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On the interpretation of combinators with weak reduction1

Published online by Cambridge University Press:  12 March 2014

L.V. Shabunin
L.V. Shabunin*
Affiliation:
Chuvashsky State University, Cheboksary, USSR
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Extract

In this paper some partial models for combinators with weak reduction are proposed. The underlying ideas are due to Church [1]. The results are extensions of the previous results of the author proved in [8].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 3 , September 1983 , pp. 558 - 563
Copyright
Copyright © Association for Symbolic Logic 1983

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Footnotes

1

(Note by Jonathan P. Seldin.) This is a revised version of a paper submitted in May, 1979 for publication in To H.B. Curry: Essays in Combinatory Logic, Lambda-Calculus, and Formalism, edited by Roger Hindley and me, Academic Press, London, 1980. At the end of May, 1979, I found an error in Lemma 2.7 of §4 of [8] and wrote to the author about it. The error turns out to be easily repaired (see footnote 4 below), but unfortunately at the time I wrote the author was in the process of moving to Moscow for six months, and so my letter did not reach him until November, 1979, and by that time a deadline set by the publishers had forced us to decide on the final contents of the book before receiving a reply from the author, and as a result this paper did not appear in the book.

References

REFERENCES

[1]Church, Alonzo, The calculi of lambda-conversion, Princeton University Press, Princeton, N.J., 1941.Google Scholar
[2]Curry, H.B. and Feys, R., Combinatory logic. Vol. I, North-Holland, Amsterdam, 1958.Google Scholar
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[8]Shabunin, L.V., An interpretation of α-words connected with simple combinatorial calculi, Vestnik Moskovskogo Universiteta. Seriya I: Matematika, Mekhanlka, vol. 30 (1975), no. 6, pp. 3–9, and vol. 31 (1976),no. 1, 12–17; English translation, Moscow University Mathematics Bulletin,vol. 30 (1975), no. 5/6, pp. 55–60, and vol. 31 (1976), no. 1/2, pp. 9–14.Google Scholar