Logo

Categories, Types, and Structures

Categories, Types, and Structures
by

Publisher: MIT Press
ISBN/ASIN: 0262011255
ISBN-13: 9780262011259
Number of pages: 300

Description:
The main methodological connection between programming language theory and category theory is the fact that both theories are essentially "theories of functions." A crucial point, though, is that the categorical notion of morphism generalizes the set-theoretical description of function in a very broad sense, which provides a unified understanding of various aspects of the theory of programs. This book is mostly inspired by this specific methodological connection and its applications to the theory of programming languages. More precisely, as expressed by the subtitle, it aims at a self-contained introduction to general category theory (part I) and at a categorical understanding of the mathematical structures that constituted the theoretical background of relevant areas of language design (part II). The impact on functional programming, for example, of the mathematical tools described in part II, is well known, as it ranges from the early dialects of Lisp, to Edinburgh ML, to the current work in polymorphisms and modularity. Other applications, such as CAML, which will be described, use categorical formalization for the purposes of implementation.

Home page url

Download or read it online for free here:
Download link
(PDF)

Similar books

Book cover: Let Over Lambda: 50 Years of LispLet Over Lambda: 50 Years of Lisp
by - Lulu.com
One of the most hardcore computer programming books out there. Starting with the fundamentals, it describes the most advanced features of the most advanced language: Common Lisp. This book is about macros, that is programs that write programs.
(20470 views)
Book cover: A Practical Theory of ProgrammingA Practical Theory of Programming
by - Springer
Understanding programming languages requires knowledge of the underlying theoretical model. This book explores aspects of programming that are amenable to mathematical proof. It describes a simple and comprehensive theory.
(13506 views)
Book cover: Structure and Interpretation of Computer ProgramsStructure and Interpretation of Computer Programs
by - McGraw-Hill
The book teaches how to program by employing the tools of abstraction and modularity. The central philosophy is that programming is the task of breaking large problems into small ones. You will learn how to program and how to think about programming.
(17238 views)
Book cover: Introduction to Programming LanguagesIntroduction to Programming Languages
- Wikibooks
This book is an attempt to describe a bit of the programming languages zoo. We use each of the particular languages to introduce fundamental notions related to the design and the implementation of general purpose programming languages.
(8775 views)