Data Type vs Abstract Data Type

Data type is set of values and set of operations on those values. and the abstract data type is a data type whose representation is hidden from the client.

Data Type (in this context)

A Data Type is not just a set of values, but also the operations you can perform on those values. In other words, it’s the combination of:
- A set of values that the data type can hold (for example, the set of integers or the set of floating-point numbers).
- A set of operations that can be performed on those values (e.g., addition for integers, or comparison for floats).

So, in this definition:

For a primitive data type like int, the set of values would be all possible integer values, and the operations could include arithmetic operations like +, -, *, and /.

This concept applies to both primitive data types (like integers or floats) and composite data types (like arrays, structs, or strings). Essentially, a data type defines both the values it can represent and how those values interact.

Abstract Data Type (ADT)

An Abstract Data Type (ADT) is a data type where its representation (how it’s structured or stored in memory) is hidden from the client (the user of the data type).
The client interacts with the ADT using a predefined set of operations, but they do not need to know how the data is stored or how those operations are implemented internally. This is what makes it “abstract.”

For example:

A Stack ADT provides operations like push() and pop(), but whether it’s implemented using an array or a linked list is hidden from the user. The client only knows what operations are available and how to use them, but the details of how those operations are implemented internally are abstracted away.

This separation of interface (the operations) from implementation (the underlying data structure) is key to the concept of abstraction.

In Summary

Data Type: A data type is a combination of values and operations that can be performed on them, such as integers with addition and subtraction.
Abstract Data Type: An ADT is a type of data type whose internal structure (representation) is hidden, exposing only the operations to the client.

In practice, ADT hides implementation details to provide flexibility and focus on what can be done with the data, rather than how it is stored or managed internally.