Theory of Bit-Vectors and Arrays
examples/api/cpp/bitvectors_and_arrays.cpp
1/******************************************************************************
2 * Top contributors (to current version):
3 * Liana Hadarean, Aina Niemetz, Mathias Preiner
4 *
5 * This file is part of the cvc5 project.
6 *
7 * Copyright (c) 2009-2022 by the authors listed in the file AUTHORS
8 * in the top-level source directory and their institutional affiliations.
9 * All rights reserved. See the file COPYING in the top-level source
10 * directory for licensing information.
11 * ****************************************************************************
12 *
13 * A simple demonstration of the solving capabilities of the cvc5
14 * bit-vector and array solvers.
15 *
16 */
17
18#include <cvc5/cvc5.h>
19
20#include <cmath>
21#include <iostream>
22
23using namespace std;
24using namespace cvc5;
25
26int main()
27{
28 Solver slv;
29 slv.setOption("produce-models", "true"); // Produce Models
30 slv.setOption("output-language", "smtlib"); // output-language
31 slv.setLogic("QF_AUFBV"); // Set the logic
32
33 // Consider the following code (where size is some previously defined constant):
34 //
35 //
36 // Assert (current_array[0] > 0);
37 // for (unsigned i = 1; i < k; ++i) {
38 // current_array[i] = 2 * current_array[i - 1];
39 // Assert (current_array[i-1] < current_array[i]);
40 // }
41 //
42 // We want to check whether the assertion in the body of the for loop holds
43 // throughout the loop.
44
45 // Setting up the problem parameters
46 unsigned k = 4; // number of unrollings (should be a power of 2)
47 unsigned index_size = log2(k); // size of the index
48
49
50 // Sorts
51 Sort elementSort = slv.mkBitVectorSort(32);
52 Sort indexSort = slv.mkBitVectorSort(index_size);
53 Sort arraySort = slv.mkArraySort(indexSort, elementSort);
54
55 // Variables
56 Term current_array = slv.mkConst(arraySort, "current_array");
57
58 // Making a bit-vector constant
59 Term zero = slv.mkBitVector(index_size, 0u);
60
61 // Asserting that current_array[0] > 0
62 Term current_array0 = slv.mkTerm(SELECT, {current_array, zero});
63 Term current_array0_gt_0 =
64 slv.mkTerm(BITVECTOR_SGT, {current_array0, slv.mkBitVector(32, 0u)});
65 slv.assertFormula(current_array0_gt_0);
66
67 // Building the assertions in the loop unrolling
68 Term index = slv.mkBitVector(index_size, 0u);
69 Term old_current = slv.mkTerm(SELECT, {current_array, index});
70 Term two = slv.mkBitVector(32, 2u);
71
72 std::vector<Term> assertions;
73 for (unsigned i = 1; i < k; ++i) {
74 index = slv.mkBitVector(index_size, i);
75 Term new_current = slv.mkTerm(BITVECTOR_MULT, {two, old_current});
76 // current[i] = 2 * current[i-1]
77 current_array = slv.mkTerm(STORE, {current_array, index, new_current});
78 // current[i-1] < current [i]
79 Term current_slt_new_current =
80 slv.mkTerm(BITVECTOR_SLT, {old_current, new_current});
81 assertions.push_back(current_slt_new_current);
82
83 old_current = slv.mkTerm(SELECT, {current_array, index});
84 }
85
86 Term query = slv.mkTerm(NOT, {slv.mkTerm(AND, assertions)});
87
88 cout << "Asserting " << query << " to cvc5 " << endl;
89 slv.assertFormula(query);
90 cout << "Expect sat. " << endl;
91 cout << "cvc5: " << slv.checkSatAssuming(slv.mkTrue()) << endl;
92
93 // Getting the model
94 cout << "The satisfying model is: " << endl;
95 cout << " current_array = " << slv.getValue(current_array) << endl;
96 cout << " current_array[0] = " << slv.getValue(current_array0) << endl;
97 return 0;
98}
examples/api/java/BitVectorsAndArrays.java
1/******************************************************************************
2 * Top contributors (to current version):
3 * Mudathir Mohamed, Morgan Deters, Liana Hadarean
4 *
5 * This file is part of the cvc5 project.
6 *
7 * Copyright (c) 2009-2022 by the authors listed in the file AUTHORS
8 * in the top-level source directory and their institutional affiliations.
9 * All rights reserved. See the file COPYING in the top-level source
10 * directory for licensing information.
11 * ****************************************************************************
12 *
13 * A simple demonstration of the solving capabilities of the cvc5
14 * bit-vector solver.
15 *
16 */
17
18import io.github.cvc5.*;
19import java.util.*;
20
21public class BitVectorsAndArrays
22{
23 private static int log2(int n)
24 {
25 return (int) Math.round(Math.log(n) / Math.log(2));
26 }
27
28 public static void main(String[] args) throws CVC5ApiException
29 {
30 Solver slv = new Solver();
31 {
32 slv.setOption("produce-models", "true"); // Produce Models
33 slv.setOption("output-language", "smtlib"); // output-language
34 slv.setLogic("QF_AUFBV"); // Set the logic
35
36 // Consider the following code (where size is some previously defined constant):
37 //
38 //
39 // Assert (current_array[0] > 0);
40 // for (unsigned i = 1; i < k; ++i) {
41 // current_array[i] = 2 * current_array[i - 1];
42 // Assert (current_array[i-1] < current_array[i]);
43 // }
44 //
45 // We want to check whether the assertion in the body of the for loop holds
46 // throughout the loop.
