[bts]

Indeed they call for new names, as they encompass far more than iterators.

If you read a bit more about them, I think you will be surprised to see the breadth of what these abstractions can be used for. To start, they've been used to build a new compositional foundation for game theory[1], and they can be used to model gradient-based learning in machine learning[2].

As for their simpler applications as getters and setters, they are programmable in the sense that you can think of lens/prism types as interfaces that can be implemented arbitrarily. So you can create your own lenses and combine them like legos to construct new, "bigger" getters and setters from the smaller components.

[1] https://arxiv.org/pdf/1603.04641 [2] https://arxiv.org/abs/2103.01931

EDIT: fixed typo

[CyberDildonics]

This thread is about traversing a tree. At what point do we take a step back and think that iterating through a data structure and "building new compositional foundations for game theory" shouldn't be conflated together?

When does someone give up on the pagentry of programming and just get something done by looping through data instead of "constructing getters and setters to model gradient based machine learning".

It really seems like the straight forward way of doing things is to make simple iteration and worry about the game theory after that is all figured out.

[throwaway17_17]

I do get, and to some extent sympathize with, your position. But the comments to the article are, in large part, fundamentally addressing a higher level of abstraction than the more narrow scope of the article’s premise. As several commenters have referenced, traversing a tree in a ‘simple’ and narrow manner is addressed at the appropriate level of abstraction using already established mechanisms, particularly in Haskell using Traversable (a typeclass with a standardized implementation for trees). The discussion of Optics and Lenses are more of a side discussion about the syntax and implementations of a more broad set of data structures than merely trees.

I think your comment is valuable in spirit because it could bring a more thorough discussion of the creation or popularization of a syntactically clean and a shift of the idiomatic-ness of such a solution to traversing trees. Leaving the more abstract and general Optics discussion to be a side dish for commenters to discuss as well.

Also, just a nitpick, but traversing a tree is a broader topic than iteration. Iteration implies, both colloquially and formally, performing a computation on each element of a data structure, while traversal is a more general algorithm that could be the basis of iteration, but may also be more akin to a search through the data structure without expectation of performing computation until the searched for ‘member’ is returned from the traversal. So it’s not an apples-to-oranges comparison with your conflation of iteration and traversal, but does seem a little like Canis Familiaris-to-Mammal comparison.

[CyberDildonics]

I read your whole comment but I'm still not getting where the actual rubber meets the road. If I have a tree data structure what am I missing? What is it that I can't do that makes this extreme iteration complexity worthwhile? To me, having simple access to the data structure is enough because that's what I want a data structure for.