22.9.1. RP 19 Part 1¶

This problem will give you practice with fixed-point combinators.

To reduce syntactic clutter in this problem, we will take some shortcuts in writing $\lambda$ expressions. First, we will drop all but the first $\lambda$ and all but the last dot for (curried) functions with two or more parameters. So, for example, we will use:

as an abbreviation for:

Second, to cut down on parentheses, we will use $(u\ v\ w\ x\ y\ z)$ as an abbreviation for $(((((u\ v)\ w)\ x)\ y)\ z)$. In essence, we are making function application left-associative. This notation is to be used only for this review problem. Do NOT use it for any assignments, exams, or other review problems.