An Effectful Way to Eliminate Addiction to Dependence
International audience 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...
Published in: | 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) |
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Main Authors: | , |
Other Authors: | , , , , , , , , , , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2017
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Subjects: | |
Online Access: | https://hal.inria.fr/hal-01441829 https://hal.inria.fr/hal-01441829/document https://hal.inria.fr/hal-01441829/file/main.pdf https://doi.org/10.1109/LICS.2017.8005113 |
Summary: | International audience 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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