Integrate homomorphism search with @migration

[kris-brown]

The @acset_colim macro is a beloved method of constructing individual ACSets. But, when people try to create rewrite rules, they need to specify a whole diagram of ACSets. After constructing the objects, they have lost the nice names they wrote down in the @acset_colim macro. The solution seems to be to use the @migration macro to directly specify the diagram. Something like:[^1]

@migration(SchGraph, begin
  L => @join begin
    (e1,e2)::E
    src(e2)==tgt(e1)
  end
  I => @join begin
    (e1,e2)::E
    (v1,v2)::V
    src(e1)==v2
  end
  R => @join begin
    e::E 
    src(e)==tgt(e)
  end
  left::(I=>L) => begin 
    e1 => e1
    e2 => e1
    v1 => v2 
   end
   right::(I=>R) => begin end
end)

Here, the maps left and right are uniquely determined by these particular generators. A homomorphisms search with those values initialized would return exactly one morphism (for starters, anything else could throw an error).

[^1]: Maybe this syntax isn't exactly compatible with @migration because it's defining the shape category at the same time. You could ignore the ::(I=>L) stuff and pretend we have a macro specific for the span diagram. It would be helpful, though for a syntax which lets you do the shape on the fly since we may have negative/positive application conditions as well as other sorts of morphisms showing up relevant to rewriting.

[ndo885]

This functionality describing the mappings in terms of the descriptive names used by the user (e.g., introduced in @acset_colim invocations) would be very helpful for elevating the transparency of the rewrite rules which are central to our application of AlgebraicABMs & AlgebraicRewriting in our health models. Creation of such models is a central focus of the ABM hackathon currently underway, and we will -- further -- be making a major investment in creating such models for my semester-long course on applying these tools to health modeling in Fall 2024.

[slwu89]

Three cheers for better programmer quality of life and more declarative rules in the same feature request!