Abstract

Lamping's optimal graph reduction technique for the -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). 1 Introduction At the end of 70's, L'evy fixed the theoretical performance of what should be considered as an optimal implementation of the -calculus. The optimal evaluator should always keep shared those redexes in a -expression that have a common origin (e.g. that are copies of a same redex). For a long time, no implementation achieved L'...

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