# F Sharp Programming/Discriminated Unions

Discriminated unions, also called tagged unions, represent a finite, well-defined set of choices. Discriminated unions are often the tool of choice for building up more complicated data structures including linked lists and a wide range of trees.

## Creating Discriminated Unions

Discriminated unions are defined using the following syntax:
By convention, union names start with a lowercase character, and union cases are written in PascalCase.

## Union Basics: an On/Off switch

Let's say we have a light switch. For most of us, a light switch has two possible states: the light switch can be ON, or it can be OFF. We can use an F# union to model our light switch's state as follows:
We've defined a union called switchstate which has two cases, On and Off. You can create and use instances of switchstate as follows:
This program has the following types:
It outputs the following:
Notice that we create an instance of switchstate simply by using the name of its cases; this is because, in a literal sense, the cases of a union are constructors. As you may have guessed, since we use the same syntax for constructing objects as for matching them, we can pattern match on unions in the following way:
The function toggle has the type val toggle : switchstate -> switchstate.
This program has the following output:

## Holding Data In Unions: a dimmer switch

The example above is kept deliberately simple. In fact, in many ways, the discriminated union defined above doesn't appear much different from an enum value. However, let's say we wanted to change our light switch model into a model of a dimmer switch, or in other words a light switch that allows users to adjust a lightbulb's power output from 0% to 100% power.
We can modify our union above to accommodate three possible states: On, Off, and an adjustable value between 0 and 100:
We've added a new case, Adjustable of float. This case is fundamentally the same as the others, except it takes a single float value in its constructor:
This program outputs:

## Creating Trees

Discriminated unions can easily model a wide variety of trees and hierarchical data structures.
For example, let's consider the following binary tree:
Each node of our tree contains exactly two branches, and each branch can either be an integer or another tree. We can represent this tree as follows:
We can create an instance of the tree above using the following code:
This program outputs the following:
Very often, we want to recursively enumerate through all of the nodes in a tree structure. For example, if we wanted to count the total number of Leaf nodes in our tree, we can use:
This program outputs:

## Generalizing Unions For All Datatypes

Note that our binary tree above only operates on integers. It is possible to construct unions that are generalized to operate on all possible data types. We can modify the definition of our union to the following:
We can use the union defined above to define a binary tree of any data type:
The functions above have the following types:
This program outputs:

## Examples
### Built-in Union Types

F# has several built-in types derived from discriminated unions, some of which have already been introduced in this tutorial. These types include:

### Propositional Logic

The ML family of languages, which includes F# and its parent language OCaml, were originally designed for the development of automated theorem provers. Union types allow F# programmers to represent propositional logic remarkably concisely. To keep things simple, let's limit our propositions to four possible cases:
Let's say we had a series of propositions and wanted to determine whether they evaluate to true or false. We can easily write an eval function by recursively enumerating through a propositional statement as follows:
The eval function has the type val eval : proposition -> bool.
Here is a full program using the eval function:
This program outputs the following:

## Additional Reading

Theorem Proving Examples (OCaml)