Semicolon-bracket notation: A hidden resource in APL

Abstract

The semicolon-bracket (SB) notation for indexing an array in APL has often been regarded unfavorably because of its anomalous character relative to other APL functions: the function symbol is a pair of brackets rather than a single character; the bracket pair is bound to the associated array at a higher precedence than any other function; and the requisite number of semicolons must appear literally within the brackets, so that the construct within the brackets when one or more semicolons are present is not an APL object, and therefore cannot be substituted for by another APL expression without semicolons. Nevertheless, this notation provides a simple way to index arrays of any rank, and has proven to be very convenient in practice. In this paper, it will be shown that the SB notation can (a) easily be extended to defined functions, and that it can also be used (b) to allow a multiplicity of names to be used unambiguously to the left of assignment, (c) to allow multiple statements on a line in a manner similar to that provided by the diamond separator in some APL systems, and (d) to extend and generalize the use of bracketed expressions as an axis operator.