{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Drawing wiring diagrams in Compose.jl\n",
    "\n",
    "\n",
    "Catlab can draw wiring diagrams using the Julia package\n",
    "[Compose.jl](https://github.com/GiovineItalia/Compose.jl).\n",
    "\n",
    "For best results, it is recommended to load the packages\n",
    "[Convex.j](https://github.com/JuliaOpt/Convex.jl) and\n",
    "[SCS.jl](https://github.com/JuliaOpt/SCS.jl). When available they are used to\n",
    "optimize the layout of the outer ports."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Catlab.WiringDiagrams, Catlab.Graphics\n",
    "\n",
    "import Convex, SCS"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Examples"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Symmetric monoidal category"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using Catlab.Theories\n",
    "\n",
    "A, B, C, D = Ob(FreeSymmetricMonoidalCategory, :A, :B, :C, :D)\n",
    "f, g = Hom(:f, A, B), Hom(:g, B, A);"
   ],
   "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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     "metadata": {},
     "execution_count": 3
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   ],
   "cell_type": "code",
   "source": [
    "to_composejl(f)"
   ],
   "metadata": {},
   "execution_count": 3
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  {
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     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(f⋅g)"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "outputs": [
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     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(f⊗g)"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here is a more complex example, involving generators with compound domains and\n",
    "codomains."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
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     "metadata": {},
     "execution_count": 6
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   "source": [
    "h, k = Hom(:h, C, D),  Hom(:k, D, C)\n",
    "m, n = Hom(:m, B⊗A, A⊗B), Hom(:n, D⊗C, C⊗D)\n",
    "q = Hom(:l, A⊗B⊗C⊗D, D⊗C⊗B⊗A)\n",
    "\n",
    "to_composejl((f⊗g⊗h⊗k)⋅(m⊗n)⋅q⋅(n⊗m)⋅(h⊗k⊗f⊗g))"
   ],
   "metadata": {},
   "execution_count": 6
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   "cell_type": "markdown",
   "source": [
    "Identities and braidings appear as wires."
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     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(id(A))"
   ],
   "metadata": {},
   "execution_count": 7
  },
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     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(braid(A,B))"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
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   "cell_type": "code",
   "source": [
    "to_composejl(braid(A,B) ⋅ (g⊗f) ⋅ braid(A,B))"
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   "metadata": {},
   "execution_count": 9
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   "source": [
    "The isomorphism $A \\otimes B \\otimes C \\to C \\otimes B \\otimes A$ induced by\n",
    "the permutation $(3\\ 2\\ 1)$ is a composite of braidings and identities."
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     "metadata": {},
     "execution_count": 10
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   ],
   "cell_type": "code",
   "source": [
    "σ = (braid(A,B) ⊗ id(C)) ⋅ (id(B) ⊗ braid(A,C) ⋅ (braid(B,C) ⊗ id(A)))\n",
    "\n",
    "to_composejl(σ)"
   ],
   "metadata": {},
   "execution_count": 10
  },
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    "By default, anchor points are added along identity and braiding wires to\n",
    "reproduce the expression structure in the layout. The anchors can be disabled\n",
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     },
     "metadata": {},
     "execution_count": 11
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(σ, anchor_wires=false)"
   ],
   "metadata": {},
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "source": [
    "### Biproduct category"
   ],
   "metadata": {}
  },
  {
   "outputs": [
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     "metadata": {},
     "execution_count": 12
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   ],
   "cell_type": "code",
   "source": [
    "A, B, C = Ob(FreeBiproductCategory, :A, :B, :C)\n",
    "f = Hom(:f, A, B)\n",
    "\n",
    "to_composejl(mcopy(A))"
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   "metadata": {},
   "execution_count": 12
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     },
     "metadata": {},
     "execution_count": 13
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(delete(A))"
   ],
   "metadata": {},
   "execution_count": 13
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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 14
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(mcopy(A)⋅(f⊗f)⋅mmerge(B))"
   ],
   "metadata": {},
   "execution_count": 14
  },
  {
   "outputs": [
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     "output_type": "execute_result",
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     },
     "metadata": {},
     "execution_count": 15
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(mcopy(A⊗B), orientation=TopToBottom)"
   ],
   "metadata": {},
   "execution_count": 15
  },
  {
   "outputs": [
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   "cell_type": "code",
   "source": [
    "to_composejl(mcopy(A⊗B⊗C), orientation=TopToBottom)"
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   "execution_count": 16
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   "cell_type": "markdown",
   "source": [
    "### Compact closed category"
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  },
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   "cell_type": "markdown",
   "source": [
    "The unit and co-unit of a compact closed category appear as caps and cups."
