Lambda Mu Calculus and Duality: Call-by-Name and Call-by-Value

TL;DR

This paper explores the computational equivalence of Lambda Mu Calculus and Lambda Bar Mu Mu Tidle Calculus under classical logic, providing translations and simulation theorems for different evaluation strategies.

Contribution

It establishes formal translations and proves simulation theorems demonstrating the computational equivalence of the two calculi.

Findings

Translations between Lambda Mu and Lambda Bar Mu Mu Tidle Calculus are defined.

Simulation theorems are proved for undirected, call-by-name, and call-by-value evaluations.

The calculi are shown to be computationally equivalent under these translations.

Abstract

Under the extension of Curry-Howard's correspondence to classical logic, Gentzen's NK and LK systems can be seen as syntax-directed systems of simple types respectively for Parigot's Lambda Mu Calculus and Curien-Herbelin's Lambda Bar Mu Mu Tidle Calculus. We aim at showing their computational equivalence. We define translations between these calculi. We prove simulation theorems for an undirected evaluation as well as for call-by-name and call-by-value evaluations.