On structural properties of eta-expansions of identity

Authors:
B. Intrigila;M. Nesi
Affiliations:
Dipartimento di Informatica, Università degli Studi di L'Aquila, via Vetoio, 67010 L'Aquila, Italy;Dipartimento di Informatica, Università degli Studi di L'Aquila, via Vetoio, 67010 L'Aquila, Italy
Venue:
Information Processing Letters
Year:
2003

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Abstract

We investigate some structural properties of a particular class of λ-terms, the so-called η-expansions of identity I, considered inside the β-calculus. This class of terms can be directly identified with a class of (unlabeled) trees, plane (or ordered) trees, which correspond to the so-called parentheses systems. By means of this identification, the class of plane trees can be equipped with an application operation as well as with a composition operation. We show that composition corresponds to a union operation on trees, while application can be characterized in terms of composition and a natural operation of shift over trees. By means of this characterization a number of results can be easily proved about the structure of this class of terms.