Affiliation:
1. National Institute of Informatics, Japan
2. Chiba University, Japan
Abstract
Transformation of programs into continuation-passing style (CPS) reveals the notion of continuations, enabling many applications such as control operators and intermediate representations in compilers. Although type preservation makes CPS transformation more beneficial, achieving type-preserving CPS transformation for implicit polymorphism with call-by-value (CBV) semantics is known to be challenging. We identify the difficulty in the problem that we call scope intrusion. To address this problem, we propose a new CPS target language Λ
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that supports two additional constructs for polymorphism: one only binds and the other only generalizes type variables. Unfortunately, their unrestricted use makes Λ
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unsafe due to undesired generalization of type variables. We thus equip Λ
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with affine types to allow only the type-safe generalization. We then define a CPS transformation from Curry-style CBV System F to type-safe Λ
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and prove that the transformation is meaning and type preserving. We also study parametricity of Λ
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as it is a fundamental property of polymorphic languages and plays a key role in applications of CPS transformation. To establish parametricity, we construct a parametric, step-indexed Kripke logical relation for Λ
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and prove that it satisfies the Fundamental Property as well as soundness with respect to contextual equivalence.
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software