 These axioms tacitly specify the arity of a combinator as well as their reduction (or contraction) pattern. Perhaps, the simplest combinaetor is the identity combinator \(\textsf{I}\), that applied to an argument \(x\) returns the same \(x\). \(\textsf{K}\) applied to \(x\) is a constant function, because when it is further applied to \(y\), it yields \(x\) as a result, that is, \(\textsf{K}\) is a cancellator with respect to its second argument. \(\textsf{W}\) and \(\textsf{M}\) are duplicators, because in the result of their application one of the arguments (always) appears twice.[10] \(\textsf{C}\), \(\textsf{T}\) and \(\textsf{V}\) are permutators, because they change the order of some of their arguments. \(\textsf{B}\) is an associator, because \(\textsf{B}xyz\) turns into a term in which \(y\) is applied to \(z\) before \(x\) is applied to the result. \(\textsf{Y}\) is the fixed point combinator, because for any function \(x\), \(\textsf{Y}x\)  is the fixed point of that function (see section 2.3). The combinator \(\textsf{B}^\prime\) is an associator and a permutator, whereas \(\textsf{S}\) and \(\textsf{J}\) are also duplicators. \(\textsf{S}\) is very special and it is called the strong composition combinator, because when applied to two functions, let us say, \(g\) and  \(f\) (in that order), as well as \(x\), then the resulting  term \(gx(fx)\) expresses the composition of \(g\) and \(f\) both applied to the same argument \(x\).