Functional Calculation 0: Numerical Apéritif ABSTRACT

This article is the first in a series expounding the joys of functional calculation. Functional calculation does with operations applied to functions and numbers what numerical calculation does with functions applied to numbers. The functional notation used as the vehicle in this series is provided by a freely available calculation tool calledJ. This article gives a detailed illustration of a few numerical uses of the notation supported by the J interpreter. This explanation is preliminary to following articles, which will review some of that tool’s support for numerical calculation. The illustration takes a simple function and shows how J, or any other tool for functional calculation, can be used to investigate special values of the function. CALCULATION Calculation is an honourable and satisfying occupation with a long history and a rich tradition [1]. Relatively recent developments in electronic computation have led to the adoption of three classes of aids to calculation, namel