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Aside from the practical interest in defining zippers as noted in another response, isn't it enough that there be this interesting and (by many, anyway) unsuspected correspondence, that holds fairly deep down? I mean---taking the Taylor series of a type! After all, we are told that "anything that gratifies one's intellectual curiosity" is suitable for an HN submission, no?

Well, the correspondence sounds interesting but if remains just on the level of the unexplained, it is hard to see it really being interesting.

If you define a function, call it a "type" and then take the Taylor series of that function, how mind blowing is that really?

My point is that without a motivation to these constructions, they are just constructions. It may be everyone in-the-know understands the motivation already, knows why this thing labeled type really has a "deep" relation to an abstract type-thing. Fair enough but I'm just saying if one omits this motivation, your whole exercise doesn't look interesting to those not in-the-know, OK?

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