back(e);
|
||||
};
|
||||
collect(d_ab, collect);
|
||||
unsigned nullable_leaves = 0;
|
||||
for (expr* l : leaves) {
|
||||
expr_ref n = rw.is_nullable(l);
|
||||
if (m.is_true(n)) ++nullable_leaves;
|
||||
}
|
||||
std::cout << "D(a|b) leaves=" << leaves.size()
|
||||
<< " nullable=" << nullable_leaves << "\n";
|
||||
ENSURE(nullable_leaves >= 2);
|
||||
|
||||
// Bisim must report the two languages are not equivalent.
|
||||
seq::regex_bisim bisim(rw);
|
||||
lbool eq = bisim.are_equivalent(a_star, ab_star);
|
||||
std::cout << "bisim(a*, (a|b)*) = "
|
||||
<< (eq == l_true ? "true" : eq == l_false ? "false" : "undef") << "\n";
|
||||
ENSURE(eq == l_false);
|
||||
}
|
||||
|
||||
// Regression for the derive top-level-cache poisoning bug.
|
||||
// Take r = (re.* "a") ++ "P" and check str.in_re "aP" r. Before the fix
|
||||
// the first per-char derivative call (wrt 'a') populated m_top_cache with
|
||||
// 'a' baked into the symbolic ITE-tree, so the next call (wrt 'P') returned
|
||||
// that stale cached value instead of computing D_P(r) = epsilon, making
|
||||
// str.in_re wrongly return false.
|
||||
static void test_derive_cache_per_ele() {
|
||||
ast_manager m;
|
||||
reg_decl_plugins(m);
|
||||
seq_util u(m);
|
||||
seq_rewriter rw(m);
|
||||
|
||||
sort_ref str_sort(u.str.mk_string_sort(), m);
|
||||
|
||||
zstring sa("a"), sP("P"), s_aP("aP");
|
||||
expr_ref re_a(u.re.mk_to_re(u.str.mk_string(sa)), m);
|
||||
expr_ref re_P(u.re.mk_to_re(u.str.mk_string(sP)), m);
|
||||
expr_ref a_star(u.re.mk_star(re_a), m);
|
||||
expr_ref r(u.re.mk_concat(a_star, re_P), m);
|
||||
expr_ref aP(u.str.mk_string(s_aP), m);
|
||||
|
||||
// Compute D_'a'(a*P) and D_'P'(a*P) directly via mk_derivative.
|
||||
// Before the fix, m_top_cache was populated while m_ele = ele (the
|
||||
// concrete char), so the second call hit the stale cached answer from
|
||||
// the first. After the fix the cache is keyed by a symbolic var, so
|
||||
// each concrete-ele substitution produces the right answer.
|
||||
expr_ref ch_a(u.mk_char('a'), m);
|
||||
expr_ref ch_P(u.mk_char('P'), m);
|
||||
expr_ref d_a = rw.mk_derivative(ch_a, r);
|
||||
expr_ref d_P = rw.mk_derivative(ch_P, r);
|
||||
std::cout << "D_a(a*P) = " << mk_pp(d_a, m) << "\n";
|
||||
std::cout << "D_P(a*P) = " << mk_pp(d_P, m) << "\n";
|
||||
|
||||
// D_P(a*P) must be nullable (it accepts the empty suffix), while
|
||||
// D_a(a*P) must not be (it still needs a trailing 'P').
|
||||
expr_ref n_a = rw.is_nullable(d_a);
|
||||
expr_ref n_P = rw.is_nullable(d_P);
|
||||
th_rewriter trw(m);
|
||||
trw(n_a);
|
||||
trw(n_P);
|
||||
std::cout << "nullable(D_a) = " << mk_pp(n_a, m) << "\n";
|
||||
std::cout << "nullable(D_P) = " << mk_pp(n_P, m) << "\n";
|
||||
ENSURE(m.is_false(n_a));
|
||||
ENSURE(m.is_true(n_P));
|
||||
}
|
||||
|
||||
void tst_seq_regex_bisim() {
|
||||
test_a_star_neq_ab_star();
|
||||
test_derive_cache_per_ele();
|
||||
}
|
||||
Loading…
Add table
Add a link
Reference in a new issue