Programs as diagrams : from categorical computability to computable categories / Dusko Pavlovic.
2023
QA169
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Details
Title
Programs as diagrams : from categorical computability to computable categories / Dusko Pavlovic.
Author
Pavlović, Dusko, author.
ISBN
9783031348273 (electronic bk.)
3031348273 (electronic bk.)
9783031348266
3031348265
3031348273 (electronic bk.)
9783031348266
3031348265
Published
Cham, Switzerland : Springer, [2023]
Language
English
Description
1 online resource (xvii, 252 pages) : illustrations.
Item Number
10.1007/978-3-031-34827-3 doi
Call Number
QA169
Dewey Decimal Classification
512/.62
Summary
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. 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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed September 25, 2023).
Series
Theory and applications of computability.
Available in Other Form
Programs As Diagrams
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Table of Contents
1. 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.
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.