Interaction systems II : the practice of optimal reductions

Lamping's optimal graph reduction technique for the l-calculus is generalized to a new class of higher order rewriting systems, called interaction systems. Interaction systems provide a nice integration of the functional paradigm with a rich class of data structures (all inductive types) and some basic control flow constructs such as conditionals and (primitive or general) recursion. We describe a uniform and optimal implementation in Lamping's style, for all these features. The paper is natural continuation where we focused on the theoretical aspects of optimal reductions in interaction systems (family relation, labeling, extraction, ...)