Coinductive Techniques in Infinitary Lambda-Calculus

A Coinductive Confluence Proof for Infinitary Lambda-Calculus

We present a new coinductive proof of confluence of Böhm reduction in infinitary lambda-calculus. The proof is simpler than previous proofs of this result. The technique of the proof is new, i.e., it is not merely a coinductive reformulation of any earlier proofs.

ar X iv : 1 41 1 . 43 80 v 3 [ cs . L O ] 2 8 Ja n 20 15 An infinitary model of linear logic

In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets. We explain how to interpret in this model the fixpoint operator Y as a Conway operator alternatively defined in an inductive or a coinductive way. We then extend the relational semantics with a notion of color or pr...

Coinductive Techniques on a Linear Quantum λ-Calculus

Infinitary Rewriting Coinductively

We provide a coinductive definition of strongly convergent reductions between infinite lambda terms. This approach avoids the notions of ordinals and metric convergence which have appeared in the earlier definitions of the concept. As an illustration, we prove the existence part of the infinitary standardization theorem. The proof is fully formalized in Coq using coinductive types. The paper co...

An Alpha-Corecursion Principle for the Infinitary Lambda Calculus

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 corec...