This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)


evaluates f applied to each element of expr in turn.
applies f to parts of expr specified by levelspec.
  • Scan 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.
  • 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:
nlevels through n
Infinitylevels through Infinity
{n}level n only
{n1,n2}levels through
  • The default value for levelspec in Scan is .
  • 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 consists of numbers, symbols, and other objects that do not have subparts.
  • Level 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 a SparseArray object, Scan applies f only to the values or subarrays that explicitly appear in expr.
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:
Scan can be used on expressions with any head:
Throw works inside Scan:
By default, heads are not scanned:
Make assignments based on data:
Find all leaves in an expression:
Leaves are visited before roots:
Scan does the same as Map, but without returning a result:
Use Sow and Reap to collect results:
New in 1 | Last modified in 5