  We study the computational model of polygraphs. For that, we consider
polygraphic programs, a subclass of these objects, as a formal description of
first-order functional programs. We explain their semantics and prove that they
form a Turing-complete computational model. Their algebraic structure is used
by analysis tools, called polygraphic interpretations, for complexity analysis.
In particular, we delineate a subclass of polygraphic programs that compute
exactly the functions that are Turing-computable in polynomial time.
