CTLNs: Recursive Match Implementation of Cover Exploitation

[jpfairbanks]

We need a recursive @match algorithm that evaluates the sheaf algorithm on the tree that is the gluing rule.

FP(gr::GluingRule) = @match gr
   CompleteGraph(n) => [1:n]
   DiscreteGraph(n) => powerset(1:n)
   CycleGraph(n) => [1:n]
   Terminal(g) => brute_force(g)
   CliqueUnion(gs) => [...]
   DisjointUnion(gs) => [...]
   CycleUnion(gs) => [...]
end

All of the [...] cases involve recursing with FP and merging the results.

Originally posted by @jpfairbanks in #147 (comment)

[jpfairbanks]

After further discussions and reviewing the gluing rules. It looks like this implementation is:

struct EMPTY end

hat(x) = union(x, EMPTY)
dehat(xs) = filter(x-> x!=EMPTY, xs)

FP(gr::GluingRule) = @match gr
   CompleteGraph(n) => [1:n]
   DiscreteGraph(n) => powerset(1:n)
   CycleGraph(n) => [1:n]
   Terminal(g) => brute_force(g)
   CliqueUnion(gs) => cartesian_product(FP.(gs))
   DisjointUnion(gs) => dehat(cartesian_product(hat.(FP.(gs))))
   CycleUnion(gs) =>  cartesian_product(FP.(gs))
end