We consider inference for the expression lambda f. lambda x. f (f x).
We assume that {} represents the empty environment.


W({} | lambda f. lambda x. f (f x)) = (a->b->c | a=d->c /\ a=b->d)
 where
     a new
     W(f:a | lambda x.f (f x)) = (b->c | a=d->c /\ a=b->d)
      where
         b new
         W(f:a,x:b | f (f x)) = (c | a=d->c /\ a=b->d)
          where
            c new
            W(f:a,x:b | f) = (a | True)
            W(f:a,x:b | f x) = (d | a=b->d)
             where
               d new
               W(f:a,x:b | f) = (a | True)
               W(f:a,x:b | x) = (b | True)



Consider a=d->c /\ a=b->d

We find phi=[a |-> b->b, c |-> b, d |-> b] is a most general unifier

That is,  phi(a->b->c) = (b->b)->b->b is the 
principal type of ({},lambda f. lambda x. f (f x))