SF-calculus builds combinators from two operators S and F that are more expressive than the usual S and K. The reduction rules are
SMNX = MX(NX)
where the factorable forms are the partially applied operators, i.e. of the form S, SM, SMN, F, FM and FMN. The operators are the atoms while the factorable forms that are applications are compounds.
The factorisation combinator cannot be represented within SK-calculus, so that SF-calculus is, in this sense, more expressive than SK-calculus or pure lambda calculus. To fully appreciate this surprising, if not controversial, claim, requires a careful definition of representation.
This, and full proofs, are in our paper A combinatorial Account of Internal Structure .
Active forum topics
New forum topics