{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "2c21cdd7", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml`\n" ] } ], "source": [ "using Pkg;\n", "Pkg.activate(\"July7_2023_Project_toml\");" ] }, { "cell_type": "code", "execution_count": 4, "id": "5046ea0a", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n", "\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml/Project.toml`\n", "\u001b[33m⌅\u001b[39m \u001b[90m[725a01d3] \u001b[39m\u001b[92m+ AlgebraicRewriting v0.2.1\u001b[39m\n", "\u001b[33m⌅\u001b[39m \u001b[90m[134e5e36] \u001b[39m\u001b[92m+ Catlab v0.15.5\u001b[39m\n", " \u001b[90m[295af30f] \u001b[39m\u001b[92m+ Revise v3.5.13\u001b[39m\n", "\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml/Manifest.toml`\n", " \u001b[90m[227ef7b5] \u001b[39m\u001b[92m+ ACSets v0.2.13\u001b[39m\n", " \u001b[90m[23cfdc9f] \u001b[39m\u001b[92m+ AlgebraicInterfaces v0.1.1\u001b[39m\n", "\u001b[33m⌅\u001b[39m \u001b[90m[725a01d3] \u001b[39m\u001b[92m+ AlgebraicRewriting v0.2.1\u001b[39m\n", "\u001b[33m⌅\u001b[39m \u001b[90m[134e5e36] \u001b[39m\u001b[92m+ Catlab v0.15.5\u001b[39m\n", " \u001b[90m[da1fd8a2] \u001b[39m\u001b[92m+ CodeTracking v1.3.5\u001b[39m\n", " \u001b[90m[3da002f7] \u001b[39m\u001b[92m+ ColorTypes v0.11.4\u001b[39m\n", " \u001b[90m[5ae59095] \u001b[39m\u001b[92m+ Colors v0.12.10\u001b[39m\n", " \u001b[90m[861a8166] \u001b[39m\u001b[92m+ Combinatorics v1.0.2\u001b[39m\n", " \u001b[90m[0fb5dd42] \u001b[39m\u001b[92m+ CompTime v0.1.2\u001b[39m\n", " \u001b[90m[34da2185] \u001b[39m\u001b[92m+ Compat v4.12.0\u001b[39m\n", " \u001b[90m[a81c6b42] \u001b[39m\u001b[92m+ Compose v0.9.5\u001b[39m\n", " \u001b[90m[a8cc5b0e] \u001b[39m\u001b[92m+ Crayons v4.1.1\u001b[39m\n", " \u001b[90m[9a962f9c] \u001b[39m\u001b[92m+ DataAPI v1.15.0\u001b[39m\n", " \u001b[90m[864edb3b] \u001b[39m\u001b[92m+ DataStructures v0.18.16\u001b[39m\n", " \u001b[90m[e2d170a0] \u001b[39m\u001b[92m+ DataValueInterfaces v1.0.0\u001b[39m\n", " \u001b[90m[53c48c17] \u001b[39m\u001b[92m+ FixedPointNumbers v0.8.4\u001b[39m\n", " \u001b[90m[6b9d7cbe] \u001b[39m\u001b[92m+ GeneralizedGenerated v0.3.3\u001b[39m\n", " \u001b[90m[c8e1da08] \u001b[39m\u001b[92m+ IterTools v1.10.0\u001b[39m\n", " \u001b[90m[82899510] \u001b[39m\u001b[92m+ IteratorInterfaceExtensions v1.0.0\u001b[39m\n", " \u001b[90m[692b3bcd] \u001b[39m\u001b[92m+ JLLWrappers v1.5.0\u001b[39m\n", " \u001b[90m[682c06a0] \u001b[39m\u001b[92m+ JSON v0.21.4\u001b[39m\n", " \u001b[90m[0f8b85d8] \u001b[39m\u001b[92m+ JSON3 v1.14.0\u001b[39m\n", " \u001b[90m[aa1ae85d] \u001b[39m\u001b[92m+ JuliaInterpreter v0.9.28\u001b[39m\n", " \u001b[90m[b14d175d] \u001b[39m\u001b[92m+ JuliaVariables v0.2.4\u001b[39m\n", " \u001b[90m[b964fa9f] \u001b[39m\u001b[92m+ LaTeXStrings v1.3.1\u001b[39m\n", " \u001b[90m[9c8b4983] \u001b[39m\u001b[92m+ LightXML v0.9.1\u001b[39m\n", " \u001b[90m[6f1432cf] \u001b[39m\u001b[92m+ LoweredCodeUtils v2.4.3\u001b[39m\n", " \u001b[90m[d8e11817] \u001b[39m\u001b[92m+ MLStyle v0.4.17\u001b[39m\n", " \u001b[90m[1914dd2f] \u001b[39m\u001b[92m+ MacroTools v0.5.12\u001b[39m\n", " \u001b[90m[442fdcdd] \u001b[39m\u001b[92m+ Measures v0.3.2\u001b[39m\n", " \u001b[90m[71a1bf82] \u001b[39m\u001b[92m+ NameResolution v0.1.5\u001b[39m\n", " \u001b[90m[bac558e1] \u001b[39m\u001b[92m+ OrderedCollections v1.6.3\u001b[39m\n", " \u001b[90m[69de0a69] \u001b[39m\u001b[92m+ Parsers v2.8.1\u001b[39m\n", " \u001b[90m[2ae35dd2] \u001b[39m\u001b[92m+ Permutations v0.4.19\u001b[39m\n", " \u001b[90m[aea7be01] \u001b[39m\u001b[92m+ PrecompileTools v1.2.0\u001b[39m\n", " \u001b[90m[21216c6a] \u001b[39m\u001b[92m+ Preferences v1.4.1\u001b[39m\n", " \u001b[90m[8162dcfd] \u001b[39m\u001b[92m+ PrettyPrint v0.2.0\u001b[39m\n", " \u001b[90m[08abe8d2] \u001b[39m\u001b[92m+ PrettyTables v2.3.1\u001b[39m\n", " \u001b[90m[189a3867] \u001b[39m\u001b[92m+ Reexport v1.2.2\u001b[39m\n", " \u001b[90m[ae029012] \u001b[39m\u001b[92m+ Requires v1.3.0\u001b[39m\n", " \u001b[90m[295af30f] \u001b[39m\u001b[92m+ Revise v3.5.13\u001b[39m\n", " \u001b[90m[90137ffa] \u001b[39m\u001b[92m+ StaticArrays v1.9.1\u001b[39m\n", " \u001b[90m[1e83bf80] \u001b[39m\u001b[92m+ StaticArraysCore v1.4.2\u001b[39m\n", " \u001b[90m[892a3eda] \u001b[39m\u001b[92m+ StringManipulation v0.3.4\u001b[39m\n", " \u001b[90m[6ec83bb0] \u001b[39m\u001b[92m+ StructEquality v2.1.0\u001b[39m\n", " \u001b[90m[856f2bd8] \u001b[39m\u001b[92m+ StructTypes v1.10.0\u001b[39m\n", " \u001b[90m[3783bdb8] \u001b[39m\u001b[92m+ TableTraits v1.0.1\u001b[39m\n", " \u001b[90m[bd369af6] \u001b[39m\u001b[92m+ Tables v1.11.1\u001b[39m\n", " \u001b[90m[94ce4f54] \u001b[39m\u001b[92m+ Libiconv_jll v1.17.0+0\u001b[39m\n", " \u001b[90m[02c8fc9c] \u001b[39m\u001b[92m+ XML2_jll v2.12.2+0\u001b[39m\n", " \u001b[90m[0dad84c5] \u001b[39m\u001b[92m+ ArgTools v1.1.1\u001b[39m\n", " \u001b[90m[56f22d72] \u001b[39m\u001b[92m+ Artifacts\u001b[39m\n", " \u001b[90m[2a0f44e3] \u001b[39m\u001b[92m+ Base64\u001b[39m\n", " \u001b[90m[ade2ca70] \u001b[39m\u001b[92m+ Dates\u001b[39m\n", " \u001b[90m[8ba89e20] \u001b[39m\u001b[92m+ Distributed\u001b[39m\n", " \u001b[90m[f43a241f] \u001b[39m\u001b[92m+ Downloads v1.6.0\u001b[39m\n", " \u001b[90m[7b1f6079] \u001b[39m\u001b[92m+ FileWatching\u001b[39m\n", " \u001b[90m[b77e0a4c] \u001b[39m\u001b[92m+ InteractiveUtils\u001b[39m\n", " \u001b[90m[b27032c2] \u001b[39m\u001b[92m+ LibCURL v0.6.3\u001b[39m\n", " \u001b[90m[76f85450] \u001b[39m\u001b[92m+ LibGit2\u001b[39m\n", " \u001b[90m[8f399da3] \u001b[39m\u001b[92m+ Libdl\u001b[39m\n", " \u001b[90m[37e2e46d] \u001b[39m\u001b[92m+ LinearAlgebra\u001b[39m\n", " \u001b[90m[56ddb016] \u001b[39m\u001b[92m+ Logging\u001b[39m\n", " \u001b[90m[d6f4376e] \u001b[39m\u001b[92m+ Markdown\u001b[39m\n", " \u001b[90m[a63ad114] \u001b[39m\u001b[92m+ Mmap\u001b[39m\n", " \u001b[90m[ca575930] \u001b[39m\u001b[92m+ NetworkOptions v1.2.0\u001b[39m\n", " \u001b[90m[44cfe95a] \u001b[39m\u001b[92m+ Pkg v1.9.2\u001b[39m\n", " \u001b[90m[de0858da] \u001b[39m\u001b[92m+ Printf\u001b[39m\n", " \u001b[90m[3fa0cd96] \u001b[39m\u001b[92m+ REPL\u001b[39m\n", " \u001b[90m[9a3f8284] \u001b[39m\u001b[92m+ Random\u001b[39m\n", " \u001b[90m[ea8e919c] \u001b[39m\u001b[92m+ SHA v0.7.0\u001b[39m\n", " \u001b[90m[9e88b42a] \u001b[39m\u001b[92m+ Serialization\u001b[39m\n", " \u001b[90m[6462fe0b] \u001b[39m\u001b[92m+ Sockets\u001b[39m\n", " \u001b[90m[2f01184e] \u001b[39m\u001b[92m+ SparseArrays\u001b[39m\n", " \u001b[90m[10745b16] \u001b[39m\u001b[92m+ Statistics v1.9.0\u001b[39m\n", " \u001b[90m[fa267f1f] \u001b[39m\u001b[92m+ TOML v1.0.3\u001b[39m\n", " \u001b[90m[a4e569a6] \u001b[39m\u001b[92m+ Tar v1.10.0\u001b[39m\n", " \u001b[90m[8dfed614] \u001b[39m\u001b[92m+ Test\u001b[39m\n", " \u001b[90m[cf7118a7] \u001b[39m\u001b[92m+ UUIDs\u001b[39m\n", " \u001b[90m[4ec0a83e] \u001b[39m\u001b[92m+ Unicode\u001b[39m\n", " \u001b[90m[e66e0078] \u001b[39m\u001b[92m+ CompilerSupportLibraries_jll v1.0.5+0\u001b[39m\n", " \u001b[90m[deac9b47] \u001b[39m\u001b[92m+ LibCURL_jll v7.84.0+0\u001b[39m\n", " \u001b[90m[29816b5a] \u001b[39m\u001b[92m+ LibSSH2_jll v1.10.2+0\u001b[39m\n", " \u001b[90m[c8ffd9c3] \u001b[39m\u001b[92m+ MbedTLS_jll v2.28.2+0\u001b[39m\n", " \u001b[90m[14a3606d] \u001b[39m\u001b[92m+ MozillaCACerts_jll v2022.10.11\u001b[39m\n", " \u001b[90m[4536629a] \u001b[39m\u001b[92m+ OpenBLAS_jll v0.3.21+4\u001b[39m\n", " \u001b[90m[bea87d4a] \u001b[39m\u001b[92m+ SuiteSparse_jll v5.10.1+6\u001b[39m\n", " \u001b[90m[83775a58] \u001b[39m\u001b[92m+ Zlib_jll v1.2.13+0\u001b[39m\n", " \u001b[90m[8e850b90] \u001b[39m\u001b[92m+ libblastrampoline_jll v5.8.0+0\u001b[39m\n", " \u001b[90m[8e850ede] \u001b[39m\u001b[92m+ nghttp2_jll v1.48.0+0\u001b[39m\n", " \u001b[90m[3f19e933] \u001b[39m\u001b[92m+ p7zip_jll v17.4.0+0\u001b[39m\n", "\u001b[36m\u001b[1m Info\u001b[22m\u001b[39m Packages marked with \u001b[33m⌅\u001b[39m have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`\n", "\u001b[32m\u001b[1mPrecompiling\u001b[22m\u001b[39m project...\n", "\u001b[32m ✓ \u001b[39mCatlab\n", "\u001b[32m ✓ \u001b[39mAlgebraicRewriting\n", " 2 dependencies successfully precompiled in 31 seconds. 56 already precompiled.\n", "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n", "\u001b[32m\u001b[1m Updating\u001b[22m\u001b[39m `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml/Project.toml`\n", " \u001b[90m[6ec83bb0] \u001b[39m\u001b[92m+ StructEquality v2.1.0\u001b[39m\n", "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml/Manifest.toml`\n", "\u001b[32m\u001b[1m Resolving\u001b[22m\u001b[39m package versions...\n", "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml/Project.toml`\n", "\u001b[32m\u001b[1m No Changes\u001b[22m\u001b[39m to `~/Usask/Research/CategoryTheory/ABMs/act-abm/July7_2023_Project_toml/Manifest.toml`\n" ] } ], "source": [ "import Pkg; Pkg.add(\"Revise\")\n", "import Pkg; Pkg.add(\"StructEquality\")\n", "import Pkg; Pkg.add(\"AlgebraicRewriting\")" ] }, { "cell_type": "code", "execution_count": 5, "id": "66492f3a", "metadata": {}, "outputs": [], "source": [ "using AlgebraicRewriting;" ] }, { "cell_type": "code", "execution_count": 6, "id": "5a06840f", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "n1\n", "\n", "V\n", "\n", "\n", "\n", "n6\n", "\n", "Eng\n", "\n", "\n", "\n", "n1->n6\n", "\n", "\n", "grass_eng\n", "\n", "\n", "\n", "n2\n", "\n", "E\n", "\n", "\n", "\n", "n2->n1\n", "\n", "\n", "src\n", "\n", "\n", "\n", "n2->n1\n", "\n", "\n", "tgt\n", "\n", "\n", "\n", "n5\n", "\n", "Dir\n", "\n", "\n", "\n", "n2->n5\n", "\n", "\n", "dir\n", "\n", "\n", "\n", "n3\n", "\n", "Sheep\n", "\n", "\n", "\n", "n3->n1\n", "\n", "\n", "sheep_loc\n", "\n", "\n", "\n", "n3->n5\n", "\n", "\n", "sheep_dir\n", "\n", "\n", "\n", "n3->n6\n", "\n", "\n", "sheep_eng\n", "\n", "\n", "\n", "n4\n", "\n", "Wolf\n", "\n", "\n", "\n", "n4->n1\n", "\n", "\n", "wolf_loc\n", "\n", "\n", "\n", "n4->n5\n", "\n", "\n", "wolf_dir\n", "\n", "\n", "\n", "n4->n6\n", "\n", "\n", "wolf_eng\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 => \"V\")), Catlab.Graphics.Graphviz.Node(\"n2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"E\")), Catlab.Graphics.Graphviz.Node(\"n3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"Sheep\")), Catlab.Graphics.Graphviz.Node(\"n4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"Wolf\")), Catlab.Graphics.Graphviz.Node(\"n5\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"point\", :xlabel => \"Dir\")), Catlab.Graphics.Graphviz.Node(\"n6\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"point\", :xlabel => \"Eng\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"src\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n2\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"tgt\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"sheep_loc\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n4\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wolf_loc\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n1\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n6\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"grass_eng\")), 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}}(:label => \"sheep_eng\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n4\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n6\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wolf_eng\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n3\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n5\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"sheep_dir\")), Catlab.Graphics.Graphviz.Edge(Catlab.Graphics.Graphviz.NodeID[Catlab.Graphics.Graphviz.NodeID(\"n4\", \"\", \"\"), Catlab.Graphics.Graphviz.NodeID(\"n5\", \"\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"wolf_dir\")), 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}}(:label => \"dir\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:margin => \"0\", :shape => \"ellipse\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Revise, Random, Test, StructEquality\n", "using Catlab, Catlab.CategoricalAlgebra, Catlab.Graphs, Catlab.Graphics, Catlab.Programs\n", "Random.seed!(124);\n", "\n", "@present SchLV <: SchGraph begin\n", " (Sheep,Wolf)::Ob\n", " sheep_loc::Hom(Sheep, V)\n", " wolf_loc::Hom(Wolf, V)\n", "\n", " (Dir,Eng)::AttrType\n", " grass_eng::Attr(V, Eng)\n", " sheep_eng::Attr(Sheep, Eng)\n", " wolf_eng::Attr(Wolf, Eng)\n", " sheep_dir::Attr(Sheep, Dir)\n", " wolf_dir::Attr(Wolf, Dir)\n", " dir::Attr(E, Dir)\n", "end;\n", "to_graphviz(SchLV; prog=\"dot\")" ] }, { "cell_type": "code", "execution_count": 9, "id": "7058095c", "metadata": {}, "outputs": [], "source": [ "@present SchLV′ <: SchLV begin\n", " Coord::AttrType \n", " coord::Attr(V,Coord)\n", "end;" ] }, { "cell_type": "code", "execution_count": 12, "id": "cfa87a0d", "metadata": {}, "outputs": [], "source": [ "import Catlab.CategoricalAlgebra: left, right\n", "\n", "function right(s::Symbol) \n", " if s == :N return :E\n", " elseif s == :S return :W \n", " elseif s == :E return :S \n", " elseif s == :W return :N \n", " end\n", "end\n", "function left(s::Symbol) \n", " if s == :N return :W\n", " elseif s == :S return :E \n", " elseif s == :E return :N \n", " elseif s == :W return :S \n", " end\n", "end\n", "\n", "\n", "\n", "@acset_type LV_Generic(SchLV) <: HasGraph\n", "const LV = LV_Generic{Symbol, Int}\n", "\n", "@acset_type LV′_Generic(SchLV′) <: