We are working on a new tutorial presentation of L, the polarized version of Curien-Herbelin’s μμ̃ calculus. The calculus μμ̃ was introduced in Curien and Herbelin [2000] as a good term calculus for classical logic, which in particular reveals a perfect symmetry (in the classical setting) between call-by-value and call-by-name evaluation. Its polarized version, L, restricts the reduction rules according to a type- or polarity-based evaluation order; as Call-By-Push-Value [Levy 1999], it can express and mix both call-by-name and call-by-value terms in the same program, and is an interesting vehicle to study side-effects.

We would like to offer a presentation of a fragment of our in-progress tutorial to the HOPE audience, as an act of popularization for newcomers, and as the best way to get feedback on our approach from newcomers and experts alike.