You can think of a calculus as a mathematical system one can use to define the essential computational basis for how a programming language or a runtime works mathematically.

Lambda calculus is often the foundation for functional programming languages, but lambda calculus is also a mathematical system you can calculate things with pencil and paper.

What makes lambda calculus interesting is it’s a relatively simple mathematical system where EVERYTHING is defined as a function. I’m serious. Imagine a programming language where you don’t have numbers, bools, if statements, while loops, gotos, etc.

You only have functions. All functions accept one argument (a function) and they always return functions.

Tree calculus is like lambda calculus, but it takes the idea a bit further. Not only can tree calculus do all this stuff where you create functions from other functions, tree calculus is fundamentally capable of reflecting on itself in a way that allows it to easily understand and transform its own interpreter.

In other words, if you base a programming language on tree calculus, your programming language or interpreter will allow you to create programs that can reflect on and transform other programs just like it was any other piece of data.

It’s pretty remarkable, especially when you find out how simple a core tree calculus based language can be implemented.

A lambda calculus variant Quite niche, so people who read about it know what a calculus is