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Diffstat (limited to 'examples/api/cpp/bitvectors.cpp')
-rw-r--r-- | examples/api/cpp/bitvectors.cpp | 128 |
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diff --git a/examples/api/cpp/bitvectors.cpp b/examples/api/cpp/bitvectors.cpp new file mode 100644 index 000000000..8768bd996 --- /dev/null +++ b/examples/api/cpp/bitvectors.cpp @@ -0,0 +1,128 @@ +/****************************************************************************** + * Top contributors (to current version): + * Aina Niemetz, Liana Hadarean, Makai Mann + * + * This file is part of the cvc5 project. + * + * Copyright (c) 2009-2021 by the authors listed in the file AUTHORS + * in the top-level source directory and their institutional affiliations. + * All rights reserved. See the file COPYING in the top-level source + * directory for licensing information. + * **************************************************************************** + * + * A simple demonstration of the solving capabilities of the CVC4 + * bit-vector solver. + * + */ + +#include <cvc5/cvc5.h> + +#include <iostream> + +using namespace std; +using namespace cvc5::api; + +int main() +{ + Solver slv; + slv.setLogic("QF_BV"); // Set the logic + + // The following example has been adapted from the book A Hacker's Delight by + // Henry S. Warren. + // + // Given a variable x that can only have two values, a or b. We want to + // assign to x a value other than the current one. The straightforward code + // to do that is: + // + //(0) if (x == a ) x = b; + // else x = a; + // + // Two more efficient yet equivalent methods are: + // + //(1) x = a ⊕ b ⊕ x; + // + //(2) x = a + b - x; + // + // We will use CVC4 to prove that the three pieces of code above are all + // equivalent by encoding the problem in the bit-vector theory. + + // Creating a bit-vector type of width 32 + Sort bitvector32 = slv.mkBitVectorSort(32); + + // Variables + Term x = slv.mkConst(bitvector32, "x"); + Term a = slv.mkConst(bitvector32, "a"); + Term b = slv.mkConst(bitvector32, "b"); + + // First encode the assumption that x must be equal to a or b + Term x_eq_a = slv.mkTerm(EQUAL, x, a); + Term x_eq_b = slv.mkTerm(EQUAL, x, b); + Term assumption = slv.mkTerm(OR, x_eq_a, x_eq_b); + + // Assert the assumption + slv.assertFormula(assumption); + + // Introduce a new variable for the new value of x after assignment. + Term new_x = slv.mkConst(bitvector32, "new_x"); // x after executing code (0) + Term new_x_ = + slv.mkConst(bitvector32, "new_x_"); // x after executing code (1) or (2) + + // Encoding code (0) + // new_x = x == a ? b : a; + Term ite = slv.mkTerm(ITE, x_eq_a, b, a); + Term assignment0 = slv.mkTerm(EQUAL, new_x, ite); + + // Assert the encoding of code (0) + cout << "Asserting " << assignment0 << " to CVC4 " << endl; + slv.assertFormula(assignment0); + cout << "Pushing a new context." << endl; + slv.push(); + + // Encoding code (1) + // new_x_ = a xor b xor x + Term a_xor_b_xor_x = slv.mkTerm(BITVECTOR_XOR, a, b, x); + Term assignment1 = slv.mkTerm(EQUAL, new_x_, a_xor_b_xor_x); + + // Assert encoding to CVC4 in current context; + cout << "Asserting " << assignment1 << " to CVC4 " << endl; + slv.assertFormula(assignment1); + Term new_x_eq_new_x_ = slv.mkTerm(EQUAL, new_x, new_x_); + + cout << " Check entailment assuming: " << new_x_eq_new_x_ << endl; + cout << " Expect ENTAILED. " << endl; + cout << " CVC4: " << slv.checkEntailed(new_x_eq_new_x_) << endl; + cout << " Popping context. " << endl; + slv.pop(); + + // Encoding code (2) + // new_x_ = a + b - x + Term a_plus_b = slv.mkTerm(BITVECTOR_ADD, a, b); + Term a_plus_b_minus_x = slv.mkTerm(BITVECTOR_SUB, a_plus_b, x); + Term assignment2 = slv.mkTerm(EQUAL, new_x_, a_plus_b_minus_x); + + // Assert encoding to CVC4 in current context; + cout << "Asserting " << assignment2 << " to CVC4 " << endl; + slv.assertFormula(assignment2); + + cout << " Check entailment assuming: " << new_x_eq_new_x_ << endl; + cout << " Expect ENTAILED. " << endl; + cout << " CVC4: " << slv.checkEntailed(new_x_eq_new_x_) << endl; + + Term x_neq_x = slv.mkTerm(EQUAL, x, x).notTerm(); + std::vector<Term> v{new_x_eq_new_x_, x_neq_x}; + cout << " Check entailment assuming: " << v << endl; + cout << " Expect NOT_ENTAILED. " << endl; + cout << " CVC4: " << slv.checkEntailed(v) << endl; + + // Assert that a is odd + Op extract_op = slv.mkOp(BITVECTOR_EXTRACT, 0, 0); + Term lsb_of_a = slv.mkTerm(extract_op, a); + cout << "Sort of " << lsb_of_a << " is " << lsb_of_a.getSort() << endl; + Term a_odd = slv.mkTerm(EQUAL, lsb_of_a, slv.mkBitVector(1u, 1u)); + cout << "Assert " << a_odd << endl; + cout << "Check satisfiability." << endl; + slv.assertFormula(a_odd); + cout << " Expect sat. " << endl; + cout << " CVC4: " << slv.checkSat() << endl; + return 0; +} |