Nested expressions with flat functions are flattened out:

Flat implements the notion of associativity:

Flat allows the pattern matcher to use associativity:

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:

Nested expressions with flat functions are automatically flattened:

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

An expression with a flat head is considered matched in its entirety when any sequence is matched:

Compare with:

ReplaceRepeated may be helpful in ensuring all occurrences are replaced:

When Blank matches a sequence inside a Flat function f, it will maintain the head f:

Sequential patterns like BlankSequence and BlankNullSequence are not affected by Flat:

For a flat function f that is not OneIdentity, when f[x_] is compared with f[expr], the pattern matcher will attempt to bind x_ to f[expr] first, and only if that fails to expr:

If the function also has attribute OneIdentity, the first attempt is skipped:

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:

For a flat function f, the pattern f[_] matches f with one or more arguments:

Repeated can be used as a pattern that only matches a single argument, even inside a flat function:

Restrictions may behave unexpectedly because x_ matches together with the head of a flat function:

The following restriction works because x_Plus matches Plus[b,c]:

However, this one will fail because x_ cannot have both head Plus and Symbol:

Using BlankSequence on the left-hand side produces more consistent results: