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A Knownbits Abstract Domain for the Toy Optimizer, Correctly
After Max' introduction to abstract interpretation for the toy optimizer in the last post, I want to present a more complicated abstract domain in this post. This abstract domain reasons about the ind
We'll spend a significant part of the post convincing ourselves that the abstract domain transfer functions that we're writing are really correct, using both property-based testing and automated proofs (again using Z3). The state space for the arguments of a binary transfer function is 3**64 * 3**64, and if only a small part of that contains wrong behaviour it would be really unlikely for us to find it with random tests by chance. Those tests aren't strict proofs, because they rely on generating random abstract values, but they can still be valuable (not for the transfer functions in this blog post, which are all optimal).
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