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arXiv · 1908.05979

A Gentzen-style monadic translation of G\"odel's System T

Chuangjie Xu
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Abstract

We introduce a syntactic translation of Goedel's System T parametrized by a weak notion of a monad, and prove a corresponding fundamental theorem of logical relation. Our translation structurally corresponds to Gentzen's negative translation of classical logic. By instantiating the monad and the logical relation, we reveal the well-known properties and structures of T-definable functionals including majorizability, continuity and bar recursion. Our development has been formalized in the Agda proof assistant.

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Chuangjie Xu. 2019-08-16. A Gentzen-style monadic translation of G\"odel's System T. https://arxiv.org/abs/1908.05979

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