# Polymorphic Variants

Thus far, whenever you've wanted to define a variant type, you have had to give it a name, such as day, shape, or 'a mylist:

type day = Sun | Mon | Tue | Wed | Thu | Fri | Sat

type shape =
| Point  of point
| Circle of point * float
| Rect   of point * point

type 'a mylist = Nil | Cons of 'a * 'a mylist


Occasionally, you might need a variant type only for the return value of a single function. For example, here's a function f that can either return an int or $\infty$; you are forced to define a variant type to represent that result:

type fin_or_inf = Finite of int | Infinity

let f = function
| 0 -> Infinity
| 1 -> Finite 1
| n -> Finite (-n)


The downside of this definition is that you were forced to defined fin_or_inf even though it won't be used throughout much of your program.

There's another kind of variant in OCaml that supports this kind of programming: polymorphic variants. Polymorphic variants are just like variants, except:

1. You don't have declare their type or constructors before using them.
2. There is no name for a polymorphic variant type. (So another name for this feature could have been "anonymous variants".)
3. The constructors of a polymorphic variant start with   (this the "grave accent", also called backquote, back tick, and reverse single quote; it is typically found on the same key as the ~ character, near the escape key).

Using polymorphic variants, we can rewrite f:

(* note: no type definition *)

let f = function
| 0 -> Infinity
| 1 -> Finite 1
| n -> Finite (-n)


With this definition, the type of f is

val f : int -> [> Finite of int | Infinity ]


This type says that f either returns Finite n for some n:int or Infinity. The square brackets do not denote a list, but rather a set of possible constructors. The > sign means that any code that pattern matches against a value of that type must at least handle the constructors Finite and Infinity, and possibly more. For example, we could write:

match f 3 with
| NegInfinity -> "negative infinity"
| Finite n    -> "finite"
| Infinity    -> "infinite"


It's perfectly fine for the pattern match to include constructors other than Finite or Infinity, because f` is guaranteed never to return any constructors other than those.

There are other, more compelling uses for polymorphic variants that we'll see later in the course. They are particularly useful in libraries. For now, we generally will steer you away from extensive use of polymorphic variants, because their types can become difficult to manage.