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Theoretical Pearls Enumerators of lambda terms are reducing
Published online by Cambridge University Press: 07 November 2008
Abstract
A closed λ-term E is called an enumerator if
Here ⋀0 is the set of closed λ-terms,. is the set of natural numbers and the ⌜n⌝ are the Church's numerals λfx.fnx. Such an E is called reducing if, moreover
An ingenious recursion theoretic proof by Statman will be presented, showing that every enumerator is reducing. I do not know any direct proof.
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