Submitted by Richard Statman
Statement. Do uniform universal generators exist?
A term is a uniform universal generator iff there is a non-trivial context such that for each closed term . The above question was ﬁrst stated in [Statman, 1993], and it is open for either CL (with weak reduction) or lambda-calculus (with - or -reduction). If the context is required to have the form , so is , then it can be shown [Statman, 1993] that uniform universal generators do not exist for combinatory logic.