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.

MORE INFORMATION

Flat corresponds to the mathematical property of associativity.

For a symbol f with attribute Flat, is automatically reduced to .

Functions like Plus, Times, and Dot are Flat.

For a Flat function f, the variables x and y in the pattern can correspond to any sequence of arguments.

The Flat attribute must be assigned before defining any values for a Flat function.

When functions that are Flat are used in pattern matching, they often also require the attribute OneIdentity.

EXAMPLES

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Basic Examples (2)

Nested expressions with flat functions are flattened out:

Flat implements the notion of associativity:

Nested expressions with flat functions are flattened out:

In[1]:=

In[2]:=

Out[2]=

Flat implements the notion of associativity:

In[1]:=

Out[1]=

In[2]:=

Out[2]=

Scope (3)

Nested expressions with associative functions are flattened out:

In pattern matching, Flat allows sequences of elements to be replaced:

For flat and orderless functions, any subset of the arguments may match:

Properties & Relations (2)

Nested expressions with flat functions are automatically flattened:

For flat functions, a definition for the two-argument case is normally sufficient:

Possible Issues (3)

Pattern matching for flat functions requires the OneIdentity attribute as well:

For flat and orderless functions, pattern matching may have to try a large number of cases:

Longest can be used to prevent additional matches for shorter subexpressions: