The LambdaMu-Calculus

Cristina Matache, Victor B. F. Gomes and Dominic P. Mulligan

16 August 2017

Abstract

The propositions-as-types correspondence is ordinarily presented as linking the metatheory of typed λ-calculi and the proof theory of intuitionistic logic. Griffin observed that this correspondence could be extended to classical logic through the use of control operators. This observation set off a flurry of further research, leading to the development of Parigots λμ-calculus. In this work, we formalise λμ- calculus in Isabelle/HOL and prove several metatheoretical properties such as type preservation and progress.
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Theories