# A Rewriting Implementation of pi-calculus

Viry, Patrick (1996) A Rewriting Implementation of pi-calculus. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

We introduce a rewriting implementation of the reduction relation of $\pi$-calculus and prove its correctness. The implementation is based on terms with De Bruijn indices and an explicit substitution operator. The resulting rewrite rules need to be applied modulo a large and complex equational theory, and are only of theoretical interest. Applying the coherence techniques introduced in a previous paper, we transform this specification into an equivalent one that only requires rewriting modulo associativity and commutativity. This latter rewrite system can then be straightforwardly encoded in currently available rewriting-based programming languages. Finally, we sketch a possible application of this implementation as the basis for adding input-output capabilities to such languages.