An alpha-corecursion principle for the infinitary lambda calculus
Coalgebraic Methods in Computer Science: 11th International Workshop, CMCS …, 2012•Springer
Gabbay and Pitts proved that lambda-terms up to alpha-equivalence 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).
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).
Abstract
Gabbay and Pitts proved that lambda-terms up to alpha-equivalence 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).
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