v0.13.5/generated/graphics/graphviz_wiring_diagrams.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Drawing wiring diagrams in Graphviz\n",
    "\n",
    "\n",
    "Catlab can draw wiring diagrams using [Graphviz](https://www.graphviz.org/).\n",
    "Directed wiring diagrams are drawn using the `dot` program and undirected\n",
    "wiring diagrams using `neato` and `fdp`. This feature requires that Graphviz\n",
    "be installed, but does not require any additional Julia packages."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Catlab.WiringDiagrams, Catlab.Graphics"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Directed wiring diagrams"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Symmetric monoidal category"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Catlab.Theories\n",
    "\n",
    "A, B = Ob(FreeSymmetricMonoidalCategory, :A, :B)\n",
    "f = Hom(:f, A, B)\n",
    "g = Hom(:g, B, A)\n",
    "h = Hom(:h, otimes(A,B), otimes(A,B));"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "To start, here are a few very simple examples."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
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   "execution_count": 3
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       "<title>n0in2:s&#45;&gt;n2:n</title>\n",
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       "<!-- n0out1 -->\n",
       "<!-- n0out2 -->\n",
       "<!-- n0out1&#45;&gt;n0out2 -->\n",
       "<!-- n1&#45;&gt;n0out1 -->\n",
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       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(otimes(f,g))"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "In the next example, notice how Graphviz automatically \"untwists\" the double\n",
    "braiding to minimize edge crossings."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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     "metadata": {},
     "execution_count": 6
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   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(compose(braid(A,A), otimes(f,f), braid(B,B)))"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here is a larger composite morphism."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "<!-- n0in1&#45;&gt;n0in2 -->\n",
       "<!-- n1 -->\n",
       "<!-- g -->\n",
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       "<!-- n0in1&#45;&gt;n1 -->\n",
       "<!-- B -->\n",
       "<g id=\"e1\" class=\"edge\">\n",
       "<title>n0in1:s&#45;&gt;n1:n</title>\n",
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       "<!-- n2 -->\n",
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       "<!-- n0in2&#45;&gt;n2 -->\n",
       "<!-- A -->\n",
       "<g id=\"e2\" class=\"edge\">\n",
       "<title>n0in2:s&#45;&gt;n2:n</title>\n",
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       "<!-- n0out1 -->\n",
       "<!-- n0out2 -->\n",
       "<!-- n0out1&#45;&gt;n0out2 -->\n",
       "<!-- n3 -->\n",
       "<!-- h -->\n",
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       "<!-- n1&#45;&gt;n3 -->\n",
       "<!-- A -->\n",
       "<g id=\"e6\" class=\"edge\">\n",
       "<title>n1:s&#45;&gt;n3:n</title>\n",
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       "<!-- n2&#45;&gt;n3 -->\n",
       "<!-- B -->\n",
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       "<g id=\"e4\" class=\"edge\">\n",
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       "<!-- B -->\n",
       "<g id=\"e3\" class=\"edge\">\n",
       "<title>n3:s&#45;&gt;n5:n</title>\n",
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       "</g>\n",
       "<!-- n4&#45;&gt;n0out1 -->\n",
       "<!-- B -->\n",
       "<g id=\"e7\" class=\"edge\">\n",
       "<title>n4:s&#45;&gt;n0out1:n</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"13.75,-6 12,-1 10.25,-6 13.75,-6\"/>\n",
       "</g>\n",
       "<!-- n5&#45;&gt;n0out2 -->\n",
       "<!-- A -->\n",
       "<g id=\"e8\" class=\"edge\">\n",
       "<title>n5:s&#45;&gt;n0out2:n</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M54,-37C54,-22.88 54,-18.1 54,-6.17\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"55.75,-6 54,-1 52.25,-6 55.75,-6\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "composite = compose(otimes(g,f), h, otimes(f,g))\n",
    "to_graphviz(composite)"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "By default, the wiring diagram is laid out from top to bottom. Other layout\n",
    "orientations can be requested, such as left-to-right or bottom-to-top:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "<title>n4:e&#45;&gt;n0out1:w</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"200,-56.25 205,-54.5 200,-52.75 200,-56.25\"/>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"199.99,-14.21 205,-12.5 200.01,-10.71 199.99,-14.21\"/>\n",
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       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(composite, orientation=LeftToRight)"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(composite, orientation=BottomToTop)"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "When working with very large diagrams (larger than the ones shown here), it is\n",
    "sometimes convenient to omit the ports of the outer box and any wires attached\n",
    "to them."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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     "metadata": {},
     "execution_count": 10
    }
   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(composite, outer_ports=false)"
   ],
   "metadata": {},
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Biproduct category"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "A, B = Ob(FreeBiproductCategory, :A, :B)\n",
    "f = Hom(:f, A, B)\n",
    "g = Hom(:g, B, A);"
   ],
   "metadata": {},
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "source": [
    "By default, copies and merges are drawn the way they are represented\n",
    "internally, as multiple wires."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
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     "metadata": {},
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   ],
   "cell_type": "code",
   "source": [
    "f1 = compose(mcopy(A), otimes(f,f))\n",
    "to_graphviz(f1)"
   ],
   "metadata": {},
   "execution_count": 12
  },
  {
   "outputs": [
    {
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   "source": [
    "f2 = compose(mcopy(A), otimes(f,f), mmerge(B))\n",
    "to_graphviz(f2)"
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   "metadata": {},
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "source": [
    "To draw nodes for copies and merges, we need to add junctions to the wiring\n",
    "diagram."
