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A Proof Theoretical Account of Continuation Passing Style

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Computer Science Logic (CSL 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2471))

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Abstract

We study the “classical proofs as programs” paradigm in Call-By-Value (CBV) setting. Specifically, we show the CBV normalization for CND (Parigot 92) can be simulated by the cut-elimination procedure for LKQ (Danos-Joinet-Schellinx 93), namely the q-protocol. We use a proof-term assignment system to prove this fact. The term calculus for CND we use follows Parigot’s λμ-Calculus and is closely related to Ong-Stewart’s(Ong-Stewart 97). A new term calculus for LKQ is presented as a variant of λ-calculus with a let-construct. We then define a translation from CND into LKQ and prove simulation theorem. We also show the translation we use can be thought of a familiar CBV CPS-translation without translation on types.

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Authors and Affiliations

  1. Information Technology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), AIST Tsukuba Central 2, 1-1-1, Umezono, Tsukuba, Ibaraki, 305-8568, Japan

    Ichiro Ogata

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  1. Ichiro Ogata
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Editor information

Editors and Affiliations

  1. Laboratory for Foundations of Computer Science Division of Informatics, University of Edinburgh, King’s Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK

    Julian Bradfield

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Ogata, I. (2002). A Proof Theoretical Account of Continuation Passing Style. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_33

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  • DOI: https://doi.org/10.1007/3-540-45793-3_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44240-0

  • Online ISBN: 978-3-540-45793-0

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