GraphRewriting.Rule

Rewrite rules are represented as nested monads: a Rule is a Pattern that returns a Rewrite the latter directly defining the transformation of the graph.

For rule construction a few functions a provided: The most basic one is rewrite. But in most cases erase, rewire, and 'replace*' should be more convenient. These functions express rewrites that replace the matched nodes of the Pattern, which comes quite close to the L -> R form in which graph rewriting rules are usually expressed.

Documentation

type Rule n = Pattern n (Rewrite n ())

A rewriting rule is defined as a Pattern that returns a Rewrite

apply :: Rule n -> Rewrite n ()

Apply rule at an arbitrary position if applicable

rewrite :: (Match -> Rewrite n a) -> Rule n

primitive rule construction with the matched nodes of the left hand side as a parameter

erase :: View [Port] n => Rule n

constructs a rule that deletes all of the matched nodes from the graph

rewire :: View [Port] n => [[Edge]] -> Rule n

Constructs a rule from a list of rewirings. Each rewiring specifies a list of hyperedges that are to be merged into a single hyperedge. All matched nodes of the left-hand side are removed.

data RHS v

Constructors

Node v

Wire Edge Edge

Merge [Edge]

replace :: (View [Port] n, View v n) => Int -> ([Edge] -> [RHS v]) -> Rule n

Constructs a rule that replaces the matched nodes of the left-hand side by new nodes and rewirings. It generates an amount of new edges specified by the Int. In most cases the functions below named replace* should be sufficient.

replace0 :: (View v n, View [Port] n) => [RHS v] -> Rule n

Replaces the matched nodes by a list of new nodes and rewirings.

replace1 :: (View v n, View [Port] n) => (Edge -> [RHS v]) -> Rule n

Replaces the matched nodes by a list of new nodes and rewirings. It also generates one new edge.

replace2 :: (View v n, View [Port] n) => (Edge -> Edge -> [RHS v]) -> Rule n

Replaces the matched nodes by a list of new nodes and rewirings. It also generates two new edges.

replace3 :: (View v n, View [Port] n) => (Edge -> Edge -> Edge -> [RHS v]) -> Rule n

You get the idea.

replace4 :: (View v n, View [Port] n) => (Edge -> Edge -> Edge -> Edge -> [RHS v]) -> Rule n

replace5 :: (View v n, View [Port] n) => (Edge -> Edge -> Edge -> Edge -> Edge -> [RHS v]) -> Rule n

replace6 :: (View v n, View [Port] n) => (Edge -> Edge -> Edge -> Edge -> Edge -> Edge -> [RHS v]) -> Rule n

replace7 :: (View v n, View [Port] n) => (Edge -> Edge -> Edge -> Edge -> Edge -> Edge -> Edge -> [RHS v]) -> Rule n

replace8 :: (View v n, View [Port] n) => (Edge -> Edge -> Edge -> Edge -> Edge -> Edge -> Edge -> Edge -> [RHS v]) -> Rule n

(>>>) :: Rule n -> Rule n -> Rule n

Apply two rules consecutively. Second rule is only applied if first one succeeds. Fails if (and only if) first rule fails.

exhaustive :: Rule n -> Rule n

Make a rule exhaustive, i.e. such that (when applied) it reduces redexes until no redexes are occur in the graph.

everywhere :: Rule n -> Rule n

Make a rule parallel, i.e. such that (when applied) all current redexes are contracted one by one. Neither new redexes or destroyed redexes are reduced.