Algebraic Networks <-> Julia Programs

[jpfairbanks]

@epatters, I would like to build programming languages from finitely presented SMCs. It looks like the Algebra.Networks module seems to be the best place to start. The goal would be one function L = language(::Presentation) which gives L::Language so that you can use a macro to define wiring diagrams in that category L. Then the @model macro would produce a Hom in the doctrine associated with the presentation object.

Here is an example of how it could work.

struct Presentation
    d::Doctrine
    obs::Vector{Ob{:generator}}
    homs::Vector{Hom{::generator}}
end

struct Language
   ...
end

p = Presentation(FreeBiproductCategory,
     Ob(FreeBiproductCategory, :A, :B, :C)
     [Hom(:f, A, B), Hom(:g, B, B), Hom(:h, otimes(B,B))]
)
L = language(p)
m = @model L (x[1], x[2]) begin
x[1] = f(x[1])
x[2] = g(x[2])
x[1] = h(x[1], x[2])
return x[1]
end
to_wiring_diagram(m) |> to_graphviz

to denote the hom expression m::Doctrine.Hom{T} = f\otimes g ; h
What would it take to get this working?

[epatters]

Maybe you know this, but we've already got a Presentation data type and corresponding macro. Example usage is in the unit tests. It should serve exactly the purpose you suggest.

The rest we will need to implement. I agree that the algebraic networks code would be a good place to start. I would like to clean that up anyway. The main thing we need to add is the ability to generate a wiring diagram from code in a fragment of the Julia language, as sketched in your post. That should be doable without too much pain. I'll think more about it and we can discuss on Friday.