SML(ID:477/sml007)MIT interactive maths systemfor Symbolic Mathematical Laboratory Martin PhD MIT 1967 On-line system under CTSS for symbolic math. Used a display screen and light pen Related languages
References: Some very interesting work has been done by Martin in preparing input-output for display on the PDP-6. He has written a program in Lisp which assigns complicated meanings to a series of simple light pen motions and accepts expressions which have been stored internally and which are to be displayed. in Advances in Computers, Vol. 8 FL Alt and M Rubinoff (Eds.), Academic Press, New York, 1967 view details in Advances in Computers, Vol. 8 FL Alt and M Rubinoff (Eds.), Academic Press, New York, 1967 view details Symbolic Mathematical Laboratory W. A. Martin (1967) describes a large computer program developed to aid applied mathematicians in the solution of problems in nonnumerical analysis that involve tedious manipulations of mathematical expressions. The mathematical laboratory was programmed for a hardware configuration consisting of a teletype, a DEC type 30 display, a lightpen, and a Calcomp plotter all communicating with a PDP-6 computer, which in turn was connected by dataphone to the Project MAC 7094 computer. The PDP-6 handles the user interface (input and output) and relays messages to and from the Project MAC time-sharing system where LISP transformation routines are applied to the mathematical expressions of the user's problem. Mathematical expressions are displayed on the CRT and manipulated by lightpen and teletype commands. In addition to the standard arithmetic operators, naming operator, etc., there are many other available operators. A somewhat random selection from a list of some 34 given in Martin (1967) will indicate the power and usefulness of the mathematical laboratory. ALLSUMEXPAND (EXP)--applies SUMEXPAND to every summation in expression EXP; BRINGOVER(EXP, X)--subexpression X, which has been indicated with the lightpen, is brought to the other side of equation EXP; DRVDO(EXP,X)--all indicated derivatives with respect to X in EXP are carried out as far as possible; DRVZERO(EXP,X)--all derivatives with respect to X in EXP are set equal to zero; EXPAND(EXP)--multiplies out all expressions of the form a.(b -~ c) in EXP. In addition d (a+ b) ~da db dx dx "~ ~ ; LIMIT (EXP, X, N)--determines the limiting value of EXP as X approaches N; MULTIPLYTHROUGH (EXP, X)-- multiplies each top level term of EXP by X; SIMPLIFY(EXP)--simplifies expression EXP; SOLVE(EXP,X)--solves equation EXP for variable X as far as possible; SPLIT(EXP)--subparts of EXP are named and replaced by their names in EXP, so that EXP will contain less than 100 subexpressions; SUBSTITUTE(EXP,X,Y)--substitutes X for each occurrence of Y in EXP; and EDISPLAY(E)--displays the expression named E on the PDP-6 scope. in [ACM] ACM Computing Surveys 2(4) Dec1970 view details in [ACM] Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation, March 23-25, 1971 Los Angeles (SYMSAM 71) view details The exact number of all the programming languages still in use, and those which are no longer used, is unknown. Zemanek calls the abundance of programming languages and their many dialects a "language Babel". When a new programming language is developed, only its name is known at first and it takes a while before publications about it appear. For some languages, the only relevant literature stays inside the individual companies; some are reported on in papers and magazines; and only a few, such as ALGOL, BASIC, COBOL, FORTRAN, and PL/1, become known to a wider public through various text- and handbooks. The situation surrounding the application of these languages in many computer centers is a similar one. There are differing opinions on the concept "programming languages". What is called a programming language by some may be termed a program, a processor, or a generator by others. Since there are no sharp borderlines in the field of programming languages, works were considered here which deal with machine languages, assemblers, autocoders, syntax and compilers, processors and generators, as well as with general higher programming languages. The bibliography contains some 2,700 titles of books, magazines and essays for around 300 programming languages. However, as shown by the "Overview of Existing Programming Languages", there are more than 300 such languages. The "Overview" lists a total of 676 programming languages, but this is certainly incomplete. One author ' has already announced the "next 700 programming languages"; it is to be hoped the many users may be spared such a great variety for reasons of compatibility. The graphic representations (illustrations 1 & 2) show the development and proportion of the most widely-used programming languages, as measured by the number of publications listed here and by the number of computer manufacturers and software firms who have implemented the language in question. The illustrations show FORTRAN to be in the lead at the present time. PL/1 is advancing rapidly, although PL/1 compilers are not yet seen very often outside of IBM. Some experts believe PL/1 will replace even the widely-used languages such as FORTRAN, COBOL, and ALGOL.4) If this does occur, it will surely take some time - as shown by the chronological diagram (illustration 2) . It would be desirable from the user's point of view to reduce this language confusion