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Michi’s blog » Computational Group Theory in Haskell (1 in a series)

 Computational Group Theory in Haskell (1 in a series)

  • October 18th, 2006
  • 3:37 pm

This term, I’m listening to a lecture course on Computational Group Theory. As a good exercise, I plan to implement everything we talk about as Haskell functions as well.

The first lecture was mainly an introduction to the area, ending with a very na

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Are you sure you want identity :: n -> a rather than identity :: a

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  • Michi
  • October 19th, 2006
  • 14:56

Actually, I do, since I view every group as a subgroup of some symmetric group. The identity is a function taking as argument which symmetric group I operate in, and returning the appropriate identity element.

Sure, translating group axioms straight off would make identity :: a be much saner; but on the other hand, I write the group type class with a specific use in mind.

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Hang on, I’m sure there was meant to be more of that comment, to the effect that what you really want is for each symmetric group to be a type in its own right. But then you’d need types parametrized by integers, which you can do in C++ or Ada, but not (IIRC) in Haskell. I remember running into this problem a while ago while implementing the algorithms from my Computational Methods in Finite Fields course.

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  • Michi
  • October 19th, 2006
  • 15:38

Parametrizing the type “Subgroup of a symmetric group” would make a lot of things much easier; handling the cycle representation would look different, as would the multiplication code. But I’m not very much inclined to start writing things like
newtype Permutation3 = ..., and Haskell does not, at the current stage, seem to allow parametrized types.

There may possibly be some extension floating around in an alpha version capable of it though…

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  • Luis
  • October 23rd, 2014
  • 8:13

I would like to use Haskell to develop some computational group modules and I am very interested in what you did time ago. I cannot find it in this blog, just the first few lines. Do you have it in another blog?
I am learning Haskell and would like to use it for managing groups and group rings.
Thank you.

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