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Computer Science > Logic in Computer Science

arXiv:1210.3116v1 (cs)
[Submitted on 11 Oct 2012]

Title:Extensional Models of Untyped Lambda-mu Calculus

Authors:Koji Nakazawa (Graduate School of Informatics, Kyoto University), Shin-ya Katsumata (Research Institute for Mathematical Sciences, Kyoto University)
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Abstract:This paper proposes new mathematical models of the untyped Lambda-mu calculus. One is called the stream model, which is an extension of the lambda model, in which each term is interpreted as a function from streams to individual data. The other is called the stream combinatory algebra, which is an extension of the combinatory algebra, and it is proved that the extensional equality of the Lambda-mu calculus is equivalent to equality in stream combinatory algebras. In order to define the stream combinatory algebra, we introduce a combinatory calculus SCL, which is an abstraction-free system corresponding to the Lambda-mu calculus. Moreover, it is shown that stream models are algebraically characterized as a particular class of stream combinatory algebras.
Comments: In Proceedings CL&C 2012, arXiv:1210.2890
Subjects: Logic in Computer Science (cs.LO)
ACM classes: F.4.1
Cite as: arXiv:1210.3116 [cs.LO]
  (or arXiv:1210.3116v1 [cs.LO] for this version)
  https://doi.org/10.48550/arXiv.1210.3116
Journal reference: EPTCS 97, 2012, pp. 35-47
Related DOI: https://doi.org/10.4204/EPTCS.97.3

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Thu, 11 Oct 2012 03:52:22 UTC (22 KB)
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