Communication Dans Un Congrès Année : 2026

Approximation theory for distant Bang calculus

Résumé

Approximation semantics capture the observable behaviour of λ-terms; Böhm Trees and Taylor Expansion are its two central paradigms, related by the Commutation Theorem. While well understood in Call-by-Name (CbN), these notions were only recently developed for Call-by-Value (CbV), motivating the search for a unified approximation framework. The Bang-calculus provides such a framework, subsuming both CbN and CbV through linear-logic translations while providing robust rewriting properties. We develop the approximation semantics of dBang-the Bang-calculus with explicit substitutions and distant reductions-by defining Böhm trees and Taylor expansion and establishing their fundamental properties. Via translations, our results recover the CbN and CbV cases within a single unifying framework capturing infinitary and resource-sensitive semantics.

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Dates et versions

hal-05518907 , version 1 (19-02-2026)
hal-05518907 , version 2 (30-04-2026)

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Kostia Chardonnet, Jules Chouquet, Axel Kerinec. Approximation theory for distant Bang calculus. FSCD 2026 - 11th International Conference on Formal Structures for Computation and Deduction, Jul 2026, Lisbonne, Portugal. ⟨hal-05518907v2⟩
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