Abstract

this paper in L a T E Xpartly supported by ARPA (ONR) grant N00014-94-1-0775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science Department, Stanford, CA 94305, (email: jmc@cs.stanford.edu), (URL: http://www-formal.stanford.edu/jmc/ ) by starting with the class of expressions called S-expressions and the functions called S-functions. 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 [2], 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. We hope to describe some of the symbolic computations for which LISP has been used in another paper, and also to give elsewhere some applications of our recursive function formalism to mathematical logic and to the problem of mechanical theorem proving. 2 Functions and Function Definitions

Citations

39	The logic theory machine - Newell, Simon - 1956
5	Programs with common sense, Paper presented at the Symposium on the Mechanization of Thought - McCARTHY
5	The Calculi of Lambda-Conversion (Princeton - CHURCH - 1941
4	International algebraic language - PERLIS, SAMELS0N - 1958