Re: [Axiom-developer] Call for help

[Martin Baker]

On 27/07/15 11:22, address@hidden wrote:
> > 3) Some categories could have exactly the same signatures but differ
> > only in their axioms.
>
> Can you give me an idea of where this might happen?
> This isn't an obvious case.

Well I was thinking of something like AbelianGroup vs. Group but that’s 
not an example in Axiom because the '*' operator is changed to '+' so 
the signature changes. So I can't think of another example.

> > 4) Axioms are operator specific and not for the whole category. For
> > instance the lattice category inherits a commutativity axiom for join
> > and another commutativity axiom for meet. There is not just one
> > commutativity axiom. For more 'numerical' categories I guess we would
> > assume a commutativity flag applies to * and that + is always
> > commutative but relying on assumptions like that does not seem to
> > generalise well.
>
> Would this be covered by the current mechanism (using 'if' as in:
>
>     if $ has Monoid
>       x ** y == exp(y * log x)
>
> Or perhaps we can re-think the 'if' and move the conditional cases
> into their own categories. This would have the benefit of
> simpliying the compiler and the inheritance machinery. It would
> have the down side of expanding the category lattice.

When you are talking about the current mechanism is this: having an 
empty category for each attribute? It seems to me that this would 
require quite a lot of categories because we don't just need 
commutativity but meet-commutativity, join-commutativity and so on.

Martin