From e21e6c7b61a2158a912247af5b0121785046a02c Mon Sep 17 00:00:00 2001
From: Luke Morris <70283489+lukem12345@users.noreply.github.com>
Date: Wed, 26 Jun 2024 12:07:52 -0400
Subject: [PATCH] Use Match-Replace strategy to alias operators (#37)

---
 src/DiagrammaticEquations.jl |   7 +-
 src/acset.jl                 |  10 ++
 src/openoperators.jl         | 247 +++++++++++++++++++++++++++++++++++
 test/Project.toml            |   1 +
 test/openoperators.jl        | 241 ++++++++++++++++++++++++++++++++++
 test/runtests.jl             |   4 +
 6 files changed, 508 insertions(+), 2 deletions(-)
 create mode 100644 src/openoperators.jl
 create mode 100644 test/openoperators.jl

diff --git a/src/DiagrammaticEquations.jl b/src/DiagrammaticEquations.jl
index 9529578..0d0de25 100644
--- a/src/DiagrammaticEquations.jl
+++ b/src/DiagrammaticEquations.jl
@@ -14,7 +14,7 @@ Collage, collate,
 oapply, unique_by, unique_by!, OpenSummationDecapodeOb, OpenSummationDecapode, Open, default_composition_diagram,
 ## acset
 SchDecapode, SchNamedDecapode, AbstractDecapode, AbstractNamedDecapode, NamedDecapode, SummationDecapode,
-contract_operators!, contract_operators, add_constant!, add_parameter, fill_names!, dot_rename!, expand_operators, infer_state_names, infer_terminal_names, recognize_types,
+contract_operators!, contract_operators, add_constant!, add_parameter, fill_names!, dot_rename!, is_expanded, expand_operators, infer_state_names, infer_terminal_names, recognize_types,
 resolve_overloads!, replace_names!,
 apply_inference_rule_op1!, apply_inference_rule_op2!,
 transfer_parents!, transfer_children!,
@@ -26,7 +26,9 @@ Plus, AppCirc1, Var, Tan, App1, App2,
 ## visualization
 to_graphviz_property_graph, typename, draw_composition,
 ## rewrite
-average_rewrite
+average_rewrite,
+## openoperators
+transfer_parents!, transfer_children!, replace_op1!, replace_op2!, replace_all_op1s!, replace_all_op2s!
 
 using Catlab
 using Catlab.Theories
@@ -56,6 +58,7 @@ include("visualization.jl")
 include("rewrite.jl")
 include("pretty.jl")
 include("colanguage.jl")
+include("openoperators.jl")
 include("deca/Deca.jl")
 include("learn/Learn.jl")
 
diff --git a/src/acset.jl b/src/acset.jl
index 19eb515..2dc7860 100644
--- a/src/acset.jl
+++ b/src/acset.jl
@@ -185,6 +185,16 @@ function recognize_types(d::AbstractNamedDecapode)
   error("Types $unrecognized_types are not recognized. CHECK: $types")
 end
 
+"""    is_expanded(d::AbstractNamedDecapode)
+
+Check that no unary operator is a composition of unary operators.
+"""
+is_expanded(d::AbstractNamedDecapode) = !any(x -> x isa AbstractVector, d[:op1])
+
+"""    function expand_operators(d::AbstractNamedDecapode)
+
+If any unary operator is a composition, expand it out using intermediate variables.
+"""
 function expand_operators(d::AbstractNamedDecapode)
   #e = SummationDecapode{Symbol, Symbol, Symbol}()
   e = SummationDecapode{Any, Any, Symbol}()
diff --git a/src/openoperators.jl b/src/openoperators.jl
new file mode 100644
index 0000000..b929463
--- /dev/null
+++ b/src/openoperators.jl
@@ -0,0 +1,247 @@
+# Opening up Op1s
+# --------------
+
+# Validate whether LHS represents a valid op1.
+function validate_op1_match(d::SummationDecapode, LHS::SummationDecapode)
+  if nparts(LHS, :Op1) != 1
+    error("Only single operator replacement is supported for now, but found Op1s: $(LHS[:op1])")
+  end
+end
+
+# Validate whether RHS represents a valid replacement for an op1.
