[lapinot]

> so not exactly the kind of thing you'd notice making a document

By "user interface" I mean (like Martin, in the linked video) the surface language, the way you interact with TeX, its syntax and how it presents itself to the user, the programming model. So definitely the kind of thing you'd notice making a document. Leaky abstractions and footguns are basically everywhere when you write a big LaTeX document.

> I mean TeX is basically an overpowered lambda calculus with a focus on text markup and generation.

No, lambda calculus has capture-avoiding substitution, aka hygienic macro expansion if you will. TeX has naive substitution. By the way, macro expansion is typically CBN, which is very much a rare and weird evaluation order (yes, Haskell, i know). TeX is much closer to some kind of assembly language for a virtual machine.