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*Originator: Richard Statman *

*Date: June 1993*

Summary: In combinatory logic, is there auniform universal generator?

Recall that *M* is a *universal generator* if each combinator
*P* has a superterm *Q* such that *M* →^{*} *Q*.
Call *M* a *uniform universal generator* if there exists a context
*C*[·] such that, for each combinator *P*, we have *M* →^{*} *C*[*P*].
Is there a uniform universal generator?
(For Combinatory Logic, if we restrict the context *C*[·]
to be of the form (*N* ·), no such term exists [Sta92].)

- [Sta92]
- Richard Statman. A short note on a problem of Ray Smullyan. Technical report, INRIA-Rocquencourt, 1992.

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