Space-Efficient Gradual Typing in Coercion-Passing Style
Herman et al. (2007, 2010) pointed out that the insertion of run-time checks into a gradually typed program could hamper tail-call optimization and, as a result, worsen the space complexity of the program. To address the problem, they proposed a space-efficient coercion calculus, which was subsequently improved by Garcia, et al. (2009) and Siek et al. (2015). The semantics of these calculi involves eager composition of run-time checks expressed by coercions to prevent the size of a term from growing. However, it relies also on a nonstandard reduction rule, which does not seem easy to implement. In fact, no compiler implementation of gradually typed languages fully supports the space-efficient semantics faithfully.
In this paper, we study coercion-passing style, which Herman et al. have already mentioned, as a technique for straightforward space-efficient implementation of gradually typed languages. A program in coercion-passing style passes “the rest of run-time checks” around—just like continuation-passing style (CPS), in which “the rest of computation” has been passed around—and (unlike CPS) composes coercions eagerly. We give a formal coercion-passing translation from $\lambda$S by Siek et al. to $\lambda$S$_1$, which is a new calculus of first-class coercions tailored for coercion-passing style, and prove correctness of the translation. We also implement our coercion-passing style transformation for the Grift compiler developed by Kuhlenschmidt et al. and give a preliminary experimental result.
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|Hypercoercions and a Framework for Equivalence of Cast Calculi
Kuang-Chen Lu Indiana University Bloomington, Jeremy G. Siek Indiana University, USA, Andre Kuhlenschmidt Indiana UniversityPre-print
|Space-Efficient Gradual Typing in Coercion-Passing Style
Yuya Tsuda Kyoto University, Atsushi Igarashi Kyoto University, Japan, Tomoya Tabuchi Kyoto UniversityPre-print