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doi:10.1016/S0304-3975(03)00324-4 
Copyright © 2003 Elsevier B.V. All rights reserved.
Confluence of the coinductive λ-calculus
Felix Joachimski
, 1
Received 5 October 2001;
revised 16 April 2003;
accepted 15 May 2003;
Communicated by M. Wirsing
Available online 11 June 2003.
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Abstract
The coinductive λ-calculus Λco arises by a coinductive interpretation of the grammar of the standard λ-calculus Λ and contains non-well-founded 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 well-founded λ-calculus, thus adding quantitative information to the classic result.
