http://www.kennknowles.com/blog Mathematics, Haskell, and little bit of Linux Sat, 12 Jul 2008 20:17:23 +0000 http://backend.userland.com/rss092 en Here I am trying to crank out something for the ICFP Programming Contest and I have a huge host of OpenGL problems with my new laptop. This stuff should come in handy for all those people out there with a Lenovo R61 running Gentoo Linux with Mesa 6.5... all ... http://www.kennknowles.com/blog/2008/07/12/debugging-mesa-dri-for-the-intel-i965-on-a-lenovo-r61/ I recently gave a little demonstration entitled "What is Defunctionalization?" for UCSC TWIGS (the acronym, stolen from a similar seminar in the the U. Mass. math department, stands for The "What Is ... ?" Graduate Seminar). The inspiration for this talk was just to present what I'd learned after ... http://www.kennknowles.com/blog/2008/05/24/what-is-defunctionalization/ The call is out for submissions to the next issue of The Monad.Reader! To get an idea of the content (and because Don Stewart told us all to read every past issue) I cracked open Issue 10, which has a nice tutorial by B Pope on the GHCi debugger. But having ... http://www.kennknowles.com/blog/2008/05/10/debugging-with-open-recursion-mixins/ As an exercise, since my reading group was discussing model checking this week, I implemented the classic model checker for CTL specifications from the 1986 paper Automatic Verification of Concurrent Systems Using Temporal Logic Specifications by EM Clarke, EM Emerson, AP Sistla. The "efficient algorithm" presented in the paper is, upon reflection, ... http://www.kennknowles.com/blog/2008/05/07/ctl-model-checking-in-haskell-a-classic-algorithm-explained-as-memoization/ I recently got a tablet to input handwritten math for slideshow presentations, but instead of using a note-taking program (Jarnal, Xournal, Gournal) I decided that I wanted the full power of image manipulation of a program like Gimp or Inkscape. Neither of these, though, has the level of support for multi-page ... http://www.kennknowles.com/blog/2008/04/20/using-haxml-to-make-a-pdf-slideshow-from-an-inkscape-svg/ I'm reading the very fun Measure, Topology, and Fractal Geometry by GA Edgar, and thought I'd hack up some of the examples in Haskell. So this post implements cursor graphics in OpenGL in (I think) DSEL style, demonstrating the StateT and Writer monad gadgets from the standard library and a ... http://www.kennknowles.com/blog/2008/04/16/drawing-fractals-in-haskell-with-a-cursor-graphics-dsel-and-a-cute-list-representation/ This is a question posed in my randomized algorithms class. If you are routing in a network whose connectivity looks "more or less" like a convex figure, what does the congestion look like? A quick way to make an educated guess is to draw a bunch of random ... http://www.kennknowles.com/blog/2008/03/23/using-opengls-blending-to-visualize-congestion-in-convex-routing-in-haskell/ I read a lot, perhaps to the detriment of my eventual graduation plans. Recently, I've been enjoying books of "recreational mathematics." This is a combined review of all such books I've read recently. http://www.kennknowles.com/blog/2007/12/29/reading-cluster-recreational-mathematics/ The Knuth-Bendix completion procedure (when it succeeds) transforms a collection of equations into a confluent, terminating rewrite system. Sometimes the procedure fails, and sometimes does not terminate, but The Handbook of Computational Group Theory by D Holt remarked that even in this case it generates an infinite set of rewrite rules that are complete, ... http://www.kennknowles.com/blog/2007/12/20/infinite-lazy-knuth-bendix-completion-for-monoids-in-haskell/ Any isometry of the plane has a unique normal form as the composition of a translation, rotation and reflection. This note computes this normal form and tests the implementation using the QuickCheck automated testing tool for Haskell. To generate random test data, I use another characterization of isometries as ... http://www.kennknowles.com/blog/2007/12/03/calculating-the-reflect-rotate-translate-normal-form-for-an-isometry-of-the-plane-in-haskell-and-verifying-it-with-quickcheck/