Meaningfulness and Genericity in a Subsuming Framework (Invited Talk)

Authors Delia Kesner , Victor Arrial , Giulio Guerrieri



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Delia Kesner
  • Université Paris Cité - CNRS - IRIF, France
Victor Arrial
  • Université Paris Cité - CNRS - IRIF, France
Giulio Guerrieri
  • University of Sussex, Department of Informatics, Brighton, United Kingdom

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Delia Kesner, Victor Arrial, and Giulio Guerrieri. Meaningfulness and Genericity in a Subsuming Framework (Invited Talk). In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 1:1-1:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.FSCD.2024.1

Abstract

This paper studies the notion of meaningfulness for a unifying framework called dBang-calculus, which subsumes both call-by-name (dCBN) and call-by-value (dCBV). We first define meaningfulness in dBang and then characterize it by means of typability and inhabitation in an associated non-idempotent intersection type system previously appearing in the literature. We validate the proposed notion of meaningfulness by showing two properties: (1) consistency of the smallest theory, called ℋ, equating all meaningless terms, and (2) genericity, stating that meaningless subterms have no bearing on the significance of meaningful terms. The theory ℋ is also shown to have a unique consistent and maximal extension ℋ*, which coincides with a well-known notion of observational equivalence. Last but not least, we show that the notions of meaningfulness and genericity in the literature for dCBN and dCBV are subsumed by the corresponding ones proposed here for the dBang-calculus.

Subject Classification

ACM Subject Classification
  • Theory of computation → Operational semantics
Keywords
  • Lambda calculus
  • Solvability
  • Meaningfulness
  • Inhabitation
  • Genericity

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