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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 [1] for the exposition of mathematical topics are used here.

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)

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)

- DIS, Leigh Clayton, Mark D. Eklof, Eugene McDonnell
- 1998

Annexes A Component Files (normative) 263 A.1 Definitions of arguments and

Certain pairs of arguments to the residue function, as implemented on many APL systems, give results which make it seem as if the ordinary decimal relationships we remember from grade school no longer hold. As far as we can tell, it looks as if a given modulus should divide the right argument, but the implementation tells us it doesn't. A definition for a… (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 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)

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)

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)