down to the most advantageous languages. Those languages still maintained should incorporate the special facets and advantages of the otherwise superfluous languages. Obviously such demands are not in the interests of computer production firms, especially when one considers that a FORTRAN program can be executed on nearly all third-generation computers. The titles in this bibliography are organized alphabetically according to programming language, and within a language chronologically and again alphabetically within a given year. Preceding the first programming language in the alphabet, literature is listed on several languages, as are general papers on programming languages and on the theory of formal languages (AAA). As far as possible, the most of titles are based on autopsy. However, the bibliographical description of sone titles will not satisfy bibliography-documentation demands, since they are based on inaccurate information in various sources. Translation titles whose original titles could not be found through bibliographical research were not included. ' In view of the fact that nany libraries do not have the quoted papers, all magazine essays should have been listed with the volume, the year, issue number and the complete number of pages (e.g. pp. 721-783), so that interlibrary loans could take place with fast reader service. Unfortunately, these data were not always found. It is hoped that this bibliography will help the electronic data processing expert, and those who wish to select the appropriate programming language from the many available, to find a way through the language Babel. We wish to offer special thanks to Mr. Klaus G. Saur and the staff of Verlag Dokumentation for their publishing work. Graz / Austria, May, 1973 in [ACM] Proceedings of the Second Symposium on Symbolic and Algebraic Manipulation, March 23-25, 1971 Los Angeles (SYMSAM 71) view details Another lost symbolic system of importance is the Symbolic Mathematical Laboratory of W. A. Martin. This system provided high-quality 2-D graphics on a DEC-340 display and was also the first to employ a lightpen for subexpression selection. In some ways, it represented a degree of interaction that has not been duplicated by any subsequent system. Nor were its innovative internal programming techniques restricted to its graphics facilities. Of particular interest is the use of hash coding for subexpression matching Extract: FORMAC The best known, purely symbolic systems are, of course, Formac and its current version PL/IFORMAC (Petrick, 1971; pp. 105-114). Formac was the first widely available general-purpose algebraic manipulation system and served for a period to define the field. Certainly, there was a time when one could have safely made the statement that the majority of all mechanical symbolic mathematical computations had been done within Formac. The practical success of these systems, in spite of their rigidity with respect to user modifications and their lack of any seminumerical facilities for rational function computations, is probably due to the overall intelligence of the facilities that were provided. Above all, they were certainly sufficient to support the dominant application area of truncated power series expansion. Current support is minimal. Extract: Symbolic systems SYMBOLIC SYSTEMS. We should mention first a sequence of three early programs for the simplification of general symbolic mathematical expressions represented as prefix-notation tree structures. The first, at M.I.T., was due to Hart, and the other two were due to Wooldridge and Korsvold at Stanford. The latter has survived in current usage as a result of its incorporation, subject to modification, into the MATHLAB, MACSYMA, and SCRATCHPAD systems. In the mid-1960s there appeared two systems, Formula Algol and FAMOUS, which, while dedicated to the symbolic manipulation of mathematical expressions, presented the user with almost no built-in automatic simplification facilities. This was due, at least in the case of FAMOUS, to a conscious decision that, since the "simplicity" of an expression is surely context- dependent, it should be reasonable to present the user with complete control over the simplification process. That is, the user'should be compelled to define all transformations, rather than, as with most systems, be permitted simply to switch on and off the transformations supplied by the system architects. No system of this species has ever solved the inherent efficiency problems to the extent that it could serve more than didactic purposes. Probably neither Formula Algol nor FAMOUS could be revived today. Another lost symbolic system of importance is the Symbolic Mathematical Laboratory of W. A. Martin. This system provided high-quality 2-D graphics on a DEC-340 display and was also the first to employ a light pen for subexpression selection. In some ways, it represented a degree of interaction that has not been duplicated by any subsequent system. Nor were its innovative internal programming techniques restricted to its graphics facilities. Of particular interest is the use of hash coding for subexpression matching (Petrick, 1971; pp. 305-310). in Encyclopedia of Computer Science, Ralston, Anthony, and Meek, Chester L. (eds) New York, NY Petrocelli/Charter 1976 view details in SIGPLAN Notices 11(09) September 1976 view details Resources
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