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Do

Do[expr,n]

evaluates expr n times.

Do[expr,{i,i_max}]

evaluates expr with the variable i successively taking on the values 1 through i_max (in steps of 1).

Do[expr,{i,i_min,i_max}]

starts with i=i_min.

Do[expr,{i,i_min,i_max,di}]

uses steps di.

Do[expr,{i,{i₁,i₂,…}}]

uses the successive values i₁, i₂, ….

Do[expr,{i,i_min,i_max},{j,j_min,j_max},…]

evaluates expr looping over different values of j etc. for each i.

Do

Do[expr,n]

evaluates expr n times.

Do[expr,{i,i_max}]

evaluates expr with the variable i successively taking on the values 1 through i_max (in steps of 1).

Do[expr,{i,i_min,i_max}]

starts with i=i_min.

Do[expr,{i,i_min,i_max,di}]

uses steps di.

Do[expr,{i,{i₁,i₂,…}}]

uses the successive values i₁, i₂, ….

Do[expr,{i,i_min,i_max},{j,j_min,j_max},…]

evaluates expr looping over different values of j etc. for each i.

Details

Do uses the standard Wolfram Language iteration specification.
You can use Return, Break, Continue, and Throw inside Do.
Unless an explicit Return is used, the value returned by Do is Null.
Do[expr,Infinity] continues evaluating expr until explicitly told to exit through a function such as Break, Return, Throw, Abort, or Quit.
Do[expr,spec] first evaluates spec, then localizes the variable specified and successively assigns values to it, each time evaluating expr.
Do effectively uses Block to localize values or variables.
Do[expr,spec₁,spec₂] is effectively equivalent to Do[Do[expr,spec₂],spec₁].
Parallelize[Do[expr,iter]] or ParallelDo[expr,iter] computes Do[expr,iter] in parallel on all subkernels. »

Examples

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Basic Examples (3)

Print the first four squares:

n goes from -3 to 5 in steps of 2:

Print 4 random integers:

Scope (8)

Evaluate Print[x] twice:

The step can be negative:

The values can be symbolic:

Loop over i and j, with j running up to i-1:

The body can be a procedure:

Break breaks out of Do:

Continue continues the loop, without executing the rest of the body:

Loop infinitely, until a condition is met:

Generalizations & Extensions (2)

Give a list of values to iterate over:

ParallelDo computes Do in parallel:

Do can be parallelized automatically, effectively using ParallelDo:

Applications (5)

Generate a symbolic continued fraction:

Build up a list of primes:

Alternatively use Reap and Sow:

Implement backsubstitution:

Implement LU triangular decomposition of matrices:

The selection sort algorithm:

Properties & Relations (2)

Equivalent loops:

Loop infinitely, until a condition is met:

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