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A Notion of a Computational Step for Partial Combinatory Algebras

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Theory and Applications of Models of Computation (TAMC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7876))

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Abstract

Working within the general formalism of a partial combinatory algebra (or PCA), we introduce and develop the notion of a step algebra, which enables us to work with individual computational steps, even in very general and abstract computational settings. We show that every partial applicative structure is the closure of a step algebra obtained by repeated application, and identify conditions under which this closure yields a PCA.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Harvard University, USA

    Nathanael L. Ackerman

  2. Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology, USA

    Cameron E. Freer

Authors
  1. Nathanael L. Ackerman
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  2. Cameron E. Freer
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Editor information

Editors and Affiliations

  1. The University of Hong Kong, Hong Kong

    T-H. Hubert Chan

  2. The Chinese University of Hong Kong, Hong Kong

    Lap Chi Lau

  3. Department of Computer Science, Stanford University, 94305, Stanford, CA, USA

    Luca Trevisan

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Ackerman, N.L., Freer, C.E. (2013). A Notion of a Computational Step for Partial Combinatory Algebras. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_13

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  • DOI: https://doi.org/10.1007/978-3-642-38236-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38235-2

  • Online ISBN: 978-3-642-38236-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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