A Substructural Type System for Delimited Continuations

13 years 10 months ago

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We propose type systems that abstractly interpret small-step rather than big-step operational semantics. We treat an expression or evaluation context as a structure in a linear logic with hypothetical reasoning. Evaluation order is not only regulated by familiar focusing rules in the operational semantics, but also expressed by structural rules in the type system, so the types track control ﬂow more closely. Binding and evaluation contexts are related, but the latter are linear. We use these ideas to build a type system for delimited continuations. It lets control operators change the answer type or act beyond the nearest dynamically-enclosing delimiter, yet needs no extra ﬁelds in judgments and arrow types to record answer types. The typing derivation of a directstyle program desugars it into continuation-passing style.

Oleg Kiselyov, Chung-chieh Shan

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