A couple of brief online discussions/justifications/derivations of the Y combinator: Matthias' legendary "Why of Y": ftp://ftp.cs.indiana.edu/pub/scheme-repository/doc/pubs/Y.ps.gz Don Blaheta's notes on the Lambda Calculus: http://www.cs.brown.edu/courses/cs173/2001/Lectures/2001-10-25.pdf