Synthesizing Loop-Free Programs with Rust and Z3

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2021-06-14 19:30:10

This post makes extensive use of math symbols, and uses MathJax.js to render them, therefore I recommend enabling JavaScript.

Automatically finding a program that implements a given specification is called program synthesis. The main difficulty is that the search space is huge: the number of programs of size \(n\) grows exponentially. Naïvely enumerating every program of size \(n\), checking whether each one satisfies the specification, and then moving on to programs of size \(n+1\) and so on doesn’t scale. However, the field has advanced by using smarter search techniques to prune the search space, leveraging performance improvements in SMT solvers, and at times limiting the scope of the problem.

In this post, I’ll explain one approach to modern program synthesis: counterexample-guided iterative synthesis of component-based, loop-free programs, as described in Synthesis of Loop-Free Programs by Gulwani et al. We’ll dissect exactly what each of those terms mean, and we’ll also walk through an implementation written in Rust that uses the Z3 solver.

I hope that people who are unfamiliar with program synthesis — just like I was not too long ago — get a little less unfamiliar and learn something new about the topic. I’ve tried to provide many examples, and break down the dense logic formulas from the paper into smaller, approachable pieces.