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.
Complete list of metadatas

https://hal.inria.fr/hal-01441829
Contributor : Nicolas Tabareau <>
Submitted on : Friday, January 20, 2017 - 11:20:25 AM
Last modification on : Tuesday, March 26, 2019 - 9:25:22 AM

File

main.pdf
Files produced by the author(s)

Identifiers

Citation

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⟩

Share

Metrics

Record views

956

Files downloads

618