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Let me advocate something even more interesting.

Take Haskell type, formally find its derivative, notice this new type is useful for traversing the original one and (optionally) explode your head.

(They call it zipper)

I just implemented a tree library using zippers without knowing this. Thanks for pointing this out.... .... .... shutdown initiated.

Zippers are really awesome data structures indeed. More people should use them. (But not for numerical computation)

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