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Programming in Martin-Lof's Type Theory: An Introduction
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  • Title: Programming in Martin-Lof's Type Theory: An Introduction
  • Author(s) Bengt Nordstrom (Author), Kent Petersson (Author), Jan M. Smith (Author)
  • Publisher: Oxford University Press; First Edition edition (July 19, 1990)
  • Hardcover: 232 pages
  • eBook: PDF and Postscript
  • Language: English
  • ISBN-10: 0198538146
  • ISBN-13: 978-0198538141
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Book Description

Several formalisms for program construction have appeared. One such formalism is the type theory developed by Per Martin-Lof. 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.

As a programming language, type theory is similar to typed functional languages such as Hope and ML, but a major difference is that the evaluation of a well-typed program always terminates. In type theory it is also possible to write specifications of programming tasks as well as to develop provably correct programs.

This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.

One of the main differences between the type theory presentation in this book and the one in Per Martin-Löf's Constructive Mathematics and Computer Programming is that this book uses a uniform notation for expressions.

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