I just came across Bob Palais’ article from 2001, entitled Pi is wrong! He makes some very interesting points; however the notation he has chosen is rather unfortunate. The definition of his three-legged ‘2π’ is given as: \def \newpi{{\pi\mskip -7.8 mu \pi}} This, when rendered by pdfLaTeX, gives: Zoomed in, we can see the problems [...]
Since XSLT is basically a pattern-matching functional programming language, we should be able to use it to compute. I’m going to use it to implement one of the most basic functions: Peano-style addition. First of all we have to have an idea of what the numbers look like. We want to simulate this in XSL: [...]
Suppose we have a functor. Let’s call it “My Functor”, because that’s a nice friendly name. I’ll call it for short. Now, a functor is—according to higher sources—something which takes any type to a type . Let’s see how we can accomplish that with our functor, using Haskell code: data MyFunctor a = Construct a [...]
After reading a recent post on Good Math, Bad Math concerning surreal numbers, I got to thinking about how to model these in Haskell. I came up with the following formulation: data Surreal = Zero | Plus Surreal | Minus Surreal … which also seems very similar to the usual construction for natural numbers: data [...]