diff --git a/src/DiagrammaticEquations.jl b/src/DiagrammaticEquations.jl
index 72cada6..558a839 100644
--- a/src/DiagrammaticEquations.jl
+++ b/src/DiagrammaticEquations.jl
@@ -69,9 +69,10 @@ include("graph_traversal.jl")
 include("deca/Deca.jl")
 include("learn/Learn.jl")
 include("SymbolicUtilsInterop.jl")
-include("acset2symbolic.jl")
 
 @reexport using .Deca
 @reexport using .SymbolicUtilsInterop
 
+include("acset2symbolic.jl")
+
 end
diff --git a/src/SymbolicUtilsInterop.jl b/src/SymbolicUtilsInterop.jl
index 61502a8..28bde3f 100644
--- a/src/SymbolicUtilsInterop.jl
+++ b/src/SymbolicUtilsInterop.jl
@@ -14,6 +14,7 @@ struct SymbolicEquation{E}
     lhs::E
     rhs::E
 end
+export SymbolicEquation
 
 Base.show(io::IO, e::SymbolicEquation) = begin
     print(io, e.lhs); print(io, " == "); print(io, e.rhs)
diff --git a/src/acset2symbolic.jl b/src/acset2symbolic.jl
index 0bf24fd..e5edd1c 100644
--- a/src/acset2symbolic.jl
+++ b/src/acset2symbolic.jl
@@ -5,14 +5,16 @@ using SymbolicUtils.Rewriters
 using SymbolicUtils.Code
 using MLStyle
 
-export extract_symexprs, apply_rewrites, merge_equations, to_acset, symbolic_rewriting, symbolics_lookup
+import SymbolicUtils: BasicSymbolic, Symbolic
+
+export symbolics_lookup, extract_symexprs, apply_rewrites, merge_equations, to_acset, symbolic_rewriting, symbolics_lookup
 
 const DECA_EQUALITY_SYMBOL = (==)
 
-to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, SymbolicUtils.BasicSymbolic}, node::TraversalNode) = to_symbolics(d, symvar_lookup, node.index, Val(node.name))
+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, SymbolicUtils.BasicSymbolic}()
+  lookup = Dict{Symbol, BasicSymbolic}()
   for i in parts(d, :Var)
     push!(lookup, d[i, :name] => decavar_to_symbolics(d, i))
   end
@@ -22,80 +24,69 @@ 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)
-  @info new_type
+
   SymbolicUtils.Sym{new_type}(var)
 end
 
-function to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, SymbolicUtils.BasicSymbolic}, op_index::Int, ::Val{:Op1})
+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 = SymbolicUtils.Sym{(SymbolicUtils.FnType){Tuple{Number}, Number}}(d[op_index, :op1])
 
   op_sym = getfield(@__MODULE__, d[op_index, :op1])
 
   S = promote_symtype(op_sym, input_sym)
   rhs = SymbolicUtils.Term{S}(op_sym, [input_sym])
-  SymbolicUtils.Term{Number}(DECA_EQUALITY_SYMBOL, [output_sym, rhs])
+  SymbolicEquation{Symbolic}(output_sym, rhs)
 end
 
-# TODO add promote_symtype as Op1
-function to_symbolics(d::SummationDecapode, symvar_lookup::Dict{Symbol, SymbolicUtils.BasicSymbolic}, op_index::Int, ::Val{:Op2})
+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]]
-  # op_sym = SymbolicUtils.Sym{(SymbolicUtils.FnType){Tuple{Number, Number}, Number}}(d[op_index, :op2])
 
   op_sym = getfield(@__MODULE__, d[op_index, :op2])
 
   S = promote_symtype(op_sym, input1_sym, input2_sym)
   rhs = SymbolicUtils.Term{S}(op_sym, [input1_sym, input2_sym])
-  SymbolicUtils.Term{Number}(DECA_EQUALITY_SYMBOL, [output_sym, rhs])
+  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, SymbolicUtils.BasicSymbolic}, op_index::Int, ::Val{:Σ})
+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]]
 
