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#!/usr/bin/env python
#####################
## bitvectors.py
## Top contributors (to current version):
## Makai Mann, Aina Niemetz
## This file is part of the CVC4 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 through the Python API. This is a direct translation
## of bitvectors-new.cpp.
##
import pycvc4
from pycvc4 import kinds
if __name__ == "__main__":
slv = pycvc4.Solver()
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 xor b xor 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
bitvector32 = slv.mkBitVectorSort(32)
# Variables
x = slv.mkConst(bitvector32, "x")
a = slv.mkConst(bitvector32, "a")
b = slv.mkConst(bitvector32, "b")
# First encode the assumption that x must be equal to a or b
x_eq_a = slv.mkTerm(kinds.Equal, x, a)
x_eq_b = slv.mkTerm(kinds.Equal, x, b)
assumption = slv.mkTerm(kinds.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.
# x after executing code (0)
new_x = slv.mkConst(bitvector32, "new_x")
# x after executing code (1) or (2)
new_x_ = slv.mkConst(bitvector32, "new_x_")
# Encoding code (0)
# new_x = x == a ? b : a
ite = slv.mkTerm(kinds.Ite, x_eq_a, b, a)
assignment0 = slv.mkTerm(kinds.Equal, new_x, ite)
# Assert the encoding of code (0)
print("Asserting {} to CVC4".format(assignment0))
slv.assertFormula(assignment0)
print("Pushing a new context.")
slv.push()
# Encoding code (1)
# new_x_ = a xor b xor x
a_xor_b_xor_x = slv.mkTerm(kinds.BVXor, a, b, x)
assignment1 = slv.mkTerm(kinds.Equal, new_x_, a_xor_b_xor_x)
# Assert encoding to CVC4 in current context
print("Asserting {} to CVC4".format(assignment1))
slv.assertFormula(assignment1)
new_x_eq_new_x_ = slv.mkTerm(kinds.Equal, new_x, new_x_)
print("Checking entailment assuming:", new_x_eq_new_x_)
print("Expect ENTAILED.")
print("CVC4:", slv.checkEntailed(new_x_eq_new_x_))
print("Popping context.")
slv.pop()
# Encoding code (2)
# new_x_ = a + b - x
a_plus_b = slv.mkTerm(kinds.BVPlus, a, b)
a_plus_b_minus_x = slv.mkTerm(kinds.BVSub, a_plus_b, x)
assignment2 = slv.mkTerm(kinds.Equal, new_x_, a_plus_b_minus_x)
# Assert encoding to CVC4 in current context
print("Asserting {} to CVC4".format(assignment2))
slv.assertFormula(assignment2)
print("Checking entailment assuming:", new_x_eq_new_x_)
print("Expect ENTAILED.")
print("CVC4:", slv.checkEntailed(new_x_eq_new_x_))
x_neq_x = slv.mkTerm(kinds.Equal, x, x).notTerm()
v = [new_x_eq_new_x_, x_neq_x]
print("Check entailment assuming: ", v)
print("Expect NOT_ENTAILED.")
print("CVC4:", slv.checkEntailed(v))
# Assert that a is odd
extract_op = slv.mkOp(kinds.BVExtract, 0, 0)
lsb_of_a = slv.mkTerm(extract_op, a)
print("Sort of {} is {}".format(lsb_of_a, lsb_of_a.getSort()))
a_odd = slv.mkTerm(kinds.Equal, lsb_of_a, slv.mkBitVector(1, 1))
print("Assert", a_odd)
print("Check satisifiability")
slv.assertFormula(a_odd)
print("Expect sat")
print("CVC4:", slv.checkSat())
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