A "signature" (in this context) is a set, whose elements are called "operations", each of which is assigned a natural number (0, 1, 2...) called its "arity". Given a signature formula_1 and a set formula_2, whose elements are called "variables", a "word" is a finite planar rooted tree in which each node is labelled by either a variable or an operation, such that every node labelled by a variable has no branches away from the root and every node labelled by an operation formula_3 has as many branches away from the root as the arity of formula_3. An "equational law" is a pair of such words; we write the axiom consisting of the words formula_5 and formula_6 as formula_7.