NOMINAL COALGEBRAIC DATA TYPES WITH APPLICATIONS TO LAMBDA CALCULUS
Contents 1. Introduction 2 2. Preliminaries on Algebra and C Page 1 Logical Methods in …

We give a coinductive proof of confluence, up to equivalence of root-active subterms, of
infinitary lambda-calculus. We also show confluence of Böhm reduction (with respect to root …

We present some highlights from the emerging theory of infinitary rewriting, both for first-
order term rewriting systems and λ-calculus. In the first section we introduce the framework …

Gabbay and Pitts proved that lambda-terms up to alpha-equivalence constitute an initial
algebra for a certain endofunctor on the category of nominal sets. We show that the terms of …

We present a new and formal coinductive proof of confluence and normalisation of B\" ohm
reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this …

Among the unsolvable terms of the lambda calculus, the mute ones are those having the
highest degree of undefinedness. In this paper, we define for each natural number n, an …

The main aim of this paper is to promote a certain style of doing coinductive proofs, similar to
inductive proofs as commonly done by mathematicians. For this purpose we provide a …

In this paper, we introduce a strong form of eta reduction called etabang that we use to
construct a confluent and normalising infinitary lambda calculus, of which the normal forms …

Since its introduction by Church, the λ-calculus has played a major role in a century of
development in theoretical computer science and mathematical logic, as well as in the birth …

We distinguish between undefined terms as used in lambda definability of partial recursive
functions and meaningless terms as used in infinite lambda calculus for the infinitary terms …