Definition of Omega combinator

[asebian]

Hello,

not considering myself an expert I wonder whether the definition of the Omega combinator is correct. Shouldn't it be like this?

Ω := MM = (λa.aa)λa.aa

That way Ω does not consume further arguments. The loop is entered when M takes M as an argument, right?

Ωx = MMx = ((λa.aa)λa.aa)x

Whereas

(λa.(aa)(aa))x = (xx)(xx)

takes one more argument and would terminate when x was I := λa.a for instance.

Accordingly, the JS expression for omega would be a function without arguments.

() => (a => a(a))(a => a(a))

I might be wrong.

Anyway, I was happy to come across your project. Thanks for sharing it!

Cheers!

[drupol]

Sorry for the delay, kinda busy with some other projects, I'll come back to this issue as soon as I have more time.