[Axiom-math] Re: [fricas-devel] Re: [open-axiom-devel] [fricas-devel] Re: [fricas-devel] Re: iterators and cartesian product.

[Bill Page]

On 10/31/07, Gabriel Dos Reis wrote:
>
> On Wed, 31 Oct 2007, Bill Page wrote:
> ...
> | It might even be interesting to consider implementing
> | something akin to monads in Aldor/SPAD,
>
> There already existe a domain called Monad in the Axiom family --
> it is a well mathematically defined notion.
>

Perhaps I am being dense but I do not see what this has to do with the
concept of Monad in Haskell. Could you please explain?

++ Description:
++  Monad is the class of all multiplicative monads, i.e. sets
++  with a binary operation.

)show Monad
 Monad  is a category constructor
 Abbreviation for Monad is MONAD
 This constructor is exposed in this frame.
 Issue )edit 
/usr/local/lib/axiom/target/i686-suse-linux/../../src/algebra/MONAD.spad
to see algebra source code for MONAD

------------------------------- Operations --------------------------------
 ?*? : (%,%) -> %                      ?**? : (%,PositiveInteger) -> %
 ?=? : (%,%) -> Boolean                coerce : % -> OutputForm
 hash : % -> SingleInteger             latex : % -> String
 ?~=? : (%,%) -> Boolean
 leftPower : (%,PositiveInteger) -> %
 rightPower : (%,PositiveInteger) -> %

-----

I think what is required "mathematically" for Haskell-like monads in
Axiom is something more related to the concept of monad in category
theory. Ref:

http://en.wikipedia.org/wiki/Monad_%28category_theory%29

perhaps implemented in the style promoted by Saul Youssef in his
article about category theory in Aldor.

> I do not however see myself implement the Haskell solution
> | for Axiom. I would prefer a more powerful effect system for
> | OpenAxiom.
>

Could you describe what you mean by "effect system"?

> | but I think you will agree that fundamentally these
> | languages were not designed to be purely functional.
>
> I do not see `purely functional' as as necessity.
>

In that case what is wrong with effects as implemented in SPAD's
imperative-style programming right now?

I am sorry. I don't mean to sound rude, but I just don't understand
where your comments lead. Could you say something more about what you
are considering for implemention in OpenAxiom?

Regards,
Bill Page.