On 19/02/07, apfelmus@quantentunnel.de
Of course, comments, corrections and criticism are welcome!
The second section, then: 1) Formatting: IMO it'd look better if the formulae were left-aligned. 2) It's currently sitting a little oddly. I think the way to take this is to write an 'Algebra on Datatypes' article which explains what 1, 0, +, * etc. mean in the concept of types and also show some elementary results like distributivity of * over +, c.f. normal algebra, and so on. We would also need to explain isomorphisms as they're really important but we can't really assume them. Then we link to that article as essential background reading before tackling the zippers bit. We should also move the differentiation bit to the Algebra on Datatypes article, which would enable the focus in the zippers article to remain a bit more; at the moment there's something of a discourse at the beginning of the second section. Nearing the end of the AoD article we would link to the Zippers article and say 'Check out a really cool development of this'. 3) The notion of a 'one-hole context' isn't fully explained; it's an odd concept to begin with and we don't really develop it enough. We should say something like 'Imagine a datastructure parameterised over a type, like trees, lists etc.. If we were to remove one of the values of this type from the structure and replace it with a placeholder indicating we've just removed something, we obtain the one-hole context for that removed object.', then back it up with examples, like: data ListHole a = LH [a] a [a] data TreeHole a = ... Then we launch into the discussion about the algebra, then we say something like: "Look! The zipper for an A is just the one-hole context plus an A! You may have already spotted that from our examples of one-hole contexts earlier. It also makes sense; the one-hole context is a structure missing an A, so couple that with an A and you can get the original structure back, but this one object is singled out, focussed. Sounds like a zipper." Let me know what you think of these ideas. I should also point out, as Eric commented, that this is a really creative and different tutorial; it's got its limitations but I think this could be another great 'Killer article' to add to our repertoire. Great work! -- -David House, dmhouse@gmail.com