I am trying to learn Lambda calculus from here
and while trying to solve some problems, I got stuck. I was trying to solve the following problem (page 14, excercise 2.6 part (i):
Simplify $M \equiv (\lambda xyz.zyx) aa (\lambda pq. q)$.
My evaluation using the beta rule reduces it to $(\lambda z. z)$ as follows: First I replace occurences of $x$ in $M$ by $aa (\lambda pq. q)$, and then since there are no occurences of $y$ in the resulting $\lambda$ term, the expression simply evaluates to $(\lambda z. z)$.
Is my reasoning correct? (Since there were no solutions to these notes, I want to ensure my understanding is correct. Any corrections, will be much appreciated! Thanks in advance.