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SFcalculusSFcalculus 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 SKcalculus, so that SFcalculus is, in this sense, more expressive than SKcalculus 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 . Yours, By Barry Jay at 20100625 02:41  LtU Forum  previous forum topic  next forum topic  other blogs  14294 reads

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