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The Church-Rosser property in dual combinatory logic. (English) Zbl 1045.03017

The dual combinatory logic considered in this paper, has not only the standard combinators such as \(S\), where \(Sxyz\triangleright xz(yz)\), but also dual combinators such as \(s\) where \(x(y(zs))\triangleright xy(xz)\). This paper shows that in any dual combinatory logic containing any proper combinators and their duals, the Church-Rosser property fails. This is not a problem in the structurally free logics in which dual combinators first appeared.

MSC:

03B40 Combinatory logic and lambda calculus
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References:

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