Abstract
We provide a new characterization of Lévy's redex-families in the λ-calculus [11] as suitable paths in the initial term of the derivation. The idea is that redexes in a same family are created by “contraction” (via β-reduction) of a unique common path in the initial term. This fact gives new evidence about the “common nature” of redexes in a same family, and about the possibility of sharing their reduction. From this point of view, our characterization underlies all recent works on optimal graph reduction techniques for the λ-calculus [9,6,7,1], providing an original and intuitive understanding of optimal implementations.
As an easy by-product, we prove that neither overlining nor underlining are required in Lévy's labelling.
Partially supported by the ESPRIT Basic Research Project 6454-CONFER. The work was mostly carried out while the first author was at INRIA Rocquencourt and the second one was at the Dipartimento di Informatica, Universitá di Pisa.
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Asperti, A., Laneve, C. (1993). Paths, computations and labels in the λ-calculus. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_13
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DOI: https://doi.org/10.1007/978-3-662-21551-7_13
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