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Current implementations of APL give one as the result of zero divided by zero. This paper gives the reasons for proposing that this quotient be changed to zero. Two conventions introduced by K. E. Iverson  for the exposition of mathematical topics are used here.
This paper gives some of the history of the early implementations of APL, and concentrates on the system aspects of these implementations, paying special attention to the evolution of the workspace concept, the time-sharing scheduling strategy, and the handling of the terminal. It contrasts the development of APL with the development of other time-sharing… (More)
This paper proposes a notation to be used for the greatest common divisor (gcd) and least common multiple (1cm) functions in APL. The notation proposed is that in use for the logical or and and functions: @@@@ for gcd and Λ for lcm. For this reason, special attention is paid to the cases of gcd and lcm for the arguments 0 and 1. Also, because we wish… (More)
Toronto NOTE: In this paper we use the linguistic terms verb and pronoun interchangeably with the mathematical terms function and variable. INTRODUCTION In standard APL [ISOSS] certain forms are ungrammatical, and new definitions could be adopted for them without conflict. Such definitions we shall call phrasal form [AHD76]. For example, if b and c are… (More)
This paper describes an efficient algorithm for the APL scans for eight Boolean functions, those whose symbols employ the caret in some orientation. The APL reduction function for each can be derived from the scan algorithm.
To characterize a much larger effort, the design and implementation of a square root routine for IPSA APL is described. The routine is perfect in the sense that, if the result can be represented exactly, the exact result is given. If the result cannot be represented exactly, it is rounded to the nearest representable floating point number. The use of APL in… (More)
This paper describes a series of functions for performing Conway's game of Life [Ga70] in APL, beginning with versions that go back to the early 1970's. The paper doesn't deal with the game itself, but rather with the expressive power of various approaches, and particularly with the increased expressiveness found in some of the new operator extensions to… (More)
Once we conceive of the real line as embedded in a pIane of complex numbers, we have entered a whole new domain of mathematics. All our old knowledge of real algebra and analysis becomes enlarged and enriched when reinterpreted in the complex domain. In addition, we immediately see countless new problems and questions which could not even have been raised… (More)
Session 1: The APL Dictionary "I'm amazed at the number of times people accuse me of having learned something." The 1985 Minnowbrook meeting began with a talk by Ken Iverson titled "The APL Dictionary". Iverson described his proposal for an APL with simpler structure and more versatility than existing APLs, but permitting an evolutionary migration of… (More)
This paper is a progress report on work undertaken to include tree data structures by means of the boxed data type available in J. Methods for displaying these boxed arrays as trees are shown. This work is part of a larger effort to provide a comprehensive set of facilities in J for working with tree structures. The facilities described were at first… (More)