Programs as Diagrams: From Categorical Computability to Computable Categories [Hardcover]

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 professorl“H