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Jespersen's formalism: problems and extensions

This article aims to give a new, rigorous, and exhaustive presentation of Jespersen's formalism published in Analytic Syntax (1937). The formalism is described by means of the Backus metalinguistic formulas (Backus, 1959), which were universally adopted for the description of the syntax of computer programming languages. A modernized version of Jespersen's algorithm is proposed and illustrated with a number of significant examples.