diff --git a/src/acset2symbolic.jl b/src/acset2symbolic.jl
index ee1898f..8df2d91 100644
--- a/src/acset2symbolic.jl
+++ b/src/acset2symbolic.jl
@@ -11,92 +11,51 @@ export symbolics_lookup, extract_symexprs, apply_rewrites, merge_equations, to_a
 
 const DECA_EQUALITY_SYMBOL = (==)
 
-to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, node::TraversalNode) = to_symbolics(d, symvar_lookup, node.index, Val(node.name))
-
 function symbolics_lookup(d::SummationDecapode)
-  lookup = Dict{Symbol, BasicSymbolic}()
-  for i in parts(d, :Var)
-    push!(lookup, d[i, :name] => decavar_to_symbolics(d, i))
-  end
-  lookup
+  Dict{Symbol, BasicSymbolic}(map(parts(d, :Var)) do i
+    (d[i, :name], decavar_to_symbolics(d, i))
+  end)
 end
 
 function decavar_to_symbolics(d::SummationDecapode, index::Int; space = :I)
-  var = d[index, :name]
   new_type = SymbolicUtils.symtype(Deca.DECQuantity, d[index, :type], space)
-
-  SymbolicUtils.Sym{new_type}(var)
-end
-
-function to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, op_index::Int, ::Val{:Op1})
-  input_sym = symvar_lookup[d[d[op_index, :src], :name]]
-  output_sym = symvar_lookup[d[d[op_index, :tgt], :name]]
-
-  op_sym = getfield(@__MODULE__, d[op_index, :op1])
-
-  S = promote_symtype(op_sym, input_sym)
-  rhs = SymbolicUtils.Term{S}(op_sym, [input_sym])
-  SymbolicEquation{Symbolic}(output_sym, rhs)
+  SymbolicUtils.Sym{new_type}(d[index, :name])
 end
 
-function to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, op_index::Int, ::Val{:Op2})
-  input1_sym = symvar_lookup[d[d[op_index, :proj1], :name]]
-  input2_sym = symvar_lookup[d[d[op_index, :proj2], :name]]
-  output_sym = symvar_lookup[d[d[op_index, :res], :name]]
+function to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, op_index::Int, op_type::Symbol)
+  input_syms = getindex.(Ref(symvar_lookup), d[edge_inputs(d,op_index,Val(op_type)), :name])
+  output_sym = getindex.(Ref(symvar_lookup), d[edge_output(d,op_index,Val(op_type)), :name])
 
-  op_sym = getfield(@__MODULE__, d[op_index, :op2])
+  op_sym = getfield(@__MODULE__, edge_function(d,op_index,Val(op_type)))
 
-  S = promote_symtype(op_sym, input1_sym, input2_sym)
-  rhs = SymbolicUtils.Term{S}(op_sym, [input1_sym, input2_sym])
+  S = promote_symtype(op_sym, input_syms...)
+  rhs = SymbolicUtils.Term{S}(op_sym, input_syms)
   SymbolicEquation{Symbolic}(output_sym, rhs)
 end
 
-#XXX: Always converting + -> .+ here since summation doesn't store the style of addition
-function to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, op_index::Int, ::Val{:Σ})
-  syms_array = [symvar_lookup[var] for var in d[d[incident(d, op_index, :summation), :summand], :name]]
-  output_sym = symvar_lookup[d[d[op_index, :sum], :name]]
-
-  S = promote_symtype(+, syms_array...)
-  rhs = SymbolicUtils.Term{S}(+, syms_array)
-  SymbolicEquation{Symbolic}(output_sym,rhs)
-end
-
 function symbolic_rewriting(old_d::SummationDecapode, rewriter = nothing)
-  d = deepcopy(old_d)
-
-  infer_types!(d)
+  d = infer_types!(deepcopy(old_d))
 
   symvar_lookup = symbolics_lookup(d)
   eqns = merge_equations(d, symvar_lookup, extract_symexprs(d, symvar_lookup))
 
-  if !isnothing(rewriter)
-    eqns = map(rewriter, eqns)
-  end
-
-  to_acset(d, eqns)
+  to_acset(d, isnothing(rewriter) ? eqns : map(rewriter, eqns))
 end
 
 function extract_symexprs(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic})
-  sym_list = SymbolicEquation{Symbolic}[]
-  for node in topological_sort_edges(d)
-    retrieve_name(d, node) != DerivOp || continue # This is not part of ThDEC
-    push!(sym_list, to_symbolics(d, symvar_lookup, node))
+  non_tangents = filter(x -> retrieve_name(d, x) != DerivOp, topological_sort_edges(d))
+  map(non_tangents) do node
+    to_symbolics(d, symvar_lookup, node.index, node.name)
   end
-  sym_list
 end
 
 function merge_equations(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, symexpr_list::Vector{SymbolicEquation{Symbolic}})
-
-  eqn_lookup = Dict()
-
   final_list = []
 
