 The first significant result in computability theory was Kleene’s (1936a) proof of the Normal Form Theorem which was presented in  Section 2.2.2.  As discussed there, the Normal Form Theorem can be understood as illustrating how it is possible to associate each \(k\)-ary partial computable function \(f(\vec{x})\) with a natural number \(e\) known as its index such that \(f(\vec{x}) \simeq \mu s(T_k(e,\vec{x},s))\). Such an \(e\) can be thought of as a name for a computer program built up from the basis functions, composition, primitive recursion, and minimization by which the values \(f(\vec{x})\) can be computed. This also leads to what is known as an indexation of \(k\)-ary partial computable functions 