Rewriting Abstract Structures: Materialization Explained Categorically
Logic in Computer Science
2019-02-14 v1
Abstract
The paper develops an abstract (over-approximating) semantics for double-pushout rewriting of graphs and graph-like objects. The focus is on the so-called materialization of left-hand sides from abstract graphs, a central concept in previous work. The first contribution is an accessible, general explanation of how materializations arise from universal properties and categorical constructions, in particular partial map classifiers, in a topos. Second, we introduce an extension by enriching objects with annotations and give a precise characterization of strongest post-conditions, which are effectively computable under certain assumptions.
Keywords
Cite
@article{arxiv.1902.04809,
title = {Rewriting Abstract Structures: Materialization Explained Categorically},
author = {Andrea Corradini and Tobias Heindel and Barbara König and Dennis Nolte and Arend Rensink},
journal= {arXiv preprint arXiv:1902.04809},
year = {2019}
}