+function validate_op1_replacement(d::SummationDecapode, LHS::Symbol, RHS::SummationDecapode)
+  if length(infer_states(RHS)) != 1 || length(infer_terminals(RHS)) != 1
+    error("The replacement for $(LHS) must have a single input and a single output, but found inputs: $(RHS[infer_states(RHS), :name]) and outputs $(RHS[infer_terminals(RHS), :name])")
+  end
+end
+
+"""    function replace_op1!(d::SummationDecapode, LHS::Symbol, RHS::SummationDecapode)
+
+Given a Decapode, d, replace at most one instance of the left-hand-side unary operator with those of the right-hand-side.
+
+Return the index of the replaced operator, 0 if no match was found.
+
+See also: [`replace_all_op1s!`](@ref)
+"""
+function replace_op1!(d::SummationDecapode, LHS::Symbol, RHS::SummationDecapode)
+  validate_op1_replacement(d, LHS, RHS)
+  isempty(incident(d, LHS, :op1)) && return 0
+
+  # Identify the "matched" operation.
+  LHS_op1 = first(incident(d, LHS, :op1))
+  LHS_input = d[LHS_op1, :src]
+  LHS_output = d[LHS_op1, :tgt]
+
+  # Add in the "replace" operation(s).
+  added_vars = copy_parts!(d, RHS).Var
+  RHS_input = only(intersect(infer_states(d), added_vars))
+  RHS_output = only(intersect(infer_terminals(d), added_vars))
+
+  # Transfer LHS_input's pointers to RHS_input.
+  transfer_parents!(d, LHS_input, RHS_input)
+  transfer_children!(d, LHS_input, RHS_input)
+  d[RHS_input, :name] = d[LHS_input, :name]
+  d[RHS_input, :type] = d[LHS_input, :type]
+
+  # Transfer LHS_output's pointers to RHS_output.
+  transfer_parents!(d, LHS_output, RHS_output)
+  transfer_children!(d, LHS_output, RHS_output)
+  d[RHS_output, :name] = d[LHS_output, :name]
+  d[RHS_output, :type] = d[LHS_output, :type]
+
+  # Remove the replaced match and variables.
+  rem_parts!(d, :Var, sort!([LHS_input, LHS_output]))
+  rem_part!(d, :Op1, LHS_op1)
+  LHS_op1
+end
+
+"""    function replace_op1!(d::SummationDecapode, LHS::SummationDecapode, RHS::SummationDecapode)
+
+Given a Decapode, d, replace at most one instance of the left-hand-side unary operator with those of the right-hand-side.
+
+Return the index of the replaced unary operator, 0 if no match was found.
+See also: [`replace_op2!`](@ref), [`replace_all_op1s!`](@ref)
+"""
+function replace_op1!(d::SummationDecapode, LHS::SummationDecapode, RHS::SummationDecapode)
+  validate_op1_match(d, LHS)
+  replace_op1!(d, only(LHS[:op1]), RHS)
+end
+
+"""    function replace_op1!(d::SummationDecapode, LHS::Symbol, RHS::Symbol)
+
+Given a Decapode, d, replace at most one instance of the left-hand-side unary operator with that of the right-hand-side.
+
+Return the index of the replaced unary operator, 0 if no match was found.
+See also: [`replace_op2!`](@ref), [`replace_all_op1s!`](@ref)
+"""
+function replace_op1!(d::SummationDecapode, LHS::Symbol, RHS::Symbol)
+  isempty(incident(d, LHS, :op1)) && return 0
+  LHS_op1 = first(incident(d, LHS, :op1))
+  d[LHS_op1, :op1] = RHS
+  LHS_op1
+end
+
+"""    function replace_all_op1s!(d::SummationDecapode, LHS::Union{Symbol, SummationDecapode}, RHS::Union{Symbol, SummationDecapode})
+
+Given a Decapode, d, replace all instances of the left-hand-side unary operator with those of the right-hand-side.
+
+Return true if any replacements were made, otherwise false.
+
+See also: [`replace_op1!`](@ref), [`replace_all_op2s!`](@ref)
+"""
+function replace_all_op1s!(d::SummationDecapode, LHS::Union{Symbol, SummationDecapode}, RHS::Union{Symbol, SummationDecapode})
+  any_replaced = false
+  while replace_op1!(d,LHS,RHS) != 0
+    any_replaced = true
+  end
+  any_replaced
+end
+
+# Opening up Op2s
+# --------------
+
+# Validate whether LHS represents a valid op2.
