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`A draft of the paper "A Combinatory Account of Internal Structure" is`

`available at`

http://www-staff.it.uts.edu.au/~cbj/Publications/factorisation.pdf

`This work may be of interest to the many readers of this list that are`

`interested in foundational issues.`

It has been accepted for publication by J Symbolic Logic.

`The paper exposes some of the limitations of SK-combinatory logic (and`

`so, by implication of lambda-calculus) by developing new combinatory`

`calculi which cannot be represented in SK-calculus. The work has been`

`controversial since each person has their own notion of representation.`

`For us, this is not merely an encoding of one calculus within another,`

`but refers to the ability to represent a symbolic function by a combinator.`

`The simplest of these new calculi has two operators, S and F which`

`satisfy the rules`

SMNX --> MX(NX) FOMN --> M if O is S or F F(PQ)MN --> NPQ if PQ is a factorable form

`where the factorable forms are those combinators of the form`

`S,SM,SMN,F,FM,FMN. These turn out to be the partially applied operators,`

`which ensures confluence. SF-calculus is able to represent static`

`pattern matching, in the sense of pattern calculus.`

All comments welcome. Barry Jay Thomas Given-Wilson