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Flat
Flat is an attribute that can be assigned to a symbol f to indicate that all expressions involving nested functions f should be flattened out. This property is accounted for in pattern matching.
Flat corresponds to the mathematical property of associativity.
For a symbol f with attribute Flat, f
[
f
[
a
,
b
],
f
[
c
]] is automatically reduced to f
[
a
,
b
,
c
].
Functions like Plus, Times and Dot are Flat.
For a Flat function f, the variables x and y in the pattern f
[x_,
y_] can correspond to any sequence of arguments.
The Flat attribute must be assigned before defining any values for a Flat function.
See the Mathematica book: Section 2.3.7, Section 2.5.3.
See also: Orderless, OneIdentity.
Further Examples
Normally, functions that you define do not have any special attributes.
In[1]:= 
Global`f
Nothing special happens with this nest of f's.
In[2]:= 
Out[2]= 
By assigning the attribute Flat to a function, you are specifying that all nestings of the functions should be flattened out.
In[3]:= 
In[4]:= 
Out[4]= 
This is how to bring back the old behavior.
In[5]:= 
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