Wiring diagrams for self-dual compact closed categories

docs/literate/graphics/composejl_wiring_diagrams.jl

@@ -49,21 +49,41 @@ to_composejl((braid(A,B) ⊗ id(C)) ⋅ (id(B) ⊗ braid(A,C) ⋅ (braid(B,C) 
 # ### Biproduct category
 
 A, B = Ob(FreeBiproductCategory, :A, :B)
-f, g = Hom(:f, A, B), Hom(:g, B, A)
+f = Hom(:f, A, B)
 
 to_composejl(mcopy(A))
 #-
 to_composejl(delete(A))
 #-
 to_composejl(mcopy(A)⋅(f⊗f)⋅mmerge(B))
 
+# ### Compact closed category
+
+# The unit and co-unit of a compact closed category appear as caps and cups.
+
+A, B = Ob(FreeBicategoryRelations, :A, :B)
+f = Hom(:f, A, B)
+
+to_composejl(dunit(A))
+#-
+to_composejl(dcounit(A))
+
+# In a self-dual compact closed category, such as a bicategory of relations,
+# every morphism $f: A \to B$ has a transpose $f^\dagger: B \to A$ given by
+# bending wires:
+
+to_composejl((dunit(A) ⊗ id(B)) ⋅ (id(A) ⊗ f ⊗ id(B)) ⋅ (id(A) ⊗ dcounit(B)))
+
 # ## Custom styles
 
 # The visual appearance of wiring diagrams can be customized by passing Compose
 # [properties](http://giovineitalia.github.io/Compose.jl/latest/gallery/properties/).
 
 using Compose: fill, stroke
 
+A, B, = Ob(FreeSymmetricMonoidalCategory, :A, :B)
+f, g = Hom(:f, A, B), Hom(:g, B, A)
+
 to_composejl(f⋅g, box_props=[fill("lavender"), stroke("black")])
 
 # ## Output formats
@@ -84,4 +104,11 @@ to_composejl(f⋅g, box_props=[fill("lavender"), stroke("black")])
 using Compose: draw, PGF
 
 pic = to_composejl(f⋅g, rounded_boxes=false)
-draw(PGF(stdout, pic.width, pic.height), pic.context)
+pgf = sprint() do io
+  pgf_backend = PGF(io, pic.width, pic.height,
+    false, # emit_on_finish
+    true,  # only_tikz
+    texfonts=true)
+  draw(pgf_backend, pic.context)
+end
+println(pgf)

docs/src/apis/wiring_diagrams.md

@@ -8,6 +8,7 @@ CurrentModule = Catlab.WiringDiagrams
 Modules = [
   WiringDiagramCore,
   WiringLayers,
+  AlgebraicWiringDiagrams,
   WiringDiagramAlgorithms,
   WiringDiagramSerialization,
   GraphMLWiringDiagrams,

src/graphics/ComposeWiringDiagrams.jl

@@ -10,9 +10,9 @@ const C = Compose
 
 using ...WiringDiagrams
 using ..WiringDiagramLayouts
-using ..WiringDiagramLayouts: AbstractVector2D, Vector2D, BoxShape,
-  RectangleShape, JunctionShape, position, size, lower_corner, upper_corner,
-  normal, tangent, wire_points
+using ..WiringDiagramLayouts: AbstractVector2D, Vector2D,
+  BoxShape, RectangleShape, JunctionShape, NoShape,
+  position, size, lower_corner, upper_corner, normal, tangent, wire_points
 
 # Data types
 ############
@@ -141,6 +141,7 @@ end
 function render_box(::Val{JunctionShape}, ::Any, opts::ComposeOptions)
   C.compose(C.context(), C.circle(), opts.junction_props...)
 end
+render_box(::Val{NoShape}, ::Any, ::ComposeOptions) = C.context()
 
