Jan Skibinski writes:
>
> It appears to me that we have reached some impasse
> in a design of basic mathematical structure for
> Haskell 2. Sergey's proposal "Basic Algebra Proposal"
> is there, but for variety of reasons (a language
> barrier being probably one of them) it does not seem to
> reverberate on this group.
>
> [...]
>
> Wouldn't it be useful to start a discussion on the future
> of math structures in Haskell 2 with something similar
> [to http://www.hep.upenn.edu/~max/toe.html] on hand? [...]
Hi. Here's my 2c worth.
I like the theory of the Basic Algebra Proposal.
In practice, it needs the support of some language features which are
research topics in their own right, such as overlapping instances, and
laws.
I'm uncomfortable about using a Haskell class to represent algebraic
groups. The reason is that group-ness is a property of a base set
*and* a function, but an instance declaration in Haskell can only
specify the type (i.e. the base set). Similarly, I wouldn't want to
equate that Theory Of Everything diagram with a Haskell class
hierarchy.
Here's an example of something which could be done, without major
language extensions: insert a partial ordering class between Eq and
Ord. (It's something I've advocated before, so I won't dwell on it
this time.)
Regards,
Tom
