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Abstract

Λμ-calculus was introduced as a Böhm-complete extension of Parigot’s λμ-calculus. Λμ-calculus, contrarily to Parigot’s calculus, is a calculus of CBN delimited control as evidenced by Herbelin and Ghilezan. In their seminal paper on (CBV) delimited control, Danvy and Filinski introduced the CPS Hierarchy of control operators (shift i /reset i ) i ∈ ω .

In a similar way, we introduce in the present paper the Stream Hierarchy, a hierarchy of calculi extending and generalizing Λμ-calculus. The \((\Lambda^n)_{n\in\omega}\)-calculi have Church-Rosser and Böhm theorems. We then present sound and complete CPS translations for the hierarchy. Next, we investigate the operational content of the hierarchy through its abstract machines, the \((\Lambda^n)_{n\in\omega}\)-KAM. Finally, we establish that the Stream hierarchy is indeed a CBN analogue to the CPS hierarchy.

Keywords

Λμ-calculus delimited control CPS hierarchy Böhm theorem CPS translation Abstract machine Streams 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Alexis Saurin
    • 1
  1. 1.PPS & INRIA πr2 

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