Re: [stack] Combining Combinators

Manfred Von Thun <[email protected]> wrote:
>"William Tanksley, Jr" <[email protected]> wrote:
> > Manfred Von Thun <[email protected]> wrote:
> >> > Years ago I sometimes wondered whether there could be
> >> > any higher order combinators.

> > I don't see how there couldn't be. Joy functions are higher-order, so
> > wouldn't Joy's combinators also be higher-order?

> My understanding is that the usual terminology is this:
> At level zero there are numbers, chars, truth values, lists...
> At level one there are functions successor, +, and ...
> At level two there are combinators, functions which take functions
> as arguments (or as values): map, fold, and many more.
> I was looking for something at level three: functions which
> take combinators as arguments, but which are distinct from
> combinators themselves.

How would that distinction be achieved? You hint below that
third-order entities would NOT take a function as a parameter; but I
must point out that every combinator IS a function.

> I never found any that are distinct
> from the existing bunch of Joy combinators.

Those are complete, right?

> a strange new world to me. But it has not led to any combinator
> N (for Œnew¹) such that [C] N is meaningful for a combinator [C]
> but [Q] N is not meaningful for a non-combinator Q. This
> is what I meant by a higher order combinator. But I do not have
> a proof that there cannot be such a beast.

It seems to me that you want a function which takes combinators as
arguments, but does not take functions (right?). But because all
combinators _are_ functions, this can't be possible.

Of course, strong type-checking can make something like this possible,
as can runtime stack checks. But I sense that's not what you mean.

>   - Manfred

-Billy


 
Yahoo! Groups Links

<*> To visit your group on the web, go to:
    http://groups.yahoo.com/group/concatenative/

<*> Your email settings:
    Individual Email | Traditional

<*> To change settings online go to:
    http://groups.yahoo.com/group/concatenative/join
    (Yahoo! ID required)

<*> To change settings via email:
    mailto:[email protected] 
    mailto:[email protected]

<*> To unsubscribe from this group, send an email to:
    [email protected]

<*> Your use of Yahoo! Groups is subject to:
    http://docs.yahoo.com/info/terms/