Finitary Corecursion for the Infinitary Lambda Calculus
Year: 2015
Type: preprint
Abstract: Kurz et al. have recently shown that infinite $λ$-trees with finitely many free variables modulo $α$-equivalence form a final coalgebra for a functor on the category of nominal sets. Here we investigate the rational fixpoint of that functor. We prove that it is formed by all rational $λ$-trees, i.e. those $λ$-trees which have only finitely many subtrees (up to isomorphism). This yields a corecursion principle that allows the definition of operations such as substitution on rational $λ$-trees.
Source: arXiv (Cornell University)
Authors: Milius, Stefan, Wißmann, Thorsten
Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W393204985