A Computational Understanding of Classical (Co)Recursion

Abstract

Recursion and induction are mature, well-understood topics in programming. Yet their duals, corecursion and coinduction, are still exotic and underdeveloped programming features. We aim to put them on equal footing by giving a foundation for corecursion based on computation, analogous to the original computational foundation of recursion. At the lower level, we show how the connection between the two can be strengthened through their implementation details in an abstract machine. At the higher level, we develop a syntactic equational theory for inductive and coinductive reasoning based on control flow. We also observe the impact of evaluation strategy: call-by-name has efficient recursion and strong coinductive reasoning, but call-by-value has efficient corecursion and strong inductive reasoning.