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# Iteration

This article discusses a concept which is exploited in computer programming (but which originated before it). For use in the Japanese and Chinese languages see iteration mark.

Iteration is the repetition of a process, typically within a computer program. 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, but typically using a recursive notation, which is typically not the case for 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.