Stability Property for the Call-by-Value $\lambda$-calculus through Taylor Expansion

TL;DR

This paper establishes the Stability Property for the call-by-value λ-calculus using Taylor resource approximation, demonstrating the calculus's sequentiality through adapted techniques from the ordinary λ-calculus.

Contribution

It extends Taylor resource approximation techniques to the call-by-value λ-calculus, proving the Stability Property and its implications for sequentiality.

Findings

Proves the Stability Property for CbV λ-calculus.

Adapts Taylor approximation techniques to the CbV setting.

Shows the calculus's sequentiality via the Stability Property.

Abstract

We prove the Stability Property for the call-by-value $\lambda$-calculus (CbV in the following). This result states necessary conditions under which the contexts of the CbV $\lambda$-calculus commute with intersections of approximants. This is an important non-trivial result, which implies the sequentiality of the calculus. We prove it via the tool of Taylor-resource approximation, whose power has been shown in several recent papers. This technique is usually conceived for the ordinary $\lambda$-calculus, but it can be easily defined for the CbV setting. Our proof is the adaptation of the one for the ordinary calculus using the same technique, with some minimal technical modification due to the fact that in the CbV setting one linearises terms in a slightly different way than usual (cfr. $!(A\multimap B)$ vs $!A\multimap B$). The content of this article is taken from the PhD thesis of the author.