Programming In Martin Lofs Type Theory
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Author | : Bengt Nordström |
Publisher | : Oxford University Press, USA |
Total Pages | : 240 |
Release | : 1990 |
Genre | : Computers |
ISBN | : |
Download Programming in Martin-Löf's Type Theory Book in PDF, Epub and Kindle
In recent years, several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Löf. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.
Author | : Per Martin-Löf |
Publisher | : |
Total Pages | : 116 |
Release | : 1984 |
Genre | : Mathematics |
ISBN | : |
Download Intuitionistic Type Theory Book in PDF, Epub and Kindle
Author | : Johan Georg Granström |
Publisher | : Springer Science & Business Media |
Total Pages | : 198 |
Release | : 2011-06-02 |
Genre | : Philosophy |
ISBN | : 9400717369 |
Download Treatise on Intuitionistic Type Theory Book in PDF, Epub and Kindle
Intuitionistic type theory can be described, somewhat boldly, as a partial fulfillment of the dream of a universal language for science. This book expounds several aspects of intuitionistic type theory, such as the notion of set, reference vs. computation, assumption, and substitution. Moreover, the book includes philosophically relevant sections on the principle of compositionality, lingua characteristica, epistemology, propositional logic, intuitionism, and the law of excluded middle. Ample historical references are given throughout the book.
Author | : Rob Nederpelt |
Publisher | : Cambridge University Press |
Total Pages | : 465 |
Release | : 2014-11-06 |
Genre | : Computers |
ISBN | : 1316061086 |
Download Type Theory and Formal Proof Book in PDF, Epub and Kindle
Type theory is a fast-evolving field at the crossroads of logic, computer science and mathematics. This gentle step-by-step introduction is ideal for graduate students and researchers who need to understand the ins and outs of the mathematical machinery, the role of logical rules therein, the essential contribution of definitions and the decisive nature of well-structured proofs. The authors begin with untyped lambda calculus and proceed to several fundamental type systems, including the well-known and powerful Calculus of Constructions. The book also covers the essence of proof checking and proof development, and the use of dependent type theory to formalise mathematics. The only prerequisite is a basic knowledge of undergraduate mathematics. Carefully chosen examples illustrate the theory throughout. Each chapter ends with a summary of the content, some historical context, suggestions for further reading and a selection of exercises to help readers familiarise themselves with the material.
Author | : Ana Bove |
Publisher | : |
Total Pages | : 117 |
Release | : 1999 |
Genre | : |
ISBN | : 9789171978615 |
Download Programming in Martin-Löf Type Theory Book in PDF, Epub and Kindle
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Download Homotopy Type Theory: Univalent Foundations of Mathematics Book in PDF, Epub and Kindle
Author | : Simon Thompson |
Publisher | : Addison Wesley Publishing Company |
Total Pages | : 396 |
Release | : 1991 |
Genre | : Computers |
ISBN | : |
Download Type Theory and Functional Programming Book in PDF, Epub and Kindle
This book explores the role of Martin-Lof s constructive type theory in computer programming. The main focus of the book is how the theory can be successfully applied in practice. Introductory sections provide the necessary background in logic, lambda calculus and constructive mathematics, and exercises and chapter summaries are included to reinforce understanding.
Author | : Giovanni Sambin |
Publisher | : Clarendon Press |
Total Pages | : 292 |
Release | : 1998-10-15 |
Genre | : Mathematics |
ISBN | : 0191606936 |
Download Twenty Five Years of Constructive Type Theory Book in PDF, Epub and Kindle
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.
Author | : Bengt Nordström |
Publisher | : |
Total Pages | : 25 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : |
Download Martin-Löf's Type Theory as a Programming Logic Book in PDF, Epub and Kindle
Author | : Elaine M. Landry |
Publisher | : Oxford University Press |
Total Pages | : 486 |
Release | : 2017 |
Genre | : Mathematics |
ISBN | : 019874899X |
Download Categories for the Working Philosopher Book in PDF, Epub and Kindle
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.