{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Layouts versus drawings of wiring diagrams\n",
"\n",
"\n",
"In Catlab, layout and drawing (rendering) of wiring diagrams are mostly\n",
"decoupled. This notebook shows how to lay out diagrams using Graphviz's\n",
"rank-based layout or Catlab's series-parallel layout and then render them\n",
"using Compose.jl or TikZ."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"The morphism we will visualize is:"
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "f⊗(f⋅g)⊗(f⋅g⋅h): X⊗X⊗X → X⊗X⊗X",
"text/latex": "$f \\otimes \\left(f \\cdot g\\right) \\otimes \\left(f \\cdot g \\cdot h\\right) : X \\otimes X \\otimes X \\to X \\otimes X \\otimes X$"
},
"metadata": {},
"execution_count": 1
}
],
"cell_type": "code",
"source": [
"using Catlab.Theories\n",
"\n",
"X = Ob(FreeSymmetricMonoidalCategory, :X)\n",
"f, g, h = (Hom(sym, X, X) for sym in (:f, :g, :h))\n",
"\n",
"expr = otimes(f, compose(f,g), compose(f,g,h))"
],
"metadata": {},
"execution_count": 1
},
{
"cell_type": "markdown",
"source": [
"Let's convert this expression into a wiring diagram. This yields a purely\n",
"combinatorial object, as evidenced by its underlying graph."
],
"metadata": {}
},
{
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "Catlab.WiringDiagrams.DirectedWiringDiagrams.WiringDiagramGraphACSet{Int64} with elements V = 1:8, E = 1:9\n┌───┬─────┐\n│ V │ box │\n├───┼─────┤\n│ 1 │ 1 │\n│ 2 │ 2 │\n│ 3 │ 3 │\n│ 4 │ 4 │\n│ 5 │ 5 │\n│ 6 │ 6 │\n│ 7 │ -2 │\n│ 8 │ -1 │\n└───┴─────┘\n┌───┬─────┬─────┬──────┐\n│ E │ src │ tgt │ wire │\n├───┼─────┼─────┼──────┤\n│ 1 │ 2 │ 3 │ 1 │\n│ 2 │ 5 │ 6 │ 2 │\n│ 3 │ 4 │ 5 │ 3 │\n│ 4 │ 7 │ 1 │ 1 │\n│ 5 │ 7 │ 2 │ 2 │\n│ 6 │ 7 │ 4 │ 3 │\n│ 7 │ 1 │ 8 │ 1 │\n│ 8 │ 3 │ 8 │ 2 │\n│ 9 │ 6 │ 8 │ 3 │\n└───┴─────┴─────┴──────┘\n",
"text/html": [
"\n",
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Catlab.WiringDiagrams.DirectedWiringDiagrams.WiringDiagramGraphACSet{Int64} with elements V = 1:8, E = 1:9\n",
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