On the one hand the n'th derivative operator is clearly a binary operator that you are composing with a function application operator.

On the other hand, OP seems to have not noticed that the ternary conditional also has this structure. That is, `f : x` could be syntactic sugar for `f(() => x)` [or perhaps `f(p => p, () => x)` if you like Church encodings] and then there are a few options for meanings of `x ? y` that have `(x ? y) : z` as a conditional.