Closure is not a functor, since we cannot map arbitrary functions over it. But it sure looks like one, and an applicative one at that. What we can do is map static pointers to arbitrary functions over it (or in general, closures). Closure is not just an applicative functor, it's also a monad, as well as a comonad, if again we limit the function space to those functions that can be statically pointed to.

In fact an entire hierarchy of classes mirroring the standard classes can be defined, where nearly the only difference lies in the fact that higher-order arguments must be a proof of static-ness (i.e. a Closure). The other difference is that composing static values requires a proof of typeability, so we carry those around (Typeable constraints).

This module and others define just such a class hierarchy in the category of static functions (aka values of type Closure (a -> b)).