By J. Diller, G.H. Müller

ISBN-10: 354007533X

ISBN-13: 9783540075332

Diller J., Mueller G.H. (eds.) ISILC facts idea Symposion. devoted to Kurt Schutte at the get together of his sixty fifth birthday, Kiel, 1974 (LNM0500, Springer, 1975)(ISBN 354007533X)(1s)_Mln_

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Example text

Is standard. Henceforth we assume secondary contractions in will be the standard reduction sought. By that lepta there is a stage U" in D2 R; D2, then D1 + Otherwise we apply Lemma 7. such that there is an is senior to the redex contracted in the next step, has and has the same beginning as and D 3. is not residual of a redex bypassed by the last step of D 2 + {R} + D 3 m > 0 R P~ in U" which as sole residual in Y , also its residuals, all of which are equiform, are interchangeable with all the redexes contracted later in D2 .

Soc. (to appear). Thesis, Oxford, 1969. spaces, A STUDY OF GENERALIZED STANDARDIZATION IN COMBINATORY LOGIC by Haskell B. ,mn) which we associated with that its normal reduction does not terminate. ,m n) We were unable at that time to con- has no normal form; for we did not have a proof, for the kind of generalized reduction there considered, that if an form XN, is unis such then the normal reduction of X must terminate in ob X XN. has a normal This question we purposely left open in accordance with the policy announced in the preface of [2].

Let Xk (0 ~ k ~ n) tracted in the k'th step be Pk+l for such that residual of Rk Pk+l for Pk k k < m, such that This is trivial for Now since It follows by Lemma 1 that Xk_ 1 which is senior to Rk k = m. Rk has Thus Pm+l R. By E7, Rk R the other hand Q contracted. Rk k, R Lemma 4. of some S i. D, Let Let and let P~, is the unique R R~ X which is a replacement for Pk of an Pm+l" in X Rk_ 1 in Rk_ 1 begins Thus by de- and begins exactly at the beginQ, R, by the hypothesis on for if it did every Q, and no residual of Q.

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ISILC - Proof Theory Symposion: Dedicated to Kurt Schütte on the Occasion of His 65th Birthday. Proceedings of the International Summer Institute and ... in Mathematics) by J. Diller, G.H. Müller


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