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Conference Papers Year : 2017

An Effectful Way to Eliminate Addiction to Dependence

Abstract

We define a monadic translation of type theory, called weaning translation, that allows for a large range of effects in dependent type theory—such as exceptions, non-termination, non-determinism or writing operation. Through the light of a call-by-push-value decomposition, we explain why the traditional approach fails with type dependency and justify our approach. Crucially, the construction requires that the universe of algebras of the monad forms itself an algebra. The weaning translation applies to a version of the Calculus of Inductive Constructions (CIC) with a restricted version of dependent elimination. Finally, we show how to recover a translation of full CIC by mixing parametricity techniques with the weaning translation. This provides the first effectful version of CIC.
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Dates and versions

hal-01441829 , version 1 (20-01-2017)

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Pierre-Marie Pédrot, Nicolas Tabareau. An Effectful Way to Eliminate Addiction to Dependence. Logic in Computer Science (LICS), 2017 32nd Annual ACM/IEEE Symposium on, Jun 2017, Reykjavik, Iceland. pp.12, ⟨10.1109/LICS.2017.8005113⟩. ⟨hal-01441829⟩
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