Since this is a discussion of Monad and not categories as parameters
as such, consider instead
Monad(A: SetCategory, M: SetCategory -> SetCategory): Category == with {
unit: A -> M A;
mult: M M A -> M A;
}
Regards,
Bill Page
On Wed, Nov 9, 2011 at 10:57 AM, Gabriel Dos Reis wrote:
> Bill Page <bill.p...@newsynthesis.org> writes:
>
> | On Wed, Nov 9, 2011 at 2:45 AM, Ralf Hemmecke wrote:
> | > Looking at http://en.wikibooks.org/wiki/Haskell/Category_theory#Monads and
> | > my previous attempt to model it in Aldor...
> | > http://groups.google.com/group/fricas-devel/msg/38e7d6dca39cc46c
> | >
> | > Actually, now I believe that
> | >
> | > #include "aldor"
> | > Monad(C: Category, A: C, M: C -> C): Category == with {
> | > unit: A -> M A;
> | > mult: M M A -> M A;
> | > }
> | >
> | > is not the way one would naturally do this in Aldor.
> | >
> |
> | What precisely do you think is wrong with what you wrote?
> |
> | Although objections might be raised about the passing of categories as
> | parameters (see Gaby's comments), I think that in principle the syntax
> | and semantics of this is well defined even if not necessarily
> | implemented in all versions of Axiom.
>
> I suspect the reason why it is not implemented is that the semantics may
> not be well-defined in the AXIOM model. In that model, there is no
> category variable/parameter and every category form is evaluated. See
> uses of compMakeCategoryObject to type check domain forms.
>
> One thing that is lost in this discussion is that Haskell does not have
> type classes as parameters. The parameter to Monad is not an arbitrary
> function, it is a type constructor. All attempts I have seen so far
> have been busy trying to pass a category (what would be a type class in
> Haskell) to a functor.
>
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