z3-src 503.3.0

Source distribution of the Z3 SMT solver, for use as a build dependency
Documentation
/*++
Copyright (c) 2016 Microsoft Corporation

--*/

#include "sat/sat_solver/inc_sat_solver.h"
#include "ast/bv_decl_plugin.h"
#include "ast/arith_decl_plugin.h"
#include "ast/datatype_decl_plugin.h"
#include "ast/pb_decl_plugin.h"
#include "ast/reg_decl_plugins.h"
#include "ast/ast_pp.h"
#include "tactic/bv/dt2bv_tactic.h"
#include "tactic/tactic.h"
#include "smt/smt_solver.h"
#include "model/model_smt2_pp.h"
#include "model/model_evaluator.h"
#include "tactic/fd_solver/fd_solver.h"
#include <iostream>
#include <string>

static expr_ref mk_const(ast_manager& m, char const* name, sort* s) {
    return expr_ref(m.mk_const(symbol(name), s), m);
}

static expr_ref mk_bool(ast_manager& m, char const* name) {
    return expr_ref(m.mk_const(symbol(name), m.mk_bool_sort()), m);
}

static expr_ref mk_bv(ast_manager& m, char const* name, unsigned sz) {
    bv_util bv(m);
    return expr_ref(m.mk_const(symbol(name), bv.mk_sort(sz)), m);
}

static void test1() {
    ast_manager m;
    reg_decl_plugins(m);
    bv_util bv(m);
    params_ref p;

    ref<solver> solver = mk_inc_sat_solver(m, p);
    expr_ref a = mk_bool(m, "a"), b = mk_bool(m, "b"), c = mk_bool(m, "c");
    expr_ref ba = mk_bv(m, "ba", 3), bb = mk_bv(m, "bb", 3), bc = mk_bv(m, "bc", 3);

    solver->assert_expr(m.mk_implies(a, b));
    solver->assert_expr(m.mk_implies(b, c));
    expr_ref_vector asms(m), vars(m), conseq(m);
    asms.push_back(a);
    vars.push_back(b);
    vars.push_back(c);
    vars.push_back(bb);
    vars.push_back(bc);
    solver->assert_expr(m.mk_eq(ba, bc));
    solver->assert_expr(m.mk_eq(bv.mk_numeral(2, 3), ba));
    solver->get_consequences(asms, vars, conseq);

    std::cout << conseq << "\n";
}


void test2() {
    ast_manager m;
    reg_decl_plugins(m);
    bv_util bv(m);
    datatype_util dtutil(m);
    params_ref p;

    datatype_decl_plugin & dt = *(static_cast<datatype_decl_plugin*>(m.get_plugin(m.get_family_id("datatype"))));
    sort_ref_vector new_sorts(m);
    constructor_decl* R = mk_constructor_decl(symbol("R"), symbol("is-R"), 0, nullptr);
    constructor_decl* G = mk_constructor_decl(symbol("G"), symbol("is-G"), 0, nullptr);
    constructor_decl* B = mk_constructor_decl(symbol("B"), symbol("is-B"), 0, nullptr);
    constructor_decl* constrs[3] = { R, G, B };
    datatype_decl * enum_sort = mk_datatype_decl(dtutil, symbol("RGB"), 0, nullptr, 3, constrs);
    VERIFY(dt.mk_datatypes(1, &enum_sort, 0, nullptr, new_sorts));
    sort* rgb = new_sorts[0].get();

    expr_ref x = mk_const(m, "x", rgb), y = mk_const(m, "y", rgb), z = mk_const(m, "z", rgb);
    ptr_vector<func_decl> const& enums = *dtutil.get_datatype_constructors(rgb);
    expr_ref r = expr_ref(m.mk_const(enums[0]), m);
    expr_ref g = expr_ref(m.mk_const(enums[1]), m);
    expr_ref b = expr_ref(m.mk_const(enums[2]), m);

    ref<solver> fd_solver = mk_fd_solver(m, p);
    fd_solver->assert_expr(m.mk_not(m.mk_eq(x, r)));
    fd_solver->assert_expr(m.mk_not(m.mk_eq(x, b)));

    expr_ref_vector asms(m), vars(m), conseq(m);
    vars.push_back(x);
    vars.push_back(y);

    VERIFY(l_true == fd_solver->get_consequences(asms, vars, conseq));
    ENSURE(!conseq.empty());
    std::cout << conseq << "\n";
    conseq.reset();

    ast_manager dst;
    reg_decl_plugins(dst);
    ref<solver> translated_solver = fd_solver->translate(dst, p);
    ast_translation tr(m, dst);
    expr_ref translated_x(tr(x.get()), dst);
    expr_ref translated_g(tr(g.get()), dst);

    VERIFY(l_true == translated_solver->check_sat(0, nullptr));
    model_ref mr;
    translated_solver->get_model(mr);
    ENSURE(mr.get());
    model_evaluator eval(*mr);
    expr_ref value(dst);
    eval(translated_x, value);
    ENSURE(dst.are_equal(value, translated_g));
    model_smt2_pp(std::cout << "model:\n", dst, *mr.get(), 0);

    VERIFY(l_true == translated_solver->check_sat(0,nullptr));
    translated_solver->get_model(mr);
    ENSURE(mr.get());
    model_smt2_pp(std::cout, dst, *mr.get(), 0);

}

static void test_bounded_int_translation() {
    ast_manager source;
    reg_decl_plugins(source);
    params_ref p;
    ref<solver> source_solver = mk_fd_solver(source, p);
    arith_util source_arith(source);
    expr_ref source_x = mk_const(source, "x", source_arith.mk_int());
    expr_ref source_three(source_arith.mk_int(3), source);
    expr_ref source_zero(source_arith.mk_int(0), source);
    expr_ref source_five(source_arith.mk_int(5), source);
    source_solver->assert_expr(source_arith.mk_le(source_zero, source_x));
    source_solver->assert_expr(source_arith.mk_le(source_x, source_five));
    source_solver->assert_expr(source.mk_eq(source_x, source_three));
    VERIFY(l_true == source_solver->check_sat(0, nullptr));

    ast_manager m;
    reg_decl_plugins(m);
    ref<solver> fd_solver = source_solver->translate(m, p);
    ast_translation tr(source, m);
    arith_util arith(m);
    expr_ref x(tr(source_x.get()), m);
    expr_ref three(arith.mk_int(3), m);

    VERIFY(l_true == fd_solver->check_sat(0, nullptr));

    model_ref mdl;
    fd_solver->get_model(mdl);
    ENSURE(mdl.get());
    model_evaluator eval(*mdl);
    expr_ref value(m);
    eval(x, value);
    ENSURE(m.are_equal(value, three));

    VERIFY(l_true == fd_solver->check_sat(0, nullptr));
}

static void test_bounded_int() {
    ast_manager source;
    reg_decl_plugins(source);
    params_ref p;
    ref<solver> source_solver = mk_fd_solver(source, p);

    ast_manager m;
    reg_decl_plugins(m);
    ref<solver> fd_solver = source_solver->translate(m, p);
    arith_util arith(m);
    expr_ref x = mk_const(m, "x", arith.mk_int());
    expr_ref three(arith.mk_int(3), m);
    expr_ref four(arith.mk_int(4), m);
    expr_ref zero(arith.mk_int(0), m);
    expr_ref five(arith.mk_int(5), m);

    fd_solver->assert_expr(arith.mk_le(zero, x));
    fd_solver->assert_expr(arith.mk_le(x, five));
    fd_solver->assert_expr(m.mk_eq(x, three));

    expr_ref_vector asms(m), vars(m), conseq(m);
    vars.push_back(x);
    VERIFY(l_true == fd_solver->get_consequences(asms, vars, conseq));
    ENSURE(!conseq.empty());

    fd_solver->push();
    fd_solver->assert_expr(m.mk_eq(x, four));
    VERIFY(l_false == fd_solver->check_sat(0, nullptr));
    fd_solver->pop(1);
    VERIFY(l_true == fd_solver->check_sat(0, nullptr));
}

static void test_cardinality_consequences_after_check() {
    ast_manager m;
    reg_decl_plugins(m);
    params_ref p;
    p.set_sym("phase", symbol("always_true"));
    ref<solver> fd_solver = mk_fd_solver(m, p);
    pb_util pb(m);

    expr_ref_vector as(m), xs(m), clause(m);
    for (unsigned i = 0; i < 5; ++i) {
        as.push_back(mk_bool(m, ("a" + std::to_string(i)).c_str()));
    }
    for (unsigned i = 0; i < 8; ++i) {
        xs.push_back(mk_bool(m, ("x" + std::to_string(i)).c_str()));
    }
    expr_ref y = mk_bool(m, "y");

    fd_solver->assert_expr(pb.mk_at_most_k(as.size(), as.data(), 1));
    fd_solver->assert_expr(m.mk_or(xs.size(), xs.data()));
    fd_solver->assert_expr(pb.mk_at_most_k(xs.size(), xs.data(), 1));
    for (unsigned i = 0; i < xs.size(); ++i) {
        if (i != 5) clause.push_back(xs[i].get());
    }
    clause.push_back(m.mk_not(y));
    fd_solver->assert_expr(m.mk_or(clause));
    VERIFY(l_true == fd_solver->check_sat(0, nullptr));
    model_ref mdl;
    fd_solver->get_model(mdl);
    model_evaluator eval(*mdl);
    expr_ref value(m);
    eval(y, value);
    ENSURE(m.is_true(value));

    expr_ref_vector asms(m), vars(m), conseq(m);
    asms.push_back(xs[5].get());
    vars.push_back(y);
    VERIFY(l_true == fd_solver->get_consequences(asms, vars, conseq));
    ENSURE(conseq.size() == 1);
    ENSURE(m.are_equal(conseq[0].get(), m.mk_implies(xs[5].get(), m.mk_not(y))));

    expr_ref_vector check_asms(m);
    check_asms.push_back(xs[5].get());
    check_asms.push_back(y);
    VERIFY(l_false == fd_solver->check_sat(check_asms));
}

static void test_datatype_accessor_consequences() {
    ast_manager m;
    reg_decl_plugins(m);
    datatype_util dt(m);
    arith_util arith(m);
    params_ref p;

    accessor_decl* accessors[] = { mk_accessor_decl(m, symbol("val"), type_ref(arith.mk_int())) };
    constructor_decl* constructors[] = {
        mk_constructor_decl(symbol("none"), symbol("is-none"), 0, nullptr),
        mk_constructor_decl(symbol("some"), symbol("is-some"), 1, accessors)
    };
    datatype_decl* option = mk_datatype_decl(dt, symbol("Option_Int"), 0, nullptr, 2, constructors);
    sort_ref_vector sorts(m);
    VERIFY(dt.plugin().mk_datatypes(1, &option, 0, nullptr, sorts));
    sort* option_sort = sorts[0].get();
    func_decl* val = (*dt.get_constructor_accessors((*dt.get_datatype_constructors(option_sort))[1]))[0];

    expr_ref a = mk_const(m, "a", option_sort);
    expr_ref b = mk_const(m, "b", option_sort);
    expr_ref t0 = mk_bool(m, "t0");
    expr_ref t1 = mk_bool(m, "t1");
    expr_ref va(m.mk_app(val, a), m);
    expr_ref vb(m.mk_app(val, b), m);
    expr_ref two(arith.mk_int(2), m);
    expr_ref nine(arith.mk_int(9), m);
    ref<solver> smt_solver = mk_smt_solver(m, p, symbol::null);
    smt_solver->assert_expr(m.mk_implies(t0, m.mk_eq(va, two)));
    smt_solver->assert_expr(m.mk_implies(t1, m.mk_eq(vb, nine)));

    expr_ref_vector assumptions(m), vars(m), consequences(m);
    assumptions.push_back(t0);
    assumptions.push_back(t1);
    vars.push_back(va);
    vars.push_back(vb);
    VERIFY(l_true == smt_solver->get_consequences(assumptions, vars, consequences));
    ENSURE(consequences.size() == 2);
    expr_ref expected_a(m.mk_implies(t0, m.mk_eq(va, two)), m);
    expr_ref expected_b(m.mk_implies(t1, m.mk_eq(vb, nine)), m);
    bool found_a = false, found_b = false;
    for (expr* consequence : consequences) {
        found_a |= m.are_equal(consequence, expected_a);
        found_b |= m.are_equal(consequence, expected_b);
    }
    ENSURE(found_a && found_b);
}

void tst_get_consequences() {
    test1();
    test2();
    test_bounded_int();
    test_bounded_int_translation();
    test_cardinality_consequences_after_check();
    test_datatype_accessor_consequences();
}