Source : Free On-Line Dictionary of Computing

algebraic data type
     
         (Or "sum of products type") In {functional
        programming}, new types can be defined, each of which has one
        or more {constructor}s.  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 type}s (only one
        constructor) and {enumeration type}s (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).
     
        (1994-11-23)