tag:blogger.com,1999:blog-11295132.post1113368024964255900..comments2016-09-24T21:29:58.885-07:00Comments on A Neighborhood of Infinity: Tries and their DerivativesDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-11295132.post-37246724535421781542009-02-22T23:38:00.000-08:002009-02-22T23:38:00.000-08:00BlackMeph: actually, to reply even LATER in the ga...BlackMeph: actually, to reply even LATER in the game:<BR/><BR/>Another way to look at the tabulate/apply functions is that they indicate that a Trie is a representable functor.<BR/><BR/>http://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/Control-Functor-Representable.html<BR/><BR/>http://en.wikipedia.org/wiki/Representable_functorEdward Kmetthttp://www.blogger.com/profile/16144424873202502715noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-11563064563671526082008-11-07T10:21:00.000-08:002008-11-07T10:21:00.000-08:00I'm sorry for commenting on this so late in the "g...I'm sorry for commenting on this so late in the "game" - what can I say, I'm a slow reader.<BR/><BR/>Anyway, isn't that 'tabulate' function in the same form as Yoneda's Lemma? Or am I missing something (not surprising)?BlackMephhttp://www.blogger.com/profile/02745499320156194052noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-512704615862874462007-10-10T13:44:00.000-07:002007-10-10T13:44:00.000-07:00Can you do something even simpler...unordered pair...Can you do something even simpler...unordered pairs (over a set; that is, not a recursive thing)?<BR/><BR/>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). <BR/><BR/>Of course, once you can do arbitrary pairs you can use it recursively.<BR/><BR/>Really, I think the best you can do is say:<BR/><BR/> X = 1 + unorderedpair(X)<BR/><BR/>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.Mitchhttp://www.blogger.com/profile/06352106235527027461noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-5033630802811635682007-10-05T15:13:00.000-07:002007-10-05T15:13:00.000-07:00To obtain overlines in HTML:<span style="text-d...To obtain overlines in HTML:<BR/><span style="text-decoration:overline">your-text-here</span>Porgeshttp://www.blogger.com/profile/02727258157936734796noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-26266732783774981102007-09-13T02:45:00.000-07:002007-09-13T02:45:00.000-07:00Hey sigfpe,This is Caroline from SocialRank.I am t...Hey sigfpe,<BR/><BR/>This is Caroline from SocialRank.<BR/><BR/><BR/>I am trying to get in touch with you but couldn't find your email address.<BR/><BR/><BR/>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.<BR/><BR/><BR/>Can you get back to me with your email address.<BR/><BR/><BR/>Mine is caroline@mathbloggers.com<BR/><BR/>Kind regards,<BR/><BR/><BR/>Caroline<BR/><BR/>www.SocialRank.comCarolinewww.socialrank.comnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-66154277272648710932007-09-09T14:47:00.000-07:002007-09-09T14:47:00.000-07:00zednenem,Cool! When I get some time I'll try to ad...zednenem,<BR/><BR/>Cool! When I get some time I'll try to adapt it to the anti- or sub-diagonal.sigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-64255285240598302922007-09-09T09:07:00.000-07:002007-09-09T09:07:00.000-07:00I have some code that implements a generic trie us...I have some code that implements a generic trie using Hinze's Generics for the Masses technique.<BR/><BR/>I've posted a <A HREF="http://hpaste.org/2642" REL="nofollow">variation that supports apply/tabulate</A>. (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.)zednenemhttp://www.blogger.com/profile/03938901010371818852noreply@blogger.com