Thursday, November 11, 2004

Bananas, Lenses, Envelopes, and Barbed Wire --- Finale

Finished the Bananas and Lenses paper on the weekend, along with another on FRP that I'll summarise later. Section 4 takes the previous work based on Lists from section 2 and combines it with the category-theory results from section 3 to develop a theory of cata/ana/hylo/para -morphisms over arbitary datatypes. Section 5 is a very brief extension to parametric types.

Unfortunately I simply don't have enough category theory to follow the discussion properly, let alone explain it here. I think it is probably time to make another visit to Amazon and pick up a book or two on category theory. I'm thinking probably Pierce's introduction, and possibly Crole's "Categories for Types" on the basis of the review there. I've already read Pierce's intro, and it is mercifully brief and yet even from a quick reading I found I remembered enough to follow fragments of the paper. Unfortunately I found it too brief to allow me to learn enough to follow the rest :/.

Anyway, this paper was just for fun; fun was had; and I come away with a fresh perspective on recursion. That counts as a win for me.

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