Finitary Corecursion for the Infinitary Lambda Calculus
Abstract
Kurz et al. have recently shown that infinite $\lambda$trees with finitely many free variables modulo $\alpha$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 $\lambda$trees, i.e. those $\lambda$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 $\lambda$trees.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 arXiv:
 arXiv:1505.07736
 Bibcode:
 2015arXiv150507736M
 Keywords:

 Mathematics  Category Theory;
 Computer Science  Logic in Computer Science;
 F.3.2;
 F.4.1;
 D.3.1