Algebraic Datatype

The most common algebraic data type is a list with two constructors: `Nil` or for an empty list, and Cons (an abbreviation of ''cons''tructor), ::, or : for the combination of a new element with a shorter list (for example (Cons 1 '(2 3 4)) or 1:[2,3,4 ). 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. Values 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). AN EXAMPLE For example, in Haskell we can define a new algebraic data type, Tree: data Tree = Empty
	Data List A	Nil Cons a (List a)

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