Re: [stack] Combining Combinators

Progress report:

I was intrigued by the possibility of combining the combinators,
restricting myself just to unary combinators ‹ those which
expect exactly one quotation parameter in addition to other
parameters that they need. In most programming the quotation
will be something such as [+], [first], [dup *], [10 *], [cons cons],
or even just [42]. But quotations such as [i], [dip], [map], [filter]
and so on seem strange as parameters to other combinators.
Does it even make sense?

So I started to investigate the possibilities, restricting myself
to just the simplest combinations. Let C and D be combinators
such as i, dip, nullary, unary, infra, step, map, filter, fold. Do
a fairly exhaustive survey of the possible combinations of the
simplest form: [C] D.

Results: For almost all quoted combinators [C] and almost all
combinators D, the combination [C] D is legal Joy ‹ provided
any additional parameters on top of the stack are correctly chosen.
For many of these combination there seem to be some good
uses, and this area deserves further investigation.

To broaden this investigation, let O be any non-combinator,
such as 42, swap, +, cons and so on, or a concatenation of
these. Investigate combinations [O C O] O D O, were the
various Os may or may not be distinct.

None of this has anything to do with my other question,
whether there are specifically higher order combinators,
These would be ones that can take quoted combinators [i],
[dip], [map] and so on as parameters, but cannot take
quoted non-combinators as parameters, such as [42], [+], [10 *].
I have not made any progress in this area.

  - Manfred


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