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.
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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.
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.
by 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.
by Kenneth Slonneger, Barry L. Kurtz - Addison Wesley Longman
The book presents the typically difficult subject of formal methods in an informal, easy-to-follow manner. Readers with a basic grounding in discreet mathematics will be able to understand the practical applications of these difficult concepts.