qudt:AlgebraicDatatype

An Algebraic Datatype is a datatype each of whose values are data from other data types wrapped in one of the constructors of the data type. Any wrapped datum is an argument to the constructor. In contrast to other data types, the constructor is not executed and the only way to operate on the data is to unwrap the constructor using pattern matching.

The most common algebraic data type is a list with two constructors: Nil or [] for an empty list, and Cons (an abbreviation of constructor), ::, 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 i.e. records (only one constructor) and enumerated types (many constructors with no arguments). Algebraic types are one kind of composite 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.