Lecture Notes On The Lambda Calculus

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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.

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.

Lecture Notes On Lambda Calculus

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Author : Piergiorgio Odifreddi
language : en
Publisher:
Release Date : 1989

Lecture Notes On Lambda Calculus written by Piergiorgio Odifreddi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.

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.

Lecture Notes On Motivic Cohomology

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Author : Carlo Mazza
language : en
Publisher: American Mathematical Soc.
Release Date : 2006

Lecture Notes On Motivic Cohomology written by Carlo Mazza and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).

Handbook Of Mathematical Logic

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Author : J. Barwise
language : en
Publisher: Elsevier
Release Date : 1982-03-01

Handbook Of Mathematical Logic written by J. Barwise and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-03-01 with Computers categories.

The handbook is divided into four parts: model theory, set theory, recursion theory and proof theory. Each of the four parts begins with a short guide to the chapters that follow. Each chapter is written for non-specialists in the field in question. Mathematicians will find that this book provides them with a unique opportunity to apprise themselves of developments in areas other than their own.

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

Foundations Of Software Science And Computation Structures

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Author : Stefan Kiefer
language : en
Publisher: Springer Nature
Release Date : 2021-03-22

Foundations Of Software Science And Computation Structures written by Stefan Kiefer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-22 with Mathematics categories.

This open access book constitutes the proceedings of the 24th International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 28 regular papers presented in this volume were carefully reviewed and selected from 88 submissions. They deal with research on theories and methods to support the analysis, integration, synthesis, transformation, and verification of programs and software systems.

Fundamentals Of Computation Theory

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Author : Gabriel Ciobanu
language : en
Publisher: Springer
Release Date : 2003-07-31

Fundamentals Of Computation Theory written by Gabriel Ciobanu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Computers categories.

This book constitutes the refereed proceedings of the 12th International Symposium on Fundamentals of Computation Theory, FCT '99, held in Iasi, Romania in August/September 1999. The 42 revised full papers presented together with four invited papers were carefully selected from a total of 102 submissions. Among the topics addressed are abstract data types, algorithms and data structures, automata and formal languages, categorical and topological approaches, complexity, computational geometry, concurrency, cryptology, distributed computing, logics in computer science, process algebras, symbolic computation, molecular computing, quantum computing, etc.