Interaction systems II: The practice of optimal reductions

AbstractLamping's optimal graph reduction technique for the λ-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 the natural continuation of [3], where we focused on the theoretical aspects of optimal reductions in Interaction Systems (family relation, labeling, extraction)