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An Introduction To Lambda Calculi For Computer Scientists
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Book Synopsis An Introduction to Lambda Calculi for Computer Scientists by : Chris Hankin
Download or read book An Introduction to Lambda Calculi for Computer Scientists written by Chris Hankin and published by College Publications. This book was released on 2004 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lambda-calculus lies at the very foundations of computer science. Besides its historical role in computability theory it has had significant influence on programming language design and implementation, denotational semantics, and domain theory. The book emphasises the proof theory for the type-free lambda-calculus. The first six chapters concern this calculus and cover the basic theory, reduction, models, computability, and the relationship between the lambda-calculus and combinatory logic. Chapter 7 presents a variety of typed calculi; first the simply typed lambda-calculus, then Milner-style polymorphism and, finally, the polymorphic lambda-calculus. Chapter 8 concerns two variants of the type-free lambda-calculus that have appeared in the research literature: the lazy lambda-calculus, and the lambda sigma-calculus. The final chapter contains references and a guide to further reading. There are exercises throughout. In contrast to earlier books on these topics, which were written by logicians, this book is written from a computer science perspective and emphasises the practical relevance of many of the key theoretical ideas. The book is intended as a course text for final year undergraduates or first year graduate students in computer science. Research students should find it a useful introduction to more specialist literature.
Download or read book Lambda Calculi written by Chris Hankin and published by . This book was released on 1994 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for final year undergraduates/first year graduates in computer science, as well as a useful introduction for research students seeking a solid introduction to more specialist literature. This text emphasises the role of calculus in programming language design and implementation, denotational semantics, and domain theory. Alternative books on the subject have been written by logicians, but this is the first to have been written from a computer science prespective, invaluable in emphasising the practical relevance of the key theortical ideas.
Book Synopsis Domains and Lambda-Calculi by : Roberto M. Amadio
Download or read book Domains and Lambda-Calculi written by Roberto M. Amadio and published by Cambridge University Press. This book was released on 1998-07-02 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
Book Synopsis An Introduction to Functional Programming Through Lambda Calculus by : Greg Michaelson
Download or read book An Introduction to Functional Programming Through Lambda Calculus written by Greg Michaelson and published by Courier Corporation. This book was released on 2013-04-10 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Well-respected text for computer science students provides an accessible introduction to functional programming. Cogent examples illuminate the central ideas, and numerous exercises offer reinforcement. Includes solutions. 1989 edition.
Book Synopsis Lambda Calculus with Types by : Henk Barendregt
Download or read book Lambda Calculus with Types written by Henk Barendregt and published by Cambridge University Press. This book was released on 2013-06-20 with total page 969 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Book Synopsis Lambda-Calculus and Combinators by : J. Roger Hindley
Download or read book Lambda-Calculus and Combinators written by J. Roger Hindley and published by Cambridge University Press. This book was released on 2008-07-24 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic and lambda-calculus, originally devised in the 1920's, have since developed into linguistic tools, especially useful in programming languages. The authors' previous book served as the main reference for introductory courses on lambda-calculus for over 20 years: this long-awaited new version is thoroughly revised and offers a fully up-to-date account of the subject, with the same authoritative exposition. The grammar and basic properties of both combinatory logic and lambda-calculus are discussed, followed by an introduction to type-theory. Typed and untyped versions of the systems, and their differences, are covered. Lambda-calculus models, which lie behind much of the semantics of programming languages, are also explained in depth. The treatment is as non-technical as possible, with the main ideas emphasized and illustrated by examples. Many exercises are included, from routine to advanced, with solutions to most at the end of the book.
Book Synopsis The Calculi of Lambda-conversion by : Alonzo Church
Download or read book The Calculi of Lambda-conversion written by Alonzo Church and published by Princeton University Press. This book was released on 1985-01-21 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description for this book, The Calculi of Lambda Conversion. (AM-6), Volume 6, will be forthcoming.
Book Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce
Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Introduction to Combinators and (lambda) Calculus by : J. R. Hindley
Download or read book Introduction to Combinators and (lambda) Calculus written by J. R. Hindley and published by CUP Archive. This book was released on 1986-05-29 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic and lambda-conversion were originally devised in the 1920s for investigating the foundations of mathematics using the basic concept of 'operation' instead of 'set'. They have now developed into linguistic tools, useful in several branches of logic and computer science, especially in the study of programming languages. These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions. The key ideas and basic results are presented, as well as a number of more specialised topics, and man), exercises are included to provide manipulative practice.
Book Synopsis The Formal Semantics of Programming Languages by : Glynn Winskel
Download or read book The Formal Semantics of Programming Languages written by Glynn Winskel and published by MIT Press. This book was released on 1993-02-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Semantic Techniques in Quantum Computation by : Simon Gay
Download or read book Semantic Techniques in Quantum Computation written by Simon Gay and published by Cambridge University Press. This book was released on 2010 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explores quantum computation from the perspective of the branch of theoretical computer science known as semantics.
Book Synopsis Central European Functional Programming School by : Zoltán Horváth
Download or read book Central European Functional Programming School written by Zoltán Horváth and published by Springer Science & Business Media. This book was released on 2008-09-29 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents eight carefully revised texts from selected lectures given by leading researchers at the Second Central European Functional Programming School, CEFP 2007, held in Cluj-Napoca, Romania, in June 2007. The eight revised full papers presented were carefully selected during two rounds of reviewing and improvement for inclusion in the book. The lectures cover a wide range of topics such as interactive workflows, lazy functional programs, lambda calculus, and object-oriented functional programming.
Book Synopsis Lectures on the Curry-Howard Isomorphism by : Morten Heine Sørensen
Download or read book Lectures on the Curry-Howard Isomorphism written by Morten Heine Sørensen and published by Elsevier. This book was released on 2006-07-04 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization corresponds to term reduction, etc.But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transformsproofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq).This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic.Key features- The Curry-Howard Isomorphism treated as common theme- Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics- Thorough study of the connection between calculi and logics- Elaborate study of classical logics and control operators- Account of dialogue games for classical and intuitionistic logic- Theoretical foundations of computer-assisted reasoning· The Curry-Howard Isomorphism treated as the common theme.· Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics.· Elaborate study of classical logics and control operators.· Account of dialogue games for classical and intuitionistic logic.· Theoretical foundations of computer-assisted reasoning
Book Synopsis Combinatory Logic by : Katalin Bimbo
Download or read book Combinatory Logic written by Katalin Bimbo and published by CRC Press. This book was released on 2011-07-27 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the auth
Book Synopsis A Theory of Objects by : Martin Abadi
Download or read book A Theory of Objects written by Martin Abadi and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: By developing object calculi in which objects are treated as primitives, the authors are able to explain both the semantics of objects and their typing rules, and also demonstrate how to develop all of the most important concepts of object-oriented programming languages: self, dynamic dispatch, classes, inheritance, protected and private methods, prototyping, subtyping, covariance and contravariance, and method specialization. An innovative and important approach to the subject for researchers and graduates.
Book Synopsis Introduction to Mathematical Logic by : Alonzo Church
Download or read book Introduction to Mathematical Logic written by Alonzo Church and published by Princeton University Press. This book was released on 1996 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classic account of mathematical logic from a pioneering giant in the field Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979. At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.
Book Synopsis Types and Programming Languages by : Benjamin C. Pierce
Download or read book Types and Programming Languages written by Benjamin C. Pierce and published by MIT Press. This book was released on 2002-01-04 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to type systems and programming languages. 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.
