We can consider interactive applied mathematics programming to be the teaming of a man and a machine to solve some problems in applied mathematics. The solution of the problem may in general consist of steps of operations upon data constructs which initially represented the problem description. The sequence of operations constitutes the program. In interactive programming, the sequence of operations is often performed alternately by the man and the machine, i.e., each member of the team does the part that he or it is good for. The importance of a programming language that can be used conveniently by man and machine alike to address the elements in the problem area is beyond dispute. Conveniences to the man are the naturalness and expressiveness possible in the language, while the convenience to the machine lies in the efficiency with which statements in the language may be interpreted. A programming language is chosen to strike an appropriate balance. This paper explores the machine architecture by describing the design of an object code which forms the internal representation of the elements in the programming language. The design is such that a PL/1 based language which is extended to cope with symbolic and expression manipulation can be implemented efficiently to provide statement incremental compilation and execution in a multiprogramming environment.
{"title":"An object code for interactive applied mathematical programming","authors":"K. Lock","doi":"10.1145/2402536.2402561","DOIUrl":"https://doi.org/10.1145/2402536.2402561","url":null,"abstract":"We can consider interactive applied mathematics programming to be the teaming of a man and a machine to solve some problems in applied mathematics. The solution of the problem may in general consist of steps of operations upon data constructs which initially represented the problem description. The sequence of operations constitutes the program. In interactive programming, the sequence of operations is often performed alternately by the man and the machine, i.e., each member of the team does the part that he or it is good for. The importance of a programming language that can be used conveniently by man and machine alike to address the elements in the problem area is beyond dispute. Conveniences to the man are the naturalness and expressiveness possible in the language, while the convenience to the machine lies in the efficiency with which statements in the language may be interpreted. A programming language is chosen to strike an appropriate balance. This paper explores the machine architecture by describing the design of an object code which forms the internal representation of the elements in the programming language. The design is such that a PL/1 based language which is extended to cope with symbolic and expression manipulation can be implemented efficiently to provide statement incremental compilation and execution in a multiprogramming environment.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128099458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Project TACT (Technological Aids to Creative Thought), in the Aiken Computation Laboratory of Harvard University, has been designing, implementing, and using on-line systems since 1964. Our investigation has concentrated on a rather small class of interactive systems which are "dedicated," that is, tailored to provide a coherent set of tools for mathematical assistance, and which use fairly powerful terminal facilities: display scopes and natural input.
{"title":"The development of systems for on-line mathematics at Harvard","authors":"Adrian Ruyle","doi":"10.1145/2402536.2402563","DOIUrl":"https://doi.org/10.1145/2402536.2402563","url":null,"abstract":"Project TACT (Technological Aids to Creative Thought), in the Aiken Computation Laboratory of Harvard University, has been designing, implementing, and using on-line systems since 1964. Our investigation has concentrated on a rather small class of interactive systems which are \"dedicated,\" that is, tailored to provide a coherent set of tools for mathematical assistance, and which use fairly powerful terminal facilities: display scopes and natural input.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133316242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Research in the real-time recognition of hand-printed characters [1--5] offers the possibility of drawing mathematical expressions on a RAND Tablet [6] or similar input device, and obtaining a list of the characters and their positions in an x-, y-coordinate system. This paper discusses the use of a set of replacement rules to recognize, or "parse," such two-dimensional configurations of characters. The replacement rules might be considered to be a generalization of the context-free Backus Normal Form rules used to describe a class of syntaxes for character strings.
手印字符的实时识别研究[1—5]提供了在RAND Tablet[6]或类似的输入设备上绘制数学表达式，并获得字符列表及其在x、y坐标系中的位置的可能性。本文讨论了使用一组替换规则来识别或“解析”这种二维字符配置。替换规则可以被认为是用于描述一类字符串语法的上下文无关的Backus Normal Form规则的泛化。
{"title":"Syntax-directed recognition of hand-printed two-dimensional mathematics","authors":"Robert H. Anderson","doi":"10.1145/2402536.2402585","DOIUrl":"https://doi.org/10.1145/2402536.2402585","url":null,"abstract":"Research in the real-time recognition of hand-printed characters [1--5] offers the possibility of drawing mathematical expressions on a RAND Tablet [6] or similar input device, and obtaining a list of the characters and their positions in an x-, y-coordinate system. This paper discusses the use of a set of replacement rules to recognize, or \"parse,\" such two-dimensional configurations of characters. The replacement rules might be considered to be a generalization of the context-free Backus Normal Form rules used to describe a class of syntaxes for character strings.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116587396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
"Coherent programming" refers to a set of conventions and techniques that we believe have the power to shape the growth of a library of programs, so that a user may draw upon them freely and with minimal concern about the details of their compatibility. The purpose of this paper is to explain the concept of coherence, and to show how it has been applied in the Lincoln Reckoner, an on-line system that provides computational assistance to scientists and engineers. The external specifications of the Reckoner, which have been presented elsewhere [1], will not be discussed here. Rather, this paper will concentrate on some of the " architectural" considerations in the design of user-oriented on-line systems.
