Twenty Five Years Of Constructive Type Theory

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Twenty Five Years Of Constructive Type Theory

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Author : Giovanni Sambin
language : en
Publisher: Clarendon Press
Release Date : 1998-10-15

Twenty Five Years Of Constructive Type Theory written by Giovanni Sambin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-15 with Mathematics categories.

Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.

Twenty Five Years Of Constructive Type Theory

DOWNLOAD
Author : Giovanni Sambin
language : en
Publisher: Clarendon Press
Release Date : 1998-10-15

Twenty Five Years Of Constructive Type Theory written by Giovanni Sambin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-15 with Mathematics categories.

Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.

Twenty Five Years Of Constructive Type Theory

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Author : Giovanni Sambin
language : en
Publisher:
Release Date : 1998

Twenty Five Years Of Constructive Type Theory written by Giovanni Sambin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification

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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2021-07-27

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-27 with Mathematics categories.

This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.

Homotopy Type Theory Univalent Foundations Of Mathematics

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Author :
language : en
Publisher: Univalent Foundations
Release Date :

Homotopy Type Theory Univalent Foundations Of Mathematics written by and has been published by Univalent Foundations this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Foundations Of Software Science And Computation Structures

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Author : Christel Baier
language : en
Publisher: Springer
Release Date : 2018-04-14

Foundations Of Software Science And Computation Structures written by Christel Baier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-14 with Computers categories.

This book constitutes the proceedings of the 21st International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2018, which took place in Thessaloniki, Greece, in April 2018, held as part of the European Joint Conference on Theory and Practice of Software, ETAPS 2018.The 31 papers presented in this volume were carefully reviewed and selected from 103 submissions. The papers are organized in topical sections named: semantics; linearity; concurrency; lambda-calculi and types; category theory and quantum control; quantitative models; logics and equational theories; and graphs and automata.

Critical Views Of Logic

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Author : Mirja Hartimo
language : en
Publisher: Taylor & Francis
Release Date : 2023-10-31

Critical Views Of Logic written by Mirja Hartimo and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-31 with Philosophy categories.

This book examines positions that challenge the Fregean logic-first view. It raises critical questions about logic by examining various ways in which logic may be entangled with mathematics and metaphysics. Is logic topic-neutral and general? Can we take the application of logic for granted? This book suggests that we should not be dogmatic about logic but ask similar critical questions about logic as those Kant raised about metaphysics and mathematics. It challenges the Fregean logic-first view according to which logic is fundamental and hence independent of any extra-logical considerations. Whereas Quine assimilated logic and mathematics to the theoretical parts of empirical science, the present volume explores views that stop short of his thoroughgoing holism but instead take logic to be answerable to or entangled with some particular disciplines. The contributions provide views that assign primacy to mathematical reasons, Kantian metaphysical grounds, Husserlian transcendental phenomenological reflection, or normative considerations about how terms ought to be defined in various fields of empirical science or mathematics. Space is thereby carved out between a Fregean position on the one hand and Quinean holism on the other. Critical Views of Logic will be a key resource for academics, researchers, and advanced students of philosophy, linguistics, mathematics, and computer science, as well as those engaged in various fields of empirical science. The chapters in this book, except for chapter 4, were originally published in the journal Inquiry.

Foundations Of Secure Computation

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Author : Friedrich L. Bauer
language : en
Publisher: IOS Press
Release Date : 2000

Foundations Of Secure Computation written by Friedrich L. Bauer and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.

The final quarter of the 20th century has seen the establishment of a global computational infrastructure. This and the advent of programming languages such as Java, supporting mobile distributed computing, has posed a significant challenge to computer sciences. The infrastructure can support commerce, medicine and government, but only if communications and computing can be secured against catastrophic failure and malicious interference.

Typed Lambda Calculi And Applications

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Author : Luke Ong
language : en
Publisher: Springer
Release Date : 2011-06-12

Typed Lambda Calculi And Applications written by Luke Ong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-12 with Mathematics categories.

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.

Epistemology Versus Ontology

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Author : P. Dybjer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-10

Epistemology Versus Ontology written by P. Dybjer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-10 with Philosophy categories.

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?