Another Word For It Patrick Durusau on Topic Maps and Semantic Diversity

November 29, 2012

Notation as a Tool of Thought

Filed under: Language,Language Design,Programming — Patrick Durusau @ 1:33 pm

Notation as a Tool of Thought by Kenneth E. Iverson.

From the introduction:

Nevertheless, mathematical notation has serious deficiencies. In particular, it lacks universality, and must be interpreted differently according to the topic, according to the author, and even according to the immediate context. Programming languages, because they were designed for the purpose of directing computers, offer important advantages as tools of thought. Not only are they universal (general-purpose), but they are also executable and unambiguous. Executability makes it possible to use computers to perform extensive experiments on ideas expressed in a programming language, and the lack of ambiguity makes possible precise thought experiments. In other respects, however, most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant by, say, an applied mathematician.

The thesis of the present paper is that the advantages of executability and universality found in programming languages can be effectively combined, in a single coherent language, with the advantages offered by mathematical notation.

Will expose you to APL but that’s not a bad thing. The history of reasoning about data structures can be interesting and useful.

Iverson’s response to critics of the algorithms in this work was in part as follows:

…overemphasis of efficiency leads to an unfortunate circularity in design: for reasons of efficiency early programming languages reflected the characteristics of the early computers, and each generation of computers reflects the needs of the programming languages of the preceding generation. (5.4 Mode of Presentation)

A good reason to understand the nature of a problem before reaching for the keyboard.

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