A type system is a syntactic method for automatically checking the absence of certain erroneous behaviors by classifying program phrases according to the kinds of values they compute. The study of type systems--and of programming languages from a type-theoretic perspective—-has important applications in software engineering, language design, high-performance compilers, and security.This text provides a comprehensive introduction both to type systems in computer science and to the basic theory of programming languages. The approach is pragmatic and operational; each new concept is motivated by programming examples and the more theoretical sections are driven by the needs of implementations. Each chapter is accompanied by numerous exercises and solutions, as well as a running implementation, available via the Web. Dependencies between chapters are explicitly identified, allowing readers to choose a variety of paths through the material.The core topics include the untyped lambda-calculus, simple type systems, type reconstruction, universal and existential polymorphism, subtyping, bounded quantification, recursive types, kinds, and type operators. Extended case studies develop a variety of approaches to modeling the features of object-oriented languages.
Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Benjamin C. Pierce received his doctoral degree from Carnegie Mellon University.Contents : Tutorial. Applications. Further Reading.
The study of type systems for programming languages now touches many areas of computer science, from language design and implementation to software engineering, network security, databases, and analysis of concurrent and distributed systems. This book offers accessible introductions to key ideas in the field, with contributions by experts on each topic.
The topics covered include precise type analyses, which extend simple type systems to give them a better grip on the run time behavior of systems; type systems for low-level languages; applications of types to reasoning about computer programs; type theory as a framework for the design of sophisticated module systems; and advanced techniques in ML-style type inference.
Advanced Topics in Types and Programming Languages builds on Benjamin Pierce's Types and Programming Languages (MIT Press, 2002); most of the chapters should be accessible to readers familiar with basic notations and techniques of operational semantics and type systems—the material covered in the first half of the earlier book.
Advanced Topics in Types and Programming Languages can be used in the classroom and as a resource for professionals. Most chapters include exercises, ranging in difficulty from quick comprehension checks to challenging extensions, many with solutions.