# Iteration¶

The primary means of iteration in q are

• atomic functions
• the distributive operators: Each and its variants
• the progressive operators Scan and Over

## Atomic functions¶

Atomic functions apply to atoms in their arguments, and preserve structure to arbitrary depth.

Many of the q operators that take numerical arguments are atomic.

The arguments of an atomic function must conform: they must be lists with the same count, or atoms.

When an atom argument is applied to a list, it is applied to every item.

q)2 3 4 + 5 6 7          / same-count lists
7 9 11
q)2 + 3 4 5              / atom and list
5 6 7


This is called scalar extension. It applies at every level of nesting.

q)2+(3 4;abc!5 6 7;(8 9;10;11 12 13);14)
5 6
abc!7 8 9
(10 11;12;13 14 15)
16


## Extendersrs¶

The distributor and progressor extenders are unary. They take maps as arguments and derive functions (extensions) that apply the maps repeatedly.

The extenders (apart from Compose)can be applied postfix, and almost always are. For example, the Over extender / takes the Add operator + to derive the extension +/, which reduces a list by summing it.

q)(+/)2 3 4 5
14


### Distributors¶

The distributors extenders – Each, Each Left, Each Right, Each Prior, and Each Parallel – apply a map to each item of a list or dictionary.

q)count "zero"                             / count the chars (items) in a string
4
q)(count')("The";"quick";"brown";"fox")    / count each string
3 5 5 3


### Progressors¶

The progressors extenders – Scan and Over – apply a map successively, first to the argument, then to the results of successive applications.

## Control words¶

The control words if, do, and while also enable iteration, but are rarely required.