For a Uni project I try to build complex lambda expressions with combinators that use only two (bound) variables.
For example I managed to create IF-THEN-ELSE $(λp.λa.λb.p a b)$ by using three combinators:
$(λx.λy. x y) (λx.λy. x y)$
Now I try the same approach for the SUCCESSOR expression $(λn.λf.λx.f ((n f) x))$ but I tried different approaches. But none worked.
Any hints? Is it even possible? How can I show that it's possible or not. Of course if I have an example that works it is possible. But how could I show that it's not possible?