 # Compose.jl forms
 ##################

src/graphics/TikZWiringDiagrams.jl

@@ -3,8 +3,6 @@
 module TikZWiringDiagrams
 export to_tikz
 
-using Match
-
 using ...Doctrines: ObExpr, HomExpr, dom, codom, head, args, compose, id
 using ...Syntax: GATExpr, show_latex
 using ...WiringDiagrams

src/graphics/WiringDiagramLayouts.jl

@@ -58,7 +58,7 @@ Specific features of the shape are determined by the graphics backend. For
 example, a rectangle could be rendered with or without rounded corners or even
 as another, similar shape, such as a rotated isosceles trapezoid.
 """
-@enum BoxShape RectangleShape CircleShape JunctionShape
+@enum BoxShape RectangleShape CircleShape JunctionShape NoShape
 
 """ Layout for box in a wiring diagram.
 """
@@ -151,13 +151,17 @@ layout_hom_expr(f::HomExpr{:mcopy}, opts) = layout_junction_expr(f, opts)
 layout_hom_expr(f::HomExpr{:delete}, opts) = layout_junction_expr(f, opts)
 layout_hom_expr(f::HomExpr{:mmerge}, opts) = layout_junction_expr(f, opts)
 layout_hom_expr(f::HomExpr{:create}, opts) = layout_junction_expr(f, opts)
-
-layout_box_expr(f::HomExpr, opts) =
-  layout_box(f, collect(dom(f)), collect(codom(f)), opts)
-layout_junction_expr(f::HomExpr, opts) =
-  layout_junction(f, collect(dom(f)), collect(codom(f)), opts)
-layout_wires_expr(f::HomExpr, opts) =
-  layout_pure_wiring(to_wiring_diagram(f), opts)
+layout_hom_expr(f::HomExpr{:dunit}, opts) =
+  layout_junction_expr(f, opts; visible=false, pad=false)
+layout_hom_expr(f::HomExpr{:dcounit}, opts) =
+  layout_junction_expr(f, opts; visible=false, pad=false)
+
+layout_box_expr(f::HomExpr, opts; kw...) =
+  layout_box(f, collect(dom(f)), collect(codom(f)), opts; kw...)
+layout_junction_expr(f::HomExpr, opts; kw...) =
+  layout_junction(f, collect(dom(f)), collect(codom(f)), opts; kw...)
+layout_wires_expr(f::HomExpr, opts; kw...) =
+  layout_pure_wiring(to_wiring_diagram(f), opts; kw...)
 
 # Diagram layout
 ################
@@ -275,12 +279,12 @@ end
 """ Lay out a circular junction and its ports.
 """
 function layout_junction(value::Any, inputs::Vector, outputs::Vector,
-                         opts::LayoutOptions)
-  radius = opts.junction_size
+                         opts::LayoutOptions; visible::Bool=true, pad::Bool=true)
+  shape, radius = visible ? (JunctionShape, opts.junction_size) : (NoShape, 0)
   size = 2*SVector(radius, radius)
-  box = Box(BoxLayout(value=value, shape=JunctionShape, size=size),
-            layout_circular_ports(InputPort, inputs, radius, opts),
-            layout_circular_ports(OutputPort, outputs, radius, opts))
+  box = Box(BoxLayout(value=value, shape=shape, size=size),
+            layout_circular_ports(InputPort, inputs, radius, opts; pad=pad),
+            layout_circular_ports(OutputPort, outputs, radius, opts; pad=pad))
   size_to_fit!(singleton_diagram(box), opts)
 end
 
@@ -318,10 +322,10 @@ end
 """ Lay out ports along a circular arc.
 """
 function layout_circular_ports(port_kind::PortKind, port_values::Vector,
-                               radius::Real, opts::LayoutOptions)
+                               radius::Real, opts::LayoutOptions; pad::Bool=true)
   n = length(port_values)
   θ1, θ2 = is_horizontal(opts.orientation) ? (π/2, -π/2) : (-π, 0)
-  θs = collect(range(θ1, θ2, length=n+2)[2:n+1])
+  θs = collect(pad ? range(θ1,θ2,length=n+2)[2:n+1] : range(θ1,θ2,length=n))
   θs = port_sign(port_kind, opts.orientation) == -1 ? reverse(θs) : θs
   dirs = [ SVector(cos(θ),-sin(θ)) for θ in θs ] # positive y-axis downwards
   PortLayout[ PortLayout(value, radius * dir, dir)