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The beginning and development of FORMAC (FORmula MAnipulation Compiler)

Published: 01 March 1993 Publication History

Abstract

The first widely available programming language for symbolic mathematical computation to have significant practical usage was FORMAC (FORmula MAnipulation Compiler). This paper discusses the earliest conceptual work in detail, and then provides information about later developments of the language. Other languages and systems of the early and mid-1960s are described briefly, with emphasis on their relation to FORMAC. There are also a few glimpses into the software management process at IBM. Finally there is an evaluation of FORMAC and its influence.

References

[1]
FORMAC MARKET STUDY, Report to IBM, C-66891, Arthur D. Little, Inc. March, 1965.
[2]
Comm. ACM, Vol. 9, No. 8, Aug. 1966, entire issue.
[3]
Bahr, Knut and Jasp Smith, Tuning an Algebraic Manipulation system through measurements, Proceedings of EUROSAM 74, ACM SIGSAM Bulletin, Vol. 8, No. 3, Aug. 1974, pp. ?
[4]
Bahr, Knut, Utilizing the FORMAC Ngveltles, ACM SIGSAM Bulletin, Vol. 9, No. i, Feb., 1975, pp. 21-24.
[5]
Bernick, M. D., E.D. Callender, and J.R. Sanford, ALGY -- An Algebraic Manipulation Program, in Proceedinas of the Western Joint computer conference, Vol. 19 1961, pp. 389-92.
[6]
Bleiweiss, L. et al., A Time-Shared Algebraic Desk Calculator Version of FORMAC, IBM Corp., TR00.1415, Systems Development Division, Poughkeepsie, N.Y. Mar., 1966 .
[7]
Bobrow, D. G., ed., Symbol Manipulation Lanquaqes and TechniQues, Proceedinqs of the IFIP Working Conference on Symbol Manipulation Lanquaqes~ Pisa, North-Holland Publishing Company, Amsterdam, 1968.
[8]
Bond, E. R. et all FORMAC -- An Experimental FORmula MAnipulation Compiler, in Proceedinqs of the ACM 19th National Conference, 1964, pp. K2.1-I-K2.1-11.
[9]
Bond, E. et al, Implementation of FORMAC, TR00.1260, IBM Systems Development Division, Poughkeepsie Laboratory, March, 1965.
[10]
Bond, Elaine R., Proposal for Language Extension to PL/I for FORMAC, internal memo, IBM, Sept. 23, 1965.
[11]
Bond, E. R. and Cundall, P. A., A Possible PL/I Extension for Mathematical Symbol Manipulation, in Symbol Manipulation Lanquages and Techniques, Proceedinqs of the IFIP Working Conference on Symbol Manipulation Lanquages, D. G. Bobrow, ed., North-Holland Publishing Co., Amsterdam, 1968, pp. 116-132.
[12]
Brown, W. S., J.P. Hyde, and B. A.Tague, The ALPAK System for Nonnumerlcal Algebra on a Digital Computer, Bell System Technical Jour., Vol. 42, No. 5, Sept., 1963, pp. 2081- 119; Vol. 43, No. 2 Mar., 1964, pp. 785-804; Vol. 43, No. 4, pt. 2 July, 1964, pp. 1547-62.
[13]
Brown, W. S., A Language and System for Symbolic Algebra on a Digital Computer, in Proceedings of the IBM Scientific Computln~Sy~oslum on Computer-Aided Experlmentatlon, IBM Corp., 320-0936-0 Data Processing Division, White Plains, N.Y. 1966, pp. 77-114.
[14]
Clapp, L. C. and Kain, R. Y., A Computer Aid for Symbolic Mathematics, in Proceedinqs of the Fall Joint Computer Conference, Vol. 24 Nov., 1963, pp. 509-17.
[15]
Collins, G. E., PM, A System for Polynomial Manipulation, Comm. ACM, Vol. 9, No. 8, Aug., 1966, pp. 578-589.
[16]
Crisman, P. A., ed., The Compatible Time-Sharinq System, A Proqrammer's Guide, Second Edition, Cambridge, MA: MIT Press, 1965.
[17]
Cuthill, E., S. Voigt, and S. Ullom, Use of Computers in the Solution of Boundary Value and Initial Value Problems, Annual Progress Report, SR011-01-01 Task 0401AML Problem 821-911, David Taylor Model Basin, Washington, D.C. June, 1965.
[18]
Duby, J. J., Sophisticated Algebra on a Computer -- Derivatives of Witt Vectors, in Symbol Manipulation Lanquages and Techniques. Proceedlnqs of the IFIP Workinq Conference on Symbol Manipulatlon Languaqes, D. G. Bobrow, ed, North-Holland Publishing Co., Amsterdam, 1968, pp. 71-85.
