30 Mar
2009
30 Mar
'09
9:55 p.m.
Hi all, I am reading the book "The lambda calculus: Its syntax and Semantics" in the chapter about Godel Numbering but I am confused in some points. We know for Church Numerals, we have Cn = \fx.f^n(x) for some n>=0, i.e. C0= \fx.x and C 1 = \fx.fx.
From the above definition, I could guess the purpose of this kind of encoding is trying to encode numeral via terms.
How about the Godel Numbering? From definition we know people say #M is the godel number of M and we also have [M] = C#M to enjoy the second fixed point theorem : for all F there exists X s.t. F[X] = X. What the mapping function # is standing for? How could I use it? What the #M will be? How to make use of the Godel Numbering? Thank you very much! alg