The lambda-gamma calculus: A language adequate for defining recursive functions

Abstract

This paper provides another formalization of the concept of an effectively calculable function motivated by the LISP language. In addition to the lambda functional abstraction operator the calculus described in this paper has a gamma decision operator of four arguments. There are two primitive relations of the calculus. The first is a denotation relation which in computer terms is the relationship holding between a name for a memory location and the contents of the location. The second is an identity relationship. An applied lambdagamma calculus with a successor function as the only primitive function is described in the paper as a fully formal theory with axioms and rules of deduction. © 1970 American Elsevier Publishing Company, Inc. All rights reserved.