+function validate_op2_match(d::SummationDecapode, LHS::SummationDecapode)
+  if nparts(LHS, :Op2) != 1
+    error("Only single operator replacement is supported for now, but found Op2s: $(LHS[:op2])")
+  end
+end
+
+# Validate whether RHS represents a valid replacement for an op2.
+function validate_op2_replacement(d::SummationDecapode, LHS::Symbol, RHS::SummationDecapode, proj1::Int, proj2::Int)
+  if length(infer_states(RHS)) != 2 || length(infer_terminals(RHS)) != 1
+    error("The replacement for $(LHS) must have two inputs and a single output, but found inputs: $(RHS[infer_states(RHS), :name]) and outputs $(RHS[infer_terminals(RHS), :name])")
+  end
+  if !issetequal(infer_states(RHS), [proj1, proj2])
+    error("The projections of the RHS of this replacement are not state variables. The projections are $(RHS[[proj1,proj2], :op2]) but the state variables are $(RHS[infer_states(RHS), :op2]).")
+  end
+end
+
+"""    function replace_op2!(d::SummationDecapode, LHS::Symbol, RHS::SummationDecapode, proj1::Int, proj2::Int)
+
+Given a Decapode, d, replace at most one instance of the left-hand-side binary operator with those of the right-hand-side.
+
+proj1 and proj2 are the indices of the intended proj1 and proj2 in RHS.
+
+Return the index of the replaced operator, 0 if no match was found.
+
+See also: [`replace_op1!`](@ref), [`replace_all_op2s!`](@ref)
+"""
+function replace_op2!(d::SummationDecapode, LHS::Symbol, RHS::SummationDecapode, proj1::Int, proj2::Int)
+  validate_op2_replacement(d, LHS, RHS, proj1, proj2)
+  isempty(incident(d, LHS, :op2)) && return 0
+
+  # Identify the "matched" operation.
+  LHS_op2 = first(incident(d, LHS, :op2))
+  LHS_proj1, LHS_proj2 = d[LHS_op2, :proj1], d[LHS_op2, :proj2]
+  LHS_output = d[LHS_op2, :res]
+
+  # Add in the "replace" operation(s).
+  added_vars = copy_parts!(d, RHS).Var
+  RHS_proj1, RHS_proj2 = intersect(infer_states(d), added_vars)
+
+  # Preserve the order of proj1 and proj2.
+  if d[RHS_proj1, :name] != RHS[proj1, :name]
+    RHS_proj1, RHS_proj2 = RHS_proj2, RHS_proj1
+  end
+  RHS_output = only(intersect(infer_terminals(d), added_vars))
+
+  # Transfer LHS_proj1's pointers to RHS_proj1.
+  transfer_parents!(d, LHS_proj1, RHS_proj1)
+  transfer_children!(d, LHS_proj1, RHS_proj1)
+  d[RHS_proj1, :name] = d[LHS_proj1, :name]
+  d[RHS_proj1, :type] = d[LHS_proj1, :type]
+
+  # Transfer LHS_proj2's pointers to RHS_proj2.
+  transfer_parents!(d, LHS_proj2, RHS_proj2)
+  transfer_children!(d, LHS_proj2, RHS_proj2)
+  d[RHS_proj2, :name] = d[LHS_proj2, :name]
+  d[RHS_proj2, :type] = d[LHS_proj2, :type]
+
+  # Transfer LHS_output's pointers to RHS_output.
+  transfer_parents!(d, LHS_output, RHS_output)
+  transfer_children!(d, LHS_output, RHS_output)
+  d[RHS_output, :name] = d[LHS_output, :name]
+  d[RHS_output, :type] = d[LHS_output, :type]
+
+  # Remove the replaced match and variables.
+  rem_parts!(d, :Var, sort!([LHS_proj1, LHS_proj2, LHS_output]))
+  rem_part!(d, :Op2, LHS_op2)
+  LHS_op2
+end
+
+"""    function replace_op2!(d::SummationDecapode, LHS::SummationDecapode, RHS::SummationDecapode, proj1::Int, proj2::Int)
+
+Given a Decapode, d, replace at most one instance of the left-hand-side binary operator with those of the right-hand-side.
+
+proj1 and proj2 are the indices of the intended proj1 and proj2 in RHS.
+
+Return the index of the replaced binary operator, 0 if no match was found.
