abstract combinatory logic?

["Meredith Gregory" <lgreg.meredith@gmail.com>]

All,

i recently ran across a use of fold (in the functional programming sense)
where i wanted to solve for the accumulator type. i realized that something
in the neighborhood of a combinatory logic would be a minimal solution. This
got me thinking... there are various versions of combinators for the
\lambda-calculus and there's Haghverdi's combinators for linear lambda and
there are Yoshida's combinators for Milner's \pi-calculus. The first two
will work in the setting i encountered, the latter will not because -- in
addition to (parallel) composition -- Yoshida's combinators require a new
and replication operator. So, i'm wondering if anyone has given an abstract
characterization of a combinatory logic/algebra? If so, does anyone have a
reference?

Best wishes,

--greg

-- 
L.G. Meredith
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