Basic Examples

Create a
Map
function that will apply a function
f
exclusively at parts of the expression lying at level 2:
[◼]
MapLevel
[f,{2}]
In[]:=
Curry[Map,{1,3,2}][f,{2}]
Out[]=
Apply the function just created to an expression that is of depth 3:
%[{{1,2,3},{4,5,{6,7}}}]
In[]:=
{{f[1],f[2],f[3]},{f[4],f[5],f[{6,7}]}}
Out[]=

Scope

MapLevel
works with integer level specifications just as
Map
does:
[◼]
MapLevel
[f,2][{{1,2,3},{4,5,{6,7}}}]
In[]:=
{f[{f[1],f[2],f[3]}],f[{f[4],f[5],f[{6,7}]}]}
Out[]=
MapLevel
works with
Association
just as
Map
does :
[◼]
MapLevel
[h,{2}][<|a<|bc|>,d<|ef|>|>]
In[]:=
abh[c],deh[f]
Out[]=
MapLevel
works at multiple levels of an association :
[◼]
MapLevel
[h,{1,3}][<|a<|bc|>,d{<|ef|>}|>]
In[]:=
ah[bh[c]],dh[{h[eh[f]]}]
Out[]=

Applications

Of people over age 40 on the Titanic, find the survival numbers broken down by cabin class, using
MapLevel
as part of a pipeline of operators:
Select[#age>40&]/*GroupBy[Key["survived"]]/*
[◼]
MapLevel
[#class&,{2}]/*
[◼]
MapLevel
[Counts,{1}][ExampleData[{"Dataset","Titanic"}]]
In[]:=
Out[]=

Properties and Relations

MapLevel
produces what can be thought of as a nested
Map
operator :
Map[Map[f]][{{1,2,3},{4,5,6}}]===
[◼]
MapLevel
[f,{2}][{{1,2,3},{4,5,6}}]
True
Out[]=
MapLevel
provides a vocabulary for understanding how
Query
works :
Query[f,g,h][Array[x,{2,3,4}]]===
[◼]
MapLevel
[h,{2}]/*
[◼]
MapLevel
[g,{1}]/*
[◼]
MapLevel
[f,{0}][Array[x,{2,3,4}]]
In[]:=
True
Out[]=