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Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 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 Depa ..."
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this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 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://wwwformal.stanford.edu/jmc/ ) by starting with the class of expressions called Sexpressions and the functions called Sfunctions. 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 Sexpressions and Sfunctions, give some examples, and then describe the universal Sfunction apply which plays the theoretical role of a universal Turing machine and the practical role of an interpreter. Then we describe the representation of Sexpressions in the memory of the IBM 704 by list structures similar to those used by Newell, Shaw and Simon [2], and the representation of Sfunctions 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
RECONSTRUCTION OF EXTENDED POLYNOMIALS FROM THE FINITE NUMBER OF EXAMPLES
"... Abstract The extended polynomials are considered the class of all functions definable in the simply typed *calculus with one basic type. The goal of the thesis was to decide, whether for every extended polynomial there exists a finite set of examples determining that polynomial, and to find an alg ..."
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Abstract The extended polynomials are considered the class of all functions definable in the simply typed *calculus with one basic type. The goal of the thesis was to decide, whether for every extended polynomial there exists a finite set of examples determining that polynomial, and to find an algorithm for constructing such a set for a given polynomial. It is proved that such a finite set exists for every extended polynomial and the cardinality of such a set depends only on the polynomial's arity. An algorithm constructing such a set is also presented.
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called ..."
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A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called the Advice Taker, whereby a machine could be instructed to handle declarati ..."
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A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called the Advice Taker, whereby a machine could be instructed to handle declarative
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called ..."
Abstract
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A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called ..."
Abstract
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A programming system called LISP (for LISt Processor) has been developed for the IBM 704 computer by the Artificial Intelligence group at M.I.T. The system was designed to facilitate experiments with a proposed system called