{
"cells": [
{
"cell_type": "markdown",
"id": "8c4b0397",
"metadata": {},
"source": [
"# Computational Category Theoretic Rewriting \n",
"### Kris Brown, Evan Patterson, Tyler Hanks, and James Fairbanks\n",
"This notebook accompanies the above paper, showing the code behind the scenes for each of the main figures.\n",
"# WARNING\n",
"This was written prior to the development of [AlgebraicRewriting.jl](https://github.com/AlgebraicJulia/AlgebraicRewriting.jl) which is the recommended way of performing rewriting within [AlgebraicJulia](https://www.algebraicjulia.org/).\n"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "df50d84b",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/code/Computational-Category-Theoretic-Rewriting`\n"
]
}
],
"source": [
"using Pkg; Pkg.activate(\"/Users/ksb/code/Computational-Category-Theoretic-Rewriting\")\n",
"#using Revise, Catlab.CategoricalAlgebra, Catlab.Graphs, Catlab.Present, Catlab.Graphics, Catlab.Theories\n",
"#import Catlab\n",
"#import Catlab.CategoricalAlgebra.CatElements\n",
"#using Catlab.CategoricalAlgebra.FinCats: FinCatGraphEq\n",
"#using CombinatorialSpaces\n",
"#using CombinatorialSpaces.SimplicialSets: get_edge!\n",
"#import AlgebraicPetri\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "5c112b63",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"┌ Info: Precompiling CombinatorialSpaces [b1c52339-7909-45ad-8b6a-6e388f7c67f2]\n",
"└ @ Base loading.jl:1423\n",
"┌ Info: Precompiling AlgebraicPetri [4f99eebe-17bf-4e98-b6a1-2c4f205a959b]\n",
"└ @ Base loading.jl:1423\n"
]
}
],
"source": [
"using Base.Iterators\n",
"using CairoMakie, GeometryBasics\n",
"using CombinatorialSpaces\n",
"import AlgebraicPetri\n",
"using CombinatorialSpaces.SimplicialSets: get_edge!\n",
"using Catlab.CategoricalAlgebra, Catlab.Graphs, Catlab.Present, Catlab.Graphics, Catlab.Theories\n",
"using Catlab.CategoricalAlgebra.FinCats: FinCatGraphEq\n",
"import Catlab \n",
"pres = Catlab.CategoricalAlgebra.CatElements.presentation; # abbreviate long name"
]
},
{
"cell_type": "markdown",
"id": "39592b20",
"metadata": {},
"source": [
"## Figure 1"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "145b2896",
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
"Catlab.Graphics.Graphviz.Graph(\"G\", true, \"dot\", Catlab.Graphics.Graphviz.Statement[Catlab.Graphics.Graphviz.Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1\")), Catlab.Graphics.Graphviz.Node(\"n2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2\")), Catlab.Graphics.Graphviz.Node(\"n3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"3\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n2\", \"\", \"\")], 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(\"n3\", \"\", \"\")], 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(\"n3\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:rankdir => \"LR\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:height => \"0.05\", :margin => \"0\", :shape => \"circle\", :width => \"0.05\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:arrowsize => \"0.5\"))"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"G = @acset Graph begin \n",
" V=3; E=3; \n",
" src=[1,2,2]; \n",
" tgt=[2,3,3] \n",
"end\n",
"to_graphviz(G; node_labels=true)"
]
},
{
"cell_type": "markdown",
"id": "e3f6f05d",
"metadata": {},
"source": [
"## Figure 2\n",
"The declaration of a new $\\mathcal{C}$-set schema and an example instance of that schema."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "0df883a6",
"metadata": {},
"outputs": [
{
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