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Well, when you really boil it down, these are the fundamental operations.

At least, I believe that is true. Someone stronger in CS theory could come along and verify/correct that statement.

This paper [1], for example, appears to argue that FOLD (foldr in particular) is universal, meaning that there is only one way to move through a list and resolve it to a single value. In other words, you may have some other algorithm that you think is not a FOLD, but if it moves through a list and resolves it to one value, then your algorithm is FOLD. (I say the paper "appears" to claim that, because in all honesty there's about 10-15% of the paper that I didn't fully grok).

I suspect that applies to map/filter/etc. After all, if you look at their definitions, they contain nothing but the essence of the operation (map/filter/fold/etc) itself.

So, map/filter/fold/etc are THE operations on lists.

[1] http://www.cs.nott.ac.uk/~gmh/fold.pdf

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