z3-src 503.2.1

Source distribution of the Z3 SMT solver, for use as a build dependency
Documentation 
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/*++
Copyright (c) 2026 Microsoft Corporation

--*/

#include "ast/reg_decl_plugins.h"
#include "cmd_context/cmd_context.h"
#include "parsers/smt2/smt2parser.h"
#include "smt/smt_context.h"
#include <sstream>

static lbool check_ho_qsolver(char const* input, bool ho_qmatcher) {
    ast_manager m;
    reg_decl_plugins(m);
    cmd_context cmd(false, &m);
    std::istringstream is(input);
    VERIFY(parse_smt2_commands(cmd, is));

    smt_params params;
    params.m_ematching = false;
    params.m_mbqi = false;
    params.m_ho_matching = true;
    params.m_ho_qmatcher = ho_qmatcher;
    params.m_term_enumeration = true;
    params.m_ho_matching_bound = 100;

    smt::context ctx(m, params);
    for (expr* assertion : cmd.assertions())
        ctx.assert_expr(assertion);
    return ctx.check();
}

void tst_ho_qsolver() {
    // Cantor/Leibniz instance: q(b) != q(a) creates the array-extensionality
    // witness delta(a,b). Matching the quantified clause uses
    // P := lambda z. a(delta(a,b)) = z and X := delta(a,b).
    char const* cantor =
        "(declare-sort U 0)\n"
        "(declare-const a (Array U U))\n"
        "(declare-const b (Array U U))\n"
        "(declare-fun q ((Array U U)) Bool)\n"
        "(assert (forall ((P (Array U Bool)) (X U))\n"
        "  (=> (select P (select a X)) (select P (select b X)))))\n"
        "(assert (q b))\n"
        "(assert (not (q a)))\n";
    VERIFY(l_undef == check_ho_qsolver(cantor, false));
    VERIFY(l_false == check_ho_qsolver(cantor, true));

    char const* reversed =
        "(declare-sort U 0)\n"
        "(declare-const a (Array U U))\n"
        "(declare-const b (Array U U))\n"
        "(declare-fun q ((Array U U)) Bool)\n"
        "(assert (forall ((P (Array U Bool)) (X U))\n"
        "  (=> (select P (select b X)) (select P (select a X)))))\n"
        "(assert (q b))\n"
        "(assert (not (q a)))\n";
    VERIFY(l_false == check_ho_qsolver(reversed, true));

    char const* many_sorted =
        "(declare-sort U 0)\n"
        "(declare-sort V 0)\n"
        "(declare-const a (Array U V))\n"
        "(declare-const b (Array U V))\n"
        "(declare-fun g ((Array U V)) Bool)\n"
        "(assert (forall ((P (Array V Bool)) (X U))\n"
        "  (=> (select P (select a X)) (select P (select b X)))))\n"
        "(assert (g b))\n"
        "(assert (not (g a)))\n";
    VERIFY(l_false == check_ho_qsolver(many_sorted, true));

    // Core of SYO300^5: the second clause becomes contradictory with the
    // first for X := lambda u. u(c).
    char const* fixed_point =
        "(declare-sort U 0)\n"
        "(declare-const P\n"
        "  (Array (Array (Array U U) U)\n"
        "         (Array (Array (Array U U) U) Bool)))\n"
        "(assert (forall ((Z (Array (Array U U) U)))\n"
        "  (select (select P Z) Z)))\n"
        "(assert (forall ((X (Array (Array U U) U)))\n"
        "  (not (select\n"
        "    (select P\n"
        "      (lambda ((u (Array U U)))\n"
        "        (select u (select X (lambda ((v U)) v)))))\n"
        "    X))))\n";
    VERIFY(l_undef == check_ho_qsolver(fixed_point, false));
    // With E-matching and MBQI disabled, neither quantifier creates the
    // ground Boolean atom needed to start qmatching.
    VERIFY(l_undef == check_ho_qsolver(fixed_point, true));
}