22.9. Recursive Functions¶
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:
\[\lambda abcd.E\]
as an abbreviation for:
\[\lambda a.\!\lambda b.\!\lambda c.\!\lambda d.E\]
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.