   ],
   "metadata": {}
  },
  {
   "outputs": [
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   "cell_type": "code",
   "source": [
    "to_graphviz(add_junctions!(to_wiring_diagram(f1)))"
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   "metadata": {},
   "execution_count": 14
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     "metadata": {},
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   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(add_junctions!(to_wiring_diagram(f2)))"
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   "metadata": {},
   "execution_count": 15
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  {
   "cell_type": "markdown",
   "source": [
    "### Traced monoidal category"
   ],
   "metadata": {}
  },
  {
   "outputs": [
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     "output_type": "execute_result",
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    "A, B, X, Y = Ob(FreeTracedMonoidalCategory, :A, :B, :X, :Y)\n",
    "f = Hom(:f, otimes(X,A), otimes(X,B))\n",
    "\n",
    "to_graphviz(trace(X, A, B, f))"
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   "metadata": {},
   "execution_count": 16
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     "metadata": {},
     "execution_count": 17
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   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(trace(X, A, B, f), orientation=LeftToRight)"
   ],
   "metadata": {},
   "execution_count": 17
  },
  {
   "outputs": [
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   ],
   "cell_type": "code",
   "source": [
    "g, h = Hom(:g, A, A), Hom(:h, B, B)\n",
    "\n",
    "trace_naturality = trace(X, A, B, compose(otimes(id(X),g), f, otimes(id(X),h)))\n",
    "to_graphviz(trace_naturality, orientation=LeftToRight)"
   ],
   "metadata": {},
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Undirected wiring diagrams"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The composite of two binary relations:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
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     "metadata": {},
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   ],
   "cell_type": "code",
   "source": [
    "using Catlab.Programs: @relation\n",
    "\n",
    "diagram = @relation (x,z) where (x,y,z) begin\n",
    "    R(x,y)\n",
    "    S(y,z)\n",
    "end\n",
    "to_graphviz(diagram, box_labels=:name)"
   ],
   "metadata": {},
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "source": [
    "A \"wheel\"-shaped composition of relations:"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Catlab.Graphics.Graphviz.Graph(\"G\", false, \"neato\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"box1\", :label => \"R\")), Catlab.Graphics.Graphviz.Node(\"n2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"box2\", :label => \"S\")), Catlab.Graphics.Graphviz.Node(\"n3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"box3\", :label => \"T\")), Catlab.Graphics.Graphviz.Node(\"n4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:height => \"0\", :id => \"outer1\", :label => \"\", :margin => \"0\", :shape => \"none\", :style => \"invis\", :width => \"0\")), Catlab.Graphics.Graphviz.Node(\"n5\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:height => \"0\", :id => 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       "<!-- n9 -->\n",
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       "</g>\n",
       "<!-- n10 -->\n",
       "<!-- junction -->\n",
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       "<title>n3&#45;&#45;n10</title>\n",
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       "<!-- n4 -->\n",
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       "<path fill=\"none\" stroke=\"black\" d=\"M1.32,-161.76C5.44,-159.72 24.11,-150.48 30.96,-147.09\"/>\n",
       "</g>\n",
       "<!-- n5 -->\n",
