Pascal nested procedures are pretty easy to parse and if they're defined before the `var` block then you don't need to worry about non-local state modification (apart from the parameters, but modifying parameters is unusual).
First-class nested functions with variable capture are harder to understand. Nested functions in e.g. JS are more like object construction than function definition, and it's generally expected that such nested functions will be capturing state from the enclosing context.
Standard Pascal permitted outer scope variable access combined with downward funargs - the nested functions could be passed to other functions, but could not be stored in variables or returned as arguments. This reduces the non-local effects, and handily doesn't require a GC to ensure memory safety, since the captured state can stay on the stack, because the nested function won't outlive the frame.
For nested decomposition of a problem, I'm more of a fan of Pascal-style nested procedures than nested function expressions like in JS. Idiomatically, one expects function expressions to capture state, while nested procedures are just more procedural decomposition.
That's probably not what you mean to say, but I don't find much to really discuss here.
I do like local functions in Python, but I don't see a huge difference from having the called function right below the calling one.
I.e. I wouldn't be inside a particular function of a particular module if I didn't have to know something about its implementation. There's a good chance I need to understand all of it at the level of abstraction of the module (often because I'm supposed to change something about it). Making that less painful leads to better and less bug-inducing experience.
Elsewhere[0], 'usrusr brings attention to nested functions, lack of which I see as a huge factor contributing to overeager splitting of code. With nested functions, you can have "best of both worlds" - a function whose implementation is divvied up into well-named pieces, while keeping those same pieces in the correct conceptual place, close to where they're used, and restricted from polluting unrelated code.
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[0] - https://news.ycombinator.com/item?id=18773691