This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)
Applying Functions to Lists
Many computations are conveniently specified in terms of applying functions in parallel to many elements in a list. Mathematica provides a suite of elegant functional programming constructs for doing this. In Mathematica, mathematical functions are automatically taken to be "listable", so that they are always applied to every element in a list.
Map (/@) map a function over a list, at specified levels
Apply (@@, @@@) — apply a function to a list, at specified levels
MapIndexed map a function, including index information
MapAt map a function at particular positions
Scan scan over every element of a list, applying a function
FoldList successively apply a function, "folding in" elements from a list
ComposeList  ▪ Outer  ▪ Inner  ▪ Accumulate  ▪ Differences  ▪ Ratios
MapThread map a function across corresponding elements in multiple lists
Thread "thread" a function across lists that appear in its arguments
Listable attribute for any function to automatically thread over lists