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36 lines
1000 B
Python
36 lines
1000 B
Python
from cvc5.pythonic import *
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if __name__ == '__main__':
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# The following example has been adapted from the book A Hacker's Delight
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# by 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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x, a, b = BitVecs('x a b', 32)
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x_is_a_or_b = Or(x == a, x == b)
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# new_x0 set per (0)
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new_x0 = If(x == a, b, a)
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# new_x1 set per (1)
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new_x1 = a ^ b ^ x
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# new_x2 set per (2)
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new_x2 = a + b - x
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prove(Implies(x_is_a_or_b, new_x0 == new_x1))
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prove(Implies(x_is_a_or_b, new_x0 == new_x2))
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