[19]
Engelman, C., MATH-LAB: A Program for On-Line Machine Assistance in Symbolic Computations, in Proceed!nqs of the Fall Joint Computer Conference, Vol. 27, Part 2, i965, pp. 413-422.
[20]
, The Legacy of MATHLAB 68, in Proceedlnqs of the Second SymDoslum on Symbollc and Alqebralc ManlpulatloD, ACM, S. R. Petrlck, ed., ACM, Mar., 1971, pp. 29-41.
[21]
Evey, R. J., S. F. Grlsoff, J.E. Sammet, and R. G. Tobey, FORMAC Prelimlnarv LanQuaQe SDeclflcatlons, IBM, Boston Advanced Programming, Advanced Computer Utilization Dept., Data Systems Division, Dec. 14, 1962.
[22]
Griesmer, J. H. and R. D. Jenks, SCRATCHPAD/I - An Interactive Facility for Symbolic Mathematics, in Proce~d- Inqs of the Second Svmposlum on Svmbollc and Algebraic ManlDulatlon, Petrlck, S. R., ed., ACM, 1971, pp. 42-58.
[23]
Haanstra, J. W., FORMAC, Memo to P. W. Knaplund, IBM, April 12, 1965.
[24]
Hearn, Anthony C., Computation of Algebraic Properties of Elementary Particle Reactions Using a Digital Computer, Comm. ACM, Vol. 9, No. 8, Aug., 1966, pp. 573-577.
[25]
REDUCE USERS' MANUAL, Memo No. 50, Stanford Artificial Intelligence Project, Feb. 1967.
[26]
, REDUCE 2, A System and Language for Algebraic Manipulation, in ProceedlnQs of the Second Symposium on Symbolic and Algebraic ManiDulatlon, Petrlck, S. R., ed., ACM, 1971, pp. 128-133.
[27]
Howard, J. C., Computer Formulation of the Equations of Motion Using Tensor Notation, Comm~ ACM, Vol. i0, No. 9 Sept., 1967, pp. 543-48.
[28]
FORMAC IOperat!nq and User's Preliminary Reference Manual), IBM Corp., No. 7090 R2IBM 0016, IBM Program Information Dept., Hawthorne, N.Y., Aug., 1965.
[29]
DESCRIPTION OF TIME-SHARED FORMAC, IBM, Boston Programming Center, No. CC-257, Computation Center, MIT, March, 1966,
[30]
PL/I-FORMAC Interpreter, IBM Corp., Contributed Program Library, 360D 03.3.004, Program Information Dept., Hawthorne, NY, Oct., 1967.
[31]
Martin, W. A., Symbolic Mathematical Laboratory, M.I.T., MAC-TR-36 (Ph.D. thesis), ProJec~ MAC, Cambrldge, Mass, Jan., 1967.
[32]
Martin, W. A. and R. J. Fateman, The MACSYMA System, in Proceedings of the Second Symposlum on Svmbollc and Algebra- Ic Manlp~lation, Petrick, S. R., ed., AcM, 197i, pp. 59-75.
[33]
Morris, A. H., Jr., The FLAP Language -- A Programmer'F Guide, U.S. Naval Weapons Lab., K-8/67, Dahlgren, VA., Jan., 1967.
[34]
Moses, Joel, Symbolic Integration, MAC-TR-47, Project MAC, MIT, Dec., 1967.
[35]
, MACSYMA--The Fifth Year, in ~roceedinqs of the Eurosam Conference, ACM SIGSAM Bullet!n, Vol. 8, No. 3, Aug., 1974, pp. 105-110.
[36]
Neldleman, L. D., An Application of FORMAC, Comm~ ACM, Vol. I0, No. 3, Mar., 1967, pp. 167-68.
[37]
~FORMAC: CONVERSATIONAL FORMAC, The Pennsylvania State University Computation Center, Aug., 1983.
[38]
Perlls, A. J. and R. Iturrlaga, An Extension to ALGOL for Manipulating Formulae, Comm, ACM, Vol. 7, No. 2, Feb., 1964, pp. 127-30.
[39]
Perlls, A. J., R. Iturriaga, and T. A. Standish, A Definition of Formula ALGOL, Carnegie Inst. of Tech., Pittsburgh, PA, Aug., 1966.
[40]
Petrlck, S. R., ed., Proceedlnqs of the Second Svmposlum on Svmbollc and Algebraic Manipulation, ACM, 1971.
[41]
Sammet, Jean E., Project Description for Symbol Manipulation Compiler, internal memo, IBM, Aug. I, 1962.
[42]
, Numerical Estimates for Justification of SYmbol MAnipulation COMpiler, internal memo, IBM, Aug. 13, 1962.
[43]
, FORMAC and NPL, internal memo, IBM, May 20, 1963.
[44]
, Implementation of FORMAC for NPL, internal memo, IBM, Nov., 23, 1963.
[45]
Sammet, Jean E. and Elaine R. Bond, Introduction to FORMAC, IEEE Trans. Elec. Com~, Vol. EC-13, No. 4, Aug., 1964, pp. 386-94.
[46]
, Proposed FORMAC Activity in 1965, internal memo, IBM, Oct. 12, 1964.
[47]
, Updated Summary of Interest on FORMAC, internal memo, IBM, Sept. 27, 1965.
[48]