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     },
     "metadata": {},
     "execution_count": 17
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   "source": [
    "A, B = Ob(FreeCompactClosedCategory, :A, :B)\n",
    "\n",
    "to_composejl(dunit(A))"
   ],
   "metadata": {},
   "execution_count": 17
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     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(dcounit(A))"
   ],
   "metadata": {},
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "source": [
    "In a self-dual compact closed category, such as a bicategory of relations,\n",
    "every morphism $f: A \\to B$ has a transpose $f^\\dagger: B \\to A$ given by\n",
    "bending wires:"
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     },
     "metadata": {},
     "execution_count": 19
    }
   ],
   "cell_type": "code",
   "source": [
    "A, B = Ob(FreeBicategoryRelations, :A, :B)\n",
    "f = Hom(:f, A, B)\n",
    "\n",
    "to_composejl((dunit(A) ⊗ id(B)) ⋅ (id(A) ⊗ f ⊗ id(B)) ⋅ (id(A) ⊗ dcounit(B)))"
   ],
   "metadata": {},
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   "source": [
    "### Abelian bicategory of relations"
   ],
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    "In an abelian bicategory of relations, such as the category of linear\n",
    "relations, the duplication morphisms $\\Delta_X: X \\to X \\oplus X$ and addition\n",
    "morphisms $\\blacktriangledown_X: X \\oplus X \\to X$ belong to a bimonoid. Among\n",
    "other things, this means that the following two morphisms are equal."
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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 20
    }
   ],
   "cell_type": "code",
   "source": [
    "X = Ob(FreeAbelianBicategoryRelations, :X)\n",
    "\n",
    "to_composejl(plus(X) ⋅ mcopy(X))"
   ],
   "metadata": {},
   "execution_count": 20
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
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       "amount2:1-d})};a.filter.invert.toString=function(){return this()};a.filter.brightness=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\"/><feFuncG type=\"linear\" slope=\"{amount}\"/><feFuncB type=\"linear\" slope=\"{amount}\"/></feComponentTransfer>',{amount:d})};a.filter.brightness.toString=function(){return this()};a.filter.contrast=function(d){null==d&&(d=1);return a.format('<feComponentTransfer><feFuncR type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncG type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/><feFuncB type=\"linear\" slope=\"{amount}\" intercept=\"{amount2}\"/></feComponentTransfer>',\n",
       "{amount:d,amount2:0.5-d/2})};a.filter.contrast.toString=function(){return this()}});return C});\n",
       "\n",
       "]]> </script>\n",
       "</svg>\n"
      ],
      "image/svg+xml": [
       "<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n",
       "<svg xmlns=\"http://www.w3.org/2000/svg\"\n",
       "     xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     version=\"1.2\"\n",
       "     width=\"36mm\" height=\"52mm\" viewBox=\"0 0 36 52\"\n",
       "     stroke=\"none\"\n",
       "     fill=\"#000000\"\n",
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       "     font-size=\"3.88\"\n",
       ">\n",
       "<defs>\n",
       "  <marker id=\"arrow\" markerWidth=\"15\" markerHeight=\"7\" refX=\"5\" refY=\"3.5\" orient=\"auto\" markerUnits=\"strokeWidth\">\n",
       "    <path d=\"M0,0 L15,3.5 L0,7 z\" stroke=\"context-stroke\" fill=\"context-stroke\"/>\n",
