The Lambda Calculus

The Lambda Calculus

The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition.

Author: Hendrik Pieter Barendregt

Publisher: Elsevier Science Limited

ISBN: UCSD:31822000132415

Category: Mathematics

Page: 621

View: 481

The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.
Categories: Mathematics

The Lambda Calculus

The Lambda Calculus

The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these.

Author: Henk Barendregt

Publisher:

ISBN: 184890066X

Category: Computers

Page: 656

View: 468

The Lambda Calculus, treated in this book mainly in its untyped version, consists of a collection of expressions, called lambda terms, together with ways how to rewrite and identify these. In the parts conversion, reduction, theories, and models the view is respectively 'algebraic', computational, with more ('coinductive') identifications, and finally set-theoretic. The lambda terms are built up from variables, using application and abstraction. Applying a term F to M has as intention that F is a function, M its argument, and FM the result of the application. This is only the intention: to actually obtain the result one has to rewrite the expression FM according to the reduction rules. Abstraction provides a way to create functions according to the effect when applying them. The power of the theory comes from the fact that computations, both terminating and infinite, can be expressed by lambda terms at a 'comfortable' level of abstraction.
Categories: Computers

Semantics of the Probabilistic Typed Lambda Calculus

Semantics of the Probabilistic Typed Lambda Calculus

Markov Chain Semantics, Termination Behavior, and Denotational Semantics Dirk Draheim. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. ... The Lambda CalculusIts Syntax and Semantics. North Holland, Amsterdam, 1984.

Author: Dirk Draheim

Publisher: Springer

ISBN: 9783642551987

Category: Computers

Page: 218

View: 669

This book takes a foundational approach to the semantics of probabilistic programming. It elaborates a rigorous Markov chain semantics for the probabilistic typed lambda calculus, which is the typed lambda calculus with recursion plus probabilistic choice. The book starts with a recapitulation of the basic mathematical tools needed throughout the book, in particular Markov chains, graph theory and domain theory, and also explores the topic of inductive definitions. It then defines the syntax and establishes the Markov chain semantics of the probabilistic lambda calculus and, furthermore, both a graph and a tree semantics. Based on that, it investigates the termination behavior of probabilistic programs. It introduces the notions of termination degree, bounded termination and path stoppability and investigates their mutual relationships. Lastly, it defines a denotational semantics of the probabilistic lambda calculus, based on continuous functions over probability distributions as domains. The work mostly appeals to researchers in theoretical computer science focusing on probabilistic programming, randomized algorithms, or programming language theory.
Categories: Computers

From Lambda Calculus to Cybersecurity Through Program Analysis

From Lambda Calculus to Cybersecurity Through Program Analysis

Barendregt, H.: The Lambda Calculus, Its Syntax and Semantics, Studies in Logic and the Foundations of Mathematics, vol. 103. Elsevier (1984) 7. Cardelli, L., Wegner, P.: On understanding types, data abstraction, and polymorphism.

Author: Alessandra Di Pierro

Publisher: Springer Nature

ISBN: 9783030411039

Category: Mathematics

Page: 293

View: 987

This Festschrift is in honor of Chris Hankin, Professor at the Imperial College in London, UK, on the Occasion of His 65th Birthday. Chris Hankin is a Fellow of the Institute for Security Science and Technology and a Professor of Computing Science. His research is in cyber security, data analytics and semantics-based program analysis. He leads multidisciplinary projects focused on developing advanced visual analytics and providing better decision support to defend against cyber attacks. This Festschrift is a collection of scientific contributions related to the topics that have marked the research career of Professor Chris Hankin. The contributions have been written to honour Chris' career and on the occasion of his retirement.
Categories: Mathematics

Lambda Calculus with Types

Lambda Calculus with Types

Barendregt, H. P. 1984. The Lambda Calculus: its Syntax and Semantics. Revised edition. North—Holland. Barendregt, H. P. 1991. Self—interpretation in lambda calculus. Journal of Functional Programming, 1(2), 229*233.

