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020 _a9783031348273
_9978-3-031-34827-3
024 7 _a10.1007/978-3-031-34827-3
_2doi
050 4 _aQA75.5-76.95
072 7 _aUYA
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aUYA
_2thema
082 0 4 _a004.0151
_223
100 1 _aPavlovic, Dusko.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aPrograms as Diagrams
_h[electronic resource] :
_bFrom Categorical Computability to Computable Categories /
_cby Dusko Pavlovic.
250 _a1st ed. 2023.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2023.
300 _aXVII, 252 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aTheory and Applications of Computability, In cooperation with the association Computability in Europe,
_x2190-6203
505 0 _a1. Drawing Types and Functions -- 2. Monoidal Computer: Computability as a Structure -- 3. Fixpoints -- 4. What can be Computed -- 5. What cannot be Computed -- 6. Computing Programs -- 7. Program-Closed Categories: Computability as a Property -- 8. Computable Categories and Effective Categorical Operations.
520 _aIt 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. Topics and features: Delivers a ‘crash’ diagram-based course in theory of computation Uses single-instruction diagrammatic programming language Offers a practical introduction into categories and string diagrams as computational tools Reveals how computability is programmability, rather than an ‘ether’ permeating computers Provides a categorical model of intensional computation is unique up to isomorphism Serves as a stepping stone into research of computable categories In addition to its early chapters introducing computability for beginners, this flexible textbook/resource also contains both middle chapters that expand for suitability to a graduate course as well as final chapters opening up new research. Dusko Pavlovic is a professor at the Department of Information and Computer Sciences at the University of Hawaii at Manoa, and by courtesy at the Department of Mathematics and the College of Engineering. He completed this book as an Excellence Professor at Radboud University in Nijmegen, The Netherlands.
650 0 _aComputer science.
650 0 _aComputable functions.
650 0 _aRecursion theory.
650 0 _aComputational complexity.
650 0 _aProgramming languages (Electronic computers).
650 1 4 _aTheory of Computation.
650 2 4 _aComputability and Recursion Theory.
650 2 4 _aComputational Complexity.
650 2 4 _aProgramming Language.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031348266
776 0 8 _iPrinted edition:
_z9783031348280
776 0 8 _iPrinted edition:
_z9783031348297
830 0 _aTheory and Applications of Computability, In cooperation with the association Computability in Europe,
_x2190-6203
856 4 0 _uhttps://doi.org/10.1007/978-3-031-34827-3
912 _aZDB-2-SCS
912 _aZDB-2-SXCS
942 _cSPRINGER
999 _c185121
_d185121