+See also: [`replace_op1!`](@ref), [`replace_all_op2s!`](@ref)
+"""
+function replace_op2!(d::SummationDecapode, LHS::SummationDecapode, RHS::SummationDecapode, proj1::Int, proj2::Int)
+  validate_op2_match(d, LHS)
+  replace_op2!(d, only(LHS[:op2]), RHS, proj1, proj2)
+end
+
+"""    function replace_op2!(d::SummationDecapode, LHS::Symbol, RHS::Symbol)
+
+Given a Decapode, d, replace at most one instance of the left-hand-side binary operator with that of the right-hand-side.
+
+Return the index of the replaced binary operator, 0 if no match was found.
+See also: [`replace_op1!`](@ref), [`replace_all_op2s!`](@ref)
+"""
+function replace_op2!(d::SummationDecapode, LHS::Symbol, RHS::Symbol)
+  isempty(incident(d, LHS, :op2)) && return 0
+  LHS_op2 = first(incident(d, LHS, :op2))
+  d[LHS_op2, :op2] = RHS
+  LHS_op2
+end
+
+# Ignoring proj1 and proj2 keeps replace_all_op2s! simple.
+replace_op2!(d::SummationDecapode, LHS::Symbol, RHS::Symbol, proj1, proj2) =
+  replace_op2!(d, LHS, RHS)
+
+"""    function replace_all_op2s!(d::SummationDecapode, LHS::Union{Symbol, SummationDecapode}, RHS::Union{Symbol, SummationDecapode}, proj1::Int, proj2::Int)
+
+Given a Decapode, d, replace all instances of the left-hand-side binary operator with those of the right-hand-side.
+
+proj1 and proj2 are the indices of the intended proj1 and proj2 in RHS.
+
+Return true if any replacements were made, otherwise false.
+
+See also: [`replace_op2!`](@ref), [`replace_all_op1s!`](@ref)
+"""
+function replace_all_op2s!(d::SummationDecapode, LHS::Union{Symbol, SummationDecapode}, RHS::Union{Symbol, SummationDecapode}, proj1::Int, proj2::Int)
+  any_replaced = false
+  while replace_op2!(d,LHS,RHS, proj1, proj2) != 0
+    any_replaced = true
+  end
+  any_replaced
+end
+
+"""    function replace_all_op2s!(d::SummationDecapode, LHS::Union{Symbol, SummationDecapode}, RHS::Union{Symbol, SummationDecapode})
+
+Given a Decapode, d, replace all instances of the left-hand-side binary operator with those of the right-hand-side.
+
+Search for distinguished variables "p1" and "p2" to serve as the proj1 and proj2 from RHS.
+
+Return true if any replacements were made, otherwise false.
+
+See also: [`replace_op2!`](@ref), [`replace_all_op1s!`](@ref)
+"""
+function replace_all_op2s!(d::SummationDecapode, LHS::Union{Symbol, SummationDecapode}, RHS::Union{Symbol, SummationDecapode})
+  p1s = incident(RHS, :p1, :name)
+  p2s = incident(RHS, :p2, :name)
+  if length(p1s) != 1 || length(p2s) != 1
+    error("proj1 and proj2 to use were not given, but unique distinguished variables p1 and p2 were not found. Found p1: $(p1s) and p2: $(p2s).")
+  end
+  proj1 = only(p1s)
+  proj2 = only(p2s)
+  any_replaced = false
+  while replace_op2!(d,LHS,RHS, proj1, proj2) != 0
+    any_replaced = true
+  end
+  any_replaced
+end
+
diff --git a/test/Project.toml b/test/Project.toml
index c36beb4..97b4819 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -1,4 +1,5 @@
 [deps]
+ACSets = "227ef7b5-1206-438b-ac65-934d6da304b8"
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
 Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
 CombinatorialSpaces = "b1c52339-7909-45ad-8b6a-6e388f7c67f2"
diff --git a/test/openoperators.jl b/test/openoperators.jl
new file mode 100644
index 0000000..1c9245c
--- /dev/null
+++ b/test/openoperators.jl
@@ -0,0 +1,241 @@
+using ACSets
+using DiagrammaticEquations
+using Test
+
+@testset "Open Operators" begin
+  # Error handling
+  # --------------
+
+  # Test erroneous left-hand side.
+  LHS = @decapode begin
+    y == Δ(X) + ∇(Z)
+  end
+  RHS = @decapode begin
+    y == -1*∘(d,⋆,d,⋆)(X)
+  end
+  Heat = @decapode begin
+    ∂ₜ(C) == Δ(C)
+  end
+  @test_throws "Only single operator replacement is supported for now, but found Op1s: [:Δ, :∇]" replace_op1!(Heat, LHS, RHS)
+
+  # Test erroneous right-hand side.
