Infinitary Lambda Calculi from a Linear Perspective

Ugo Dal Lago 1, 2
2 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : We introduce a linear infinitary λ-calculus, called Λ∞, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted coinductively. The obtained calculus embeds the infinitary applica-tive λ-calculus and is universal for computations over infinite strings. What is particularly interesting about Λ∞, is that the refinement induced by linear logic allows to restrict both modalities so as to get calculi which are terminating inductively and productive coin-ductively. We exemplify this idea by analysing a fragment of Λ built around the principles of SLL and 4LL. Interestingly, it enjoys confluence, contrarily to what happens in ordinary infinitary λ-calculi.
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Ugo Dal Lago. Infinitary Lambda Calculi from a Linear Perspective. Logic in Computer Science, Jul 2016, New York, United States. ⟨10.1145/2933575.2934505⟩. ⟨hal-01400883⟩

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