We defined what it means to curry a function and how to write curried functions in SML.
(If you have forgotten about closures, please revisit Lecture 2.)
We discussed higher-order functions. A function that takes another function as an argument is classified as a higher-order function, as are functions that return higher-order functions. (Some authors broaden the definition to also include any function that returns a first-order function.)
We discussed passing functions as arguments, returning functions as values, and mapping functions over recursive data structures. Key to understanding functions as first class values is understanding the lexical scoping rules.
We discussed several important higher-order functions on lists, including filter, map, foldl, and foldr.
Here is some extra material about folding: How to Fold, along with code.