A data *structure* is an abstract description of a way of organizing data to allow certain operations on it to be performed efficiently. For example, a binary tree is a data structure, as is a Fibonacci heap, AVL tree, or skiplist. Theoreticians describe data structures and prove their properties in order to show that certain algorithms or problems can be solved efficiently under certain assumptions.

A data *type* is a (potentially infinite) class of concrete objects that all share some property. For example, “integer” is a data type containing all of the infinitely many integers, “string” is a data type containing all of the infinitely many strings, and “32-bit integer” is a data type containing all integers expressible in thirty-two bits. There is no requirement that a data type be a primitive in a language – for example, in C++, the type `int`

is a primitive, as is this one:

```
struct MyStruct {
int x, y;
};
```

In this case, `MyStruct`

is a data type representing all possible objects labeled `MyStruct`

that have two `int`

s in them labeled `x`

and `y`

.

It is possible to have a data type representing all possible instances of a data structure. For example, you could encode a binary search tree with this data type:

```
struct BST {
int data;
BST* left, *right;
};
```

In short, a data *structure* is a mathematical object with some set of properties that can be realized in many different ways as data *types.* A data *type* is just a class of values that can be concretely constructed and represented.