Bill Page <bill.p...@newsynthesis.org> writes:
| 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;
| }
OK, then what is the question?
-- Gaby
|
| 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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