Formalizing the Curry-Howard Correspondence

Juan Ferrer Meleiro; Hugo Luiz Mariano

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arXiv · 1912.10961

Formalizing the Curry-Howard Correspondence

Juan Ferrer Meleiro·Hugo Luiz Mariano

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Abstract

The Curry-Howard Correspondence has a long history, and still is a topic of active research. Though there are extensive investigations into the subject, there doesn't seem to be a definitive formulation of this result in the level of generality that it deserves. In the current work, we introduce the formalism of p-institutions that could unify previous aproaches. We restate the tradicional correspondence between typed $λ$-calculi and propositional logics inside this formalism, and indicate possible directions in which it could foster new and more structured generalizations. Furthermore, we indicate part of a formalization of the subject in the programming-language Idris, as a demonstration of how such theorem-proving enviroments could serve mathematical research.

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BibTeX RIS

Juan Ferrer Meleiro, Hugo Luiz Mariano. 2019-12-23. Formalizing the Curry-Howard Correspondence. https://arxiv.org/abs/1912.10961

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