Kenneth E. Iverson

A formal description of SYSTEM/360

All SYSTEM/360 functional characteristics having programming significance are completely and concisely described. The description, which is formal rather than verbal, is accomplished by a set of programs, interacting through common variables, used in conjunction with auxiliary tables. The language used in the programs involves operators and notation selected from mathematics and logic, together with additional operators and conventions defined to facilitate system description. Although the formal description is complete and self-contained, text is provided as an aid to initial study. Examples to illustrate the application of the formal description are given in an appendix.

A dictionary of APL

APL is a formal, imperative language. Because it is imperative, a sentence may be called an instruction, and may be executed to produce a result. In illustrations used here, an instruction will be indented, and the result of its execution will be shown on the following line without indentation.

The role of operators in APL

Operators, which apply to functions to produce functions, are an important component of APL. Despite their importance, their role is not well understood, and they are often lumped with functions in expositions of the language. This paper attempts to clarify the role of operators in APL by tracing their development, outlining possible future directions, and commenting briefly on their roles in other languages, both natural and programming.

A personal view of APL

This essay portrays a personal view of the development of several influential dialects of APL: APL2 and J. The discussion traces the evolution of the treatment of arrays, functions, and operators, as well as function definition, grammar, terminology, and spelling.

A function definition operator

This paper proposes two related extensions to APL: the extension of assignment to allow a name <italic>F</italic> to be assigned to a derived function by an expression of the form <italic>F</italic>←+.x, and the introduction of a dyadic operator @@@@ to apply to character arrays <italic>D</italic> and <italic>M</italic> so that <italic>D</italic>@@@@<italic>M</italic> produces an ambivalent function in which the dyadic case is defined by <italic>D</italic> and the monadic case by <italic>M</italic>.

The evolution of APL

This paper is a discussion of the evolution of the APL language, and it treats implementations and applications only to the extent that they appear to have exercised a major influence on that evolution. Other sources of historical information are cited in References 1-3; in particular, The Design of APL [1] provides supplementary detail on the reasons behind many of the design decisions made in the development of the language. Readers requiring background on the current definition of the language should consult APL Language [4]. Although we have attempted to confirm our recollections by reference to written documents and to the memories of our colleagues, this remains a personal view which the reader should perhaps supplement by consulting the references provided. In particular, much information about individual contributions will be found in the Appendix to The Design of APL [1], and in the Acknowledgements in A Programming Language [10] and in APL\360 Users Manual [23]. Because Reference 23 may no longer be readily available, the acknowledgements from it are reprinted in Appendix A.

A method of syntax specification

The addition of a few simple conventions to the Backus Normal Form specification of a language provides a mode of description which is more compact and easier to prepare and use than either the standard BNF description [1] or the corresponding syntactical chart [2].

The derivative operator

This paper defines a single derivative operator which, together with certain related operators, provides a coherent treatment of many aspects of the derivative including the Jacobian, Laplacian, gradient, divergence, and curl. Working models of all operators are provided in a set of APL functions.

Programming notation in systems design

The function of programming notation in systems design and the characteristics of a suitable language are discussed. A brief introduction is given to a particular language (developed by the author and detailed elsewhere) which has many of the desired properties. Application of the language is illustrated by the use of familiar examples.

Practical uses of a model of APL

This paper discusses the use of a general model of APL (written in APL) which allows convenient definition of new operators and functions and experimentation with their use. Use of the model is illustrated by a number of functions and operators, some of which have been previously discussed, and some (such as the operator til) which are new. Details of the model itself are not treated. The effective use of new facilities introduced into APL systems is often long delayed, not only because of a programmers tendency to cling to familiar ways, but also because the abstract, formal treatment necessary to the specification of a new facility often makes its assimilation and use seem unduly difficult. Working models of new facilities available before their actual introduction can be very helpful in teaching their use, and very effective in speeding their widespread application. However, the development of an accurate model for each new facility can, especially in the case of new operators, be burdensome, and we have found that a general model of the APL interpreter, developed primarily for use by the language designers in the design and modelling of new extensions, can also be useful in providing specific models for the enlightenment of users. This paper discusses such uses of the general model, employing illustrations executed by the version available on the I.P. Sharp Associates APL system. Except for information necessary for understanding its use, details of the model will not be discussed here. The model incorporates a number of facilities proposed in earlier papers [1 2 3]; the more fundamental among them are illustrated below. The model, invoked by executing the function ΔAPL, accepts character input and parses and executes the expression entered. 0-origin indexing is used throughout the paper.