47
48 // Setting up the problem parameters
49 int k = 4; // number of unrollings (should be a power of 2)
50 int index_size = log2(k); // size of the index
51
52 // Sorts
53 Sort elementSort = slv.mkBitVectorSort(32);
54 Sort indexSort = slv.mkBitVectorSort(index_size);
55 Sort arraySort = slv.mkArraySort(indexSort, elementSort);
56
57 // Variables
58 Term current_array = slv.mkConst(arraySort, "current_array");
59
60 // Making a bit-vector constant
61 Term zero = slv.mkBitVector(index_size, 0);
62
63 // Asserting that current_array[0] > 0
64 Term current_array0 = slv.mkTerm(Kind.SELECT, current_array, zero);
65 Term current_array0_gt_0 =
66 slv.mkTerm(Kind.BITVECTOR_SGT, current_array0, slv.mkBitVector(32, 0));
67 slv.assertFormula(current_array0_gt_0);
68
69 // Building the assertions in the loop unrolling
70 Term index = slv.mkBitVector(index_size, 0);
71 Term old_current = slv.mkTerm(Kind.SELECT, current_array, index);
72 Term two = slv.mkBitVector(32, 2);
73
74 List<Term> assertions = new ArrayList<Term>();
75 for (int i = 1; i < k; ++i)
76 {
77 index = slv.mkBitVector(index_size, i);
78 Term new_current = slv.mkTerm(Kind.BITVECTOR_MULT, two, old_current);
79 // current[i] = 2 * current[i-1]
80 current_array = slv.mkTerm(Kind.STORE, current_array, index, new_current);
81 // current[i-1] < current [i]
82 Term current_slt_new_current = slv.mkTerm(Kind.BITVECTOR_SLT, old_current, new_current);
83 assertions.add(current_slt_new_current);
84
85 old_current = slv.mkTerm(Kind.SELECT, current_array, index);
86 }
87
88 Term query = slv.mkTerm(Kind.NOT, slv.mkTerm(Kind.AND, assertions.toArray(new Term[0])));
89
90 System.out.println("Asserting " + query + " to cvc5 ");
91 slv.assertFormula(query);
92 System.out.println("Expect sat. ");
93 System.out.println("cvc5: " + slv.checkSatAssuming(slv.mkTrue()));
94
95 // Getting the model
96 System.out.println("The satisfying model is: ");
97 System.out.println(" current_array = " + slv.getValue(current_array));
98 System.out.println(" current_array[0] = " + slv.getValue(current_array0));
99 }
100 }
101}
examples/api/python/pythonic/bitvectors_and_arrays.py
1from cvc5.pythonic import *
2
3if __name__ == '__main__':
4 # Consider the following (where k is some previously defined constant):
5 #
6 #
7 # Assert (current_array[0] > 0);
8 # for (unsigned i = 1; i < k; ++i) {
9 # current_array[i] = 2 * current_array[i - 1];
10 # Assert (current_array[i-1] < current_array[i]);
11 # }
12 #
13 # We want to check whether the assertion in the body of the for loop holds
14 # throughout the loop.
15 k = 4
16 idx_bits = int(math.ceil(math.log(k, 2)))
17
18 init_array = Array('init_arr', BitVecSort(idx_bits), BitVecSort(32))
19 array = init_array
20 assertions = []
21 for i in range(1, k):
22 array = Store(array, i, 2 * Select(array, i - 1))
23 assertions.append(Select(array, i - 1) < Select(array, i))
24 # Does *not* hold.
25 # If the first element is large enough, the multiplication overflows.
26 prove(Implies(Select(init_array, 0) > 0, And(*assertions)))
examples/api/python/bitvectors_and_arrays.py
1#!/usr/bin/env python
2###############################################################################
3# Top contributors (to current version):
4# Makai Mann, Aina Niemetz, Alex Ozdemir
5#
6# This file is part of the cvc5 project.
7#
8# Copyright (c) 2009-2022 by the authors listed in the file AUTHORS
9# in the top-level source directory and their institutional affiliations.
10# All rights reserved. See the file COPYING in the top-level source
11# directory for licensing information.
12# #############################################################################
13#
14# A simple demonstration of the solving capabilities of the cvc5
15# bit-vector and array solvers through the Python API. This is a direct
16# translation of bitvectors_and_arrays-new.cpp.
17##
18
19import cvc5
20from cvc5 import Kind
21
22import math
23
24if __name__ == "__main__":
25 slv = cvc5.Solver()
26 slv.setOption("produce-models", "true")
27 slv.setOption("output-language", "smtlib")
28 slv.setLogic("QF_AUFBV")
29
30 # Consider the following code (where size is some previously defined constant):
31 #
32 #
33 # Assert (current_array[0] > 0);
34 # for (unsigned i = 1; i < k; ++i) {
35 # current_array[i] = 2 * current_array[i - 1];
36 # Assert (current_array[i-1] < current_array[i]);
37 # }
38 #
39 # We want to check whether the assertion in the body of the for loop holds
40 # throughout the loop.
