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- Дата: 10-04-2023, 20:36
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![Category Theory: Invariances and Symmetries in Computer Science](/uploads/posts/2023-04/1681148254_7271_cat_gory_th_ory__invarianc_s_and_symm_tri_s_in_comput_r_sci_nc_.jpg)
Автор: Zoran Majkic
Издательство: De Gruyter
Год: 2023
Страниц: 436
Язык: английский
Формат: pdf (true), epub
Размер: 54.2 MB
This book presents the formal definition of fundamental transformations in Category Theory as a mathematical language to be used in Computer Science modelling. The book focuses in particular on models with Global and Internal symmetries (in analogy to Field Theories like Quantum Mechanics and General Relativity). The second part of the book is dedicated to more advanced applications of Category Theory to Computer Science. In computer science, the lambda calculus made its first appearance in programming language LISP, which has been also the first formal programming language to use the procedures as objects of the language. Consequently, in LISP the programs and data are not distinguished, but they are all elements of a unique untyped universe. Anyway, in each programming practice, the types arise naturally, even starting from untyped universes, when the programming objects are categorized according to their usage or behavior. Since the first appearance of types in the programming language Algol 60, when the typing of variables was introduced to check at compile time the connection of instances of use with associated declarations, typing has been considered an essential method that guides a programmer in a design of a programming code.