Maddy Bowers

Zeng Ren, Maddy Bowers, Xinyi Guan et al.

Humans can acquire a highly structured intuitive understanding of musical patterns, yet these patterns often require multiple iterations of reflection and re-listening to internalize fully. To capture such an internalization process, we present a computational model for the learning of jazz harmonic patterns based on library learning. Given a corpus of harmonic progressions, our model searches over a space of programs composed of primitive harmonic relations in order to discover concise generative explanations of the corpus. The model first enumerates possible programs for each piece, and then jointly learns a library of harmonic patterns and refactored programs. To efficiently navigate the vast joint space of programs and libraries, we integrate deductive parsing with library learning on e-graphs. We explore how well our model captures aspects of human musical pattern learning by evaluating the intuitiveness of both programs and libraries, as well as similarities to human-written harmonic derivations.

Zeng Ren, Maddy Bowers

Folding over a recursive data structure (also known as "catamorphism") is an essential operation in functional programming. It allows one to declaratively define a recursive computation by focusing on how solutions of subproblems are combined into the solution of the parent problem. Folding in the context of e-graphs can have several benefits. Not only do we get memoization for free, but also computation is drastically reduced since the subproblems are defined over e-classes as opposed to concrete sub-terms. This short report presents our initial attempt at defining and implementing catamorphism, a general notion of a fold, in pure egglog. We discuss a reusable implementation trick to stage the inference rules so that there is no re-propagation of updated values.