+  LHS = @decapode begin
+    y == Δ(X)
+  end
+  RHS = @decapode begin
+    y == -1*∘(d,⋆,d,⋆)(X) + 10*Z
+  end
+  Heat = @decapode begin
+    ∂ₜ(C) == Δ(C)
+  end
+  @test_throws "The replacement for Δ must have a single input and a single output, but found inputs: [:X, :Z] and outputs [:y]" replace_op1!(Heat, LHS, RHS)
+
+  # Transfering variables
+  # ---------------------
+
+  # Test transfering variables on the Brusselator.
+  Brusselator = @decapode begin
+    (U, V)::Form0
+    U2V::Form0
+    (U̇, V̇)::Form0
+    (α)::Constant
+    F::Parameter
+    U2V == (U .* U) .* V
+    U̇ == 1 + U2V - (4.4 * U) + (α * Δ(U)) + F
+    V̇ == (3.4 * U) - U2V + (α * Δ(V))
+    ∂ₜ(U) == U̇
+    ∂ₜ(V) == V̇
+  end
+  U_idx = only(incident(Brusselator, :U, :name))
+  V_idx = only(incident(Brusselator, :V, :name))
+  transfer_children!(Brusselator, U_idx, V_idx)
+  @test Brusselator == @decapode begin
+    (U, V)::Form0
+    U2V::Form0
+    (U̇, V̇)::Form0
+    (α)::Constant
+    F::Parameter
+    U2V == (V .* V) .* V
+    U̇ == 1 + U2V - (4.4 * V) + (α * Δ(V)) + F
+    V̇ == (3.4 * V) - U2V + (α * Δ(V))
+    ∂ₜ(V) == U̇
+    ∂ₜ(V) == V̇
+  end
+
+  # Opening Op1s
+  # ------------
+
+  # Test expanding the Heat equation.
+  LHS = @decapode begin
+    y == Δ(X)
+  end
+  RHS = @decapode begin
+    y == -1*∘(d,⋆,d,⋆)(X)
+  end
+  Heat = @decapode begin
+    ∂ₜ(C) == Δ(C)
+  end
+  replace_op1!(Heat, LHS, RHS)
+  @test Heat == @acset SummationDecapode{Any,Any,Symbol} begin
+    Var=4
+    type=[:Literal, :infer, :infer, :infer]
+    name=[Symbol("-1"), Symbol("•1"), :Ċ, :C]
+    TVar=1
+    incl=[3]
+    Op1=2
+    src=[4,4]
+    tgt=[3,2]
+    op1=[:∂ₜ, [:d, :⋆, :d, :⋆]]
+    Op2=1
+    proj1=[1]
+    proj2=[2]
+    res=[3]
+    op2=[:*]
+  end
+
+  # Test expanding a vector calculus equivalent.
+  LHS = @decapode begin
+    y == div(X)
+  end
+  RHS = @decapode begin
+    y == ∘(⋆,d,⋆)(X)
+  end
+  Divergence = @decapode begin
+    C::Form0
+    V::Form1
+    ∂ₜ(C) == C*div(V)
+  end
+  replace_op1!(Divergence, LHS, RHS)
+  @test Divergence == @acset SummationDecapode{Any,Any,Symbol} begin
+    Var = 4
+    TVar = 1
+    Op1 = 2
+    Op2 = 1
+    src = [1, 4]
+    tgt = [3, 2]
+    proj1 = [1]
+    proj2 = [2]
+    res = [3]
+    incl = [3]
+    op1 = Any[:∂ₜ, [:⋆, :d, :⋆]]
+    op2 = [:*]
+    type = [:Form0, :infer, :infer, :Form1]
+    name = [:C, Symbol("•2"), :Ċ, :V]
+  end
+
+  # Test expanding the vector laplacian.
