Combinatory completeness in partial groupoids

TL;DR

This paper characterizes combinatorially complete partial applicative systems (pargoids) using expandability with two constants satisfying specific identities, revealing a broader class than just partial combinatory algebra reducts.

Contribution

It introduces a new characterization of combinatorially complete pargoids through expandability with constants, expanding understanding beyond known partial combinatory algebra reducts.

Findings

Identifies conditions for combinatorial completeness in partial groupoids.

Shows that the class of such systems exceeds partial combinatory algebra reducts.

Provides an example illustrating the broader class.

Abstract

I characterize the combinatorially complete pargoids (partial applicative systems) by expandability with two constants that satisfy the well-known identities. An example shows that this class contains more than just the reducts of partial combinatory algebras.