{"title":"Coherent programming in the Lincoln Reckoner","authors":"R. Wiesen, D. Yntema, J. Forgie, Arthur N. Stowe","doi":"10.1145/2402536.2402552","DOIUrl":"https://doi.org/10.1145/2402536.2402552","url":null,"abstract":"\"Coherent programming\" refers to a set of conventions and techniques that we believe have the power to shape the growth of a library of programs, so that a user may draw upon them freely and with minimal concern about the details of their compatibility. The purpose of this paper is to explain the concept of coherence, and to show how it has been applied in the Lincoln Reckoner, an on-line system that provides computational assistance to scientists and engineers. The external specifications of the Reckoner, which have been presented elsewhere [1], will not be discussed here. Rather, this paper will concentrate on some of the \" architectural\" considerations in the design of user-oriented on-line systems.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127124337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For approximately three and one-half years a continuous modest-level effort has been maintained at Aerospace Corporation to support the development of analyst-oriented computer languages which could be used for both off-line and interactive applications. Initially, this effort produced a block-oriented macro language called EASL (Engineering Analysis and Simulation Language) [1].
{"title":"Two analyst-oriented computer languages: EASL, POSE","authors":"S. Schlesinger, L. Sashkin, K. C. Reed","doi":"10.1145/2402536.2402545","DOIUrl":"https://doi.org/10.1145/2402536.2402545","url":null,"abstract":"For approximately three and one-half years a continuous modest-level effort has been maintained at Aerospace Corporation to support the development of analyst-oriented computer languages which could be used for both off-line and interactive applications. Initially, this effort produced a block-oriented macro language called EASL (Engineering Analysis and Simulation Language) [1].","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123982033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
As a programming language, AMTRAN is designed to satisfy two objectives: the reduction of programming cost and effort by at least an order of magnitude, and the provision of a semiautomatic numerical analytical problem solving system. It resembles a blend of FORTRAN and ALGOL but possesses certain additional features. These include the following.
{"title":"What is different about AMTRAN?","authors":"Richard J. Plocica","doi":"10.1145/2402536.2402560","DOIUrl":"https://doi.org/10.1145/2402536.2402560","url":null,"abstract":"As a programming language, AMTRAN is designed to satisfy two objectives: the reduction of programming cost and effort by at least an order of magnitude, and the provision of a semiautomatic numerical analytical problem solving system. It resembles a blend of FORTRAN and ALGOL but possesses certain additional features. These include the following.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115426780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of time-sharing is twofold: to increase the efficiency of the computer system and, while attaining this increase, to permit efficient communication between a programmer and his programs. This communication we may call conversation. Prevailing programming languages like FORTRAN, PL/1, ALGOL, COBOL, etc., are poorly designed for such interactive programming. However, languages like JOSS [1], APL [2], and the to be described LC2 are much more suited to this task.
{"title":"LC2: a language for conversational computing","authors":"J. Mitchell, A. Perlis, H. V. Zoeren","doi":"10.1145/2402536.2402558","DOIUrl":"https://doi.org/10.1145/2402536.2402558","url":null,"abstract":"The purpose of time-sharing is twofold: to increase the efficiency of the computer system and, while attaining this increase, to permit efficient communication between a programmer and his programs. This communication we may call conversation. Prevailing programming languages like FORTRAN, PL/1, ALGOL, COBOL, etc., are poorly designed for such interactive programming. However, languages like JOSS [1], APL [2], and the to be described LC2 are much more suited to this task.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123101655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The theme of these symposium proceedings is Interactive Systems for Experimental Applied Mathematics. Certainly, there can be little confusion about the basic meaning or broad fundamentals of applied mathematics. However, questions as to the value of the experimental approach toward mathematics are an entirely different matter. The present state-of-the-art is so scant in empirical or theoretical guidelines that this approach must be acknowledged as an expression of faith that a computer, used to explore ill-defined mathematical constructs and problems, might yield powerful insights and a fruitful methodology. The term interactive is difficult to define and I cannot pretend that I fully understand the relevance of the term as applied to some specific systems. However, in some sense, we would suppose that what we mean is close to the definition used by the physicist. When two effects interact, they do so in a nonseparable and usually nonlinear way. Usually, the effect of the interaction is that the whole is not simply equal to the sum of its parts, and that the characteristics of the interacted system can be surprisingly different from the qualities of its constituent parts. Therefore, in the man-machine interaction, we would expect more than in the old process of inputting a well-formulated set of directions with the machine performing in its capacity as an idiot savant. Obviously we can expect that any serious attempt at man-machine interaction will involve on-line response. However, I would not entirely exclude the possibility that significant interaction can occur off-line.
