Recursive data type

In computer programming, a recursive data type is a data type whose definition contains values of the same type. It is also known as a recursively defined, inductively defined or inductive data type. Data of recursive types are usually viewed as directed graphs.^{[citation needed]}

An important application of recursion in computer science is in defining dynamic data structures such as Lists and Trees. Recursive data structures can dynamically grow to an arbitrarily large size in response to runtime requirements; in contrast, a static array's size requirements must be set at compile time.

Sometimes the term "inductive data type" is used for algebraic data types which are not necessarily recursive.

An example is the list type, in Haskell:

This indicates that a list of a's is either an empty list or a cons cell containing an 'a' (the "head" of the list) and another list (the "tail").

Another example is a similar singly linked type in Java:

This indicates that non-empty list of type E contains a data member of type E, and a reference to another List object for the rest of the list (or a null reference to indicate that this is the end of the list).

Data types can also be defined by mutual recursion. The most important basic example of this is a tree, which can be defined mutually recursively in terms of a forest (a list of trees). Symbolically: