The ÎÎ-calculus Cristina Matache, Victor B. F. Gomes, and Dominic P. MulliganThe propositions-as-types correspondence is ordinarily presented as linking the metatheory of typed Î-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 ÎÎ-calculus. In this work, we formalise ÎÎ- calculus in Isabelle/HOL and prove several metatheoretical properties such as type preservation and progress.
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