The simplest functional programming language

Abstract

This paper describes a prefix version of Alonzo Church's Lambda Calculus called "$", named for its single operator, "$". The $ language is the simplest form of functional programming, consisting as it does in the iterative application of a simple substitution rule on well-formed strings of the language. The $ language is capable of modeling Boolean algebra and number theory and probably has the computational power of a single-tape Turing machine. It is fun to experiment with, especially interactively on a computer, using an interpreter.