The untyped stack calculus and Bohm's theorem

TL;DR

This paper introduces an extension to the stack calculus, a classical logic-oriented functional language, addressing its limitations related to Bohm's theorem, similar to how Saurin's extension improves lambda-mu.

Contribution

The paper proposes a simple extension to the stack calculus that restores properties analogous to Bohm's theorem, enhancing its theoretical robustness.

Findings

Extension restores Bohm's theorem-like properties

Maintains confluence in the extended calculus

Bridges gap between stack calculus and classical logic

Abstract

The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We present a simple extension of stack calculus which is for the stack calculus what Saurin's Lambda-mu is for lambda-mu.