ENH: Wiring diagrams for bicategories of relations (#49).

AlgebraicJulia · Jan 5, 2020 · 86b0f02 · 86b0f02
1 parent 5294f55
commit 86b0f02
Show file tree

Hide file tree

Showing 2 changed files with 40 additions and 3 deletions.
diff --git a/src/wiring_diagrams/Algebraic.jl b/src/wiring_diagrams/Algebraic.jl
@@ -9,15 +9,16 @@ module AlgebraicWiringDiagrams
 export Ports, Junction, PortOp, BoxOp,
   functor, dom, codom, id, compose, ⋅, ∘, otimes, ⊗, munit, braid, permute,
   mcopy, delete, Δ, ◇, mmerge, create, ∇, □, dual, dunit, dcounit, mate, dagger,
-  ocompose, junction_diagram, junction_caps, junction_cups, add_junctions,
-  add_junctions!, rem_junctions, merge_junctions
+  meet, top, ocompose, junction_diagram, junction_caps, junction_cups,
+  add_junctions, add_junctions!, rem_junctions, merge_junctions
 
 using AutoHashEquals
 using LightGraphs
 
 using ...GAT, ...Doctrines
 import ...Doctrines: dom, codom, id, compose, ⋅, ∘, otimes, ⊗, munit, braid,
-  mcopy, delete, Δ, ◇, mmerge, create, ∇, □, dual, dunit, dcounit, mate, dagger
+  mcopy, delete, Δ, ◇, mmerge, create, ∇, □, dual, dunit, dcounit, mate, dagger,
+  meet, top
 import ...Syntax: functor
 using ..WiringDiagramCore, ..WiringLayers
 import ..WiringDiagramCore: Box, WiringDiagram, input_ports, output_ports
@@ -269,6 +270,25 @@ dagger(f::WiringDiagram{DaggerCompactCategory.Hom}) =
 mate(f::WiringDiagram{DaggerCompactCategory.Hom}) =
   functor(f, dual, mate, contravariant=true, monoidal_contravariant=true)
 
+# Bicategory of relations
+#------------------------
+
+mcopy(A::Ports{BicategoryRelations.Hom}, n::Int) = junctioned_mcopy(A, n)
+mmerge(A::Ports{BicategoryRelations.Hom}, n::Int) = junctioned_mmerge(A, n)
+delete(A::Ports{BicategoryRelations.Hom}) = junctioned_delete(A)
+create(A::Ports{BicategoryRelations.Hom}) = junctioned_create(A)
+
+dagger(f::WiringDiagram{BicategoryRelations.Hom}) =
+  functor(f, identity, dagger, contravariant=true)
+
+dunit(A::Ports{BicategoryRelations.Hom}) = junction_caps(A)
+dcounit(A::Ports{BicategoryRelations.Hom}) = junction_cups(A)
+
+meet(f::WiringDiagram{BicategoryRelations.Hom}, g::WiringDiagram{BicategoryRelations.Hom}) =
+  compose(mcopy(dom(f)), otimes(f,g), mmerge(codom(f)))
+top(A::Ports{BicategoryRelations.Hom}, B::Ports{BicategoryRelations.Hom}) =
+  compose(delete(A), create(B))
+
 # Operadic interface
 ####################
 

diff --git a/test/wiring_diagrams/Algebraic.jl b/test/wiring_diagrams/Algebraic.jl
@@ -203,6 +203,23 @@ g = singleton_diagram(CompactClosedCategory.Hom, Box(:g,[:B],[:A]))
 @test mate(mate(compose(f,g))) == compose(f,g)
 @test mate(mate(otimes(f,g))) == otimes(f,g)
 
+# Bicategory of relations
+#------------------------
+
+A, B = [ Ports{BicategoryRelations.Hom}([sym]) for sym in [:A, :B] ]
+R = singleton_diagram(BicategoryRelations.Hom, Box(:R,[:A],[:B]))
+S = singleton_diagram(BicategoryRelations.Hom, Box(:S,[:A],[:B]))
+
+# Domains and codomains
+@test dom(meet(R,S)) == A
+@test codom(meet(R,S)) == B
+@test dom(top(A,B)) == A
+@test codom(top(A,B)) == B
+
+# Units and counits
+@test dunit(A) == merge_junctions(compose(create(A), mcopy(A)))
+@test dcounit(A) == merge_junctions(compose(mmerge(A), delete(A)))
+
 # Operadic interface
 ####################