Confluence of the Coinductive

Abstract

The coinductive λ-calculus Λ co 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/Martin-Löf style development argument. This yields bounds for the lengths of those joining reduction sequences that are guaranteed to exist by confluence. These bounds also apply to the wellfounded λ-calculus, thus adding quantitative information to the classic result