A list comprehension is a syntactic construct available in some programming languages for creating a list based on existing lists. It follows the form of the mathematical set-builder notation (set comprehension) as distinct from the use of map and filter functions.

Consider the following example in mathematical set-builder notation.

or often

This can be read, "${\displaystyle S}$ is the set of all numbers "2 times ${\displaystyle x}$" SUCH THAT ${\displaystyle x}$ is an ELEMENT or MEMBER of the set of natural numbers (${\displaystyle \mathbb {N} }$), AND ${\displaystyle x}$ squared is greater than ${\displaystyle 3}$."

The smallest natural number, x = 1, fails to satisfy the condition x²>3 (the condition 1²>3 is false) so 2 ·1 is not included in S. The next natural number, 2, does satisfy the condition (2²>3) as does every other natural number. Thus x consists of 2, 3, 4, 5... Since the set S consists of all numbers "2 times x" it is given by S = {4, 6, 8, 10,...}. S is, in other words, the set of all even numbers greater than 2.

In this annotated version of the example:

A list comprehension has the same syntactic components to represent generation of a list in order from an input list or iterator:

The order of generation of members of the output list is based on the order of items in the input.