**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

**Programming Languages: Application and Interpretation**

by

**Shriram Krishnamurthi**-

**Lulu.com**

The textbook for a programming languages course, taken primarily by advanced undergraduate and beginning graduate students. This book assumes that students have modest mathematical maturity, and are familiar with the existence of the Halting Problem.

(

**11878**views)

**Semantics of Programming Languages**

by

**Andrew M. Pitts**-

**University of Cambridge**

These notes introduce the structural, operational approach to programming language semantics. The course shows how to specify the meaning of some simple programming language constructs and to reason formally about semantic properties of programs.

(

**8195**views)

**Programming and Programming Languages**

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.

(

**7092**views)

**Semantics With Applications: A Formal Introduction**

by

**Hanne Riis Nielson, Flemming Nielson**-

**John Wiley & Sons**

The book covers the foundations of structural operational semantics and natural semantics. It shows how to describe the semantics of declarative as well as imperative language constructs and will also touch upon non-sequential constructs.

(

**12431**views)