APL and a Black-Box theory of electric circuits

Abstract

The paper presents the rudiments of a theory of resistive electric circuits viewed as black boxes. The relevant mathematical model is a function mapping voltage vectors to current vectors and having two properties which can be regarded as analogous to Kirchhoff's laws. This treatment of electric circuit theory is unconventional and in fact appears to be new. The purpose of the paper is not to develop the theory itself but to show the convenience and precision of the APL notation in such a theory, and also to illustrate the need, even in a relatively simple application, for general arrays of functions and numbers, and for a notation for and a means of specifying user-defined operators.