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

[Gabriel Dos Reis]

On Wed, 31 Oct 2007, Bill Page wrote:

| 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.

They are the same categorial notion.  What youhave in Haskell is a
computer scientist application of the categorial notion of `monad'.
Haskell's take derive from Moggi's work on applying monads to defined
program semantics.  See his seminal work.  And it is also true that you
don't need to understand category theory before using `monad's in
Haskell.  Which makes some haskellers say that they did a really bad job
at picking the name.

[...]

| > 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"?


  http://www.irisa.fr/prive/talpin/papers/jfp92.pdf

| > | 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 did not make a statement to that effect, so I do not exactly what
you mean. Could you clarify?

| 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?

Among other things, a type and effect system so that I can know which
domain are purely functional -- therefore the caching implementation
technique is sound for them -- and which have effects, therefore
should not be cached. 

-- Gaby