[Haskell-cafe] A question about algebra and dependent typing

[Henning Thielemann]

On Mon, 14 Jul 2008, Nathan Bloomfield wrote:

> There's something I want to do with Haskell, and after tinkering for a while
> I think it's not possible. Before giving up entirely, I thought I'd try this
> mailing list.
>
> I'm working on an abstract algebra library, using the "types are sets"
> strategy. For the algebraists out there, I'm trying to implement as much as
> I can of "Abstract Algebra" by Dummit & Foote in Haskell. I've got a Ring
> class definition that looks approximately like

It follows my usual pointer to NumericPrelude where some
algebraic structures are implemented including residue classes.
However a quotient by a general ideal is missing.
   http://darcs.haskell.org/numericprelude/src/Number/ResidueClass/Func.hs
   http://hackage.haskell.org/cgi-bin/hackage-scripts/package/numeric-prelude