Confluence of the coinductive λ-calculus

Confluence of the coinductive [lambda]-calculus

The coinductive λ-calculus Λ arises by a coinductive interpretation of the grammar of the standard λ-calculus Λ and contains non-wellfounded λ-terms. An appropriate notion of reduction is analyzed and proven to be confluent by means of a detailed analysis of the usual Tait/MartinLöf style development argument. This yields bounds for the lengths of those joining reduction sequences that are guar...

Confluence of the BS λ - calculus

The BSλ -calculus, a formal basis for functional languages expressing bulk synchronous parallel algorithms, is presented. It is then shown to be confluent. 1 High-level languages and parallel programming For parallel programming to become as widespread as sequential programming, the languages supporting it should incorporate all the standard abstraction mechanisms including higher-order functio...

A Coinductive Confluence Proof for Infinitary Lambda-Calculus

We present a new coinductive proof of confluence of Böhm reduction in infinitary lambda-calculus. The proof is simpler than previous proofs of this result. The technique of the proof is new, i.e., it is not merely a coinductive reformulation of any earlier proofs.

On the confluence of λ-calculus with conditional rewriting

The confluence of untyped λ-calculus with unconditional rewriting is now well understood. In this paper, we investigate the confluence of λ-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Müller and Dougherty for unconditional rewriting. Two cases are considered, whether betareduction is allo...

Coinductive Techniques on a Linear Quantum λ-Calculus