Comments on A Neighborhood of Infinity: Tries and their Derivatives

BlackMeph: actually, to reply even LATER in the ga...

2009-02-22T23:38:00.000-08:00

BlackMeph: actually, to reply even LATER in the game:

Another way to look at the tabulate/apply functions is that they indicate that a Trie is a representable functor.

http://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/Control-Functor-Representable.html

http://en.wikipedia.org/wiki/Representable_functor

I'm sorry for commenting on this so late in the "g...

2008-11-07T10:21:00.000-08:00

I'm sorry for commenting on this so late in the "game" - what can I say, I'm a slow reader.

Anyway, isn't that 'tabulate' function in the same form as Yoneda's Lemma? Or am I missing something (not surprising)?

Can you do something even simpler...unordered pair...

2007-10-10T13:44:00.000-07:00

Can you do something even simpler...unordered pairs (over a set; that is, not a recursive thing)?

I have trouble seeing this in terms of an algebra (er..I can't), but it is certainly 'computable' (one can rank and unrank these kinds of pairs).

Of course, once you can do arbitrary pairs you can use it recursively.

Really, I think the best you can do is say:

X = 1 + unorderedpair(X)

where 'unordered pair' is a blackbox that (somehow) computes the set of unordered pairs of X. google for Flajolet, Salvy, and van Cutsem, or look at the maple package for combinatorial structures.

To obtain overlines in HTML:
<span style=&qu...

2007-10-05T15:13:00.000-07:00

To obtain overlines in HTML:
<span style="text-decoration:overline">your-text-here</span>

Hey sigfpe,

This is Caroline from SocialRan...

2007-09-13T02:45:00.000-07:00

Hey sigfpe,

This is Caroline from SocialRank.

I am trying to get in touch with you but couldn't find your email address.

We will index your blog posts as part of our content filter. I'd like to send you an invite to a beta preview of our new Web 2.0 site.

Can you get back to me with your email address.

Mine is caroline@mathbloggers.com

Kind regards,

Caroline

www.SocialRank.com

zednenem,

Cool! When I get some time I'll t...

2007-09-09T14:47:00.000-07:00

zednenem,

Cool! When I get some time I'll try to adapt it to the anti- or sub-diagonal.

I have some code that implements a generic trie us...

2007-09-09T09:07:00.000-07:00

I have some code that implements a generic trie using Hinze's Generics for the Masses technique.

I've posted a variation that supports apply/tabulate. (The original wouldn't work because it's defined for partial maps, i.e. apply would have type Trie a t => t b -> a -> Maybe b.)