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       "<title>n5&#45;&#45;n9</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M197.07,-181.84C193.36,-179.12 176.59,-166.78 170.43,-162.25\"/>\n",
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       "<!-- n6 -->\n",
       "<!-- n6&#45;&#45;n10 -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>n6&#45;&#45;n10</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M118.93,-1.4C118.17,-5.94 114.71,-26.48 113.44,-34.02\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "cell_type": "code",
   "source": [
    "diagram = @relation (x,y,z) where (w,x,y,z) begin\n",
    "    R(x,w)\n",
    "    S(y,w)\n",
    "    T(z,w)\n",
    "end\n",
    "to_graphviz(diagram, box_labels=:name)"
   ],
   "metadata": {},
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "source": [
    "As these examples show, the `box_labels` keyword argument specifies the data\n",
    "attribute of boxes to use for box labels, if any. The boolean argument\n",
    "`port_labels` controls the labeling of ports by numerical values and the\n",
    "argument `junction_labels` specifies the data attribute of junctions to use\n",
    "for junction labels. Note that the macro `@relation` creates wiring diagrams\n",
    "with `name` attribute for boxes and `variable` attribute for junctions."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "<g id=\"junction4\" class=\"node\">\n",
       "<title>n10</title>\n",
       "<ellipse fill=\"black\" stroke=\"black\" cx=\"112.97\" cy=\"-36.81\" rx=\"2.5\" ry=\"2.5\"/>\n",
       "<text text-anchor=\"middle\" x=\"106.47\" y=\"-43.11\" font-family=\"Serif\" font-size=\"14.00\">z</text>\n",
       "</g>\n",
       "<!-- n3&#45;&#45;n10 -->\n",
       "<g id=\"edge8\" class=\"edge\">\n",
       "<title>n3&#45;&#45;n10</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M111.07,-56.49C111.72,-49.83 112.37,-43.03 112.72,-39.43\"/>\n",
       "</g>\n",
       "<!-- n4 -->\n",
       "<!-- n4&#45;&#45;n8 -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>n4&#45;&#45;n8</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M1.32,-161.76C5.44,-159.72 24.11,-150.48 30.96,-147.09\"/>\n",
       "</g>\n",
       "<!-- n5 -->\n",
       "<!-- n5&#45;&#45;n9 -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>n5&#45;&#45;n9</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M197.07,-181.84C193.36,-179.12 176.59,-166.78 170.43,-162.25\"/>\n",
       "</g>\n",
       "<!-- n6 -->\n",
       "<!-- n6&#45;&#45;n10 -->\n",
       "<g id=\"edge9\" class=\"edge\">\n",
       "<title>n6&#45;&#45;n10</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M118.93,-1.4C118.17,-5.94 114.71,-26.48 113.44,-34.02\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(diagram, box_labels=:name,\n",
    "            port_labels=false, junction_labels=:variable)"
   ],
   "metadata": {},
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "source": [
    "By default, all junctions are shown. The keyword argument `implicit_junctions`\n",
    "omits any junctions which have exactly two incident ports."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Catlab.Graphics.Graphviz.Graph(\"G\", false, \"neato\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"box1\", :label => \"R\")), Catlab.Graphics.Graphviz.Node(\"n2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"box2\", :label => \"S\")), Catlab.Graphics.Graphviz.Node(\"n3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"box3\", :label => \"T\")), Catlab.Graphics.Graphviz.Node(\"n4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:height => \"0\", :id => \"outer1\", :label => \"\", :margin => \"0\", :shape => \"none\", :style => \"invis\", :width => \"0\")), Catlab.Graphics.Graphviz.Node(\"n5\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:height => \"0\", :id => \"outer2\", :label => \"\", :margin => \"0\", :shape => \"none\", :style => \"invis\", :width => \"0\")), Catlab.Graphics.Graphviz.Node(\"n6\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:height => \"0\", :id => \"outer3\", :label => \"\", :margin => \"0\", :shape => \"none\", :style => \"invis\", :width => \"0\")), Catlab.Graphics.Graphviz.Node(\"n7\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"junction\", :fillcolor => \"black\", :height => \"0.075\", :id => \"junction1\", :label => \"\", :shape => \"circle\", :style => \"filled\", :width => \"0.075\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n7\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}()), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n7\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}()), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n7\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}()), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n4\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}()), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n5\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}()), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n6\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :shape => \"ellipse\", :margin => \"0.05,0.025\", :width => \"0.5\", :height => \"0.5\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :len => \"0.5\"))",
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.43.0 (0)\n",
       " -->\n",
       "<!-- Title: G Pages: 1 -->\n",
       "<svg width=\"139pt\" height=\"135pt\"\n",
       " viewBox=\"0.00 0.00 139.34 134.56\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 130.56)\">\n",
       "<title>G</title>\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-130.56 135.34,-130.56 135.34,4 -4,4\"/>\n",
       "<!-- n1 -->\n",
       "<g id=\"box1\" class=\"node\">\n",
       "<title>n1</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"35.42\" cy=\"-88.53\" rx=\"18\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"35.42\" y=\"-84.83\" font-family=\"Serif\" font-size=\"14.00\">R</text>\n",
       "</g>\n",
       "<!-- n4 -->\n",
       "<!-- n1&#45;&#45;n4 -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>n1&#45;&#45;n4</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M18.37,-94.74C11.17,-97.36 3.87,-100.02 1.39,-100.92\"/>\n",
       "</g>\n",
       "<!-- n7 -->\n",
       "<!-- junction -->\n",
       "<g id=\"junction1\" class=\"node\">\n",
       "<title>n7</title>\n",
       "<ellipse fill=\"black\" stroke=\"black\" cx=\"72.89\" cy=\"-75.73\" rx=\"2.5\" ry=\"2.5\"/>\n",
       "</g>\n",
       "<!-- n1&#45;&#45;n7 -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>n1&#45;&#45;n7</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M52.84,-82.58C59.56,-80.28 66.52,-77.9 70.21,-76.64\"/>\n",
       "</g>\n",
       "<!-- n2 -->\n",
       "<g id=\"box2\" class=\"node\">\n",
       "<title>n2</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"102.77\" cy=\"-101.68\" rx=\"18\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"102.77\" y=\"-97.98\" font-family=\"Serif\" font-size=\"14.00\">S</text>\n",
       "</g>\n",
       "<!-- n5 -->\n",
       "<!-- n2&#45;&#45;n5 -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>n2&#45;&#45;n5</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M116.48,-113.58C122.27,-118.61 128.13,-123.7 130.13,-125.44\"/>\n",
       "</g>\n",
       "<!-- n2&#45;&#45;n7 -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>n2&#45;&#45;n7</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M88.88,-89.62C83.51,-84.96 77.97,-80.14 75.02,-77.58\"/>\n",
       "</g>\n",
       "<!-- n3 -->\n",
       "<g id=\"box3\" class=\"node\">\n",
       "<title>n3</title>\n",
       "<ellipse fill=\"none\" stroke=\"black\" cx=\"80.29\" cy=\"-36.83\" rx=\"18\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"80.29\" y=\"-33.13\" font-family=\"Serif\" font-size=\"14.00\">T</text>\n",
       "</g>\n",
       "<!-- n6 -->\n",
       "<!-- n3&#45;&#45;n6 -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>n3&#45;&#45;n6</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M84.12,-19.09C85.8,-11.31 87.5,-3.42 87.99,-1.15\"/>\n",
       "</g>\n",
