ENH: Operadic interface for substitution of wiring diagrams.

Closes #40.

src/wiring_diagrams/Core.jl

@@ -28,7 +28,7 @@ export AbstractBox, Box, WiringDiagram, Wire, Ports, PortValueError, Port,
   singleton_diagram, induced_subdiagram, encapsulated_subdiagram,
   substitute, encapsulate,
   dom, codom, id, compose, otimes, munit, braid, mcopy, delete, mmerge, create,
-  permute, is_permuted_equal
+  ocompose, permute, is_permuted_equal
 
 using Compat
 using AutoHashEquals
@@ -555,7 +555,8 @@ end
 Performs one or more substitutions. When performing multiple substitutions, the
 substitutions are simultaneous.
 
-This operation is the operadic composition of wiring diagrams.
+This operation implements the operadic composition of wiring diagrams
+(`ocompose`).
 """
 function substitute(d::WiringDiagram, v::Int)
   substitute(d, v, box(d,v)::WiringDiagram)
@@ -900,6 +901,23 @@ function mmerge(A::Ports, n::Int)::WiringDiagram
   return f
 end
 
+""" Operadic composition of wiring diagrams.
+
+This generic function has two different signatures, corresponding to the two
+standard definitions of an operad (Yau, 2018, Operads of Wiring Diagrams,
+Definitions 2.3 and 2.10).
+
+This operation is a simple wrapper around substitution (`substitute`).
+"""
+function ocompose(f::WiringDiagram, gs::Vector{WiringDiagram})
+  @assert length(gs) == nboxes(f)
+  substitute(f, box_ids(f), gs)
+end
+function ocompose(f::WiringDiagram, i::Int, g::WiringDiagram)
+  @assert 1 <= i <= nboxes(f)
+  substitute(f, box_ids(f)[i], g)
+end
+
 function collect_values(ob::ObExpr)::Vector
   exprs = collect(ob)
   @assert all(head(expr) == :generator for expr in exprs)

test/wiring_diagrams/Core.jl

@@ -315,4 +315,35 @@ X = Ports([:A])
 # Unit
 @test compose(otimes(id(X),create(X)), mmerge(X)) == id(X)
 
+# Operadic composition
+#---------------------
+
+f, g, h = map([:f, :g, :h]) do sym
+  (i::Int) -> singleton_diagram(Box(Hom(Symbol("$sym$i"), A, A)))
+end
+
+# Identity
+d = compose(f(1),f(2))
+@test ocompose(g(1), 1, d) == d
+@test ocompose(g(1), [d]) == d
+@test ocompose(d, [f(1),f(2)]) == d
+@test ocompose(d, 1, f(1)) == d
+@test ocompose(d, 2, f(2)) == d
+
+# Associativity
+@test ocompose(compose(f(1),f(2)), [
+  ocompose(compose(g(1),g(2)), [compose(h(1),h(2)), compose(h(3),h(4))]),
+  ocompose(compose(g(3),g(4)), [compose(h(5),h(6)), compose(h(7),h(8))])
+]) == ocompose(
+  ocompose(compose(f(1),f(2)), [compose(g(1),g(2)), compose(g(3),g(4))]),
+  [compose(h(1),h(2)), compose(h(3),h(4)), compose(h(5),h(6)), compose(h(7),h(8))]
+)
+@test ocompose(
+  ocompose(compose(f(1),f(2)), 1, compose(g(1),g(2))),
+  3, compose(g(3),g(4))
+) == ocompose(
+  ocompose(compose(f(1),f(2)), 2, compose(g(3),g(4))),
+  1, compose(g(1),g(2))
+)
+
 end