Wiring diagrams for bicategories of relations

[jpfairbanks]

Wiring diagrams for bicategories of relations

[epatters]

Probably a bug. I'll look into it soon.

[jpfairbanks]

Thanks, here is a related problem,

X,Y = Ob(FreeAbelianBicategoryRelations, :X, :Y)
f = Hom(:f, X,Y)
to_wiring_diagram(f)
wd(mplus(X))

MethodError: no method matching mplus(::Ports{Symbol})

[epatters]

Having refreshed myself on the situation, I'd say that these are not so much bugs as features that I never implemented. Bicategories of relations in Catlab have been neglected, since I'm not currently using them in any computational project. But I would like to improve this.

I see two different issues here:

1. Wiring diagrams for bicategories of relations: I need to implement the dagger and possibly a few other things. This should be fairly straightforward.

2. Wiring diagrams for abelian bicategories of relations: there are now two different diagonal and codiagonal structures. How to best handle this will require some thought. The obvious strategy is to have two different kinds of junction nodes, but the Junction type is currently not very flexible.

[epatters]

The first step is probably to resolve #54. Then we can make sure that all the operations in a bicategory of relations get properly translated into wiring diagrams.

[jpfairbanks]

For making WDs for Rel, should we introduce a DaggerBox that has an AbstractBox in it tells you to flip it? I am thinking like this:

struct DaggerBox{T} where T<: AbstractBox
  box::T
end

dagger(b::Box) = DaggerBox(b)
dagger(b::DaggerBox) = b.box

Do you think this is the right approach?

[epatters]

PR #68 is a start towards a proper implementation of wiring diagrams for bicategories of relations.

If I'm not mistaken, the dagger is now the only missing operation. I like the strategy suggested here. We would further write:

input_ports(box::DaggerBox) = output_ports(box.box)
output_ports(box::DaggerBox) = input_ports(box.box)

[epatters]

Issues related to abelian bicategories of relations will be taken up in #70.