       "<!-- n3&#45;&#45;n7 -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>n3&#45;&#45;n7</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M76.85,-54.91C75.49,-62.05 74.08,-69.44 73.37,-73.2\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "cell_type": "code",
   "source": [
    "to_graphviz(diagram, box_labels=:name,\n",
    "            port_labels=false, implicit_junctions=true)"
   ],
   "metadata": {},
   "execution_count": 22
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Custom styles"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The visual appearance of wiring diagrams can be customized by setting Graphviz\n",
    "[attributes](https://www.graphviz.org/doc/info/attrs.html) at the graph, node,\n",
    "edge, and cell levels. Graph, node, and edge attributes are described in the\n",
    "Graphviz documentation. Cell attributes are passed to the primary cell of the\n",
    "[HTML-like label](https://www.graphviz.org/doc/info/shapes.html#html) used for\n",
    "the boxes."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"dot\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Subgraph(\"\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n0in1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"in1\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rank => \"source\", :rankdir => \"LR\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\", :shape => \"none\", :label => \"\", :width => \"0.333\", :height => \"0\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\")), Catlab.Graphics.Graphviz.Subgraph(\"\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n0out1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:id => \"out1\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rank => \"sink\", :rankdir => \"LR\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\", :shape => \"none\", :label => \"\", :width => \"0.333\", :height => \"0\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:style => \"invis\")), Catlab.Graphics.Graphviz.Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:color => \"black\", :comment => \"f\", :fillcolor => \"white\", :id => \"n1\", :label => Catlab.Graphics.Graphviz.Html(\"<TABLE BORDER=\\\"0\\\" CELLPADDING=\\\"0\\\" CELLSPACING=\\\"0\\\">\\n<TR><TD><TABLE BORDER=\\\"0\\\" CELLPADDING=\\\"0\\\" CELLSPACING=\\\"0\\\"><TR><TD HEIGHT=\\\"0\\\" WIDTH=\\\"24\\\" PORT=\\\"in1\\\"></TD></TR></TABLE></TD></TR>\\n<TR><TD BORDER=\\\"1\\\" CELLPADDING=\\\"4\\\" BGCOLOR=\\\"lavender\\\">f</TD></TR>\\n<TR><TD><TABLE BORDER=\\\"0\\\" CELLPADDING=\\\"0\\\" CELLSPACING=\\\"0\\\"><TR><TD HEIGHT=\\\"0\\\" WIDTH=\\\"24\\\" PORT=\\\"out1\\\"></TD></TR></TABLE></TD></TR>\\n</TABLE>\"), :style => \"solid\")), Catlab.Graphics.Graphviz.Node(\"n2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:color => \"black\", :comment => \"g\", :fillcolor => \"white\", :id => \"n2\", :label => Catlab.Graphics.Graphviz.Html(\"<TABLE BORDER=\\\"0\\\" CELLPADDING=\\\"0\\\" CELLSPACING=\\\"0\\\">\\n<TR><TD><TABLE BORDER=\\\"0\\\" CELLPADDING=\\\"0\\\" CELLSPACING=\\\"0\\\"><TR><TD HEIGHT=\\\"0\\\" WIDTH=\\\"24\\\" PORT=\\\"in1\\\"></TD></TR></TABLE></TD></TR>\\n<TR><TD BORDER=\\\"1\\\" CELLPADDING=\\\"4\\\" BGCOLOR=\\\"lavender\\\">g</TD></TR>\\n<TR><TD><TABLE BORDER=\\\"0\\\" CELLPADDING=\\\"0\\\" CELLSPACING=\\\"0\\\"><TR><TD HEIGHT=\\\"0\\\" WIDTH=\\\"24\\\" PORT=\\\"out1\\\"></TD></TR></TABLE></TD></TR>\\n</TABLE>\"), :style => \"solid\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n0in1\", \"s\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n1\", \"in1\", \"n\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"A\", :headlabel => \"A\", :id => \"e1\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n1\", \"out1\", \"s\"), Catlab.Graphics.Graphviz.NodeID(\"n2\", \"in1\", \"n\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"B\", :headlabel => \"B\", :id => \"e2\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n2\", \"out1\", \"s\"), Catlab.Graphics.Graphviz.NodeID(\"n0out1\", \"n\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"C\", :headlabel => \"C\", :id => \"e3\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :rankdir => \"TB\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Courier\", :shape => \"none\", :width => \"0\", :height => \"0\", :margin => \"0\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:arrowsize => \"0.5\", :fontname => \"Courier\", :labelangle => \"25\", :labeldistance => \"2\"))",
