Categories, Types, and Structures
by Andrea Asperti, Giuseppe Longo
Publisher: MIT Press 1991
Number of pages: 300
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:
by Shuly Wintner - ESSLLI
This text is a mild introduction to Formal Language Theory for students with little or no background in formal systems. The motivation is Natural Language Processing, and the presentation is geared towards NLP applications, with extensive examples.
by Mira Balaban - Ben-Gurion University of the Negev
This course is about building computational processes. We need computational processes for computing functions. The means for performing computational processes are programs. The emphasis is on programming languages and their properties.
by Eric C.R. Hehner - 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.
by Shriram Krishnamurthi - Brown University
Many people would regard this as being two books in one. One book is an introduction to programming, teaching you basic concepts of organizing data and the programs that operate over them. The other book is an introduction to programming languages.