Dactl Rewriting Is Categorical

The graph-manipulating core of the general term graph rewriting language DACTL, namely contraction building and redirection, is reexamined from a categorical viewpoint. The essentials of this rather complex two-phase operational semantics is recast as a Grothendieck opfibration of a category of graph rewrites over a base of rewrite rules. This generalises previous attempts to categorise contractum building and redirection as pushouts and is able to describe more DACTL rewrites than pushout models. The full operational core model conforms to a more restricted version of this construction and is able to successfully cope with examples such as the infamous circular I example a : I[ a ].