graph-rewriting-0.5: Monadic graph rewriting of hypergraphs with ports and multiedges



This is a monadic graph rewriting library for port graphs with a strong emphasis on nodes. It aims primarily at making it as convenient as possible to specify graph rewriting systems in Haskell and to experiment with them. There are a few aspects of the design to be pointed out:

  1. The port graph is actually a hypergraph, therefore if we speak of edges we are in fact referring hyperedges.
  2. The graph structure is essentially representated as a collection of nodes. The nodes have a user-defined type, where each node features a list of Ports to each of which an Edge is attached. Edges are unlabeled and can not exist autonomously, i.e. each edge is connected to at least one port. Each port is connetected to exactly one edge. Two ports are connected if (and only if) they share the same edge. What is particularly convenient is how these ports can be modeled as constructor fields of a user-defined node type.
  3. An important abstraction used in this library is the multi-parameter type-class View. It permits to expose a certain aspect of a node, allowing both to inspect or update it, while hiding the internal representation of the node. By that it is easy to specify the rewrite system in a way, that it can not only be applied to a graph with nodes of a fixed node type, but also to a Graph with polymorphic node type n. The nodes merely have to expose values of type v by means of defining a View v on n. The View abstraction is also used to expose the nodes' ports (and therefore the graph structure) to this library.
  4. Rewrite Rule are represented as Patterns that return a Rewrite. A Pattern is a branching scrutinisation of the graph that returns a result for every possible matching position in the graph. A Rule is essentially a Pattern that returns a Rewrite. A Rewrite is a monadic modification of the graph structure. In a Rule the Rewrite part can conveniently use the variables bound in the Pattern code.

See the graph-rewriting-ski package for an example of a simple rewrite system. Together with the graph-rewriting-layout and the graph-rewriting-gl packages it is easy to build a graphical and interactive application to experiment with your rewrite system.

What the library does not (yet) offer combinators to define strategies, since the emphasis of the project was to create an interactive graph-rewriting tool where rules and rewriting positions are selected manually.



graph representation, Rewrite monad

mapping over nodes, graph creation, applying a Rewrite

monadic graph scrutinisation

monadic graph modification

branching graph scrutinisation that keeps track of scrutinised nodes

combine a Pattern with a Rewrite to obtain a rewrite rule

module Data.View