General computable functions can be described either functionally (in terms of closure of the coordinate functions, constant functions, composition, primitive recursion, and $\mu$-recursion), or in terms of a Turing machine.
I have only seen primitive recursion defined in the functional language, i.e. functions obtained by coordinates, constants, composition, primitive recursion.
Is there a similar type of machine model for primitive recursion?
I am aware of some (pedagogical) programming languages, such as Hofstadter's BLOOP, that are PR-complete, but this approach doesn't really look like a Turing machine to me.