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124 lines
4.2 KiB
Python
124 lines
4.2 KiB
Python
#!/usr/bin/env python
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###############################################################################
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# Top contributors (to current version):
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# Makai Mann, Aina Niemetz, Andrew Reynolds
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#
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# This file is part of the cvc5 project.
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#
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# Copyright (c) 2009-2022 by the authors listed in the file AUTHORS
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# in the top-level source directory and their institutional affiliations.
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# All rights reserved. See the file COPYING in the top-level source
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# directory for licensing information.
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# #############################################################################
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#
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# A simple demonstration of the solving capabilities of the cvc5 bit-vector
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# solver through the Python API. This is a direct translation of
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# bitvectors-new.cpp.
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##
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import cvc5
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from cvc5 import Kind
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if __name__ == "__main__":
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slv = cvc5.Solver()
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slv.setLogic("QF_BV") # Set the logic
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# The following example has been adapted from the book A Hacker's Delight by
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# Henry S. Warren.
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#
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# Given a variable x that can only have two values, a or b. We want to
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# assign to x a value other than the current one. The straightforward code
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# to do that is:
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#
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#(0) if (x == a ) x = b;
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# else x = a;
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#
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# Two more efficient yet equivalent methods are:
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#
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#(1) x = a xor b xor x;
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#
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#(2) x = a + b - x;
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#
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# We will use cvc5 to prove that the three pieces of code above are all
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# equivalent by encoding the problem in the bit-vector theory.
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# Creating a bit-vector type of width 32
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bitvector32 = slv.mkBitVectorSort(32)
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# Variables
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x = slv.mkConst(bitvector32, "x")
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a = slv.mkConst(bitvector32, "a")
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b = slv.mkConst(bitvector32, "b")
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# First encode the assumption that x must be equal to a or b
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x_eq_a = slv.mkTerm(Kind.EQUAL, x, a)
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x_eq_b = slv.mkTerm(Kind.EQUAL, x, b)
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assumption = slv.mkTerm(Kind.OR, x_eq_a, x_eq_b)
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# Assert the assumption
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slv.assertFormula(assumption)
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# Introduce a new variable for the new value of x after assignment.
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# x after executing code (0)
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new_x = slv.mkConst(bitvector32, "new_x")
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# x after executing code (1) or (2)
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new_x_ = slv.mkConst(bitvector32, "new_x_")
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# Encoding code (0)
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# new_x = x == a ? b : a
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ite = slv.mkTerm(Kind.ITE, x_eq_a, b, a)
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assignment0 = slv.mkTerm(Kind.EQUAL, new_x, ite)
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# Assert the encoding of code (0)
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print("Asserting {} to cvc5".format(assignment0))
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slv.assertFormula(assignment0)
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print("Pushing a new context.")
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slv.push()
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# Encoding code (1)
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# new_x_ = a xor b xor x
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a_xor_b_xor_x = slv.mkTerm(Kind.BITVECTOR_XOR, a, b, x)
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assignment1 = slv.mkTerm(Kind.EQUAL, new_x_, a_xor_b_xor_x)
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# Assert encoding to cvc5 in current context
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print("Asserting {} to cvc5".format(assignment1))
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slv.assertFormula(assignment1)
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new_x_eq_new_x_ = slv.mkTerm(Kind.EQUAL, new_x, new_x_)
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print("Checking sat assuming:", new_x_eq_new_x_.notTerm())
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print("Expect UNSAT.")
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print("cvc5:", slv.checkSatAssuming(new_x_eq_new_x_.notTerm()))
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print("Popping context.")
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slv.pop()
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# Encoding code (2)
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# new_x_ = a + b - x
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a_plus_b = slv.mkTerm(Kind.BITVECTOR_ADD, a, b)
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a_plus_b_minus_x = slv.mkTerm(Kind.BITVECTOR_SUB, a_plus_b, x)
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assignment2 = slv.mkTerm(Kind.EQUAL, new_x_, a_plus_b_minus_x)
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# Assert encoding to cvc5 in current context
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print("Asserting {} to cvc5".format(assignment2))
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slv.assertFormula(assignment2)
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print("Checking sat assuming:", new_x_eq_new_x_.notTerm())
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print("Expect UNSAT.")
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print("cvc5:", slv.checkSatAssuming(new_x_eq_new_x_.notTerm()))
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x_neq_x = slv.mkTerm(Kind.EQUAL, x, x).notTerm()
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query = slv.mkTerm(Kind.AND, new_x_eq_new_x_, x_neq_x)
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print("Check sat assuming: ", query.notTerm())
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print("Expect SAT.")
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print("cvc5:", slv.checkSatAssuming(query.notTerm()))
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# Assert that a is odd
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extract_op = slv.mkOp(Kind.BITVECTOR_EXTRACT, 0, 0)
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lsb_of_a = slv.mkTerm(extract_op, a)
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print("Sort of {} is {}".format(lsb_of_a, lsb_of_a.getSort()))
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a_odd = slv.mkTerm(Kind.EQUAL, lsb_of_a, slv.mkBitVector(1, 1))
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print("Assert", a_odd)
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print("Check satisifiability")
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slv.assertFormula(a_odd)
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print("Expect sat")
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print("cvc5:", slv.checkSat())
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