## [REBOL] Re: Functional programming in REBOL

### From: larry:ecotope at: 12-Aug-2001 21:42

Hi Ladislav, all
Latest News Flash from the Y front.
I just blew a mental fuse and possibly discovered a new way of defining the
Y-combinator in REBOL which is much simpler than the previous ones. Given
the wrapped version of the factorial function:
fact*: func [fact][
func [n][
either zero? n [1][n * fact n - 1]
]
]
Define Y like this:
Y2: func [f][f f :f]
This is another combinator, (i.e., a higher order function with no free
variables). Now at the console:

>> fact: Y2 :fact*
>> fact 16.0

== 20922789888000
fact seems to calculate the correct answers.

>> do fact* Y2 :fact* 5

== 120

>> do fact* fact* Y2 :fact* 5

== 120
It seems to satisfy the fixed-point property for Y.
Question 1: Is Y2 really a valid definition of Y? Or have I missed something
important.
One warning sign is that the same formulation does not work in Scheme. In
Scheme you have to put as many applications of f into the definition of Y2
as the n you want the recursion to work for.
Possibly it works for all cases in REBOL with just the 2 applications of f
to f because of the difference in the evaluation model for local variables
between REBOL and Scheme.
I'll have another look at this when brain function is restored.
Puzzled
-Larry