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-Relations and the Actual Meaning of -Renaming

-Relations and the Actual Meaning of -Renaming In this work we provide an alternative, and equivalent, formulation of the concept of -theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We call -relations our alternative versions of -theories. We also clarify the actual role of -renaming in the lambda calculus: it expresses a property of extensionality for a certain class of terms. To motivate the necessity of -renaming, we construct an unusual denotational model of the lambda calculus that validates all structural and beta conditions but not -renaming. The article also has a survey character. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

-Relations and the Actual Meaning of -Renaming

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2021 ACM
ISSN
1529-3785
eISSN
1557-945X
DOI
10.1145/3426471
Publisher site
See Article on Publisher Site

Abstract

In this work we provide an alternative, and equivalent, formulation of the concept of -theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We call -relations our alternative versions of -theories. We also clarify the actual role of -renaming in the lambda calculus: it expresses a property of extensionality for a certain class of terms. To motivate the necessity of -renaming, we construct an unusual denotational model of the lambda calculus that validates all structural and beta conditions but not -renaming. The article also has a survey character.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Jan 15, 2021

Keywords: -renaming

References