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Colloquium on Trees in Algebra and Programming

CAAP 1983: CAAP'83 pp 405–416Cite as

Cofinality in reduction graphs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 159))

Abstract

Reductions from an arbitrary term of the λβ-calculus are considered in this paper in the framework of the reduction graph that can be associated to that term. The graph approach allows to have a global view of all reductions starting from a term with a criterium of significance for reductions according to which cofinal reductions are the most significant ones. A new class of cofinal reductions are defined, namely, the quasi-complete reductions. A sufficient condition (conjectured to be also necessary) concerning cofinality in reduction graphs which is weaker than one already known is stated.

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References

  1. H.P. Barendregt, The Lambda Calculus. Its Syntax and Semantics (North-Holland, Amsterdam 1981).

    Google Scholar 

  2. A. Church, The Calculi of Lambda Conversion (Princeton University Press, 1941).

    Google Scholar 

  3. H.B. Curry, R. Feys, Combinatory Logic, vol. I (North-Holland, Amsterdam 1958).

    Google Scholar 

  4. H.B. Curry, J.R. Hindley, J.P. Seldin, Combinatory Logic, vol. II (North-Holland, Amsterdam 1972).

    Google Scholar 

  5. F. Harary, Graph Theory (addison-Wesley Pub. Co. 1969).

    Google Scholar 

  6. J.W. Klop, Reduction Cycles in Combinatory Logic, in: J.P. Seldin and J.R. Hindley, Eds., To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism (Academic Press, London 1980).

    Google Scholar 

  7. J.W. Klop, Combinatory Reduction Systems, Mathematical Centre Tracts n.127, (Mathematical Centre, Amsterdam 1980).

    Google Scholar 

  8. G. Jacopini, M. Venturini Zilli, Equating for Recurrent Terms of λ-Calculus and Combinatory Logic, Quaderno IAC s.III, n.85 (Roma 1978).

    Google Scholar 

  9. J.J. Lévy, Réductions correctes et optimales dans le lambda-calculi, Thèse de doctorat, Paris (1978).

    Google Scholar 

  10. C. St. J. Nash-Williams, Infinite Graphs: A Survey, Journal of Combinatorial Theory 3, (1967) 286–301.

    Google Scholar 

  11. M. Venturini Zilli, Head — recurrent Terms in Combinatory Logic: a Generalization of the Notion of Head-normal form, in: G. Ausiello and C. Böhm, Eds., Automata, Languages and Programming (Springer-Verlag 1978) 477–493.

    Google Scholar 

  12. M. Venturini Zilli, Recurrence and Head-recurrence in Combinatory Logic and λ-Calculus, IAC Internal Report, 1981.

    Google Scholar 

  13. M. Venturini Zilli, Reduction Graphs in the Lambda Calculus, 1982, submitted for publication to Theoretical Computer Science.

    Google Scholar 

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Authors and Affiliations

  1. IAC-CNR, Viale del Policlinico 137, 00161, Roma, Italy

    M. Venturini Zilli

Authors
  1. M. Venturini Zilli
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Giorgio Ausiello Marco Protasi

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© 1983 Springer-Verlag Berlin Heidelberg

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Zilli, M.V. (1983). Cofinality in reduction graphs. In: Ausiello, G., Protasi, M. (eds) CAAP'83. CAAP 1983. Lecture Notes in Computer Science, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12727-5_26

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  • DOI: https://doi.org/10.1007/3-540-12727-5_26

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12727-7

  • Online ISBN: 978-3-540-38714-5

  • eBook Packages: Springer Book Archive

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