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Titlebook: Isomorphisms of Types; from ?-calculus to i Roberto Cosmo Book 1995 Birkhäuser Boston 1995 Mathematica.Permutation.calculus.logic.mathemati

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书目名称Isomorphisms of Types
副标题from ?-calculus to i
编辑Roberto Cosmo
视频video
丛书名称Progress in Theoretical Computer Science
图书封面Titlebook: Isomorphisms of Types; from ?-calculus to i Roberto Cosmo Book 1995 Birkhäuser Boston 1995 Mathematica.Permutation.calculus.logic.mathemati
描述This is a book about isomorphisms 0/ types, arecent difficult research topic in type theory that turned out to be able to have valuable practical applications both for programming language design and far more human­ centered information retrieval in software libraries. By means of a deep study of the syntax of the now widely known typed A-ca1culus, it is possible to identify some simple equations between types that on one hand allow to improve the design of the ML language, and on the other hand provide the basis for building radically new information retrieval systems for functional software libraries. We present in this book both the theoretical aspects of these researches and a fully functional implementation of some of their applications in such a way to provide interesting material both for the theoretician looking for proofs and for the practitioner interested in implementation details. In order to make it possible for these different types of readers to use this book effectively, some special signs are used to designate material that is particularly technical or applied or that represents a digression. When the symbol appears at the beginning of a section or a subsection, it
出版日期Book 1995
关键词Mathematica; Permutation; calculus; logic; mathematical logic; optimization; programming; programming langu
版次1
doihttps://doi.org/10.1007/978-1-4612-2572-0
isbn_softcover978-1-4612-7585-5
isbn_ebook978-1-4612-2572-0
copyrightBirkhäuser Boston 1995
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Confluence Results,In the λ-calculus there are plenty of programs (or λ-terms) where it is pos­sible to apply the reduction rule ., introduced in 1.3.4, in more than one position. The λ-calculus does not specify a unique evaluation order, or ., that associates to each program or term a unique position where the reduction will proceed.
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,Strong normalization for subsystems of λ,,✻,Our proof of confluence in Theorem 2.4.5 relies upon the strong normalization of . over the set of . normal forms, while we need the strong normalization of . less .. and .. over the full set of terms in order to provide an effective weakly normalizing strategy for . in Theorem 2.5.2.
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Second-Order Isomorphic Types,This chapter is dedicated to the proof of completeness of Th.. for iso­morphisms in λ..✻. This proof is by far the most complex present in this book, because in the second-order case we have to face the problem of invertibility of terms almost anew, and we can no longer avoid it as we did for the first-order systems.
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Introduction,l relevance. A . is simply seen as a useful means of classification of the objects that a program manipulates: types help to understand better what a program does, and they also provide a valuable firewall against many common programming errors.
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