HasGraph\n", "const LV′ = LV′_Generic{Symbol, Int, Tuple{Int,Int}};\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "980575a3", "metadata": {}, "outputs": [], "source": [ "using AlgebraicRewriting\n", "Swap = Migrate(\n", " Dict(:Sheep=>:Wolf, :Wolf=>:Sheep), \n", " Dict([:sheep_loc=>:wolf_loc, :wolf_loc=>:sheep_loc,\n", " :sheep_eng=>:wolf_eng, :wolf_eng=>:sheep_eng,:grass_eng =>:grass_eng,\n", " :sheep_dir=>:wolf_dir, :wolf_dir=>:sheep_dir,]), LV);" ] }, { "cell_type": "code", "execution_count": 16, "id": "fcf1780a", "metadata": {}, "outputs": [], "source": [ "Coords = Migrate(\n", " Dict(x=>x for x in Symbol.(SchLV.generators[:Ob])), \n", " Dict(x=>x for x in Symbol.(SchLV.generators[:Hom])), \n", " LV′; delta=false);" ] }, { "cell_type": "code", "execution_count": 14, "id": "24acd69b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Vgrass_engcoord
11(0, 0)
215(0, 1)
322(1, 0)
40(1, 1)
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Esrctgtdir
113E
213W
312N
412S
524E
624W
721N
821S
931E
1031W
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1234S
1342E
1442W
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Sheepsheep_locsheep_engsheep_dir
135N
245E
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Wolfwolf_locwolf_engwolf_dir
115N
225N
\n", "
\n" ], "text/plain": [ "LV′ {V:4, E:16, Sheep:2, Wolf:2, Dir:0, Eng:0, Coord:0}\n", "┌───┬───────────┬────────┐\n", "│\u001b[1m V \u001b[0m│\u001b[1m grass_eng \u001b[0m│\u001b[1m coord \u001b[0m│\n", "├───┼───────────┼────────┤\n", "│\u001b[1m 1 \u001b[0m│ 1 │ (0, 0) │\n", "│\u001b[1m 2 \u001b[0m│ 15 │ (0, 1) │\n", "│\u001b[1m 3 \u001b[0m│ 22 │ (1, 0) │\n", "│\u001b[1m 4 \u001b[0m│ 0 │ (1, 1) │\n", "└───┴───────────┴────────┘\n", "┌────┬─────┬─────┬─────┐\n", "│\u001b[1m E \u001b[0m│\u001b[1m src \u001b[0m│\u001b[1m tgt \u001b[0m│\u001b[1m dir \u001b[0m│\n", "├────┼─────┼─────┼─────┤\n", "│\u001b[1m 1 \u001b[0m│ 1 │ 3 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 3 │ W │\n", "│\u001b[1m 3 \u001b[0m│ 1 │ 2 │ N │\n", "│\u001b[1m 4 \u001b[0m│ 1 │ 2 │ S │\n", "│\u001b[1m 5 \u001b[0m│ 2 │ 4 │ E │\n", "│\u001b[1m 6 \u001b[0m│ 2 │ 4 │ W │\n", "│\u001b[1m 7 \u001b[0m│ 2 │ 1 │ N │\n", "│\u001b[1m 8 \u001b[0m│ 2 │ 1 │ S │\n", "│\u001b[1m 9 \u001b[0m│ 3 │ 1 │ E │\n", "│\u001b[1m 10 \u001b[0m│ 3 │ 1 │ W │\n", "│\u001b[1m 11 \u001b[0m│ 3 │ 4 │ N │\n", "│\u001b[1m 12 \u001b[0m│ 3 │ 4 │ S │\n", "│\u001b[1m 13 \u001b[0m│ 4 │ 2 │ E │\n", "│\u001b[1m 14 \u001b[0m│ 4 │ 2 │ W │\n", "│\u001b[1m 15 \u001b[0m│ 4 │ 3 │ N │\n", "│\u001b[1m 16 \u001b[0m│ 4 │ 3 │ S │\n", "└────┴─────┴─────┴─────┘\n", "┌───────┬───────────┬───────────┬───────────┐\n", "│\u001b[1m Sheep \u001b[0m│\u001b[1m sheep_loc \u001b[0m│\u001b[1m sheep_eng \u001b[0m│\u001b[1m sheep_dir \u001b[0m│\n", "├───────┼───────────┼───────────┼───────────┤\n", "│\u001b[1m 1 \u001b[0m│ 3 │ 5 │ N │\n", "│\u001b[1m 2 \u001b[0m│ 4 │ 5 │ E │\n", "└───────┴───────────┴───────────┴───────────┘\n", "┌──────┬──────────┬──────────┬──────────┐\n", "│\u001b[1m Wolf \u001b[0m│\u001b[1m wolf_loc \u001b[0m│\u001b[1m wolf_eng \u001b[0m│\u001b[1m wolf_dir \u001b[0m│\n", "├──────┼──────────┼──────────┼──────────┤\n", "│\u001b[1m 1 \u001b[0m│ 1 │ 5 │ N │\n", "│\u001b[1m 2 \u001b[0m│ 2 │ 5 │ N │\n", "└──────┴──────────┴──────────┴──────────┘\n" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function create_grid(n::Int)\n", " lv = LV′()\n", " coords = Dict()\n", " # Initialize grass 50% green, 50% uniformly between 0-30\n", " for i in 0:n-1\n", " for j in 0:n-1\n", " coords[i=>j] = add_part!