Resource approximation for the λμ-calculus

Barbarossa, Davide

doi:10.1145/3531130.3532469

Cited by 1 publication

(1 citation statement)

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“…This Commutation theorem enables one to deduce properties of some λ-terms from the properties of their Taylor expansion; typically, properties of the (possibly) non-terminating execution of a λ-term, previously characterized by coinductive objects like its Böhm tree, are proved via the Taylor expansion by mere induction. This approach has been successfully applied not only to the ordinary λ-calculus [ER06; Oli18; Oli20; BM20], but also to nondeterministic [BEM12; VA19], probabilistic [DZ12; DL19], call-by-value [KMP20], and call-by-push-value [CT20] calculi, as well as Parigot's λμ-calculus [Bar22].…”

Section: Introductionmentioning

confidence: 99%

Finitary Simulation of Infinitary $\beta$-Reduction via Taylor Expansion, and Applications

Cerda,

Auclair

2023

Logical Methods in Computer Science

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Originating in Girard's Linear logic, Ehrhard and Regnier's Taylor expansion of $\lambda$-terms has been broadly used as a tool to approximate the terms of several variants of the $\lambda$-calculus. Many results arise from a Commutation theorem relating the normal form of the Taylor expansion of a term to its B\"ohm tree. This led us to consider extending this formalism to the infinitary $\lambda$-calculus, since the $\Lambda_{\infty}^{001}$ version of this calculus has B\"ohm trees as normal forms and seems to be the ideal framework to reformulate the Commutation theorem. We give a (co-)inductive presentation of $\Lambda_{\infty}^{001}$. We define a Taylor expansion on this calculus, and state that the infinitary $\beta$-reduction can be simulated through this Taylor expansion. The target language is the usual resource calculus, and in particular the resource reduction remains finite, confluent and terminating. Finally, we state the generalised Commutation theorem and use our results to provide simple proofs of some normalisation and confluence properties in the infinitary $\lambda$-calculus.

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Section: Introductionmentioning

confidence: 99%