Primitive recursion in the abstract - Leivant, Daniel; Marion, Jean-Yves (Mathematical structures in computer science, 2020)
Recurrence can be used as a function definition schema for any nontrivial free algebra, yielding the same computational complexity in all cases. We show that primitive-recursive computing is in fact independent of free algebras altogether, and can be characterized by a generic programming principle, namely the control of iteration by the depletion of finite components of the underlying structure.