Iteration is the repetition of a process, typically within a computer program. Confusingly, it can be used both as a general term, synonymous with repetition, and to describe a specific form of repetition with a mutable state.

When used in the first sense, recursion is an example of iteration.

However, when used in the second (more restricted) sense, iteration describes the style of programming used in imperative programming languages. This contrasts with recursion, which has a more declarative approach.

Here is an example of iteration, in imperative pseudocode:

 var i, a := 0 // initialize a before iteration for i from 1 to 3 { // loop three times a := a + i // increment a by the current value of i } print a // the number 6 is printed 

In this program fragment, the value of the variable i changes over time, taking the values 1, 2 and 3. This changing value—or mutable state—is characteristic of iteration.

Iteration can be done in functional programming languages. The following example is in Scheme:

 (define (sum n) (define (iter i result) (if (<= i n) (+ i (iter (+ i 1) result)) result)) (iter 0 0)) 

An iterator is an object that wraps iteration.

See also

• iterative method
• Nash embedding theorem
• Iterative and Incremental development