Hi all,<br><br>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.<br><br>We know for Church Numerals, we have C<font size="1">n</font> = \fx.f^n(x) for some n>=0, i.e. C<font size="1">0</font> = \fx.x and C<font size="1">1</font> = \fx.fx.<br>
<br>From the above definition, I could guess the purpose of this kind of encoding is trying to encode numeral via terms.<br><br>How about the Godel Numbering? From definition we know people say #M is the godel number of M and we also have [M] = C<font size="1">#M</font> to enjoy the second fixed point theorem : for all F there exists X s.t. F[X] = X.<br>
<br>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?<br><br>Thank you very much!<br><br>alg<br>