I'm trying to find a combinator that can derive all other combinators, so there is an expression in terms of this combinator (I'll call it U, for universal), for any (computable) combinator. I also want a proper combinator, which means that Uabc..., will be entirely in terms of a,b,c, etc. With such a combinator, I can make a new minimalist version of the Xi function. I've worked out a few properties such a combinator must posess:
1) The Cancellation Effect, which means when Uabc... is betareduced, one of the variables will disappear. As an example, the combinator K is defined as: Kxy=x, so y disaapears. No combinator with the cancellative property can be derived solely from combinators without said property.
2) The Duplicative Effect, whi…Read more >