Relationship of algebraic theories to powerset theories and fuzzy topological theories for lattice-valued mathematics.
Rewriting on cyclic structures : equivalence between the operational and the categorical description
Rewriting on cyclic structures: Equivalence between the operational and the categorical description
We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2-theories. We show 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 allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and...