Re: [Axiom-developer] BINGO, Curiosities with Axiom mathematical structures

[Gabriel Dos Reis]

"Bill Page" <address@hidden> writes:

| Martin,
| 
| I think you have a rather beautiful idea... but I see some
| problems.
| 
| On March 9, 2006 11:08 AM you wrote:
| > 
| > I am satisfied now:
| > -----------------
| > #include "axiom"
| > 
| > MyMonoid(T: Type, m: (T, T) -> T): Category == with {
| >    square: T-> T;
| >    default {square(t: T): T == m(t, t)}
| > }
| 
| This definition of the category MyMonoid looks quite strange
| because it does not export any binary operation!
| 
| Also, I think you should write:
| 
|    square: % -> %;
|    default {square(t: %): % == m(t pretend T, t pretend T) pretend %
| 
| although apparently the compiler does not worry about this since
| your representation of the domain MyWord below is the same as the
| operation that you pass to MyMonoid.

we should also probably find a way to minimize the "pretend"s :-)

-- Gaby