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https://github.com/Z3Prover/z3
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b544f7e58c
Add two rewrite rules in mk_mod_core: 1. mod(a + k*y, y) → mod(a, y): removes summands equal to (or integer multiples of) the symbolic modulus. Valid for all y including y=0 since k*0=0. 2. mod(mod(x, y), y) for symbolic y: rewrites via ite to terminate the E-matching chain created by the quantifier idempotency rule. Also add regression tests in src/test/arith_rewriter.cpp covering both new rules.
105 lines
3.3 KiB
C++
105 lines
3.3 KiB
C++
/*++
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Copyright (c) 2015 Microsoft Corporation
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--*/
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#include "ast/rewriter/arith_rewriter.h"
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#include "ast/bv_decl_plugin.h"
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#include "ast/ast_pp.h"
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#include "ast/reg_decl_plugins.h"
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#include "ast/rewriter/th_rewriter.h"
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#include "model/model.h"
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#include "parsers/smt2/smt2parser.h"
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#include <iostream>
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static expr_ref parse_fml(ast_manager& m, char const* str) {
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expr_ref result(m);
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cmd_context ctx(false, &m);
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ctx.set_ignore_check(true);
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std::ostringstream buffer;
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buffer << "(declare-const x Real)\n"
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<< "(declare-const y Real)\n"
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<< "(declare-const z Real)\n"
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<< "(declare-const a Real)\n"
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<< "(declare-const b Real)\n"
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<< "(assert " << str << ")\n";
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std::istringstream is(buffer.str());
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VERIFY(parse_smt2_commands(ctx, is));
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ENSURE(!ctx.assertions().empty());
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result = ctx.assertions().get(0);
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return result;
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}
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static char const* example1 = "(<= (+ (* 1.3 x y) (* 2.3 y y) (* (- 1.1 x x))) 2.2)";
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static char const* example2 = "(= (+ 4 3 (- (* 3 x x) (* 5 y)) y) 0)";
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static expr_ref parse_int_fml(ast_manager& m, char const* str) {
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expr_ref result(m);
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cmd_context ctx(false, &m);
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ctx.set_ignore_check(true);
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std::ostringstream buffer;
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buffer << "(declare-const I Int)\n"
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<< "(declare-const S Int)\n"
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<< "(assert " << str << ")\n";
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std::istringstream is(buffer.str());
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VERIFY(parse_smt2_commands(ctx, is));
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ENSURE(!ctx.assertions().empty());
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result = ctx.assertions().get(0);
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return result;
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}
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void tst_arith_rewriter() {
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ast_manager m;
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reg_decl_plugins(m);
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arith_rewriter ar(m);
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arith_util au(m);
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expr_ref t1(m), t2(m), result(m);
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t1 = au.mk_numeral(rational(0),false);
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t2 = au.mk_numeral(rational(-3),false);
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expr* args[2] = { t1, t2 };
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ar.mk_mul(2, args, result);
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std::cout << mk_pp(result, m) << "\n";
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th_rewriter rw(m);
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expr_ref fml = parse_fml(m, example1);
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rw(fml);
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std::cout << mk_pp(fml, m) << "\n";
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fml = parse_fml(m, example2);
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rw(fml);
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std::cout << mk_pp(fml, m) << "\n";
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// Issue #7507: (>= (* I (+ I 1)) 0) should simplify to true
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fml = parse_int_fml(m, "(>= (* I (+ I 1)) 0)");
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rw(fml);
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std::cout << "consecutive product >= 0: " << mk_pp(fml, m) << "\n";
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ENSURE(m.is_true(fml));
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// (>= (* I (+ I (- 1))) 0) should also simplify to true (x*(x-1))
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fml = parse_int_fml(m, "(>= (* I (+ I (- 1))) 0)");
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rw(fml);
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std::cout << "consecutive product (minus) >= 0: " << mk_pp(fml, m) << "\n";
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ENSURE(m.is_true(fml));
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// Issue #7403: mod (a + b) b should simplify to mod a b for symbolic b
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// i.e. (= (mod (+ I S) S) (mod I S)) should reduce to true
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fml = parse_int_fml(m, "(= (mod (+ I S) S) (mod I S))");
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rw(fml);
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std::cout << "mod (a+b) b = mod a b: " << mk_pp(fml, m) << "\n";
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ENSURE(m.is_true(fml));
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// mod (a + 2*b) b should simplify to mod a b (multiple of modulus dropped)
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fml = parse_int_fml(m, "(= (mod (+ I (* 2 S)) S) (mod I S))");
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rw(fml);
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std::cout << "mod (a+2b) b = mod a b: " << mk_pp(fml, m) << "\n";
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ENSURE(m.is_true(fml));
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// mod (mod a b) b should simplify for non-zero numeral b
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fml = parse_int_fml(m, "(= (mod (mod I 3) 3) (mod I 3))");
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rw(fml);
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std::cout << "mod (mod a 3) 3 = mod a 3: " << mk_pp(fml, m) << "\n";
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ENSURE(m.is_true(fml));
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}
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