Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Functional programming, design and analysis of algorithms / 1 / c

The base value can have any type a. The recursive result has that same type, so the step must accept and return a. Thus the most general polymorphic type signature of the natural-number fold is

foldNat :: (a -> a) -> a -> Natural -> a

In mathematical type notation, $\boxed{(\alpha \to \alpha )\to \alpha \to \mathrm{Natural}\to \alpha }$. No equality, ordering or numeric constraint is needed: the natural-number fold manipulates constructors, rather than performing arithmetic on the result.