You'd be interested in Grammar-Guided Genetic Programming. It's tangential, but along similar lines. You generate a grammar of what a successful program looks

You'd be interested in Grammar-Guided Genetic Programming. It's tangential, but along similar lines. You generate a grammar of what a successful program looks like, and then that grammar can spit out programs of that "shape" ad infinitum. The main difference is that you don't have the same verifiable guarantees as logic-al solutions because the grammar is generated and evolved over time instead of induced from a ruleset.