   # TODO pls test
   S = promote_symtype(+, syms_array...)
   rhs = SymbolicUtils.Term{S}(+, syms_array)
-  SymbolicUtils.Term{Number}(DECA_EQUALITY_SYMBOL, [output_sym, rhs])
+  SymbolicEquation{Symbolic}(output_sym,rhs)
 end
 
-function symbolic_rewriting(old_d::SummationDecapode)
+function symbolic_rewriting(old_d::SummationDecapode, rewriter = nothing)
   d = deepcopy(old_d)
 
   infer_types!(d)
-  # resolve_overloads!(d)
 
   symvar_lookup = symbolics_lookup(d)
-  merge_equations(d, symvar_lookup, extract_symexprs(d, symvar_lookup))
-end
+  eqns = merge_equations(d, symvar_lookup, extract_symexprs(d, symvar_lookup))
 
-function extract_symexprs(d::SummationDecapode, symvar_lookup::Dict{Symbol, SymbolicUtils.BasicSymbolic})
-  topo_list = topological_sort_edges(d)
-  sym_list = []
-  for node in topo_list
-    retrieve_name(d, node) != DerivOp || continue
-    push!(sym_list, to_symbolics(d, symvar_lookup, node))
+  if !isnothing(rewriter)
+    eqns = map(rewriter, eqns)
   end
-  sym_list
-end
 
-function apply_rewrites(symexprs, rewriter)
+  to_acset(d, eqns)
+end
 
-  rewritten_list = []
-  for sym in symexprs
-    res_sym = rewriter(sym)
-    rewritten_sym = isnothing(res_sym) ? sym : res_sym
-    push!(rewritten_list, rewritten_sym)
+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))
   end
-
-  rewritten_list
+  sym_list
 end
 
-function merge_equations(d::SummationDecapode, symvar_lookup::Dict{Symbol, SymbolicUtils.BasicSymbolic}, rewritten_syms)
+function merge_equations(d::SummationDecapode, symvar_lookup::Dict{Symbol, BasicSymbolic}, symexpr_list::Vector{SymbolicEquation{Symbolic}})
 
   eqn_lookup = Dict()
 
@@ -108,22 +99,35 @@ function merge_equations(d::SummationDecapode, symvar_lookup::Dict{Symbol, Symbo
 
   final_nodes = infer_terminal_names(d)
 
-  for expr in rewritten_syms
+  for expr in symexpr_list
 
-    merged_eqn = SymbolicUtils.substitute(expr, eqn_lookup)
-    lhs = merged_eqn.arguments[1]
-    rhs = merged_eqn.arguments[2]
+    merged_rhs = SymbolicUtils.substitute(expr.rhs, eqn_lookup)
 
-    push!(eqn_lookup, (lhs => rhs))
+    push!(eqn_lookup, (expr.lhs => merged_rhs))
 
-    if lhs.name in final_nodes
-      push!(final_list, merged_eqn)
+    if expr.lhs.name in final_nodes
+      push!(final_list, formed_deca_eqn(expr.lhs, merged_rhs))
     end
   end
 
   final_list
 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
+    res_sym = rewriter(sym)
+    rewritten_sym = isnothing(res_sym) ? sym : res_sym
+    push!(rewritten_list, rewritten_sym)
+  end
+
+  rewritten_list
+end
+
+
 function to_acset(og_d, sym_exprs)
   final_exprs = SymbolicUtils.Code.toexpr.(sym_exprs)
 
@@ -159,7 +163,6 @@ function to_acset(og_d, sym_exprs)
   d = SummationDecapode(parse_decapode(deca_block))
 
   infer_types!(d)
-  # resolve_overloads!(d)
 
   d
 end
diff --git a/src/graph_traversal.jl b/src/graph_traversal.jl
index 43b8860..f2875b2 100644
--- a/src/graph_traversal.jl
+++ b/src/graph_traversal.jl
@@ -1,7 +1,7 @@
 using DiagrammaticEquations
 using ACSets
 
