ADT is the mathematical model for the data types.
So, what is Mathematical model?
Representing the system using the mathematical concepts and mathematical language is called
Now, What is Mathematical Language?
Mathematical language is representing some information using mathematical vocabulary. Mathematical vocabulary is nothing but equal sign, arithmetic symbols,range symbol.
For Eg to represent the range of the integer:
-32768 <= x <= 32767
Data type is nothing but classification of data based on their characteristics.
Finally, type which is represented using mathematical concepts and mathematical language is called as an abstract data type.
What is difference between data structure and Abstract data type?
Abstract data type is logical description of type, where as the data structure is concrete description of type.
In simple, ADT is a Plan and data structure is an implementation of that plan.
Data structure implements the ADT.
ADT designs the type based on point of view of user of the data, where as the data structure is designed based on the point of view of implementer of that ADT.
For instance, Integer is an ADT, which simply says possible values and operation that can be performed on the integer whereas, data structure is the implementation of that integer in any of the programming language. Implementation can be of any form such as binary format at low level, using the 2’s complement for the storing the negative numbers and so on.