recursion schemes

This is the third post in a three-post series. In the first post we developed a stack-safe, ergonomic, and concise method for working with recursive data structures (using a simple expression language as an example). In the second post we made it fully generic, providing a set of generic tools for expanding and collapsing any recursive data structure in Rust.

In this post we will see how to combine these two things - expanding a structure and collapsing it at the same time, performing both operations in a single pass. In the process, we will gain the ability to write arbitrary recursive functions over traditional boxed-pointer recursive structures (instead of the novel RecursiveTree type introduced in my previous post) while retaining stack safety.

Previously, we introduced a method for writing performant stack safe recursion in Rust for a single recursive data structure. This post uses the same ideas to implement a single recursion backend that can collapse or expand any recursive data structure.

This is a post about writing elegant and performant recursive algorithms in Rust. It makes heavy use of a pattern from Haskell called recursion schemes, but you don’t need to know anything about that; it’s just an implementation detail. Instead, as motivation, I have benchmarks showing a 14-34% improvement over the typical boxed pointer representation of recursive data structures in Rust.