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
       "<!-- Generated by graphviz version 2.43.0 (0)\n",
       " -->\n",
       "<!-- Title: G Pages: 1 -->\n",
       "<svg width=\"33pt\" height=\"168pt\"\n",
       " viewBox=\"0.00 0.00 32.95 168.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 164)\">\n",
       "<title>G</title>\n",
       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-164 28.95,-164 28.95,4 -4,4\"/>\n",
       "<!-- n0in1 -->\n",
       "<!-- n1 -->\n",
       "<!-- f -->\n",
       "<g id=\"n1\" class=\"node\">\n",
       "<title>n1</title>\n",
       "<polygon fill=\"lavender\" stroke=\"transparent\" points=\"0.95,-97.5 0.95,-122.5 24.95,-122.5 24.95,-97.5 0.95,-97.5\"/>\n",
       "<polygon fill=\"none\" stroke=\"black\" points=\"0.95,-97.5 0.95,-122.5 24.95,-122.5 24.95,-97.5 0.95,-97.5\"/>\n",
       "<text text-anchor=\"start\" x=\"8.45\" y=\"-106.3\" font-family=\"Courier,monospace\" font-size=\"14.00\">f</text>\n",
       "</g>\n",
       "<!-- n0in1&#45;&gt;n1 -->\n",
       "<!-- A -->\n",
       "<g id=\"e1\" class=\"edge\">\n",
       "<title>n0in1:s&#45;&gt;n1:n</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M12.95,-159C12.95,-144.88 12.95,-140.1 12.95,-128.17\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"14.7,-128 12.95,-123 11.2,-128 14.7,-128\"/>\n",
       "<text text-anchor=\"middle\" x=\"4.5\" y=\"-137.43\" font-family=\"Courier,monospace\" font-size=\"14.00\">A</text>\n",
       "</g>\n",
       "<!-- n0out1 -->\n",
       "<!-- n2 -->\n",
       "<!-- g -->\n",
       "<g id=\"n2\" class=\"node\">\n",
       "<title>n2</title>\n",
       "<polygon fill=\"lavender\" stroke=\"transparent\" points=\"0.95,-36.5 0.95,-61.5 24.95,-61.5 24.95,-36.5 0.95,-36.5\"/>\n",
       "<polygon fill=\"none\" stroke=\"black\" points=\"0.95,-36.5 0.95,-61.5 24.95,-61.5 24.95,-36.5 0.95,-36.5\"/>\n",
       "<text text-anchor=\"start\" x=\"8.45\" y=\"-45.3\" font-family=\"Courier,monospace\" font-size=\"14.00\">g</text>\n",
       "</g>\n",
       "<!-- n1&#45;&gt;n2 -->\n",
       "<!-- B -->\n",
       "<g id=\"e2\" class=\"edge\">\n",
       "<title>n1:s&#45;&gt;n2:n</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M12.95,-98C12.95,-83.88 12.95,-79.1 12.95,-67.17\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"14.7,-67 12.95,-62 11.2,-67 14.7,-67\"/>\n",
       "<text text-anchor=\"middle\" x=\"4.5\" y=\"-76.43\" font-family=\"Courier,monospace\" font-size=\"14.00\">B</text>\n",
       "</g>\n",
       "<!-- n2&#45;&gt;n0out1 -->\n",
       "<!-- C -->\n",
       "<g id=\"e3\" class=\"edge\">\n",
       "<title>n2:s&#45;&gt;n0out1:n</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M12.95,-37C12.95,-22.88 12.95,-18.1 12.95,-6.17\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"14.7,-6 12.95,-1 11.2,-6 14.7,-6\"/>\n",
       "<text text-anchor=\"middle\" x=\"4.5\" y=\"-15.43\" font-family=\"Courier,monospace\" font-size=\"14.00\">C</text>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "cell_type": "code",
   "source": [
    "A, B, C = Ob(FreeSymmetricMonoidalCategory, :A, :B, :C)\n",
    "f, g = Hom(:f, A, B), Hom(:g, B, C)\n",
    "\n",
    "to_graphviz(compose(f,g),\n",
    "  labels = true, label_attr=:headlabel,\n",
    "  node_attrs = Dict(\n",
    "    :fontname => \"Courier\",\n",
    "  ),\n",
    "  edge_attrs = Dict(\n",
    "    :fontname => \"Courier\",\n",
    "    :labelangle => \"25\",\n",
    "    :labeldistance => \"2\",\n",
    "  ),\n",
    "  cell_attrs = Dict(\n",
    "    :bgcolor => \"lavender\",\n",
    "  )\n",
    ")"
   ],
   "metadata": {},
   "execution_count": 23
