Abstract. The notion of delimited continuations has been proved useful in various areas of computer programming such as partial evaluation, mobile computing, and web transaction. In our previous work, we proposed polymorphic calculi with control operators for delimited continuations. This paper presents a proof of strong normalization (SN) of these calculi based on a refined (i.e. administrative redex-free) CPS translation.

We study the control operators ”control” and ”prompt” which manage part of continuations, that is, delimited continuations. They are similar to the well-known control operators ”shift” and ”reset”, but differ in that the former is dynamic, while the latter is static. In this paper, we introduce a static type system for ”control ” and ”prompt” which does not use recursive types. We design our type system based on the dynamic CPS transformation recently proposed by Biernacki, Danvy and Millikin. We also introduce let-polymorphism into our type system, and show that our type system satisfies several important properties such as strong type soundness.

We describe the implementation of first-class polymorphic delimited continuations in the programming language Scala. We use Scala’s pluggable typing architecture to implement a simple type and effect system, which discriminates expressions with control effects from those without and accurately tracks answer type modification incurred by control effects. To tackle the problem of implementing first-class continuations under the adverse conditions brought upon by the Java VM, we employ a selective CPS transform, which is driven entirely by effect-annotated types and leaves pure code in direct style. Benchmarks indicate that this high-level approach performs competitively.