Functorial Semantics for Multi-algebras
WADT '98 Selected papers from the 13th International Workshop on Recent Trends in Algebraic Development Techniques
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We present a categorical formulation of the rewriting of possibly cyclic term graphs, and the proof that this presentation is equivalent to the well-accepted operational definition proposed by Barendregt et al., but for the case of circular redexes, for which we propose (and justify formally) a different treatment. The categorical framework, based on suitable 2-categories, allows to model also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures. Furthermore, it can be used for defining various extensions of term graph rewriting, and for relating it to other rewriting formalisms.