-  for node in start_nodes(d)
+  eqn_lookup = Dict{Any,Any}(map(start_nodes(d)) do node
     sym = symvar_lookup[d[node, :name]]
-    push!(eqn_lookup, (sym => sym))
-  end
-
-  final_nodes = infer_terminal_names(d)
+    (sym, sym)
+  end)
 
   for expr in symexpr_list
 
@@ -112,7 +71,7 @@ function merge_equations(d::SummationDecapode, symvar_lookup::Dict{Symbol, Basic
 
     push!(eqn_lookup, (expr.lhs => merged_rhs))
 
-    if expr.lhs.name in final_nodes
+    if expr.lhs.name in infer_terminal_names(d)
       push!(final_list, formed_deca_eqn(expr.lhs, merged_rhs))
     end
   end
@@ -123,22 +82,13 @@ end
 formed_deca_eqn(lhs, rhs) = SymbolicUtils.Term{Number}(DECA_EQUALITY_SYMBOL, [lhs, rhs])
 
 function apply_rewrites(symexprs, rewriter)
-
-  rewritten_list = []
-  for sym in symexprs
+  map(symexprs) do sym
     res_sym = rewriter(sym)
-    rewritten_sym = isnothing(res_sym) ? sym : res_sym
-    push!(rewritten_list, rewritten_sym)
+    isnothing(res_sym) ? sym : res_sym
   end
-
-  rewritten_list
 end
 
-"""
-og_d = original reference decapode which provides type information, state and terminal information
-"""
-function to_acset(og_d, sym_exprs)
-
+function to_acset(d::SummationDecapode, sym_exprs)
   #TODO: This step is breaking up summations
   final_exprs = SymbolicUtils.Code.toexpr.(sym_exprs)
 
@@ -151,28 +101,18 @@ function to_acset(og_d, sym_exprs)
     end
     sym => nothing
   end
-  map(recursive_descent, final_exprs)
-
-  deca_block = quote end
-
-  states = infer_states(og_d)
-  terminals = infer_terminals(og_d)
+  foreach(recursive_descent, final_exprs)
 
-  deca_type_gen = idx -> :($(og_d[idx, :name])::$(og_d[idx, :type]))
-
-  append!(deca_block.args, map(deca_type_gen, vcat(states, terminals)))
-
-  for op1 in parts(og_d, :Op1)
-    if og_d[op1, :op1] == DerivOp
-      push!(deca_block.args, :($(og_d[og_d[op1, :tgt], :name]) == $DerivOp($(og_d[og_d[op1, :src], :name]))))
-    end
+  states_terminals = map([infer_states(d)..., infer_terminals(d)...]) do idx
+    :($(d[idx, :name])::$(d[idx, :type]))
   end
 
-  append!(deca_block.args, final_exprs)
-
-  d = SummationDecapode(parse_decapode(deca_block))
-
-  infer_types!(d)
+  tangents = map(incident(d, DerivOp, :op1)) do op1
+    :($(d[d[op1, :tgt], :name]) == $DerivOp($(d[d[op1, :src], :name])))
+  end
 
-  d
+  deca_block = quote end
+  deca_block.args = [states_terminals..., tangents..., final_exprs...]
+  infer_types!(SummationDecapode(parse_decapode(deca_block)))
 end
+
diff --git a/src/graph_traversal.jl b/src/graph_traversal.jl
index f2875b2..cc47435 100644
--- a/src/graph_traversal.jl
+++ b/src/graph_traversal.jl
@@ -1,13 +1,34 @@
 using DiagrammaticEquations
 using ACSets
 
-export TraversalNode, topological_sort_edges, n_ops, retrieve_name, start_nodes
+export TraversalNode, topological_sort_edges, n_ops, retrieve_name, start_nodes, edge_inputs, edge_outputs, edge_function
 
 struct TraversalNode{T}
   index::Int
   name::T
 end
 
+edge_inputs(d::SummationDecapode, idx::Int, ::Val{:Op1}) =
+  [d[idx,:src]]
+edge_inputs(d::SummationDecapode, idx::Int, ::Val{:Op2}) =
+  [d[idx,:proj1], d[idx,:proj2]]
+edge_inputs(d::SummationDecapode, idx::Int, ::Val{:Σ}) =
+  d[incident(d, idx, :summation), :summand]
+
+edge_output(d::SummationDecapode, idx::Int, ::Val{:Op1}) =
+  d[idx,:tgt]
+edge_output(d::SummationDecapode, idx::Int, ::Val{:Op2}) =
+  d[idx,:res]
+edge_output(d::SummationDecapode, idx::Int, ::Val{:Σ}) =
+  d[idx, :sum]
+
+edge_function(d::SummationDecapode, idx::Int, ::Val{:Op1}) =
+  d[idx,:op1]
+edge_function(d::SummationDecapode, idx::Int, ::Val{:Op2}) =
+  d[idx,:op2]
+edge_function(d::SummationDecapode, idx::Int, ::Val{:Σ}) =
+  :+
+
 function topological_sort_edges(d::SummationDecapode)
   visited_Var = falses(nparts(d, :Var))
   visited_Var[start_nodes(d)] .= true