This introduction to this paper explains the motivation:

https://dl.acm.org/doi/pdf/10.1145/3704253.3706138

Tree Calculus is an alternative to lambda calculus that is capable of doing meta-theory without having to construct or bolt on something else entirely.

If lambda calculus provides a theoretical foundation for a language like Lisp. Tree calculus provides a theoretical foundation for a Lisp with a macro system that is fundamentally part of the core calculus.

You don’t have to write parsers and other stuff to do meta programming. It’s fundamentally built in and the paper I posted above explores how to construct type systems as a library, not as something that is outside of the runtime environment.

Here’s what’s really cool about it too: Just like lambda calculus, you can evaluate tree calculus with pencil and paper.

It’s very slick.