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On the interpretation of combinators with weak reduction1

Published online by Cambridge University Press:  12 March 2014

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

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
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
[3]Curry, H.B., Hindley, J.R., and Seldin, J.P., Combinatory logic. Vol. II, North-Holland, Amsterdam, 1972.Google Scholar
[4]Curry, H.B., The undecidability of λK-conversion, Foundations of mathematics (Bulloff, J.J., Holyoke, T.C., and Hahn, S.W., editors), Springer-Verlag, Berlin, 1969, pp. 1014.CrossRefGoogle Scholar
[5]Kearns, J.T., The completeness of combinatory logic with discriminators, Notre Dame Journal of Formal Logic, vol. 14 (1973), pp. 323330.CrossRefGoogle Scholar
[6]Rogers, H., Theory of recursive functions and effective computability, McGraw-Hill, New York, 1967.Google Scholar
[7]Shabunin, L.V., A variant of combinatory logic with discriminators, Vestnik Moskovskogo Universiteta. Serlya I: Matematika, Mekhanlka, vol. 27 (1972), no. 4,pp. 5358; English translation, Moscow University Matematlcs Bulletin, vol. 27 (1972), no. 3/4, pp. 115–120.Google Scholar
[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. 39, 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