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Recursion from cyclic sharing: Traced monoidal categories and models of cyclic lambda calculi

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Typed Lambda Calculi and Applications (TLCA 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1210))

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Abstract

Cyclic sharing (cyclic graph rewriting) has been used as a practical technique for implementing recursive computation efficiently. To capture its semantic nature, we introduce categorical models for lambda calculi with cyclic sharing (cyclic lambda graphs), using notions of computation by Moggi/Power and Robinson and traced monoidal categories by Joyal, Street and Verity. The former is used for representing the notion of sharing, whereas the latter for cyclic data structures. Our new models provide a semantic framework for understanding recursion created from cyclic sharing, which includes traditional models for recursion created from fixed points as special cases. Our cyclic lambda calculus serves as a uniform language for this wider range of models of recursive computation.

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Authors and Affiliations

  1. LFCS, Department of Computer Science, University of Edinburgh JCMB, King's Buildings, EH9 3JZ, Edinburgh, Scotland

    Masahito Hasegawa

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  1. Masahito Hasegawa
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Philippe de Groote J. Roger Hindley

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© 1997 Springer-Verlag Berlin Heidelberg

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Hasegawa, M. (1997). Recursion from cyclic sharing: Traced monoidal categories and models of cyclic lambda calculi. In: de Groote, P., Roger Hindley, J. (eds) Typed Lambda Calculi and Applications. TLCA 1997. Lecture Notes in Computer Science, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62688-3_37

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  • DOI: https://doi.org/10.1007/3-540-62688-3_37

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62688-6

  • Online ISBN: 978-3-540-68438-1

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