______, Faults with FORMAC, internal memo, IBM, May 28, 1965.
[49]
, Efficient polynomial manipulation capablllty for 0S/360 FORMAC, internal memo, IBM, March 23, 1965.
[50]
_____, Survey of Formula Manipulation, Comm. ACM, Vol. 9, No. 8, Aug., 1966, pp. 555-569.
[51]
, An Annotated Descriptor Based Bibliography on the Use of Computers for Non-Numerlcal Mathematics, ComDutlng Revlew_________ss, Vol. 7, No. 4, July-Aug., 1966, pp. B-I-B-31.
[52]
___~_, Survey of the Use of Computers for Doing Non-Numerlcal Mathematics, IBM Systems Development Division, Poughkeepsie Laboratory, TR 00.1428, March, 1966.
[53]
, Formula Manipulation by Computer, in Advances in Computers, Vol. 8, Alt, F. L. and M. Rubinoff, eds., NY: Academic Press, 1967, pp. 47-102.
[54]
~, Revised annotated descriptor based bibliography on the use of computers for non-numerical mathematics, in ~oI Manipulatlon Lanquaqes and Technl~ues, Bobrow, D. G., ed., North-Holland, Amsterdam, 1968, pp. 358-484.
[55]
~, PROGRAMMING LANGUAGES: History and Fundamental~, Englewood Cliffs, NJ: Prentlce-Hall, 1969.
[56]
~, Software for Nonnumerlcal Mathematics, in ~HEMATICAL SOFTWARE, Rice, John ed., N~: Academic Press, 1971, pp. 295-330.
[57]
__, Symbolic Computation: The Early Days {1950-1971, in COMPUTERS IN MATHEMATIC SS, Chudnovsky, David V. and Richard D. Jenks, eds., NY: Marcel Dekker, Inc., 1990, pp. 351-366.
[58]
Sconzo, P., A. R. LeSchack, and R. G. Tobey, Symbolic Computation of f, and g, Series by Computer, Astronomical Jour., Vol. 70, No. 4, May, 1965, pp. 269-271.
[59]
SHARE-FORMAC, No. 360D-03.3.013 II, Aug. 1983.
[60]
Slagle, J.R., A heuristic program that solves symbolic integration problems in freshman calculus, J.__~, Vol. I0, No. 4, Oct. 1963, pp. 507-520.
[61]
Tobey, R. G., et a_____!l, Preliminary specifications for FORMAL NPL (System/360 FORMAC), internal report, IBM, Jan. 28, 1965.
[62]
Tobey, R. G., R. J. Bobrow, and S. N. Zilles, Automatic Simplification in FORMAC, in Proceedlnqs of the AFIPS Fall Joint Computer Conference, Vol. 27, Nov., 1965, pp. 37-52.
[63]
~, Experience with FORMAC Algorithm Design, Comm. ACM, Vol. 9, No. 8, Aug., 1966, pp. 589-595.
[64]
Tobey, R. G., Eliminating Monotonous Mathematics with FORMAC, Comm. ACM, Vol. 9, No. I0, Oct., 1966, pp. 742-51.
[65]
Tobey, Robert G., ed., Proceedings Q~ the 1968 Summer Institute on Symbolic Mathematical Computation, Programming Laboratory Report #FSC69-0312, IBM Federal Systems Division, June 1969.
[66]
van Hulzen, J. A., FONMAC Today, or What Can Happen to an Orphan, ACM SIGSAM Bulletlnn, Vol. 8, No. I, Feb. 1974, pp. 5-7.
[67]
Walton, J. J., Tensor Calculations on Computer: Appendix, Comm. ACM, Vol. I0, No. 3, Mar., 1967, pp. 183-86.
[68]
Xenakls, J., The PL/I--Formac Interpreter, in Proceedings of the Second Svmposium on S .~bollc and Alqebraic M~nIDulatlon, Petrlck, S. R., ed., ACM, Mar., 1971, pp. 105-114.

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Published In

cover image ACM SIGPLAN Notices
ACM SIGPLAN Notices  Volume 28, Issue 3
March 1993
363 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/155360
Issue’s Table of Contents
  • cover image ACM Conferences
    HOPL-II: The second ACM SIGPLAN conference on History of programming languages
    April 1993
    370 pages
    ISBN:0897915704
    DOI:10.1145/154766
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 March 1993
Published in SIGPLAN Volume 28, Issue 3

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  • (2022)History and Present Scenario of Computers in Pharmaceutical Research and DevelopmentComputer Aided Pharmaceutics and Drug Delivery10.1007/978-981-16-5180-9_1(1-38)Online publication date: 31-May-2022
  • (2018)Computer algebra in gravity researchLiving Reviews in Relativity10.1007/s41114-018-0015-621:1Online publication date: 20-Aug-2018

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