[Haskell-cafe] Mathematics in Haskell Re: Why the Prelude must die

[jasonm]

Jacques Carette wrote:
> 
>> perhaps i was mistaken in thinking that there is a group of 
>> math-interested
>> haskellers out there discussing, developing, and documenting the area? or
>> perhaps that group needs introductory tutorials presenting its work?
> My guess is that there are a number of people "waiting in the wings", 
> waiting for a critical mass of features to show up before really diving 
> in.  See
> http://www.cas.mcmaster.ca/plmms07/
> for my reasons for being both interested and wary).
> 
> Probably the simplest test case is the difficulties that people are 
> (still) encountering doing matrix/vector algebra in Haskell.  One either 
> quickly encounters efficiency issues (although PArr might help), or 
> typing issues (though many tricks are known, but not necessarily 
> simple).  Blitz++ and the STL contributed heavily to C++ being taken 
> seriously by people in the scientific computation community.  Haskell 
> has even more _potential_, but it is definitely unrealised potential.
> 

I am one of those mathematicians "waiting in the wings."  Haskell looked
very appealing at first, and the type system seems perfect, especially for
things like multilinear algebra where currying and duality is fundamental.
I too was put off by the Num issues though--strange mixture of sophisticated
category theory and lack of a sensible hierarchy of algebraic objects.

However, I've decided I'm more interested in helping to fix it than wait;
so count me in on an effort to make Haskell more mathematical.  For me that
probably starts with the semigroup/group/ring setup, and good
arbitrary-precision as well as approximate linear algebra support.

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