On Sun, Feb 15, 2009 at 11:09 AM, Tillmann Rendel <[email protected]> wrote:
> Gregg Reynolds wrote: > >> Came up with an alternative to the container metaphor for functors that >> you >> might find amusing: http://syntax.wikidot.com/blog:9 >> > > You seem to describe Bifunctors (two objects from one category are mapped > to one object in another category), but Haskell's Functor class is about > Endofunctors (one object in one category is mapped to an object in the same > category). Therefore, your insistence on the alien Yeah, it needs work, but close enough for a sketch. 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. > universe being totally different from our own is somewhat misleading, since > in Haskell, we are specifically dealing with the case that the alien > universe is just our own. > The idea is that each type (category) is a distinct universe. The essential point about functors cross boundaries from one category to another. > > 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 > 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.
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