What are abstract data types and why are they useful?

Abstract data types (ADTs) are high-level data structures that hide the implementation details and only expose operations relevant to the data.

In more detail, an abstract data type is a theoretical concept used in computer science that defines a type by its behaviour, but not by its implementation. It is a way of looking at a data structure focusing on what it does, not on how it does it. The actual implementation is hidden (or 'abstracted') away from the user, who interacts with the ADT through a defined set of operations.

For example, consider a list ADT. The operations might include adding an item to the list, removing an item from the list, or checking whether the list contains a certain item. However, the underlying implementation of the list - whether it's an array, a linked list, or some other data structure - is hidden from the user.

ADTs are useful for several reasons. Firstly, they promote modularity and reusability. Once an ADT is defined, it can be used in multiple programs without needing to be redefined or understood in detail. This can save time and effort in programming.

Secondly, ADTs provide a way to manage complexity in large software systems. By hiding the details of data structures, they allow programmers to focus on the high-level design of their software without getting bogged down in the details of data manipulation.

Thirdly, ADTs can improve the reliability and correctness of software. By defining a clear interface for a data structure, they help to prevent misuse and errors. For example, if a list ADT only allows items to be added with an 'add' operation, it's not possible to accidentally overwrite an item in the list by directly accessing its underlying array.

Finally, ADTs can make software more flexible and easier to maintain. If the implementation of a data structure needs to change - for example, if an array needs to be replaced with a linked list for efficiency reasons - this can be done without affecting the rest of the software, as long as the interface of the ADT remains the same. This separation of interface and implementation is a key principle of good software design.