Really fun question. One partial idea: you can give the space of programs a finite group structure by using ideas from https://en.wikipedia.org/wiki/Reversible_computing …. And then take a discrete Fourier transform over a finite group. But what does a linear combination of programs mean, initially? Hmm.https://twitter.com/warrenm/status/997326005411897344 …
And that question is related the thought that provoked this: how can one preserve well-formedness (and ideally some sort of useful semantics) across transformations in the program "frequency" domain?
