Inside the lambda calculus, the only thing you can do with a lambda abstraction is apply it. And one thing you can't do using your numbering scheme (which is b

Inside the lambda calculus, the only thing you can do with a lambda abstraction is apply it. And one thing you can't do using your numbering scheme (which is basically a Gödel numbering) is establish whether two syntactically different functions are extensionally equal (under some fixed reduction strategy).