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       "  <g transform=\"translate(32,38)\">\n",
       "    <path fill=\"none\" d=\"M-4,-0 C0,-0 0,0 4,0\" class=\"primitive\"/>\n",
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       "  <g transform=\"translate(32,14)\">\n",
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       "  </g>\n",
       "</g>\n",
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       "  <g transform=\"translate(18,26)\">\n",
       "    <path fill=\"none\" d=\"M-8.13,11.5 C2.95,5.1 -2.95,-5.1 8.13,-11.5\" class=\"primitive\"/>\n",
       "  </g>\n",
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       "  <g transform=\"translate(18,26)\">\n",
       "    <path fill=\"none\" d=\"M-8.13,-11.5 C2.95,-5.1 -2.95,5.1 8.13,11.5\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-c1173036-5\">\n",
       "  <g transform=\"translate(22.02,10.14)\">\n",
       "    <path fill=\"none\" d=\"M-4.02,-2.14 C0.04,-2.14 -0.13,0.91 4.11,3.36\" class=\"primitive\"/>\n",
       "  </g>\n",
       "  <g transform=\"translate(13.98,10.14)\">\n",
       "    <path fill=\"none\" d=\"M-4.11,3.36 C0.13,0.91 -0.04,-2.14 4.02,-2.14\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-c1173036-6\">\n",
       "  <g transform=\"translate(22.02,41.86)\">\n",
       "    <path fill=\"none\" d=\"M-4.02,2.14 C0.04,2.14 -0.13,-0.91 4.11,-3.36\" class=\"primitive\"/>\n",
       "  </g>\n",
       "  <g transform=\"translate(13.98,41.86)\">\n",
       "    <path fill=\"none\" d=\"M-4.11,-3.36 C0.13,-0.91 -0.04,2.14 4.02,2.14\" class=\"primitive\"/>\n",
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       "  <g transform=\"translate(4,38)\">\n",
       "    <path fill=\"none\" d=\"M-4,0 C0,0 0,-0 4,-0\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-c1173036-8\">\n",
       "  <g transform=\"translate(4,14)\">\n",
       "    <path fill=\"none\" d=\"M-4,-0 C0,-0 0,0 4,0\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g fill=\"#000000\" fill-opacity=\"0.000\" stroke=\"#000000\" id=\"img-c1173036-9\">\n",
       "  <g transform=\"translate(27,38)\">\n",
       "    <circle cx=\"0\" cy=\"0\" r=\"1\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g fill=\"#000000\" fill-opacity=\"0.000\" stroke=\"#000000\" id=\"img-c1173036-10\">\n",
       "  <g transform=\"translate(27,14)\">\n",
       "    <circle cx=\"0\" cy=\"0\" r=\"1\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-c1173036-11\">\n",
       "  <g transform=\"translate(9,38)\">\n",
       "    <circle cx=\"0\" cy=\"0\" r=\"1\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-c1173036-12\">\n",
       "  <g transform=\"translate(9,14)\">\n",
       "    <circle cx=\"0\" cy=\"0\" r=\"1\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 21
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl((mcopy(X)⊕mcopy(X)) ⋅ (id(X)⊕swap(X,X)⊕id(X)) ⋅ (plus(X)⊕plus(X)))"
   ],
   "metadata": {},
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Custom styles"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The visual appearance of wiring diagrams can be customized by passing Compose\n",
    "[properties](http://giovineitalia.github.io/Compose.jl/latest/gallery/properties/)."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "\n",
       "]]> </script>\n",
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      "image/svg+xml": [
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       "     xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     version=\"1.2\"\n",
