The CTalk programming language: a strategic evolution of APL
APL '92 Proceedings of the international conference on APL
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The extended abstract below outlines the main points of a more complete paper in preparation. The purpose of the paper is to trace seven lines of development that have carried array theory from some of its original questions through a succession of intermediate answers to current suggestions for a more coherent theory. The paper explains the algebraic motivations for the theory and how and why the treatment of empty arrays in the Nested Interactive Array Language, Nial, differ from that in APL2. The paper introduces modular indexing, indexing from the end of an axis with negative indices, arrays viewed as tori, arithmetical and Boolean operations on non-numbers and nontruth values, and a purely structural operation underlying reshaping.