{"title":"Interactive programming and automated mathematics","authors":"M. Klerer","doi":"10.1145/2402536.2402538","DOIUrl":"https://doi.org/10.1145/2402536.2402538","url":null,"abstract":"The theme of these symposium proceedings is Interactive Systems for Experimental Applied Mathematics. Certainly, there can be little confusion about the basic meaning or broad fundamentals of applied mathematics. However, questions as to the value of the experimental approach toward mathematics are an entirely different matter. The present state-of-the-art is so scant in empirical or theoretical guidelines that this approach must be acknowledged as an expression of faith that a computer, used to explore ill-defined mathematical constructs and problems, might yield powerful insights and a fruitful methodology. The term interactive is difficult to define and I cannot pretend that I fully understand the relevance of the term as applied to some specific systems. However, in some sense, we would suppose that what we mean is close to the definition used by the physicist. When two effects interact, they do so in a nonseparable and usually nonlinear way. Usually, the effect of the interaction is that the whole is not simply equal to the sum of its parts, and that the characteristics of the interacted system can be surprisingly different from the qualities of its constituent parts. Therefore, in the man-machine interaction, we would expect more than in the old process of inputting a well-formulated set of directions with the machine performing in its capacity as an idiot savant. Obviously we can expect that any serious attempt at man-machine interaction will involve on-line response. However, I would not entirely exclude the possibility that significant interaction can occur off-line.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134527560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In our previous work [1, 2], an effort was made to determine which of the many methods and orders available for the numerical integration of ordinary differential equations was best. While it was possible to show that, under certain circumstances, some methods and orders outperformed others, no one method was clearly superior under all circumstances.
{"title":"A learning program for the integration of systems of ordinary differential equations","authors":"L. Gallaher, I. E. Perlin","doi":"10.1145/2402536.2402573","DOIUrl":"https://doi.org/10.1145/2402536.2402573","url":null,"abstract":"In our previous work [1, 2], an effort was made to determine which of the many methods and orders available for the numerical integration of ordinary differential equations was best. While it was possible to show that, under certain circumstances, some methods and orders outperformed others, no one method was clearly superior under all circumstances.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"17 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132831060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Slave Interactive System (SIS) is a software system that makes available an interactive computing facility on a multiprogramming, remote-batch computer system. SIS runs under the computer's operating system in the same manner as a batch (or slave) job. The other slave programs continue as background work during an interactive run. However, SIS is intended to serve only one interactive user at a time; it is not built for multiple-access, time-sharing usage. SIS is a research vehicle designed to continue exploratory programming in user-oriented computing which requires a high degree of interaction and system flexibility.
{"title":"The Slave Interactive System: a one-user interactive executive grafted on a remote-batch computing system","authors":"K. J. Busch, G. Luderer","doi":"10.1145/2402536.2402562","DOIUrl":"https://doi.org/10.1145/2402536.2402562","url":null,"abstract":"The Slave Interactive System (SIS) is a software system that makes available an interactive computing facility on a multiprogramming, remote-batch computer system. SIS runs under the computer's operating system in the same manner as a batch (or slave) job. The other slave programs continue as background work during an interactive run. However, SIS is intended to serve only one interactive user at a time; it is not built for multiple-access, time-sharing usage. SIS is a research vehicle designed to continue exploratory programming in user-oriented computing which requires a high degree of interaction and system flexibility.","PeriodicalId":148361,"journal":{"name":"Symposium on Interactive Systems for Experimental Applied Mathematics","volume":"309 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1967-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134197508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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