+  LHS = @decapode begin
+    y == Δ(X)
+  end
+  RHS = @decapode begin
+    y == ∘(d,⋆,d,⋆)(X) + ∘(⋆,d,⋆,d)(X)
+  end
+  Heat = @decapode begin
+    ∂ₜ(C) == -1*Δ(V)
+  end
+  replace_op1!(Heat, LHS, RHS)
+  @test Heat == @acset SummationDecapode{Any,Any,Symbol} begin
+    Var = 7
+    TVar = 1
+    Op1 = 3
+    Op2 = 1
+    Σ = 1
+    Summand = 2
+    src = [2, 3, 3]
+    tgt = [1, 5, 7]
+    proj1 = [4]
+    proj2 = [6]
+    res = [1]
+    incl = [1]
+    summand = [7, 5]
+    summation = [1, 1]
+    sum = [6]
+    op1 = Any[:∂ₜ, [:⋆, :d, :⋆, :d], [:d, :⋆, :d, :⋆]]
+    op2 = [:*]
+    type = [:infer, :infer, :infer, :Literal, :infer, :infer, :infer]
+    name = [:Ċ, :C, :V, Symbol("-1"), Symbol("•2"), Symbol("•2"), Symbol("•1")]
+  end
+
+  # Test expanding multiple op1s.
+  LHS = @decapode begin
+    y == Δ(X)
+  end
+  RHS = @decapode begin
+    y == ∘(d,⋆,d,⋆)(X)
+  end
+  LapLap = @decapode begin
+    ∂ₜ(C) == Δ(Δ(C))
+  end
+  replace_all_op1s!(LapLap, LHS, RHS)
+  @test LapLap == @acset SummationDecapode{Any,Any,Symbol} begin
+    Var = 3
+    TVar = 1
+    Op1 = 3
+    src = [3, 3, 2]
+    tgt = [1, 2, 1]
+    incl = [1]
+    op1 = Any[:∂ₜ, [:d, :⋆, :d, :⋆], [:d, :⋆, :d, :⋆]]
+    type = [:infer, :infer, :infer]
+    name = [:Ċ, Symbol("•2"), :C]
+  end
+
+  # Test expanding the Brusselator.
+  Brusselator = @decapode begin
+    (U, V)::Form0
+    U2V::Form0
+    (U̇, V̇)::Form0
+    (α)::Constant
+    F::Parameter
+    U2V == (U .* U) .* V
+    U̇ == 1 + U2V - (4.4 * U) + (α * Δ(U)) + F
+    V̇ == (3.4 * U) - U2V + (α * Δ(V))
+    ∂ₜ(U) == U̇
+    ∂ₜ(V) == V̇
+  end
+  LHS = @decapode begin
+    y == Δ(X)
+  end
+  RHS = @decapode begin
+    y == -1*∘(d,⋆,d,⋆)(X)
+  end
+  replace_all_op1s!(Brusselator, LHS, RHS)
+  @test Brusselator[:op1] == Any[[:d,:⋆,:d,:⋆], [:d,:⋆,:d,:⋆], :∂ₜ, :∂ₜ]
+
+  # Opening Op2s
+  # ------------
+
+  # Test expanding the interior product.
+  Interior = @decapode begin
+    ∂ₜ(C) == ι(A, B)
+  end
+  LHS = @decapode begin
+    y == ι(X, Z)
+  end
+  RHS = @decapode begin
+    y == -1*⋆((⋆p1) ∧ p2)
+  end
+  replace_all_op2s!(Interior, LHS, RHS)
+  @test Interior == @acset SummationDecapode{Any,Any,Symbol} begin
+    Var = 8
+    TVar = 1
+    Op1 = 3
+    Op2 = 2
+    src = [2, 4, 1]
+    tgt = [5, 3, 8]
+    proj1 = [7, 3]
+    proj2 = [8, 6]
+    res = [5, 1]
+    incl = [5]
+    op1 = [:∂ₜ, :⋆, :⋆]
+    op2 = [:*, :∧]
+    type = [:infer, :infer, :infer, :infer, :infer, :infer, :Literal, :infer]
+    name = [Symbol("•2"), :C, Symbol("•3"), :A, :Ċ, :B, Symbol("-1"), Symbol("•1")]
+  end
+  Interior = @decapode begin
+    ∂ₜ(C) == ι(A, B)
+  end
+  @test replace_all_op2s!(copy(Interior), LHS, RHS) ==
+    replace_all_op2s!(copy(Interior), LHS, RHS,
+      only(incident(RHS, :p1, :name)), only(incident(RHS, :p2, :name)))
+end
+
diff --git a/test/runtests.jl b/test/runtests.jl
index 1e64509..0cb0f30 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -35,3 +35,7 @@ end
 @testset "SummationDecapode Deconstruction" begin
   include("colanguage.jl")
 end
+
+@testset "Open Operators" begin
+  include("openoperators.jl")
+end