Define return values for a function that is not of type Boolean

Question

I have a function with more than two possible return values.

A simplified example is the following function that classifies vertices of a graph according to their degrees:

VertexRole[g_, v_] := Which[
  VertexDegree[g, v] == 1, BadVertex,
  VertexDegree[g, v] == 2, MediocreVertex,
  VertexDegree[g, v] == 3, GoodVertex
  ]

However, defining the function in this way would be bad practice since the symbols BadVertex etc. are undefined. Furthermore, I want to evaluate expressions such as

VertexRole[graph, vertex] == BadVertex

Defining BadVertex to be a number (e.g. 42) would also be bad since I actually want

BadVertex == x

to evaluate to False for all x other than BadVertex.

Therefore BadVertex etc. should be symbols similar to True, False, Automatic, All, None. How can I implement that?

[One could use a string as the return value (e.g. "BadVertex"), but that kind of misses the syntactical point I am trying to make. I am rather looking for something that resembles the enum type in C.]

Answer 1

Your code looks reasonable to me. If I were doing this, I would

• manually Protect those symbols on the off chance that for some reason I accidentally assigned them values (though this is not necessary for them to work),
• assign them ::usage messages so they register correctly into the system (and therefore display in black instead of blue, and
• use === (i.e. SameQ) instead of == (i.e. Equal) if I wanted to make it very explicit that "BadVertex == x should evaluate to False for all x other than BadVertex".

If you're really worried about it, it would also be acceptable to use strings instead of symbols, but really it looks fine as is.