[Haskell-beginners] Re: fixpoint operator for ULC with specific reduction property

ben wrote:

I'm looking for a fixpoint operator Z for the untyped lambda calculus that has the property

Z g --> g (Z g)

for any g.

The best-known fixpoint operator Y := \f. (\x. f (x x)) (\x. f (x x)) does not have this property, but only

Y g --> T <-- g (Y g)

for some T.

Does anybody know such a Z I'm looking for?

I think the Turing fixed point combinator does exactly that. It's defined as Theta = (λxf.f(xxf))(λxf.f(xxf)) Related: http://www.mail-archive.com/haskell-cafe@haskell.org/msg43467.html Regards, Heinrich Apfelmus -- http://apfelmus.nfshost.com