\begin{definition}[Definition:Self Distributive]
Let $\circ$ be a binary operation on the set $S$.
Then $\circ$ is '''self-distributive''' {{iff}}:
* $\forall a, b, c \in S: \paren {a \circ b} \circ c = \paren {a \circ c} \circ \paren {b \circ c}$
* $\forall a, b, c \in S: a \circ \paren {b \circ c} = \paren {a \circ b} \circ \paren {a \circ c}$
\end{definition}