α β-Relations and the Actual Meaning of α-Renaming
In this work we provide an alternative, and equivalent, formulation of the concept of λ-theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We call α β-relations our alternative versions of λ-theories. We also clarify the actual role of α-renaming in the lambda calculus: it expresses a property of extensionality for a certain class of terms. To motivate the necessity of α-renaming, we construct an unusual denotational model of the lambda calculus that validates all structural and beta conditions but not α-renaming. The article also has a survey character.
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1974 ◽
Vol 65
(3)
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pp. 287-290
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2002 ◽
Vol 386
(8)
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pp. 545-546
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