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Output formats"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The function `to_graphviz` returns an object of a type `Graphviz.Graph`,\n",
    "representing a Graphviz graph as an abstract syntax tree. When displayed\n",
    "interactively, this object is automatically run through Graphviz and rendered\n",
    "as an SVG image. Sometimes it is convenient to perform this process manually,\n",
    "to change the output format or further customize the generated dot file."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "To generate a dot file, use the builtin pretty-printer. This feature does not\n",
    "require Graphviz to be installed."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "digraph G {\n",
      "  graph [fontname=\"Serif\",rankdir=\"TB\"];\n",
      "  node [fontname=\"Serif\",shape=\"none\",width=\"0\",height=\"0\",margin=\"0\"];\n",
      "  edge [arrowsize=\"0.5\",fontname=\"Serif\"];\n",
      "  {\n",
      "    graph [rank=\"source\",rankdir=\"LR\"];\n",
      "    node [style=\"invis\",shape=\"none\",label=\"\",width=\"0.333\",height=\"0\"];\n",
      "    edge [style=\"invis\"];\n",
      "    n0in1 [id=\"in1\"];\n",
      "  }\n",
      "  {\n",
      "    graph [rank=\"sink\",rankdir=\"LR\"];\n",
      "    node [style=\"invis\",shape=\"none\",label=\"\",width=\"0.333\",height=\"0\"];\n",
      "    edge [style=\"invis\"];\n",
      "    n0out1 [id=\"out1\"];\n",
      "  }\n",
      "  n1 [color=\"black\",comment=\"f\",fillcolor=\"white\",id=\"n1\",label=<<TABLE BORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\">\n",
      "<TR><TD><TABLE BORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\"><TR><TD HEIGHT=\"0\" WIDTH=\"24\" PORT=\"in1\"></TD></TR></TABLE></TD></TR>\n",
      "<TR><TD BORDER=\"1\" CELLPADDING=\"4\">f</TD></TR>\n",
      "<TR><TD><TABLE BORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\"><TR><TD HEIGHT=\"0\" WIDTH=\"24\" PORT=\"out1\"></TD></TR></TABLE></TD></TR>\n",
      "</TABLE>>,style=\"solid\"];\n",
      "  n2 [color=\"black\",comment=\"g\",fillcolor=\"white\",id=\"n2\",label=<<TABLE BORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\">\n",
      "<TR><TD><TABLE BORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\"><TR><TD HEIGHT=\"0\" WIDTH=\"24\" PORT=\"in1\"></TD></TR></TABLE></TD></TR>\n",
      "<TR><TD BORDER=\"1\" CELLPADDING=\"4\">g</TD></TR>\n",
      "<TR><TD><TABLE BORDER=\"0\" CELLPADDING=\"0\" CELLSPACING=\"0\"><TR><TD HEIGHT=\"0\" WIDTH=\"24\" PORT=\"out1\"></TD></TR></TABLE></TD></TR>\n",
      "</TABLE>>,style=\"solid\"];\n",
      "  n0in1:s -> n1:in1:n [comment=\"A\",id=\"e1\"];\n",
      "  n1:out1:s -> n2:in1:n [comment=\"B\",id=\"e2\"];\n",
      "  n2:out1:s -> n0out1:n [comment=\"C\",id=\"e3\"];\n",
      "}\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "using Catlab.Graphics: Graphviz\n",
    "\n",
    "graph = to_graphviz(compose(f,g))\n",
    "Graphviz.pprint(graph)"
   ],
   "metadata": {},
   "execution_count": 24
  },
  {
   "cell_type": "markdown",
   "source": [
    "Catlab provides a simple wrapper around the Graphviz command-line programs.\n",
    "For example, here is the JSON output for the graph."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Dict{String, Any} with 9 entries:\n  \"name\"          => \"G\"\n  \"strict\"        => false\n  \"bb\"            => \"0,0,24,160\"\n  \"objects\"       => Any[Dict{String, Any}(\"rank\"=>\"source\", \"name\"=>\"%3\", \"nod…\n  \"fontname\"      => \"Serif\"\n  \"rankdir\"       => \"TB\"\n  \"directed\"      => true\n  \"edges\"         => Any[Dict{String, Any}(\"headport\"=>\"in1:n\", \"tail\"=>2, \"hea…\n  \"_subgraph_cnt\" => 2"
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "cell_type": "code",
   "source": [
    "import JSON\n",
    "\n",
    "JSON.parse(Graphviz.run_graphviz(graph, format=\"json0\"))"
   ],
   "metadata": {},
   "execution_count": 25
  }
 ],
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