Typing, Representing, and Abstracting Control: Functional Pearl
by Philipp Schuster and Jonathan Brachthäuser
In Proceedings of the International Workshop on Type-Driven Development. ACM Press, 2018.
This publication is related to the Effekt: Algebraic Effect Handlers research project.
A well known technique to implement a programming language with delimited control operators shift and reset is to translate programs into continuation passing style (CPS). We can iterate the CPS translation to implement a family of control operators shift_i and reset_i . This functional pearl retells the story of a family of delimited control operators and their translation to lambda calculus via the CPS hierarchy. Prior work on the CPS hierarchy fixes a level of n control operators for the entire program upfront. In contrast, we allow different parts of the program to live at different levels. It turns out that taking shift_0 rather than shift as the basis for the family of control operators is essential for this. Our source language is a typed embedding in the dependently typed language Idris. Our target language is a HOAS embedding in Idris. Guided by the types, the translation applies well known techniques to avoiding administrative beta- and eta-redexes at all levels of the CPS hierarchy.