Re: [stack] Meta-combinators?

On 1/24/07, William Tanksley, Jr <[email protected]> wrote:
>
> Christopher Diggins <[email protected]> wrote:
> > I have been intrigued by two typed-combinators which I haven't noticed
> > in Joy, and that I am considering adding to Cat.
> > I am calling them producer and consumer.
>
> > consumer : (('A -> 'B) -> ('A -> ))
> > producer : ('A ('A -> 'B) -> 'A ( -> 'B))
>
> > The consumer transforms any function into a new function which
> > produces nothing, but consumes what was expected.
>
> A more general form might be a word that "consumes" only the first
> argument of a multiargument function, ala:
>
> consumer : ('A -> B 'C) -> ('A -> 'C))
>
> (I hope I got your notation right. I'm also not particular on which
> side of the function the arguments get consumed.)

The notation is correct except I use little letters for single
arguments and big letters for multiple-arguments. The tick indicates
that it is a type variable.

> The obvious implementation, in terms of Joy quotations, would be to
> concatenate the original function with a stack shuffle that destroys
> the appropriate output.

So the solution is simple in Cat (and Joy as well) to this case:

In Cat "[quote] dip compose"

And in Joy: "[unit] dip cat"

What I am looking for though is something which curries all of the
consumed arguments, or pops all the produced results.

The more general problem is how to construct a combinator which can
curry all arguments for any given function. Stated differently the
challenge is to write a function which can compute the number of
arguments or number of results of any given function.

> > The producer transforms any function into a new function which
> > consumes nothing, but produces the result as if it was fed the stack
> > configuration when it was created.
>
> > Production is like a generalized form of currying.
>
> So you'd prepend the input data value onto (a copy of) the input function.

Yes.

> > How would this be possible in the general case in Joy? Or Factor, or
> > any other concatenative language for that matter?
>
> Currying is equivalent to concatenation.

Yes.

> > Christopher

Thanks for your comments.

P.S. Let me know when you have a chance to review the Cat paper
(http://www.cat-language.com/paper.html). I am considering submitting
it (with revisisons) to the upcopming Trends in Functional Programming
symposium (deadline is February 1st.)

Thanks
-- 
http://www.cdiggins.com