[Haskell-cafe] Re: [Haskell] Math behind Haskell

[Derek Elkins]

On Sun, 2007-09-23 at 20:03 -0400, Cale Gibbard wrote:
> On 23/09/2007, Neil Mitchell <ndmitchell at gmail.com> wrote:
> > Hi
> >
> > The haskell-cafe@ mailing list is more appropriate for messages such
> > as this. haskell@ is just for announcements (it should be called
> > haskell-annouce@ !)
> >
> > >  * Lambda calculus - the basis of functional languages
> > >
> > >  * Category theory - where all these mysterious things like monads,
> > > arrows, and functors come from.
> >
> > I'd add:
> >
> > * Discrete Maths - booleans, relations, functions etc.
> >
> > * Type theory
> >
> > * Logic programming (Prolog)
> >
> > * Semantics
> >
> 
> Although it might technically be covered by "Discrete Maths", I'd like
> to add algebraic and enumerative combinatorics to the list. That is,
> the sort of mathematics where one deals with bijective decompositions
> of combinatorial structures and generating series (generating
> functions). The overall picture is that you put collections of
> discrete structures in correspondence with algebraic objects of some
> sort, typically the elements of a suitable ring, and make use of that
> correspondence to move results back and forth.
> 
> I've found that a lot of the recent stuff like the theory of zippers
> and differentiation of data structures directly reflects the sort of
> combinatorial operations which go on in algebraic combinatorics. (See,
> for instance, "Combinatorial Enumeration", by Jackson and Goulden, or
> Joyal's combinatorial species.) No doubt there are more ideas which
> could be fruitfully imported from there.

A few words by me on this general topic on LtU:
http://lambda-the-ultimate.org/node/2342#comment-34980