IThe theory of optimal reductions
نویسندگان
چکیده
We introduce a new class of higher order rewriting systems, called Interaction Systems (IS's). IS's come from Lafont's (Intuitionistic) Interaction Nets Lafont 1990] by dropping the linearity constraint. In particular, we borrow from Interaction Nets the syntactical bipartitions of operators into constructors and destructors and the principle of binary interaction. As a consequence, IS's are a subclass of Klop's Combinatory Reduction Systems Klop 1980] where the Curry-Howard analogy still \makes sense". Destructors and constructors respectively corresponds to left and right logical introduction rules, interaction is cut and reduction is cut-elimination. Interaction Systems have been primarily motivated by the necessity of extending the practice of optimal evaluators for-calculus Lamping 1990, Gonthier et al. 1992a] to other computational constructs as conditionals and recursion. In this paper we focus on the theoretical aspects of optimal reductions. In particular, we generalize the family relation in L evy 1978, L evy 1980], thus deening the amount of sharing an optimal evaluator is required to perform. We comfort our notion of family by approaching to it in two diierent ways (generalizing labeling and extraction in L evy 1980]) and proving their coincidence. The reader is referred to Asperti and Laneve 1993c] for the paradigmatic description of optimal evaluators of IS's.
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