TITLE: Encode lambda calculus in arithmetic?
QUESTION [8 upvotes]: There is plenty of information about how to encode arithmetic given the lambda calculus.  The wikipedia article on Church Encoding seems complete to my inexpert eye.  My question is "how about the other direction?"  What's a good way to encode the lambda calculus in ordinary real or integer (or even matrix) arithmetic?  It would seem that an application of Godel Numbering would do it, but I have been unable to find any writing on Godel Numbering for the lambda calculus specifically.  It also seems plausible to encode the lambda calculus in arithmetic in some way more efficient than Godel Numbering; perhaps someone has done that?  I might settle for the SKI calculus or some other Turing-complete language that's easier to encode than the lambda calculus.

REPLY [3 votes]: Binary coded Lambda calculus is effectively a Gödel encoding of LC.