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[Axiom-math] Re: [fricas-devel] Re: [open-axiom-devel] [fricas-devel] Re


From: Bill Page
Subject: [Axiom-math] Re: [fricas-devel] Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel] Re: iterators and cartesian product.
Date: Thu, 1 Nov 2007 00:16:43 -0400

On 10/31/07, Gabriel Dos Reis wrote:
>
> On Wed, 31 Oct 2007, Bill Page wrote:
> | ...
> | I mean: What does Monad as defined in the Axiom library right now:
> |
> | ++  Monad is the class of all multiplicative monads, i.e. sets
> | ++  with a binary operation.
> |
> | have to do with Monads in Haskell?
>
> That is explained in the reference to Philip Wadler's paper I pointed
> to in my earlier message.
>

Philip Wadler's paper is well known and was published in 1992. The
Axiom category

)abbrev category MONAD Monad
++ Authors: J. Grabmeier, R. Wisbauer
++ Date Created: 01 March 1991
++ Date Last Updated: 11 June 1991

and the associated domains:

AlgebraicGivenbyStructuralConstants
AssociatedJoranAlgebra
AssociatedLieAlgebra
FreeNilpotentLie
GenericNonAssociativeAlgebra
LieSquareMatrix

seem to me to refer to subjects very different than Philip Wadler's
paper. I do not see any higher-order functions like 'map', 'unit' or
'join' defined here at all. Certainly Axiom does have various forms of
list comprehensions and functions like 'map' defined for many domains
but I do not see that generalized in any way in the existing Monad
category and associated domains.

Please, what do you see that I am missing?

> | Isn't that what you implied by your comment?
>
> Yes.
>

Sorry, I don't understand that at all. Maybe this discussion is best
saved for another time after I have had more time to think about how
to do these things in Axiom.

Regards,
Bill Page.




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