Patch graph rewriting

[kris-brown]

PBPO+ is for the most part a generalization of patch graph rewriting (PGR), but it seems promising to implement PGR because it is simpler to understand and could be implemented more efficiently (e.g. no need to search for adherence morphisms).

One downside is that PGR is described set theoretically rather than categorically.

Note the following (from "Graph rewriting and relabeling with PBPO+: A unifying theory for quasitoposes")

PBPO+ does not provide a strict generalization of PGR ... This is because patch edge endpoints that lie in the context graph can be redefined in PGR (e.g., the direction of edges between context and pattern can be inverted), but not in PBPO+.

The most obvious utility of using PBR is to have a painless way of using rewrites to change the values of certain homs (e.g. modifying the src of an edge). In DPO this requires deletion and re-addition, but that causes problems once there are other objects which have homs into $E$.

[kris-brown]

Implementing this in a user-friendly way would obviate the need for #61

[kris-brown]

Paper here