Re: [stack] Combining Combinators

> At level one there are functions which take zero level entities
> as arguments. At level two there are combinators which take
> level one entities as arguments but cannot take level zero
> entities as arguments. Examples: dip, nullary, map, filter, fold.
> At level three there would be functions which take level two
> entities as arguments but cannot take level one entities as
> arguments.

Interesting.

I propose a function called `compose'. It takes a quoted combinator
[C1] and alters that combinator to expect TWO functions on top of the
stack, compose them, and then execute C1.

For example:
[1 2 3] [2 *] [1 +] [map] compose i
=> [3 5 7]
['a] 123 ['b] [cons] [dip] compose i
=> ['a 'b]

This can be written in Joy as follows:
compose == [concat] swap concat

Note that applying compose to a non-combinator is not `meaningful':
[+] compose
=> [concat +]
it results in the meaningless function [concat +] which will throw an
error no matter what kind of input you give it.

I think we can construct other third- and even higher-level functions
using a similar technique. Of course, they are all really functions
stack->stack at heart; the distinction comes with the fact that
third-level functions only make sense when they modify second-level
functions (combinators).

~Daniel