A Neighborhood of Infinity: Eleven Reasons to use Haskell as a Mathematician
As a mathematician, what programming language should you use when you need to do anything algorithmic? For some specific domains there are languages tailored for the task, for example Macaulay2 is great for some types of algebra. For general problems many turn to Mathematica or Maple. But although they are universal (in the sense of Turing) they're not great platforms for general purpose algorithm
Beautiful differentiation
March 2009 Appeared in ICFP 2009 Abstract Automatic differentiation (AD) is a precise, efficient, and convenient method for computing derivatives of functions. Its forward-mode implementation can be quite simple even when extended to compute all of the higher-order derivatives as well. The higher-dimensional case has also been tackled, though with extra complexity. This paper develops an implement
A Neighborhood of Infinity: Beyond Regular Expressions: More Incremental String Matching
In my last post I showed how to incrementally match long strings against regular expressions. I now want to apply similar methods to matching languages that can't be described by regular expressions. (Note that 'language' is just jargon for a set of strings that meet some criterion.) In particular, regular expressions can't be used to test a string for balanced parentheses. This is because we need
evan_tech -- powerset
For those of us who found this somwhat (but not totally) unaccessible, i'd recommend reading [[Schwartzian Transform]] to get into apprximately the right head-space, then [[Monads in functional programming]]. Oh man is that hard for me to grok, mostly because I haven't internalized the list monad. avva and I were puzzling over it too; here's how we figured it out. First, in terms of types, yes, it
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Welcome to Haskell for Maths
