<programming> (Or "sum of products type") In functional
programming, new types can be defined, each of which has one
or more constructors. Such a type is known as an algebraic
data type. E.g. in Haskell we can define a new type,
"Tree":

data Tree = Empty | Leaf Int | Node Tree Tree

with constructors "Empty", "Leaf" and "Node". The
constructors can be used much like functions in that they can
be (partially) applied to arguments of the appropriate type.
For example, the Leaf constructor has the functional type Int
-> Tree.

A constructor application cannot be reduced (evaluated) like a
function application though since it is already in normal
form. Functions which operate on algebraic data types can be
defined using pattern matching:

depth :: Tree -> Int
depth Empty = 0
depth (Leaf n) = 1
depth (Node l r) = 1 + max (depth l) (depth r)

The most common algebraic data type is the list which has
constructors Nil and Cons, written in Haskell using the
special syntax "[]" for Nil and infix ":" for Cons.

Special cases of algebraic types are product types (only one
constructor) and enumeration types (many constructors with
no arguments). Algebraic types are one kind of constructed
type (i.e. a type formed by combining other types).

An algebraic data type may also be an abstract data type
(ADT) if it is exported from a module without its
constructors. Objects of such a type can only be manipulated
using functions defined in the same module as the type
itself.

In set theory the equivalent of an algebraic data type is a
discriminated union - a set whose elements consist of a tag
(equivalent to a constructor) and an object of a type
corresponding to the tag (equivalent to the constructor
arguments).