Great question. For the benefit of those without a functioning DrRacket installation (myself included) I’ll try to answer it. First, let’s use some sane (short) variable names, easily trackable by a human eye/mind: ((lambda (h) ; A. (h h)) ; apply h to h (lambda (g) (lambda (lst) (if (null? lst) 0 (add1 ((g g) … Read more
I’m going to disagree with other answers: The fixed-point (Y) combinator does have practical applications, but it takes a very imaginative mind to find them. Like Bruce McAdam. Here’s the abstract from his paper That About Wraps it Up: The Y combinator for computing fixed points can be expressed in Standard ML. It is frequently … Read more
As the compiler points out, there is no type that can be assigned to x so that the expression (x x) is well-typed (this isn’t strictly true; you can explicitly type x as obj->_ – see my last paragraph). You can work around this issue by declaring a recursive type so that a very similar … Read more
Here’s a non-recursive definition of the y-combinator in haskell: newtype Mu a = Mu (Mu a -> a) y f = (\h -> h $ Mu h) (\x -> f . (\(Mu g) -> g) x $ x) hat tip
Unless you’re deeply into theory, you can regard the Y combinator as a neat trick with functions, like monads. Monads allow you to chain actions, the Y combinator allows you to define self-recursive functions. Python has built-in support for self-recursive functions, so you can define them without Y: > def fun(): > print “bla” > … Read more
The only way I can think of to do this amounts to giving the function a name: fact = lambda x: 1 if x == 0 else x * fact(x-1) or alternately, for earlier versions of python: fact = lambda x: x == 0 and 1 or x * fact(x-1) Update: using the ideas from … Read more