(lv, :V; grass_eng=max(0,rand(-30:30)), coord=(i,j))\n", " end\n", " end\n", " for i in 0:n-1\n", " for j in 0:n-1\n", " add_part!(lv, :E; src=coords[i=>j], tgt=coords[mod(i+1,n)=>j], dir=:E)\n", " add_part!(lv, :E; src=coords[i=>j], tgt=coords[mod(i-1,n)=>j], dir=:W)\n", " add_part!(lv, :E; src=coords[i=>j], tgt=coords[i=>mod(j+1,n)], dir=:N)\n", " add_part!(lv, :E; src=coords[i=>j], tgt=coords[i=>mod(j-1,n)], dir=:S)\n", " end\n", " end\n", " return lv\n", "end\n", "\n", "\"\"\"\n", "`n` is the length of the grid.\n", "`sheep` and `wolves` are the fraction of spaces that are \n", "populated with that animal\n", "\"\"\"\n", "function initialize(n::Int, sheep::Float64, wolves::Float64)::LV′\n", " grid = create_grid(n)\n", " args = [(sheep, :Sheep, :sheep_loc, :sheep_eng, :sheep_dir),\n", " (wolves, :Wolf, :wolf_loc, :wolf_eng, :wolf_dir)]\n", " for (n_, name, loc, eng, d) in args\n", " for _ in 1:round(Int,n_*n^2)\n", " dic = Dict([eng => 5, loc => rand(vertices(grid)),\n", " d => rand([:N,:E,:S,:W])])\n", " add_part!(grid, name; dic...)\n", " end\n", " end\n", " return grid\n", "end" ] }, { "cell_type": "code", "execution_count": 31, "id": "01e93812", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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Vgrass_engcoord
10(0, 0)
212(0, 1)
30(1, 0)
40(1, 1)
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Esrctgtdir
113E
213W
312N
412S
524E
624W
721N
821S
931E
1031W
1134N
1234S
1342E
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1543N
1643S
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Sheepsheep_locsheep_engsheep_dir
145W
215N
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Wolfwolf_locwolf_engwolf_dir
135E
235N
\n", "
\n" ], "text/plain": [ "LV′ {V:4, E:16, Sheep:2, Wolf:2, Dir:0, Eng:0, Coord:0}\n", "┌───┬───────────┬────────┐\n", "│\u001b[1m V \u001b[0m│\u001b[1m grass_eng \u001b[0m│\u001b[1m coord \u001b[0m│\n", "├───┼───────────┼────────┤\n", "│\u001b[1m 1 \u001b[0m│ 0 │ (0, 0) │\n", "│\u001b[1m 2 \u001b[0m│ 12 │ (0, 1) │\n", "│\u001b[1m 3 \u001b[0m│ 0 │ (1, 0) │\n", "│\u001b[1m 4 \u001b[0m│ 0 │ (1, 1) │\n", "└───┴───────────┴────────┘\n", "┌────┬─────┬─────┬─────┐\n", "│\u001b[1m E \u001b[0m│\u001b[1m src \u001b[0m│\u001b[1m tgt \u001b[0m│\u001b[1m dir \u001b[0m│\n", "├────┼─────┼─────┼─────┤\n", "│\u001b[1m 1 \u001b[0m│ 1 │ 3 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 3 │ W │\n", "│\u001b[1m 3 \u001b[0m│ 1 │ 2 │ N │\n", "│\u001b[1m 4 \u001b[0m│ 1 │ 2 │ S │\n", "│\u001b[1m 5 \u001b[0m│ 2 │ 4 │ E │\n", "│\u001b[1m 6 \u001b[0m│ 2 │ 4 │ W │\n", "│\u001b[1m 7 \u001b[0m│ 2 │ 1 │ N │\n", "│\u001b[1m 8 \u001b[0m│ 2 │ 1 │ S │\n", "│\u001b[1m 9 \u001b[0m│ 3 │ 1 │ E │\n", "│\u001b[1m 10 \u001b[0m│ 3 │ 1 │ W │\n", "│\u001b[1m 11 \u001b[0m│ 3 │ 4 │ N │\n", "│\u001b[1m 12 \u001b[0m│ 3 │ 4 │ S │\n", "│\u001b[1m 13 \u001b[0m│ 4 │ 2 │ E │\n", "│\u001b[1m 14 \u001b[0m│ 4 │ 2 │ W │\n", "│\u001b[1m 15 \u001b[0m│ 4 │ 3 │ N │\n", "│\u001b[1m 16 \u001b[0m│ 4 │ 3 │ S │\n", "└────┴─────┴─────┴─────┘\n", "┌───────┬───────────┬───────────┬───────────┐\n", "│\u001b[1m Sheep \u001b[0m│\u001b[1m sheep_loc \u001b[0m│\u001b[1m sheep_eng \u001b[0m│\u001b[1m sheep_dir \u001b[0m│\n", "├───────┼───────────┼───────────┼───────────┤\n", "│\u001b[1m 1 \u001b[0m│ 4 │ 5 │ W │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 5 │ N │\n", "└───────┴───────────┴───────────┴───────────┘\n", "┌──────┬──────────┬──────────┬──────────┐\n", "│\u001b[1m Wolf \u001b[0m│\u001b[1m wolf_loc \u001b[0m│\u001b[1m wolf_eng \u001b[0m│\u001b[1m wolf_dir \u001b[0m│\n", "├──────┼──────────┼──────────┼──────────┤\n", "│\u001b[1m 1 \u001b[0m│ 3 │ 5 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 3 │ 5 │ N │\n", "└──────┴──────────┴──────────┴──────────┘\n" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X = initialize(2, 0.5,0.5)" ] }, { "cell_type": "code", "execution_count": 15, "id": "7f7cd0b5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "view_LV (generic function with 2 methods)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "using Catlab.Graphics.Graphviz: Attributes, Statement, Node, Digraph\n", "using Catlab.Graphics.Graphviz\n", "\n", "supscript_d = Dict([\n", " '1'=>'¹', '2'=>'²', '3'=>'³', '4'=>'⁴', '5'=>'⁵','6'=>'⁶', '7'=>'⁷', '8'=>'⁸', \n", " '9'=>'⁹', '0'=>'⁰', 'x'=>'ˣ', 'y'=>'ʸ','z'=>'ᶻ','a'=>'ᵃ','b'=>'ᵇ','c'=>'ᶜ',\n", " 'd'=>'ᵈ'])\n", "supscript(x::String) = join([get(supscript_d, c, c) for c in x])\n", "\n", "function view_LV(p::ACSetTransformation; name=\"G\", title=\"\")\n", " if nparts(dom(p),:Wolf) == 1 \n", " star = :Wolf=>p[:Wolf](1)\n", " elseif nparts(dom(p),:Sheep) == 1 \n", " star = :Sheep=>p[:Sheep](1)\n", " elseif nparts(dom(p),:V) == 1 \n", " star = :V=>p[:V](1)\n", " else\n", " star = nothing\n", " end\n", " view_LV(codom(p); name=name, title=title, star=star)\n", "end \n", "function view_LV(p::LV′; name=\"G\", title=\"\", star=nothing)\n", " pstr = [\"$(i),$(j)!\" for (i,j) in p[:coord]]\n", " stmts = Statement[]\n", " for s in 1:nv(p)\n", " st = (star == (:V=>s)) ? \"*\" : \"\"\n", " gv = p[s, :grass_eng]\n", " col = gv == 0 ? \"lightgreen\" : \"tan\"\n", " push!(stmts,Node(\"v$s\", Attributes(\n", " :label=>gv == 0 ? \"\" : string(gv)*st,\n", " :shape=>\"circle\",\n", " :color=> col, :pos=>pstr[s])))\n", " end\n", " d = Dict([:E=>(1,0),:N=>(0,1), :S=>(0,-1),:W=>(-1,0),])\n", "\n", " args = [(:true,:Wolf,:wolf_loc,:wolf_eng,:wolf_dir),\n", " (false, :Sheep, :sheep_loc, :sheep_eng,:sheep_dir)]\n", "\n", " for (is_wolf, prt, loc, eng, dr) in args\n", " for w in parts(p, prt)\n", " st = (star == ((is_wolf ? :Wolf : :Sheep) => w)) ? \"*\" : \"\"\n", " e = only(incident(p,p[w,loc], :src) ∩ incident(p,p[w,dr], :dir))\n", " s = src(p,e)\n", " dx, dy = d[p[e, :dir]]\n", " (sx,sy) = p[s,:coord]\n", "\n", " L, R = 0.25, 0.1\n", " wx = sx+L*dx+R*rand()\n", " wy = sy+L*dy+R*rand()\n", " ID = \"$(is_wolf ? :w : :s)$w\"\n", " append!(stmts,[Node(ID, Attributes(\n", " :label=>\"$w\"*supscript(\"$(p[w,eng])\")*st,\n", " :shape=>\"square\", :width=>\"0.3px\", :height=>\"0.3px\", :fixedsize=>\"true\",\n", " :pos=>\"$(wx),$(wy)!\",:color=> is_wolf ? \"red\" : \"lightblue\"))])\n", " end\n", " end\n", "\n", " g = Graphviz.Digraph(name, Statement[stmts...]; prog=\"neato\",\n", " graph_attrs=Attributes(:label=>title, :labelloc=>\"t\"),\n", " node_attrs=Attributes(:shape=>\"plain\", :style=>\"filled\"))\n", " return g\n", "end" ] }, { "cell_type": "code", "execution_count": 17, "id": "24639e21", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "1\n", "\n", "\n", "\n", "v2\n", "\n", "15\n", "\n", "\n", "\n", "v3\n", "\n", "22\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n", "s2\n", "\n", "2⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1\", :shape => \"circle\", :color => \"tan\", :pos => \"0,0!