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Unique Fixed Point Induction for McCarthy’s Amb

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Mathematical Foundations of Computer Science 1999 (MFCS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1672))

Abstract

We develop an operational theory of higher-order functions, recursion, and fair non-determinism for a non-trivial, higher-order, call-by-name functional programming language extended with McCarthy’s amb. Implemented via fair parallel evaluation, functional programming with amb is very expressive. However, conventional semantic fixed point principles for reasoning about recursion fail in the presence of fairness. Instead, we adapt higher-order operational methods to deal with fair non-determinism. We present two natural semantics, describing may-and must-convergence, and define a notion of contextual equivalence over these two modalities. The presence of amb raises special difficulties when reasoning about contextual equivalence. In particular, we report on a challenging open problem with regard to the validity of bisimulation proof methods. We develop two sound and useful reasoning methods which, in combination, enable us to prove a rich collection of laws for contextual equivalence and also provide a unique fixed point induction rule, the first proof rule for reasoning about recursion in the presence of fair non-determinism.

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Author information

Authors and Affiliations

  1. University of Cambridge Computing Laboratory, Pembroke Street, Cambridge, CB2 3QG, UK

    Søren B. Lassen

  2. Department of Computing Science, Chalmers University of Technology, 412 96, Göteborg, Sweden

    Andrew Moran

Authors
  1. Søren B. Lassen
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  2. Andrew Moran
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Wrocław, Przesmyckiego 20, PL-51-151, Wrocław, Poland

    Mirosław Kutyłowski , Leszek Pacholski  & Tomasz Wierzbicki ,  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Lassen, S.B., Moran, A. (1999). Unique Fixed Point Induction for McCarthy’s Amb. In: Kutyłowski, M., Pacholski, L., Wierzbicki, T. (eds) Mathematical Foundations of Computer Science 1999. MFCS 1999. Lecture Notes in Computer Science, vol 1672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48340-3_18

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  • DOI: https://doi.org/10.1007/3-540-48340-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66408-6

  • Online ISBN: 978-3-540-48340-3

  • eBook Packages: Springer Book Archive

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