A General Schema for Constructing One-Point Bases in the Lambda Calculus

Abstract

In this paper, we present a schema for constructing one-point bases for recursively enumerable sets of lambda terms. The novelty of the approach is that we make no assumptions about the terms for which the one-point basis is constructed: They need not be combinators and they may contain constants and free variables. The significance of the construction is twofold: In the context of the lambda calculus, it characterises one-point bases as ways of ``packaging'' sets of terms into a single term; And in the context of realistic programming languages, it implies that we can define a single procedure that generates any given recursively enumerable set of procedures, constants and free variables in a given programming language.