       "     width=\"40mm\" height=\"16mm\" viewBox=\"0 0 40 16\"\n",
       "     stroke=\"none\"\n",
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       "     font-size=\"3.88\"\n",
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       "    </g>\n",
       "  </g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 22
    }
   ],
   "cell_type": "code",
   "source": [
    "using Compose: fill, stroke\n",
    "\n",
    "A, B, = Ob(FreeSymmetricMonoidalCategory, :A, :B)\n",
    "f, g = Hom(:f, A, B), Hom(:g, B, A)\n",
    "\n",
    "to_composejl(f⋅g, props=Dict(\n",
    "  :box => [fill(\"lavender\"), stroke(\"black\")],\n",
    "))"
   ],
   "metadata": {},
   "execution_count": 22
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "  </g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 23
    }
   ],
   "cell_type": "code",
   "source": [
    "X = Ob(FreeAbelianBicategoryRelations, :X)\n",
    "\n",
    "to_composejl(plus(X) ⋅ mcopy(X), props=Dict(\n",
    "  :junction => [fill(\"red\"), stroke(\"black\")],\n",
    "  :variant_junction => [fill(\"blue\"), stroke(\"black\")],\n",
    "))"
   ],
   "metadata": {},
   "execution_count": 23
  },
  {
   "cell_type": "markdown",
   "source": [
    "The background color can also be changed."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
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       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(f⋅g, background_color=\"lightgray\", props=Dict(\n",
    "  :box => [fill(\"white\"), stroke(\"black\")],\n",
    "))"
   ],
   "metadata": {},
   "execution_count": 24
  },
  {
   "cell_type": "markdown",
   "source": [
    "By default, the boxes are rectangular (`:rectangle`). Other available shapes\n",
    "include circles (`:circle`) and ellipses (`:ellipse`)."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
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       "     xmlns:xlink=\"http://www.w3.org/1999/xlink\"\n",
       "     version=\"1.2\"\n",
       "     width=\"40mm\" height=\"16mm\" viewBox=\"0 0 40 16\"\n",
       "     stroke=\"none\"\n",
       "     fill=\"#000000\"\n",
       "     stroke-width=\"0.3\"\n",
       "     font-size=\"3.88\"\n",
       ">\n",
       "<defs>\n",
       "  <marker id=\"arrow\" markerWidth=\"15\" markerHeight=\"7\" refX=\"5\" refY=\"3.5\" orient=\"auto\" markerUnits=\"strokeWidth\">\n",
       "    <path d=\"M0,0 L15,3.5 L0,7 z\" stroke=\"context-stroke\" fill=\"context-stroke\"/>\n",
       "  </marker>\n",
       "</defs>\n",
       "<g stroke=\"#000000\" id=\"img-441ba1d8-1\">\n",
       "  <g transform=\"translate(36,8)\">\n",
       "    <path fill=\"none\" d=\"M-4,0 C0,0 0,0 4,0\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-441ba1d8-2\">\n",
       "  <g transform=\"translate(20,8)\">\n",
       "    <path fill=\"none\" d=\"M-4,0 C0,0 0,-0 4,-0\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g stroke=\"#000000\" id=\"img-441ba1d8-3\">\n",
       "  <g transform=\"translate(4,8)\">\n",
       "    <path fill=\"none\" d=\"M-4,0 C0,0 0,0 4,0\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g fill=\"#000000\" fill-opacity=\"0.000\" stroke=\"#000000\" id=\"img-441ba1d8-4\">\n",
       "  <g transform=\"translate(28,8)\">\n",
       "    <circle cx=\"0\" cy=\"0\" r=\"4\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g fill=\"#000000\" id=\"img-441ba1d8-5\">\n",
       "  <g transform=\"translate(28,8)\">\n",
       "    <g class=\"primitive\">\n",
       "      <text text-anchor=\"middle\" dy=\"0.35em\">g</text>\n",
       "    </g>\n",
