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Theoretical Pearl Yet yet a counterexample for λ+SP

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Pierre-Louis Curien  and
Thérèse Hardin
Pierre-Louis Curien
Affiliation:
CNRS-ENS, 45 rue d'Ulm 75230, Paris Cedex 05, France (e-mail: cuhen@dmi.ens.fr)
Thérèse Hardin
Affiliation:
LITP-Université Paris VI, 2 pl. Jussieu, 75005 Paris, France (e-mail: hardin@margaux.inria.fr)
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In 1979, Klop (1980), answering a question raised by Mann in 1972, showed that the extension of λ-calculus with subjective pairing is not confluent. We refer to Klop (1980) and Barendregt (1981, revised 1984) for a perspective. The term presented by Klop to provide a counterexample is fairly simple, but the proof of non-confluence, although intuitively quite simple, involves some technical properties. Among others, a suitable standardization result on derivations in the extended system is needed in the proof. Klop's proof was revisited by Bunder (1985), who seemingly used less technical apparatus than Klop, starting with the same term as Klop. Although Bunder's proof does not explicitly use a standardization result, his proof proceeds internally with some rearrangements of derivations, so that it is fair to say that some standardization technique is present in Bunder (1985).

Type
Articles
Information
Journal of Functional Programming , Volume 4 , Issue 1 , January 1994 , pp. 113 - 115
Copyright
Copyright © Cambridge University Press 1994

References

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