Method overriding and pattern matching actually solve the same problem in precisely opposite ways. In the functional programming community, this is referred to

Method overriding and pattern matching actually solve the same problem in precisely opposite ways. In the functional programming community, this is referred to as "the expression problem". To understand this problem properly you must first accept the idea that every object (or class of objects) in an OO context is essentially an interpreter defined by how it responds to sequential messages (methods). The crux of the expression problem is the tension between adding new operations over a type (i.e. new methods on the base class of a hierarchy) which requires implanting that method for every existing subclass... and adding new types (new subclases) over which an existing operation (method from the parent class) applies, which requires implementing every existing for the new type (subclass). There are some "clever" approaches to "solving" this problem, but they only really make sense for types that look and act like ASTs. Despite many complex programs essentially being interpreters for some internal "language", this isn't as useful as one might hope, and the machinery necessary to "solve" the problem relies on a lot of compiler and language extensions. If you want an example of (uh) "solving" the expression problem, the canonical starting point is Wouter Swierstra's "Data Types a la Carte" paper.