Categories, Types, and Structures
by Andrea Asperti, Giuseppe Longo
Publisher: MIT Press 1991
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.
Download or read it online for free here:
Download link
(PDF)
Similar books
Practical Foundations for Programming Languagesby Robert Harper - Carnegie Mellon University
This is a book on the foundations of programming languages. The emphasis is on the concept of type, which organizes the computational universe in the same way that the concept of set may be seen as an organizing principle for mathematics.
(17161 views)
Lecture Notes on the Lambda Calculusby Peter Selinger - Dalhousie University
Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, type inference, etc.
(12256 views)
The Theory of Languages and Computationby Jean Gallier, Andrew Hicks - University of Pennsylvania
From the table of contents: Automata; Formal Languages (A Grammar for Parsing English, Context-Free Grammars, Derivations and Context-Free Languages, Normal Forms for Context-Free Grammars, Chomsky Normal Form, ...); Computability; Current Topics.
(9381 views)
Proofs and Typesby J. Girard, Y. Lafont, P. Taylor - Cambridge University Press
This little book comes from a short graduate course on typed lambda-calculus given at the Universite Paris. It is not intended to be encyclopedic and the selection of topics was really quite haphazard. Some very basic knowledge of logic is needed.
(18573 views)