WolframLang: Map Function to List

Map[f, expr]

(Short syntax: f /@ expr)
Like many language's map, but can map to specific level of a nested list, such as at leafs of a tree. e.g. Map[ f, {1, {{2}, 3}}, {-1} ] === {f[1], {{f[2]}, f[3]}} Map

Scan[f, expr]

Same as Map, but return Null. use this if you no need return value. Scan

Map a builtin function to list:

xx = {1, {2, 3}};

Map[ Length, xx ] === {0, 2}

(* short syntax *)
Length /@ xx === {0, 2}

Map a user-defined function to list:

xx = {1, 2, 3};

Map[ Function[x, x+1 ], xx ] === { 2, 3, 4}

(* short syntax *)
(#+1 &) /@ xx === { 2, 3, 4}

Map a function to different levels of a rectangular array:

(xx = Table[{i, j}, {i, 2}, {j, 2}]) ===
{{{1, 1}, {1, 2}}, {{2, 1}, {2, 2}}}

(* map to 1st level, as in flat map *)
Map[ f, xx, {1} ] ===
{f[{{1, 1}, {1, 2}}], f[{{2, 1}, {2, 2}}]}

(* map to 2nd level *)
Map[ f, xx, {2} ] ===
{{f[{1, 1}], f[{1, 2}]}, {f[{2, 1}], f[{2, 2}]}}

(* map to 3rd level *)
Map[ f, xx, {3} ] ===
{{{f[1], f[1]}, {f[1], f[2]}}, {{f[2], f[1]}, {f[2], f[2]}}}

(* map to deepest level, the leafs. in this case, same as 3rd level *)
Map[ f, xx, {-1} ] ===
{{{f[1], f[1]}, {f[1], f[2]}}, {{f[2], f[1]}, {f[2], f[2]}}}

Map to a tree.

xx = {a, {{b,c}, d}, e};

(* map to top level *)
Map[ f, xx ] ===
{f[a], f[{{b, c}, d}], f[e]}

(* same as 1st level *)
Map[ f, xx, {1} ] ===
{f[a], f[{{b, c}, d}], f[e]}

(* map to leafs *)
Map[ f, xx, {-1} ] ===
{f[a], {{f[b], f[c]}, f[d]}, f[e]}