Added proof of concept

Added a short script showcasing how rewriting could be done with the `Sort` types and a reference ACSet.

Project.toml

@@ -10,7 +10,6 @@ Catlab = "134e5e36-593f-5add-ad60-77f754baafbe"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
 MLStyle = "d8e11817-5142-5d16-987a-aa16d5891078"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
-Revise = "295af30f-e4ad-537b-8983-00126c2a3abe"
 StructEquality = "6ec83bb0-ed9f-11e9-3b4c-2b04cb4e219c"
 SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Unicode = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"

src/sym_rewrite.jl

@@ -0,0 +1,60 @@
+using DiagrammaticEquations
+using SymbolicUtils
+using MLStyle
+
+test_space = Space(:X, 2)
+
+test_type = Form(0, false, test_space)
+
+Heat = @decapode begin
+  C::Form0
+  D::Constant
+  ∂ₜ(C) == (D+2)*Δ(C)
+end
+
+infer_types!(Heat)
+resolve_overloads!(Heat)
+
+function oldtype_to_new(old::Symbol, space::Space = Space(:I, 2))::Sort
+  @match old begin
+    :Form0 => PrimalForm(0, space)
+    :Form1 => PrimalForm(1, space)
+    :Form2 => PrimalForm(2, space)
+
+    :DualForm0 => DualForm(0, space)
+    :DualForm1 => DualForm(1, space)
+    :DualForm2 => DualForm(2, space)
+
+    :Constant => Scalar()
+    :Parameter => Scalar()
+  end
+end
+
+function isform_zero(x)
+  getmetadata(x, Sort).dim == 0
+end
+
+function isform_two(x)
+  getmetadata(x, Sort).dim == 2
+end
+
+@syms Δ(x) d(x) ⋆(x)
+
+@syms C D Ċ sum_1
+
+C = setmetadata(C, Sort, oldtype_to_new(Heat[1, :type]))
+
+lap_0_rule = @rule Δ(~x::(isform_zero)) => ⋆(d(⋆(d(~x))))
+lap_2_rule = @rule Δ(~x::(isform_two)) => d(⋆(d(⋆(~x))))
+
+test_eq = Δ(C)
+lap_0_rule(test_eq)
+lap_2_rule(test_eq) === nothing
+
+rewriter = SymbolicUtils.Postwalk(SymbolicUtils.Chain([lap_0_rule]))
+test_eq_long = (D + 2) * Δ(C)
+rewriter(test_eq_long)
+
+# Δ₀(x) = ⋆₀⁻¹(dual_d₁(⋆₁(d₀(x))))
+# @syms Δ₀(x) d₀(x) ⋆₁(x) dual_d₁(x) ⋆₀⁻¹(x)
+# lap_0_rule = @rule Δ₀(~x::(isform_zero)) => ⋆₀⁻¹(dual_d₁(⋆₁(d₀(~x))))