You may want to consult: "Denotational Semantics-A Methodology for Language Development" by David A. Schmidt, ISBN 0-697-06849-8. I think that the Y combinator is: Y = lambda h.(lambda x. h(x x)) (lambda x. h(x x)) . I think that this does what it should is pretty patent from it, but as for deriving it, this involves insight that I don't yet have. john