An effectful way to eliminate addiction to dependence

Pierre-Marie Pedrot, Nicolas Tabareau
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
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
more » ... ies 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.
doi:10.1109/lics.2017.8005113 dblp:conf/lics/PedrotT17 fatcat:n6zg5i4anfgkje44g5ntcltkpq