Formal language
History

In the 17th century, Gottfried Leibniz imagined and described the characteristica universalis, a universal and formal language which utilised pictographs. Later, Carl Friedrich Gauss investigated the problem of Gauss codes.

Gottlob Frege attempted to realize Leibniz's ideas, through a notational system first outlined in Begriffsschrift (1879) and more fully developed in his 2-volume Grundgesetze der Arithmetik (1893/1903). This described a "formal language of pure language."

In the first half of the 20th century, several developments were made with relevance to formal languages. Axel Thue published four papers relating to words and language between 1906 and 1914. The last of these introduced what Emil Post later termed 'Thue Systems', and gave an early example of an undecidable problem. Post would later use this paper as the basis for a 1947 proof "that the word problem for semigroups was recursively insoluble", and later devised the canonical system for the creation of formal languages.

In 1907, Leonardo Torres Quevedo introduced a formal language for the description of mechanical drawings (mechanical devices), in Vienna. He published "Sobre un sistema de notaciones y símbolos destinados a facilitar la descripción de las máquinas" ("On a system of notations and symbols intended to facilitate the description of machines"). Heinz Zemanek rated it as an equivalent to a programming language for the numerical control of machine tools.

Noam Chomsky devised an abstract representation of formal and natural languages, known as the Chomsky hierarchy. In 1959 John Backus developed the Backus-Naur form to describe the syntax of a high level programming language, following his work in the creation of FORTRAN. Peter Naur was the secretary/editor for the ALGOL60 Report in which he used Backus–Naur form to describe the Formal part of ALGOL60.
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