The article surveys a recent series of papers by the authors investigating the categorical foundations of various rule-based formalisms. The starting point is the well-known representation of term rewriting systems as cartesian 2-categories, based on the characterization of finite terms as arrows of a Lawvere theory. We first show that many term-like structures (including cyclic term graphs, mu-terms and rational terms) can be characterized as arrows of suitable theories. Next we represent rules as cells over a theory, and we show that the free 2-category generated by these cells faithfully represents the rewrite sequences of the original rewriting system.

Categorical rewriting of term-like structures

CORRADINI, ANDREA;GADDUCCI, FABIO
2001

Abstract

The article surveys a recent series of papers by the authors investigating the categorical foundations of various rule-based formalisms. The starting point is the well-known representation of term rewriting systems as cartesian 2-categories, based on the characterization of finite terms as arrows of a Lawvere theory. We first show that many term-like structures (including cyclic term graphs, mu-terms and rational terms) can be characterized as arrows of suitable theories. Next we represent rules as cells over a theory, and we show that the free 2-category generated by these cells faithfully represents the rewrite sequences of the original rewriting system.
Corradini, Andrea; Gadducci, Fabio
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/192361
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