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 Muhammad Tanvir Afzal (ed.) - InTech
The book is a blend of a number of great ideas, theories, mathematical models, and practical systems in the domain of Semantics. Topics include: Background; Queries, Predicates, and Semantic Cache; Algorithms and Logic Programming; etc.
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 Robert Harper
Provides an account of the role of type theory in programming language design and implementation. The stress is on the use of types as a tool for analyzing programming language features and studying their implementation.
by Keijo Ruohonen - Tampere University of Technology
In these notes the classical Chomskian formal language theory is fairly fully dealt with, omitting however much of automata constructs and computability issues. Surveys of Lindenmayer system theory and the mathematical theory of codes are given.