Combinatory Arithmetic

  • Sören Stenlund
Part of the Synthese Library book series (SYLI, volume 42)


The aim of this chapter is to show how to develop an arithmetic of natural numbers within the pure theory of combinators. In section 2 we shall give a simple proof of the combinatory definability of all partial recursive functions. This result is essentially due to Kleene 1936, who developed arithmetic within the λI-calculus without an analog to the combinator K. In the presence of K it is possible to simplify the proof a bit. The first to develop arithmetic within the theory of combinators was Curry 1941.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1972

Authors and Affiliations

  • Sören Stenlund

There are no affiliations available

Personalised recommendations