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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