Scan[f,expr]

evaluates f applied to each element of expr in turn.

Scan[f,expr,levelspec]

applies f to parts of expr specified by levelspec.

Scan[f]

represents an operator form of Scan that can be applied to an expression.

• Scan[f,expr] discards the results of applying f to the subexpressions in expr. Unlike Map, Scan does not build up a new expression to return.
• You can use Return to exit from Scan. Return[ret] causes the final value of Scan to be ret. If no explicit return values are specified, the final result from Scan is Null.
• You can also use Throw to exit from Scan. »
• Scan is useful in carrying out an operation on parts of expressions where the operation has a "side effect", such as making an assignment.
• Scan uses standard level specifications:

• 	n	levels 1 through n
  	Infinity	levels 1 through Infinity
  	{n}	level n only
  	{n1,n2}	levels n1 through n2

• The default value for levelspec in Scan is {1}.
• A positive level n consists of all parts of expr specified by n indices.
• A negative level -n consists of all parts of expr with depth n.
• Level -1 consists of numbers, symbols, and other objects that do not have subparts.
• Level 0 corresponds to the whole expression.
• With the option setting Heads->True, Scan includes heads of expressions and their parts. »
• Scan traverses the parts of expr in a depth-first order, with leaves visited before roots.
• If expr is an Association object, Scan[f,expr] applies f only to the values in the association.
• If expr is a SparseArray object, Scan[f,expr] applies f only to the values or subarrays that explicitly appear in expr.
• Scan[f][expr] is equivalent to Scan[f,expr].
• Parallelize[Scan[f,expr]] computes Scan[f,expr] in parallel on all subkernels. »

Basic Examples  (6)

Scan elements of an Association:

Scan elements up to the second level:

Scan elements including the 0 level:

Use the operator form of Scan:

Scope  (5)

Level Specifications  (5)

Scan level 1 (default):

Scan down to level 2:

Scan only level 2:

Scan levels 0 through 2:

Scan down to level 3:

Scan all levels, starting at level 1:

Scan also level 0:

Negative levels:

Positive and negative levels can be mixed:

Different heads at each level:

Generalizations & Extensions  (2)

Scan can be used on expressions with any head:

Throw works inside Scan:

Options  (1)

Heads  (1)

By default, heads are not scanned:

Applications  (2)

Properties & Relations  (4)

Leaves are visited before roots:

Scan does the same as Map, but without returning a result:

Use Sow and Reap to collect results:

Compute Scan in parallel: