I have been trying to decode an old paper of J. Lambek from 1980: "From λ-Calculus to Cartesian Closed Categories".
The first proposition in the paper concerns some early results in combinatory algebra and reads as follows:
Every polynomial $\varphi(x)$ over a Schonfinkel algebra $A$ can be written in the form $f^{\wr} x$, where $f \in |A|$.
and the second is similar, but for "Curry" algebras.
In the context of this material, what kind of objects would the "algebra" and "polynomial" be? It's never really spelled out in the paper and I assume I'm supposed to just know from whatever background I should have picked up before reading the paper, which I have clearly not done.
I've done some snooping around but can't find any other exposition on combinatory logic that uses this sort of algebraic language.
Thanks,
Pete