Definition: A set of data values & related operations that are accurately specified independent of any particular implementation.

As the data values and operations are described with mathematical precision, instead of as an implementation in a computer language, we might reason about effects of the operations, relationship to other abstract data types, whether a programming language implements the particular data type, etc.

Regard the given abstract data type:

Structure data tree

type Tree = nil | fork (Element , Tree , Tree)

Operations:

null : Tree -> Boolean leaf : Tree -> Boolean

fork : (Element , Tree , Tree) -> Tree

left : Tree -> Tree                 // It illustrated the properties of tree that left of a tree is also a tree.

right: Tree -> Tree contents: Tree -> Element height (nil) = 0 |

height (fork(e,T,T')) = 1+max(height(T), height(T'))

weight (nil) = 0 |

weight (fork(e,T,T')) = 1+weight(T)+weight(T')

 Figure: A binary tree