To me it was the recursive mapping over a closed set of types, whatever you do you should end up with an element of your type/grammar. That and the graph walk space of the AST.
The closed set of types describes how each pass in a compiler pipeline tends to build an intermediate representation of some sort, analyze/modify it, and then output it to the next stage. The IR is closed in that it is not open for everyone to extend willy-nilly. It is this property that makes it even possible to analyze and manipulate in a sound manner.
In a sense, compilers literally build a bunch of linguistic 'worlds' within their pipeline, each one emphasizing something different.