I'd like to call out the work from Nada Amin in this area:

Dafny and verification-aware programming, including proof by induction to verify properties of programs (for example, that an optimizer preserves semantics). Dafny Sketcher (https://github.com/namin/dafny-sketcher)

Multi-stage programming, a principled approach to writing programs that write programs, and its incarnation in multi-stage relational programming for faster synthesis of programs with holes—with the theoretical insight that a staged interpreter is a compiler, and a staged relational interpreter for a functional language can turn functions into relations running backwards for synthesis. multi-stage miniKanren (https://github.com/namin/staged-miniKanren)

Monte Carlo Tree Search, specifically the VerMCTS variant, and when this exploration-exploitation sweet spot is a good match for synthesis problems. VerMCTS (https://github.com/namin/llm-verified-with-monte-carlo-tree-...), and Holey (https://github.com/namin/holey).

Nada is the best! Don't forget the mind bending https://dl.acm.org/doi/10.1145/3158140 (not quite on topic, but in the multi-stage rabbit hole)

Very Interesting; thanks for the pointer.

Nada Amin website - https://namin.seas.harvard.edu/