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
powerset
Beautiful Haskell implementation of math's "power set": import Control.Monad powerset :: [a] -> [[a]] powerset = filterM (const [True, False]) And powerset [1,2,3] produces [[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3],[]]. Oh man is that hard for me to grok, mostly because I haven't internalized the list monad. (It helped me to write out the definition of filterM, which has type Monad m => (a -> m Bool)
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Welcome to Haskell for Maths
