\begin{definition}[Definition:Basic Primitive Recursive Function/Identity Function]
The identity function $I_\N: \N \to \N$ is a basic primitive recursive function, defined as:
:$\forall n \in \N: \map {I_\N} n = n$
Note that this is an implementation of the projection function:
:$\pr_1^1: \N \to \N: \map {\pr_1^1} {n_1} = n_1$
It is URM computable by a single-instruction URM program.
Category:Definitions/Primitive Recursive Functions
\end{definition}