An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

Authors

Alexander Kurz, Chapman UniversityFollow
Daniela Petrişan, University of Leicester
Paula Severi, University of Leicester
Fer-Jan de Vries, University of Leicester

Document Type

Conference Proceeding

Publication Date

2012

Abstract

Gabbay and Pitts proved that lambda-terms up to alphaequivalence constitute an initial algebra for a certain endofunctor on the category of nominal sets. We show that the terms of the infinitary lambda-calculus form the final coalgebra for the same functor. This allows us to give a corecursion principle for alpha-equivalence classes of finite and infinite terms. As an application, we give corecursive definitions of substitution and of infinite normal forms (Böhm, Lévy-Longo and Berarducci trees).

Comments

This paper was originally presented at International Workshop on Coalgebraic Methods in Computer Science (CMCS) in 2012. DOI: 10.1007/978-3-642-32784-1_8

Recommended Citation

Kurz A., Petrişan D., Severi P., de Vries FJ. (2012) An Alpha-Corecursion Principle for the Infinitary Lambda Calculus. In: Pattinson D., Schröder L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg

Copyright

Springer