41
42 # Setting up the problem parameters
43 k = 4
44 index_size = int(math.ceil(math.log(k, 2)))
45
46 # Sorts
47 elementSort = slv.mkBitVectorSort(32)
48 indexSort = slv.mkBitVectorSort(index_size)
49 arraySort = slv.mkArraySort(indexSort, elementSort)
50
51 # Variables
52 current_array = slv.mkConst(arraySort, "current_array")
53
54 # Making a bit-vector constant
55 zero = slv.mkBitVector(index_size, 0)
56
57 # Test making a constant array
58 constarr0 = slv.mkConstArray(arraySort, slv.mkBitVector(32, 0))
59
60 # Asserting that current_array[0] > 0
61 current_array0 = slv.mkTerm(Kind.SELECT, current_array, zero)
62 current_array0_gt_0 = slv.mkTerm(Kind.BITVECTOR_SGT,
63 current_array0,
64 slv.mkBitVector(32, 0))
65 slv.assertFormula(current_array0_gt_0)
66
67 # Building the assertions in the loop unrolling
68 index = slv.mkBitVector(index_size, 0)
69 old_current = slv.mkTerm(Kind.SELECT, current_array, index)
70 two = slv.mkBitVector(32, 2)
71
72 assertions = []
73 for i in range(1, k):
74 index = slv.mkBitVector(index_size, i)
75 new_current = slv.mkTerm(Kind.BITVECTOR_MULT, two, old_current)
76 # current[i] = 2*current[i-1]
77 current_array = \
78 slv.mkTerm(Kind.STORE, current_array, index, new_current)
79 # current[i-1] < current[i]
80 current_slt_new_current = \
81 slv.mkTerm(Kind.BITVECTOR_SLT, old_current, new_current)
82 assertions.append(current_slt_new_current)
83 old_current = slv.mkTerm(Kind.SELECT, current_array, index)
84
85 query = slv.mkTerm(Kind.NOT, slv.mkTerm(Kind.AND, *assertions))
86
87 print("Asserting {} to cvc5".format(query))
88 slv.assertFormula(query)
89 print("Expect sat.")
90 print("cvc5:", slv.checkSatAssuming(slv.mkTrue()))
91
92 # Getting the model
93 print("The satisfying model is: ")
94 print(" current_array =", slv.getValue(current_array))
95 print(" current_array[0]", slv.getValue(current_array0))
examples/api/smtlib/bitvectors_and_arrays.smt2
1(set-logic QF_AUFBV)
2(set-option :produce-models true)
3
4; Consider the following code (where size is some previously defined constant):
5
6
7; Assert (current_array[0] > 0);
8; for (unsigned i = 1; i < k; ++i) {
9; current_array[i] = 2 * current_array[i - 1];
10; Assert (current_array[i-1] < current_array[i]);
11; }
12
13; We want to check whether the assertion in the body of the for loop holds
14; throughout the loop. We will do so for k = 4.
15
16
17(define-sort Index () (_ BitVec 2))
18(define-sort Element () (_ BitVec 32))
19(define-sort ArraySort () (Array Index Element))
20
21; Declaring the array
22(declare-const current_array ArraySort)
23
24; Making utility bit-vector constants
25(define-const zeroI Index (_ bv0 2))
26(define-const oneI Index (_ bv1 2))
27(define-const twoI Index (_ bv2 2))
28(define-const threeI Index (_ bv3 2))
29
30(define-const zeroE Element (_ bv0 32))
31(define-const twoE Element (_ bv2 32))
32
33; Asserting that current_array[0] > 0
34(assert (bvsgt (select current_array zeroI) zeroE))
35
36; Building the formulas representing loop unrolling
37
38; current_array[0] < array [1]
39(define-const unroll1 Bool (bvslt (select current_array zeroI) (bvmul twoE (select current_array zeroI))))
40; current_array[1] = 2 * current_array[0]
41(define-const current_array_ ArraySort (store current_array oneI (bvmul twoE (select current_array zeroI))))
42
43; current_array[1] < array [2]
44(define-const unroll2 Bool (bvslt (select current_array_ oneI) (bvmul twoE (select current_array_ oneI))))
45; current_array[2] = 2 * current_array[1]
46(define-const current_array__ ArraySort (store current_array_ twoI (bvmul twoE (select current_array_ oneI))))
47
48; current_array[2] < array [3]
49(define-const unroll3 Bool (bvslt (select current_array_ twoI) (bvmul twoE (select current_array_ twoI))))
50; current_array[3] = 2 * current_array[2]
51(define-const current_array___ ArraySort (store current_array_ threeI (bvmul twoE (select current_array_ twoI))))
52
53(assert (not (and unroll1 unroll2 unroll3)))
54
55(check-sat)
56(get-value (current_array___ (select current_array___ zeroI)))