Gregg Reynolds wrote:
BTW, I'm not talking about Haskell's Functor class, I guess I should
have made that clear. I'm talking about category theory, as the
semantic framework for thinking about Haskell.
In that case, I even less see why you are not introducing category
theory proper. Certainly, if one wants to use a semantic framework for
thinking about something, one should use the real thing, not some
metaphors.
The idea is that each type (category) is a distinct universe. The essential
point about functors cross boundaries from one category to another.
What are the categories you are talking about here?
Moreover, you are mixing in the subject of algebraic data types (all we
know about (a, b) is that (,), fst and snd exist).
It's straight out of category theory. See Pierce
http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=7986
Which part specifically?
Personally, I do not see why one should explain something easy like
functors in terms of something complicated like quantum entanglement.
The metaphor is action-at-a-distance. Quantum entanglement is a vivid way
of conveying it since it is so strange, but true. Obviously one is not
expected to understand quantum entanglement, only the idea of two things
linked "invisibly" across a boundary.
How does the fact that a morphism exists between two objects in some
category link these objects together? It doesn't change the objects at
all. In your own words: How can action (at-a-distance) be about
mathematical values?
Tillmann
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