tag:blogger.com,1999:blog-11295132.post115765077990439901..comments2016-09-24T21:29:58.885-07:00Comments on A Neighborhood of Infinity: Learn Maths with HaskellDan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-11295132.post-1157793912217509512006-09-09T02:25:00.000-07:002006-09-09T02:25:00.000-07:00Hm. Sounds like something I'm working on (I'm usin...Hm. Sounds like something I'm working on (I'm using ML rather than Haskell, with an intent to port it to OCaml, but there's not much difference in the implementations really.)<BR/><BR/>Someone I know has a database of topological spaces, mostly extracted from the book "Counterexamples in Topology". There are various nice properties of topological spaces which are best described by assigning cardinal numbers to them. So it occurred to me that it would be really quite nice to expand the database to include these properties.<BR/><BR/>Which means that one needs the computer to be able to deal with cardinal numbers (ok, you could just represent them as strings. But that would suck, as it might get confused between max{ aleph_2, 2^aleph_0 } and max { 2^aleph_0, aleph_2 } and I wouldn't for example be able to search for all spaces with weight <= aleph_7). <BR/><BR/>This turns out to be harder than it looks. <BR/><BR/>I'm currently treating it as an algebraic datatype with constructors pow, succ, max, min and aleph0 and then applying various redunction rules based on these. It's rather fiddly, and will probably be embarassingly inefficient when it's finished. Also it doesn't handle things like Aleph_omega, and won't until I get around to writing an ordinal datatype and reimplementing this entirely. :-)David R. MacIverhttp://www.blogger.com/profile/12893796777558636623noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-1157668568478630312006-09-07T15:36:00.000-07:002006-09-07T15:36:00.000-07:00There is The Haskell Road to Logic, Maths and Prog...There is <A HREF="http://homepages.cwi.nl/~jve/HR/" REL="nofollow">The Haskell Road to Logic, Maths and Programming</A>.Dave Menendezhttp://www.blogger.com/profile/10628628100970152906noreply@blogger.com