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Termination tests inside λ-calculus

  • C. Böhm
  • M. Coppo
  • M. Dezani-Ciancaglini
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)

Abstract

Let be associated to each element N of the set
of the normal forms of the λ-κ-β calculus and to each integer r > 0 the semi but non - decidable domain D [N,r] \( \subseteq \)
r onto which N, considered as partial map ping
r
, is total (that is the computation starting from NX1 ... Xr where N ∈
and X1, ..., xrD [N,r] and evolging through a β -reduction algorithm terminates). The decidability of the relation D [N,r] =
r has been proved in a previous paper. In the present paper, for any N and r, an infinite, decidable subdomain C [N,r] \( \subseteq \)D [N,r] is defined in a constructive way. The ensuing sufficient condition for the termination of a computation starting from N X1 ... Xr can be tested in a number of steps negligible with respect to those needed for reaching the n.f., if there is one.

Keywords

Normal Form Composition Operator Free Variable Combinatory Logic Access Path 
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.

References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • C. Böhm
    • 1
  • M. Coppo
    • 2
  • M. Dezani-Ciancaglini
    • 3
  1. 1.Istituto Matematico G. Castelnuovo (Università di Roma)Italy
  2. 2.Istituto di Scienza dell'Informazione (Università di Torino)Italy
  3. 3.Istituto di Scienza dell'Informazione (Università di Torino)Italy

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