Here, the term "generalized regex" refers to something that can be used to match, say, the lists [1, 2, 3] and [4, 5, 6] (but not [3, 2, 1]) using regex-style syntax such as [_, _+1, _+2]. Instead of applying only to strings or lists, though, the goal is to develop a syntax that is applicable to a wide variety of objects.
