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.

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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.

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:

In[1]:=

In[2]:=

Out[2]=

Flat implements the notion of associativity:

Scope (3)

Properties & Relations (2)

Possible Issues (2)