Roadmap: GAT of GATs

[jpfairbanks]

@epatters @mehalter @bosonbaas, here are some tasks I think we should address for the next push on Catlab (aka Gatlab).

• [ ] CT constructions
  • [ ] Product/Sum
  • [ ] Span/Cospan
  • [ ] Functor/Instance
  • [ ] Category of Elements
• [ ] GAT Functors, injective, surjective to talk about relationships between algebraic theories
  • [ ] Causal Theories
  • [ ] Statistical Theories
  • [ ] Physical Theories
• [ ] Compute pushout/pullback of GAT functors
  • [ ] Cospan category for open GATs
• [ ] Pushout/pullback within a Cat, can we infer the rules for composition of FinSet cospans from the definition of FinSet morphisms?
• [ ] Relation orient computing: functors from an arbitrary GAT into Rel
• [ ] Generic Operads
  • [ ] Syntax
  • [ ] Drawing
  • [ ] Substitution based on term matching
• [ ] Axiom Support
  • [ ] Generating term rewriting rules from the specification of the axioms of a GAT

[mehalter]

• [x] Task 0: Refactor SemanticModels -> (Catlab.jl, AlgebraicX.jl)
• [ ] Task 1: Refactor Catlab.jl implementation of GAT to provide more efficient and easier to work with data structures