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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.
ACM Transactions on Computational Logic (TOCL) – Association for Computing Machinery
Published: Jan 15, 2021
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