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 and Section 2.5.3.

See also: Orderless, OneIdentity.

Further Examples