mirror of
https://github.com/Z3Prover/z3
synced 2026-07-15 11:35:42 +00:00
21c23e78db
The arith rewriter now recognizes that x * (x + 1) >= 0 for all integers, since no integer lies strictly between -1 and 0. Two changes: 1. is_non_negative: detect products where unpaired factors are consecutive integer expressions (differ by exactly 1), handling both +1 and -1 offsets and n-ary additions 2. is_separated: return true for (>= non_negative_mul 0), restricted to multiplication expressions to avoid disrupting other theories Also adds regression tests for the new simplification. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
86 lines
2.5 KiB
C++
86 lines
2.5 KiB
C++
/*++
|
|
Copyright (c) 2015 Microsoft Corporation
|
|
|
|
--*/
|
|
|
|
#include "ast/rewriter/arith_rewriter.h"
|
|
#include "ast/bv_decl_plugin.h"
|
|
#include "ast/ast_pp.h"
|
|
#include "ast/reg_decl_plugins.h"
|
|
#include "ast/rewriter/th_rewriter.h"
|
|
#include "model/model.h"
|
|
#include "parsers/smt2/smt2parser.h"
|
|
#include <iostream>
|
|
|
|
static expr_ref parse_fml(ast_manager& m, char const* str) {
|
|
expr_ref result(m);
|
|
cmd_context ctx(false, &m);
|
|
ctx.set_ignore_check(true);
|
|
std::ostringstream buffer;
|
|
buffer << "(declare-const x Real)\n"
|
|
<< "(declare-const y Real)\n"
|
|
<< "(declare-const z Real)\n"
|
|
<< "(declare-const a Real)\n"
|
|
<< "(declare-const b Real)\n"
|
|
<< "(assert " << str << ")\n";
|
|
std::istringstream is(buffer.str());
|
|
VERIFY(parse_smt2_commands(ctx, is));
|
|
ENSURE(!ctx.assertions().empty());
|
|
result = ctx.assertions().get(0);
|
|
return result;
|
|
}
|
|
|
|
static char const* example1 = "(<= (+ (* 1.3 x y) (* 2.3 y y) (* (- 1.1 x x))) 2.2)";
|
|
static char const* example2 = "(= (+ 4 3 (- (* 3 x x) (* 5 y)) y) 0)";
|
|
|
|
static expr_ref parse_int_fml(ast_manager& m, char const* str) {
|
|
expr_ref result(m);
|
|
cmd_context ctx(false, &m);
|
|
ctx.set_ignore_check(true);
|
|
std::ostringstream buffer;
|
|
buffer << "(declare-const I Int)\n"
|
|
<< "(declare-const S Int)\n"
|
|
<< "(assert " << str << ")\n";
|
|
std::istringstream is(buffer.str());
|
|
VERIFY(parse_smt2_commands(ctx, is));
|
|
ENSURE(!ctx.assertions().empty());
|
|
result = ctx.assertions().get(0);
|
|
return result;
|
|
}
|
|
|
|
|
|
void tst_arith_rewriter() {
|
|
ast_manager m;
|
|
reg_decl_plugins(m);
|
|
arith_rewriter ar(m);
|
|
arith_util au(m);
|
|
expr_ref t1(m), t2(m), result(m);
|
|
t1 = au.mk_numeral(rational(0),false);
|
|
t2 = au.mk_numeral(rational(-3),false);
|
|
expr* args[2] = { t1, t2 };
|
|
ar.mk_mul(2, args, result);
|
|
std::cout << mk_pp(result, m) << "\n";
|
|
|
|
|
|
th_rewriter rw(m);
|
|
expr_ref fml = parse_fml(m, example1);
|
|
rw(fml);
|
|
std::cout << mk_pp(fml, m) << "\n";
|
|
|
|
|
|
fml = parse_fml(m, example2);
|
|
rw(fml);
|
|
std::cout << mk_pp(fml, m) << "\n";
|
|
|
|
// Issue #7507: (>= (* I (+ I 1)) 0) should simplify to true
|
|
fml = parse_int_fml(m, "(>= (* I (+ I 1)) 0)");
|
|
rw(fml);
|
|
std::cout << "consecutive product >= 0: " << mk_pp(fml, m) << "\n";
|
|
ENSURE(m.is_true(fml));
|
|
|
|
// (>= (* I (+ I (- 1))) 0) should also simplify to true (x*(x-1))
|
|
fml = parse_int_fml(m, "(>= (* I (+ I (- 1))) 0)");
|
|
rw(fml);
|
|
std::cout << "consecutive product (minus) >= 0: " << mk_pp(fml, m) << "\n";
|
|
ENSURE(m.is_true(fml));
|
|
}
|