One way of looking at regular expressions is as a constructive proof of the following fact: it's possible to construct the regular languages by starting with a small set of languages and combining them via a small, fixed set of closure properties. Specifically, if we start with the empty language, the language containing the empty string, and the languages of all single-character strings, we can assemble all possible regular languages using union, concatenation, and Kleene star.
Is there a set of base languages and closure properties that can be used to generate all and only the context-free languages? (To clarify: I'm not asking whether you can write regular expressions for all CFLs, which I know is impossible. Instead, I'm wondering whether there is a way to design a regular-expression-like framework for CFLs based on the same basic principles.)