Lambda Calculus With Types
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Lambda Calculus With Types
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Author : Henk Barendregt
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-20
Lambda Calculus With Types written by Henk Barendregt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Mathematics categories.
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.
An Introduction To Functional Programming Through Lambda Calculus
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Author : Greg Michaelson
language : en
Publisher: Courier Corporation
Release Date : 2013-04-10
An Introduction To Functional Programming Through Lambda Calculus written by Greg Michaelson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-10 with Mathematics categories.
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.
Lambda Calculus Types And Models
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Author : Jean Louis Krivine
language : en
Publisher: Prentice Hall
Release Date : 1993
Lambda Calculus Types And Models written by Jean Louis Krivine and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
This introduction to lambda-calculus looks at aspects of the theory: combinatory logic, models, and type streams, showing how they interlink and underpin computer science.
Lambda Calculus With Types
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Author : Hendrik Pieter Barendregt
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-20
Lambda Calculus With Types written by Hendrik Pieter Barendregt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Mathematics categories.
This handbook with exercises reveals the mathematical beauty of formalisms hitherto mostly used for software and hardware design and verification.
Domains And Lambda Calculi
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Author : Roberto M. Amadio
language : en
Publisher: Cambridge University Press
Release Date : 1998-07-02
Domains And Lambda Calculi written by Roberto M. Amadio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-02 with Computers categories.
Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
Lecture Notes On The Lambda Calculus
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Author : Peter Selinger
language : en
Publisher:
Release Date : 2018-10-04
Lecture Notes On The Lambda Calculus written by Peter Selinger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-04 with Science categories.
This is a set of lecture notes that developed out of courses on the lambda calculus that the author taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. 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, polymorphism, type inference, denotational semantics, complete partial orders, and the language PCF.
Lectures On The Curry Howard Isomorphism
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Author : Morten Heine Sørensen
language : en
Publisher: Elsevier
Release Date : 2006-07-04
Lectures On The Curry Howard Isomorphism written by Morten Heine Sørensen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-07-04 with Mathematics categories.
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
Types And Programming Languages
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Author : Benjamin C. Pierce
language : en
Publisher: MIT Press
Release Date : 2002-01-04
Types And Programming Languages written by Benjamin C. Pierce and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-04 with Computers categories.
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.
Type Theory And Formal Proof
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Author : Rob Nederpelt
language : en
Publisher: Cambridge University Press
Release Date : 2014-11-06
Type Theory And Formal Proof written by Rob Nederpelt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-06 with Computers categories.
A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.