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In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior from the point of view of a user of the data, specifically in terms of possible values, possible operations on data of this type, and the behavior of these operations.
For example, Lua provides tables. Although Lua stores lists that have numerical indices as arrays internally, they still appear as dictionaries. [4] In Lisp, lists are the fundamental data type and can represent both program code and data. In most dialects, the list of the first three prime numbers could be written as (list 2 3 5).
Some collections maintain a linear ordering of items – with access to one or both ends. The data structure implementing such a collection need not be linear. For example, a priority queue is often implemented as a heap, which is a kind of tree. Notable linear collections include: list; stack; queue; priority queue; double-ended queue
The abstract data type (ADT) can be represented in a number of ways, including a list of parents with pointers to children, a list of children with pointers to parents, or a list of nodes and a separate list of parent-child relations (a specific type of adjacency list).
A stack may be implemented as, for example, a singly linked list with a pointer to the top element. A stack may be implemented to have a bounded capacity. If the stack is full and does not contain enough space to accept another element, the stack is in a state of stack overflow. A stack is needed to implement depth-first search.
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A queue is an example of a linear data structure, or more abstractly a sequential collection. Queues are common in computer programs, where they are implemented as data structures coupled with access routines, as an abstract data structure or in object-oriented languages as classes.
The way I've found that is the most successful way to explain what an ADT is, to give tangible examples. The ADT for an ordered set of information provides the same API for accessing the data, regardless of it being stored in an array, an unordered linked-list, an ordered linked-list, a binary tree, a 3-2 tree, etc.