Author: Henk Barendregt

Publisher: Cambridge University Press

ISBN: 9780521766142

Category: Mathematics

Page: 833

View: 372

This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.
Categories: Mathematics

The Parametric Lambda Calculus

The Parametric Lambda Calculus

The Lambda Calculus: Its Syntax and Semantics (2nd edition). North-Holland, Amsterdam, 1984. Henk Barendregt, Mario Coppo, and Mariangiola Dezani-Ciancaglini. A filter lambda model and the completeness of type assignment.

Author: Simona Ronchi Della Rocca

Publisher: Springer Science & Business Media

ISBN: 9783662103944

Category: Mathematics

Page: 248

View: 998

The book contains a completely new presentation of classical results in the field of Lambda Calculus, together with new results. The text is unique in that it presents a new calculus (Parametric Lambda Calculus) which can be instantiated to obtain already known lambda-calculi. Some properties, which in the literature have been proved separately for different calculi, can be proved once for the Parametric one. The lambda calculi are presented from a Computer Science point of view, with a particular emphasis on their semantics, both operational and denotational.
Categories: Mathematics

Computer Science Logic

Computer Science Logic

Barendregt, H.P.: The lambda calculus: Its syntax and semantics. North-Holland Publishing Co, Amsterdam (1984) 5. Berline, C.: From computation to foundations via functions and application: The λ- calculus and its webbed models.

Author: Jacques Duparc

Publisher: Springer Science & Business Media

ISBN: 9783540749141

Category: Computers

Page: 600

View: 238

This book constitutes the refereed proceedings of the 21st International Workshop on Computer Science Logic, CSL 2007, held as the 16th Annual Conference of the EACSL in Lausanne, Switzerland. The 36 revised full papers presented together with the abstracts of six invited lectures are organized in topical sections on logic and games, expressiveness, games and trees, logic and deduction, lambda calculus, finite model theory, linear logic, proof theory, and game semantics.
Categories: Computers

Typed Lambda Calculi and Applications

Typed Lambda Calculi and Applications

Thispaperhasraised many questions, mainly concerninga possible implementation of lambda calculus with constructors.The first one is about recursively defined data types, ... Barendregt, H.: The Lambda Calculus: Its Syntax and Semantics.

Author: Pierre-Louis Curien

Publisher: Springer Science & Business Media

ISBN: 9783642022722

Category: Computers

Page: 417

View: 366

This book constitutes the refereed proceedings of the 9th International Conference on Typed Lambda Calculi and Applications, TLCA 2009, held in Brasilia, Brazil in July 2008 in conjunction with RTA 2007, the 19th International Conference on Rewriting Techniques and Applications as part of RDP 2009, the 5th International Conference on Rewriting, Deduction, and Programming. The 27 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 53 submissions. The papers present original research results that are broadly relevant to the theory and applications of typed calculi and address a wide variety of topics such as proof-theory, semantics, implementation, types, and programming.
Categories: Computers

Typed Lambda Calculi and Applications

Typed Lambda Calculi and Applications

Barendregt, H.: The Lambda Calculus: its Syntax and Semantics. North-Holland, Amsterdam (1984) 8. Barendregt, H., Coppo, M., Dezani-Ciancaglini, M.: A filter lambda model and the completeness of type assignment.

Author: Luke Ong

Publisher: Springer Science & Business Media

ISBN: 9783642216909

Category: Computers

Page: 245

View: 938

This book constitutes the refereed proceedings of the 10th International Conference on Typed Lambda Calculi and Applications, TLCA 2011, held in Novi Sad, Serbia, in June 2011 as part of RDP 2011, the 6th Federated Conference on Rewriting, Deduction, and Programming. The 15 revised full papers presented were carefully reviewed and selected from 44 submissions. The papers provide prevailing research results on all current aspects of typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts addressing a wide variety of topics such as proof-theory, semantics, implementation, types, and programming.
Categories: Computers