       "  </g>\n",
       "</g>\n",
       "<g fill=\"#000000\" fill-opacity=\"0.000\" stroke=\"#000000\" id=\"img-441ba1d8-6\">\n",
       "  <g transform=\"translate(12,8)\">\n",
       "    <circle cx=\"0\" cy=\"0\" r=\"4\" class=\"primitive\"/>\n",
       "  </g>\n",
       "</g>\n",
       "<g fill=\"#000000\" id=\"img-441ba1d8-7\">\n",
       "  <g transform=\"translate(12,8)\">\n",
       "    <g class=\"primitive\">\n",
       "      <text text-anchor=\"middle\" dy=\"0.35em\">f</text>\n",
       "    </g>\n",
       "  </g>\n",
       "</g>\n",
       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "cell_type": "code",
   "source": [
    "to_composejl(f⋅g, default_box_shape=:circle)"
   ],
   "metadata": {},
   "execution_count": 25
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Output formats"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The function `to_composejl` returns a `ComposePicture` object, which contains\n",
    "a Compose.jl context as well as a recommended width and height. When displayed\n",
    "interactively, this object is rendered using Compose's SVG backend."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "Any backend can be used by calling Compose's `draw` function. The SVG and\n",
    "[PGF](https://ctan.org/pkg/pgf) (LaTeX) backends are always available. To use\n",
    "the PNG or PDF backends, the extra packages\n",
    "[Cairo.jl](https://github.com/JuliaGraphics/Cairo.jl) and\n",
    "[Fontconfig.jl](https://github.com/JuliaGraphics/Fontconfig.jl) must be\n",
    "installed."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "For example, here is how to use the PGF backend."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\\begin{tikzpicture}[x=1mm,y=-1mm]\n",
      "\\definecolor{mycolor000000}{rgb}{0,0,0}\n",
      "\\begin{scope}\n",
      "\\path [fill=mycolor000000,draw=mycolor000000] (32,8) .. controls (36,8) and (36,8) .. (40,8);\n",
      "\\end{scope}\n",
      "\\begin{scope}\n",
      "\\path [fill=mycolor000000,draw=mycolor000000] (16,8) .. controls (20,8) and (20,8) .. (24,8);\n",
      "\\end{scope}\n",
      "\\begin{scope}\n",
      "\\path [fill=mycolor000000,draw=mycolor000000] (0,8) .. controls (4,8) and (4,8) .. (8,8);\n",
      "\\end{scope}\n",
      "\\begin{scope}\n",
      "\\path [fill=mycolor000000,fill opacity=0,draw=mycolor000000] (24,4) rectangle +(8,8);\n",
      "\\end{scope}\n",
      "\\begin{scope}\n",
      "\\draw (28,8) node [text=mycolor000000,rotate around={-0: (0,0)},inner sep=0.0]{\\fontsize{12mm}{14.4mm}\\selectfont $\\text{g}$};\n",
      "\\end{scope}\n",
      "\\begin{scope}\n",
      "\\path [fill=mycolor000000,fill opacity=0,draw=mycolor000000] (8,4) rectangle +(8,8);\n",
      "\\end{scope}\n",
      "\\begin{scope}\n",
      "\\draw (12,8) node [text=mycolor000000,rotate around={-0: (0,0)},inner sep=0.0]{\\fontsize{12mm}{14.4mm}\\selectfont $\\text{f}$};\n",
      "\\end{scope}\n",
      "\\end{tikzpicture}\n",
      "\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "using Compose: draw, PGF\n",
    "\n",
    "pic = to_composejl(f⋅g, rounded_boxes=false)\n",
    "pgf = sprint() do io\n",
    "  pgf_backend = PGF(io, pic.width, pic.height,\n",
    "    false, # emit_on_finish\n",
    "    true,  # only_tikz\n",
    "    texfonts=true)\n",
    "  draw(pgf_backend, pic.context)\n",
    "end\n",
    "println(pgf)"
   ],
   "metadata": {},
   "execution_count": 26
  }
 ],
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  "kernelspec": {
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