[klibertp]

You should be familiar with the terms "essential" and "accidental complexity", right?

Lambda calculus, primitive recursion, Brainf*ck (Turing machine) are all models that discard all of the accidental complexity - all of it: syntax, higher-level constructs, abstractions, etc. What's left is the bare computation itself, amenable to analysis.

It's not meant to be practical - it's a research vehicle that shows what's possible and what's not possible in the realm of ideas, without looking at any real-world constraints (you would, in practice, want to see the result of your computation in less than 100 years - that's not the consideration when using one of the models).

So yeah, it's not something you use, it's something you learn to arm your brain with tools that will help you debug and write complex code that works. It's really worth spending a year or two deep-diving into these "pure theory CS" things; considering that you're going to be writing code for 20+ years (AI allowing), spending 10% of that time learning the foundations on which everything else rests is not that big of a task.

[brazzy]

I'm not sure the concepts of accidental vs. essential complexity really applies here. Is it really "accidental complexity" that is being removed when the result is harder to understand and less practically usable?

[klibertp]

"Essential" here means something that cannot, in any way, be further removed from consideration. In this view, things that simplify the understanding and make the program more practical are not essential - they are add-ons on top of the most primitive computational model(s). You can drastically simplify the reading of the lambda calculus by giving it direct support for integers, for example - however, you now polluted the model with an additional element that you need to describe and always keep in mind. Using Church encoding lets you get integers without introducing any new elements to the model, keeping the model simpler - but yes, the implementations of programs within that model will get much more complex to read.

[brazzy]

Yes, I get that. I just don't think that interpretation is a good fit for the concept, since that was formulated from the POV of practical usability and cognitive load.

Though... now that I think about it, maybe it does fit - it's all about the question "practical usability for what?"

I suppose that if what you actually want to do is model and reason about theoretical computability, then most things that make languages convenient to implement things in actually are accidental complexity!