-export TraversalNode, topological_sort_edges, number_of_ops, retrieve_name, start_nodes
+export TraversalNode, topological_sort_edges, n_ops, retrieve_name, start_nodes
 
 struct TraversalNode{T}
   index::Int
@@ -20,7 +20,7 @@ function topological_sort_edges(d::SummationDecapode)
   # FIXME: this is a quadratic implementation of topological_sort inlined in here.
   op_order = TraversalNode{Symbol}[]
 
-  for _ in 1:number_of_ops(d)
+  for _ in 1:n_ops(d)
     for op in parts(d, :Op1)
       if !visited_1[op] && visited_Var[d[op, :src]]
 
@@ -49,12 +49,12 @@ function topological_sort_edges(d::SummationDecapode)
     end
   end
 
-  @assert length(op_order) == number_of_ops(d)
+  @assert length(op_order) == n_ops(d)
 
   op_order
 end
 
-function number_of_ops(d::SummationDecapode)
+function n_ops(d::SummationDecapode)
   return nparts(d, :Op1) + nparts(d, :Op2) + nparts(d, :Σ)
 end
 
diff --git a/src/sym_rewrite.jl b/src/sym_rewrite.jl
index 73f4cd9..cec55de 100644
--- a/src/sym_rewrite.jl
+++ b/src/sym_rewrite.jl
@@ -8,9 +8,15 @@ Heat = @decapode begin
   C::Form0
   G::Form1
   D::Constant
-  ∂ₜ(G) == D*Δ(d(C))
+  ∂ₜ(G) == D*Δ(C)
 end;
 infer_types!(Heat)
+test_heat_same = symbolic_rewriting(Heat)
+
+r = rules(Δ, Val(1))
+
+rwr = Fixpoint(Prewalk(Chain(r)))
+test_heat_open = symbolic_rewriting(Heat, rwr)
 
 Brusselator = @decapode begin
   (U, V)::Form0
@@ -35,24 +41,7 @@ Phytodynamics = @decapode begin
   ∂ₜ(n) == w + m*n + Δ(n)
 end
 infer_types!(Phytodynamics)
-test = to_acset(Phytodynamics, symbolic_rewriting(Phytodynamics))
-
-# resolve_overloads!(Heat)
-
-# lap_0_convert = @rule Δ₀(~x) => Δ(~x)
-# lap_1_convert = @rule Δ₁(~x) => Δ(~x)
-# lap_2_convert = @rule Δ₂(~x) => Δ(~x)
-
-# d_0_convert = @rule d₀(~x) => d(~x)
-
-# overloaders = [lap_0_convert, lap_1_convert, lap_2_convert, d_0_convert]
-
-# lap_0_rule = @rule Δ(~x) => ⋆(d(⋆(d(~x))))
-# lap_1_rule = @rule Δ(~x) => d(⋆(d(⋆(~x)))) + ⋆(d(⋆(d(~x))))
-# lap_2_rule = @rule Δ(~x) => d(⋆(d(⋆(~x))))
-
-# openers = [lap_0_rule, lap_1_rule, lap_2_rule]
-
+test_phy = symbolic_rewriting(Phytodynamics)
 
 # it seems that type-instability or improper type promotion is happening. expressions derived from this have BasicSymbolic{Number} type, which means we can't conditionally rewrite on forms.
 heat_exprs = symbolic_rewriting(Heat)
@@ -103,8 +92,6 @@ R1 = @rule Δ(~~x::(x->isForm1(x))) => ★(d(★(d(~x))))
 # pulling out the subexpression
 rewriter = SymbolicUtils.Fixpoint(SymbolicUtils.Prewalk(SymbolicUtils.Chain(r)))
 
-
-
 res_exprs =  apply_rewrites(heat_exprs, rewriter)
 sub_exprs =  apply_rewrites([sub], rewriter)
 
diff --git a/test/graph_traversal.jl b/test/graph_traversal.jl
index 7a5d6ac..b09fd24 100644
--- a/test/graph_traversal.jl
+++ b/test/graph_traversal.jl
@@ -4,7 +4,7 @@ using MLStyle
 using Test
 
 function is_correct_length(d::SummationDecapode, result)
-  return length(result) == number_of_ops(d)
+  return length(result) == n_ops(d)
 end
 
 @testset "Topological Sort on Edges" begin