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Church-Rosser theorems for replacement systems

Part of the Lecture Notes in Mathematics book series (LNM,volume 450)

Abstract

Replacement systems with the Church-Rosser property promise to be of great interest for the theory of parallel programming languages; particular systems have long been of interest in theories of combinatory logic and lambda conversion. This paper reviews known methods for proving the Church-Rosser property for general replacement systems and adds some new results. Finally some open problems are listed.

Keywords

  • Inductive Hypothesis
  • Binary Relation
  • Local System
  • Terminal Node
  • Base Node

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. BARENDREGT, H.P. Some extensional term models for combinatory logics and λ-calculi. Ph.D. thesis, U. Utrecht, 1971.

    Google Scholar 

  2. CURRY, H.B. and R. FEYS Combinatory logic, North-Holland, Amsterdam, 1958.

    MATH  Google Scholar 

  3. HINDLEY, R. The Church-Rosser property and a result in combinatory logic. Ph.D. thesis, U. Newcastle-upon-Tyne, 1964.

    Google Scholar 

  4. An abstract form of the Church-Rosser theorem, I. J. Symbolic Logic 34, 1969, 545–560.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. An abstract Church-Rosser theorem, II: applications. J. Symbolic Logic, 39, 1974, 1–21.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. MITSCHKE, G. Ein algebraischer Beweis für das Church-Rosser Theorem, Arch. math. Logik 15, 1973, 146–157.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. ROSEN, B.K. Tree-manipulating systems and Church-Rosser theorems. J.A.C.M. 20, 1973, 160–187.

    MathSciNet  MATH  Google Scholar 

  8. SCHROER, D.E. The Church-Rosser theorem. Ph.D. thesis, Cornell University, 1965.

    Google Scholar 

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© 1975 Springer-Verlag

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Staples, J. (1975). Church-Rosser theorems for replacement systems. In: Crossley, J.N. (eds) Algebra and Logic. Lecture Notes in Mathematics, vol 450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062861

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  • DOI: https://doi.org/10.1007/BFb0062861

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07152-5

  • Online ISBN: 978-3-540-37480-0

  • eBook Packages: Springer Book Archive