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Mathematical Preliminaries - Untyped Systems - Untyped Arithmetic Expressions - An ML Implementation of Arithmetic Expressions - The Untyped Lambda-Calculus - Nameless Representation of Terms - An ML Implementation of the Lambda-Calculus - Types Arithmetic Expressions - Simply Typed Lambda-Calculus - An ML Implementation of Simple Types - Simple Extensions - Normalization - Exceptions - Subtyping - Metatheory of Subtyping - An ML Implementation of Subtyping - Recursive Types - Metatheory of Recursive Types - Polymorphism - Type Reconstruction - Universal Types - Existential Types - An ML Implementation of System F - Bounded Quantification - Higher-Order Systems - Higher-Order Polymorphism - Higher-Order Subtyping.
A thorough and accessible introduction to a range of key ideas in type systems for programming language. 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.
The Formal Semantics of Programming Languages provides the basic mathematical techniques necessary for those who are beginning a study of the semantics and logics of programming languages. These techniques will allow students to invent, formalize, and justify rules with which to reason about a variety of programming languages. Although the treatment is elementary, several of the topics covered are drawn from recent research, including the vital area of concurency. The book contains many exercises ranging from simple to miniprojects.Starting with basic set theory, structural operational semantics is introduced as a way to define the meaning of programming languages along with associated proof techniques. Denotational and axiomatic semantics are illustrated on a simple language of while-programs, and fall proofs are given of the equivalence of the operational and denotational semantics and soundness and relative completeness of the axiomatic semantics. A proof of Godel's incompleteness theorem, which emphasizes the impossibility of achieving a fully complete axiomatic semantics, is included. It is supported by an appendix providing an introduction to the theory of computability based on while-programs.Following a presentation of domain theory, the semantics and methods of proof for several functional languages are treated. The simplest language is that of recursion equations with both call-by-value and call-by-name evaluation. This work is extended to lan guages with higher and recursive types, including a treatment of the eager and lazy lambda-calculi. Throughout, the relationship between denotational and operational semantics is stressed, and the proofs of the correspondence between the operation and denotational semantics are provided. The treatment of recursive types - one of the more advanced parts of the book - relies on the use of information systems to represent domains. The book concludes with a chapter on parallel programming languages, accompanied by a discussion of methods for specifying and verifying nondeterministic and parallel programs.
Semantics of Programming Languages exposes the basic motivations and philosophy underlying the applications of semantic techniques in computer science. It introduces the mathematical theory of programming languages with an emphasis on higher-order functions and type systems. Designed as a text for upper-level and graduate-level students, the mathematically sophisticated approach will also prove useful to professionals who want an easily referenced description of fundamental results and calculi.Basic connections between computational behavior, denotational semantics, and the equational logic of functional programs are thoroughly and rigorously developed. Topics covered include models of types, operational semantics, category theory, domain theory, fixed point (denotational). semantics, full abstraction and other semantic correspondence criteria, types and evaluation, type checking and inference, parametric polymorphism, and subtyping. All topics are treated clearly and in depth, with complete proofs for the major results and numerous exercises.
The Structure of Typed Programming Languages describes the fundamental syntactic and semantic features of modern programming languages, carefully spelling out their impacts on language design. Using classical and recent research from lambda calculus and type theory, it presents a rational reconstruction of the Algol-like imperative languages such as Pascal, Ada, and Modula-3, and the higher-order functional languages such as Scheme and ML. David Schmidt's text is based on the premise that although few programmers ever actually design a programming language, it is important for them to understand the structuring techniques. His use of these techniques in a reconstruction of existing programming languages and in the design of new ones allows programmers and would-be programmers to see why existing languages are structured the way they are and how new languages can be built using variations on standard themes. The text is unique in its tutorial presentation of higher-order lambda calculus and intuitionistic type theory. The latter in particular reveals that a programming language is a logic in which its typing system defines the propositions of the logic and its well-typed programs constitute the proofs of the propositions. The Structure of Typed Programming Languages is designed for use in a first or second course on principles of programming languages. It assumes a basic knowledge of programming languages and mathematics equivalent to a course based on books such as Friedman, Wand, and Haynes': Essentials of Programming Languages. As Schmidt covers both the syntax and the semantics of programming languages, his text provides a perfect precursor to a more formal presentation of programming language semantics such as Gunter's Semantics of Programming Languages.
This textbook offers an understanding of the essential concepts of programming languages. The text uses interpreters, written in Scheme, to express the semantics of many essential language elements in a way that is both clear and directly executable.
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. 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. Contents Tutorial * Applications * Further Reading

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