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| The '''Laning and Zierler system''' (sometimes called "George" by its users) was one of the first operating algebraic [[compiler]]s, that is, a system capable of accepting mathematical formulae in [[Infix notation|algebraic notation]] and producing equivalent [[machine code]] (the term compiler had not yet been invented and the system was referred to as "an [[interpreter|interpretive]] program"). It was implemented in 1954 for the [[Massachusetts Institute of Technology|MIT]] [[Whirlwind (computer)|WHIRLWIND]] by [[J. Halcombe Laning]] and Neal Zierler. It is preceded by the [[UNIVAC]] A-2, [[IBM]] [[Speedcoding]] and a number of systems that were proposed but never implemented.
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| ==Description==
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| The system accepted formulae in a more or less algebraic notation. It respected the standard rules for [[operator precedence]], allowed nested parentheses, and used superscripts to indicate [[Exponentiation|exponents]]. It was among the first programming systems to allow [[variable (computer science)|symbolic variable]] names and allocate storage automatically.
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| The system also automated the following tasks: [[floating point]] computation, linkage to [[subroutine]]s for the basic functions of analysis (sine, etc.) and printing, and arrays and indexing.
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| The system accepted input on [[punched tape]] produced by a [[Friden Flexowriter]]. The [[character set]] in use at the Whirlwind installation included "[[upper-case]]" (superscript) digits and a hyphen, which were used to indicate array indices, function codes, and (integer) exponents. Like other programming notations of its time, the system accepted only single-letter variable names and multiplication was indicated by juxtaposition of operands. A raised dot was available to indicate multiplication explicitly (the character was created by filing off the lower half of a colon!) The system also included support for solution of linear differential equations via the [[Runge-Kutta methods|Runge-Kutta method]].
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| The system was described in an 18-page typewritten manual written for people familiar with mathematics but perhaps unfamiliar with computers. It contains almost nothing in the way of an introduction to computer hardware.
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| ==Sample Program==
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| The following example, taken from page 11 of the system's manual, evaluates <math>\cos x</math> for <math>x = 0, 0.1, ..., 1</math> using the [[Taylor series]] expansion. The implementation is not terribly efficient, and the system already includes <math>\cos x</math> in its subroutine library, but the example serves to give a flavor of the system's syntax. Note that division in the system is evaluated after multiplication:
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| 1 ''x'' = 0,
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| ''z'' = 1 - ''x''<sup>2</sup>/2 + ''x''<sup>4</sup>/2·3·4 - ''x''<sup>6</sup>/2·3·4·5·6
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| + ''x''<sup>8</sup>/2·3·4·5·6·7·8 - ''x''<sup>10</sup>/2·3·4·5·6·7·8·9·10,
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| PRINT ''x'', ''z''.
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| ''e'' = ''x'' - 1.05,
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| CP 1,
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| STOP
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| ==Applications==
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| Few applications were written for the system. One documented application, authored by Laning and Zierler themselves, involved a problem in aeronautics. The problem required seven systems of differential equations to express, and had been given to the Whirlwind because it was too large for MIT's [[Differential Analyzer]] to handle. The authors, exploiting the Runge-Kutta feature of their programming system, produced a 97-statement program in two and half hours. The program ran successfully the first time.
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| ==Influence on FORTRAN==
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| Some sources have said that the Laning and Zierler system was the inspiration for [[FORTRAN]]. [[John Backus]] himself admitted to having contributed to this misconception:
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| <blockquote>
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| The effect of the Laning and Zierler system on the development of FORTRAN is a question which has been muddled by many misstatements on my part. For many years I believed that we had gotten the idea for using algebraic notation in FORTRAN from seeing a demonstration of the Laning and Zierler system at MIT. (Backus {{ref|Backus}})
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| </blockquote> | |
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| After reviewing documentation from the time, Backus learned that the FORTRAN project was "well underway" when he and his team got a chance to see Laning and Zierler's work:
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| <blockquote> | |
| [W]e were already considering algebraic input considerably more sophisticated than that of Laning and Zierler's system when we first heard of their pioneering work... [I]t is difficult to know what, if any, new ideas we got from seeing the demonstration of their system. (Backus, ''op cit'')
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| </blockquote>
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| ==Notes==
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| # {{note|Backus}} J. W. Backus, The history of FORTRAN I, II and III. Proceedings First ACM SIGPLAN conference on History of programming languages
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| ==References==
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| * Backus, J. W. The history of FORTRAN I, II and III. Proceedings First ACM SIGPLAN conference on History of programming languages (Available [http://www.stanford.edu/group/mmdd/SiliconValley/Backus/backus.html on line]).
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| * Laning, J.H. and N. Zierler. A Program For Translation of Mathematical Equations for Whirlwind I. Engineering Memorandum E-364, Instrumentation Laboratory, Massachusetts Institute of Technology. (Available [http://archive.computerhistory.org/resources/text/Fortran/102653982.05.01.acc.pdf on line]).
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| * Sammet, Jean E., "Programming Languages: History and Fundamentals" Prentice-Hall, 1969
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| * "The Early Development of Programming Languages" in ''A History of Computing in the Twentieth Century'', New York, Academic Press, 1980. ISBN 0-12-491650-3
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| ==See also==
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| *[[History of programming languages]]
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| *[[Timeline of programming languages]]
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| [[Category:Compilers]]
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