I'm reading Types and Programming Languages and trying to understand the solution to exercise 5.2.4 on untyped lambda calculus / Church numerals:
Define a term for raising one number to the power of another.
The proposed solution says:
$\textrm{power2} = \lambda m. \lambda n. m~n$
In an attempt to understand how this solution works, I tried it on 01 as follows:
$$ \begin{array}{ll} & \textrm{power2}~c_0~c_1 \\ \rightarrow & c_0~c_1 \\ = & (\lambda s.\lambda z.z)~c_1 \\ \rightarrow & \lambda z.z \end{array}$$
The result doesn't look like a Church numeral to me. Is it an error in the solution, or have I misunderstood something?