# M. P. Barnett

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Mechanization of tedious algebra—the e coefficients of theoretical chemistry

A table of formulas for certain integrals involving Legendre functions has been constructed mechanically by a program which performed algebraic operations. The formulas are all rational algebraic expressions in a single variable and were constructed by a recurrence procedure. They are of interest in molecular quantum chemistry. Trivial coding techniques were used to write the relevant programs in FORTRAN. The results were photocomposed on a Photon S-560 system, that was controlled by tapes which were punched directly from the computer output, so avoiding manual keyboarding, transcription errors and keyboarded correction.

Symbol manipulation in FORTRAN: SASP I subroutines

A set of subroutines for use in FORTRAN are described whose purpose is to synthesize output strings from (i) input strings which have been analysed by the SHADOW general syntactic analysis subroutine reported earlier, and/or (ii) packed BCD strings formed in any way. Function-type subroutines are included for intermediate manipulations, which are performed on the strings which are stored in an abbreviated internal representation. The automatic way in which an internal representation for each newly created substring is stored sequentially in a block of common storage, and the manner in which a storage block is dynamically allocated for that purpose, are discussed.

Comments on “a continued operation notation”

This note is intended to clarify and correct several points in a recent paper describing some notations for symbol manipulation by M. P. Barnett [Comm. ACM 6(August, 1963)].

Continued operation notation for symbol manipulation and array processing

A brief account is given of a notational device that is very useful in the formal representation of syntaxes, string relationships and string transformation procedures and also of computing procedures that deal with arrays of functions of many variables. The device consists of the use of certain “continued operation” or “collective” symbols that are analogous to the summation symbol ∑ and continued multiplication symbol ∏ of conventional mathematics.

Syntactic analysis by digital computer

This paper provides an account of the Shadow language that is used to describe syntax and of a corresponding subroutine that enables a computer to perform syntactic analysis. The input to this subroutine consists of a string to be analyzed and a description of the syntax that is to be used. The syntax is expressed in the Shadow language. The output consists of a trace table that expresses the results of the syntactic analysis in a tabular form. Several versions of the subroutine and some associated programs have been in use now for over three years. The present account of the language and the subroutine contains a summary of material that has been described previously in unpublished reports and also some additional discussion of the work in relation to the more general questions of problem-oriented languages and string transformations.

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