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::Boolean logic may be implemented in lambda calculus. See [[Church encoding]]. You can give an expression for Y F in this case, but the calculation would never terminate (beta reduce to normal form). So no fixed point.
::<math>\operatorname{not}_1 = \lambda p.\lambda a.\lambda b.p\ b\ a</math>
::<math>(\lambda f.(\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))) (\lambda p.\lambda a.\lambda b.p\ b\ a) </math>
::<math>(\lambda f.(\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))) (\lambda p.\lambda a.\lambda b.p\ b\ a) </math>
::<math>(\lambda x.(\lambda p.\lambda a.\lambda b.p\ b\ a)\ (x\ x))\ (\lambda x.(\lambda p.\lambda a.\lambda b.p\ b\ a)\ (x\ x)) </math>
::<math>(\lambda p.\lambda a.\lambda b.p\ b\ a)\ ((\lambda x.(\lambda p.\lambda a.\lambda b.p\ b\ a)\ (x\ x))\ (\lambda x.(\lambda p.\lambda a.\lambda b.p\ b\ a)\ (x\ x)))) </math>
::<math>(\lambda p.\lambda a.\lambda b.p\ b\ a)\ ((\lambda x.(\lambda p.\lambda a.\lambda b.p\ b\ a)\ (x\ x))\ (\lambda x.(\lambda p.\lambda a.\lambda b.p\ b\ a)\ (x\ x))) </math>
[[User:Thepigdog|Thepigdog]] ([[User talk:Thepigdog|talk]]) 01:10, 10 January 2014 (UTC)
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