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It is copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. A few typographical changes have been made, but the notation has not been modernized. There are also some new explanatory footnotes. Part II, which never appeared, was to have had some Lisp programs for algebraic computation.
In this article, we first describe a formalism for defining functions recursively. We believe this formalism has advantages both as a programming language and as a vehicle for developing a theory of computation. Next, we describe S-expressions and S-functions, give some examples, and then describe the universal S-function apply which plays the theoretical role of a universal Turing machine and the practical role of an interpreter. Then we describe the representation of S-expressions in the memory of the IBM 704 by list structures similar to those used by Newell, Shaw and Simon, and the representation of S-functions by program. Then we mention the main features of the LISP programming system for the IBM 704. Next comes another way of describing computations with symbolic expressions, and finally we give a recursive function interpretation of flow charts.