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Автор: Dusko Pavlovic
Издательство: Springer
Год: 2023
Страниц: 261
Язык: английский
Формат: pdf (true)
Размер: 10.1 MB
It is not always clear what computer programs mean in the various languages in which they can be written, yet a picture can be worth 1000 words, a diagram 1000 instructions. In this unique textbook/reference, programs are drawn as string diagrams in the language of categories, which display a universal syntax of mathematics (Computer scientists use them to analyze the program semantics; programmers to display the syntax of computations). Here, the string-diagrammatic depictions of computations are construed as programs in a single-instruction programming language. Such programs as diagrams show how functions are packed in boxes and tied by strings. Readers familiar with categories will learn about the foundations of computability; readers familiar with computability gain access to category theory. Additionally, readers familiar with both are offered many opportunities to improve the approach. While programmers program computers in a great variety of languages, mathematicians study mathematics in a great variety of completely different languages. A great variety of languages is a good thing, provided that the languages do not isolate but diversify the views of the world and that there are multi-lingual communities to connect them. Many mathematicians speak programming languages; many programmers are conversant with mathematics. The language of categories seems convenient for both, and to some extent connects the communities.