2019/12/23 by Juan Ferrer Meleiro, Meleiro, Juan Ferrer, Hugo Luiz Mariano +1
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Formal Methods in Verification #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1912.10961
openalex publication_date 2019/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.