Space-Efficient Polymorphic Gradual Typing, Mostly Parametric

Atsushi Igarashi, Shota Ozaki, Taro Sekiyama, Yudai Tanabe

Abstract: Since the arrival of gradual typing, which allows partially typed code in a single program, efficient implementations of gradual typing have been an active research topic. In this paper, we study the space-efficiency problem of gradual typing in the presence of parametric polymorphism. Based on the existing work that showed the impossibility of a space-efficient implementation that supports fully parametric polymorphism, this paper will show that a space-efficient implementation is, in principle, possible by slightly relaxing parametricity. We first develop λCmp, which is a coercion calculus with mostly parametric polymorphism, and show its relaxed parametricity. Then, we present λSmp, a space-efficient version of λCmp, and prove that λSmp programs can be executed in a space-efficient manner and that translation from λCmp to λSmp is type- and semantics-preserving.