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- Carlos Lombardi, Alejandro Ríos, Roel de Vrijer
- RTA-TLCA
- 2014

Barendregt’s Lemma in its original form is a statement on Combinatory Logic that holds also for the lambda calculus and gives important insight into the syntactic interplay between substitution and reduction. Its origin lies in undefinablity proofs, but there are other applications as well. It is connected to the so-called Square Brackets Lemma, introduced… (More)

This paper is dedicated to my longtime friend and colleague Roel de Vrijer on the occasion of his sixtieth birthday. With its subject I have tried to go a little in his direction by taking a very syntactic subject. The work is part of a project in progress in cooperation with Rosalie Iemhoff and Nick Vaporis. It concerns the disjunction property in… (More)

for any n ≥ 0 and 0 ≤ k ≤ n. A combinatorial interpretation of the formula (1) is as follows. The left-hand side counts the number of ways to select k balls (numbered with the corresponding number) from a bin of n balls. This is equivalent to the sum of the following two cases: (a) if the ball n is selected, the number of ways to select the remaining k − 1… (More)

- Carlos Lombardi, Alejandro Ríos, Roel de Vrijer
- Electr. Notes Theor. Comput. Sci.
- 2017

Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g. simultaneous from sequential reduction. Proof terms for finitary, first-order, left-linear term rewriting are described in [15], ch. 8. In a previous work [12] we defined an extension of the finitary… (More)

- Carlos Lombardi, Alejandro Ríos, Roel de Vrijer
- ArXiv
- 2014

Proof. This is an easy consequence of some properties of ordinals. Namely, β < Σ i<ω αi implies that the set {k < ω / β < α0 + . . . + αk} is nonempty; we take n as the minimum of this set. Then α0 + . . . + αn−1 ≤ β < (α0 + . . . + αn−1) + αn. Basic properties of ordinals entail the existence and uniqueness of an ordinal γ verifying (α0 + . . .+αn−1) + γ =… (More)

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