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"15\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"22\", :shape => \"circle\", :color => \"tan\", :pos => \"1,0!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.06849654266579729,0.2933390970151203!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.004255329021628751,1.3339814389671707!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.010499613794431,0.2616284602207712!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.301572086719917,1.013784448366333!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "view_LV(X)" ] }, { "cell_type": "code", "execution_count": 18, "id": "deda5c79", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "1\n", "\n", "\n", "\n", "v2\n", "\n", "15\n", "\n", "\n", "\n", "v3\n", "\n", "22\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵*\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n", "s2\n", "\n", "2⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1\", :shape => \"circle\", :color => \"tan\", :pos => \"0,0!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"15\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"22\", :shape => \"circle\", :color => \"tan\", :pos => \"1,0!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵*\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.04055871848385959,0.28953034194361493!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.04544456128547683,1.3352441625858422!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.053629505296321,0.31738803366916657!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.2585447432953236,1.0485103191268235!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "const Var = AttrVar # shorthand\n", "Base.isless(x::Var,y::Var) = x.val < y.val\n", "\n", "\"\"\"Visualize a LV with a distinguished focus\"\"\"\n", "function view_LV(p::ACSetTransformation; name=\"G\", title=\"\")\n", " if nparts(dom(p),:Wolf) == 1 \n", " star = :Wolf=>p[:Wolf](1)\n", " elseif nparts(dom(p),:Sheep) == 1 \n", " star = :Sheep=>p[:Sheep](1)\n", " elseif nparts(dom(p),:V) == 1 \n", " star = :V=>p[:V](1)\n", " else\n", " star = nothing\n", " end\n", " view_LV(codom(p); name=name, title=title, star=star)\n", "end\n", "\n", "yLV = yoneda_cache(LV); # compute representables\n", "\n", "# Empty agent type\n", "I = LV()\n", "# Generic sheep agent\n", "S = @acset_colim yLV begin s::Sheep end\n", "# Generic wolf agent\n", "W = Swap(S)\n", "# Generic grass agent\n", "G = @acset_colim yLV begin v::V end\n", "\n", "N = Dict(W=>\"W\",S=>\"S\",G=>\"G\", I=>\"\") # names for visualization\n", "\n", "\n", "view_LV(homomorphism(Coords(W), X)) # a distinguished wolf" ] }, { "cell_type": "code", "execution_count": 19, "id": "b741afba", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "22\n", "\n", "\n", "\n", "v2\n", "\n", "1\n", "\n", "\n", "\n", "v3\n", "\n", "15\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n", "s2\n", "\n", "2⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"22\", :shape => \"circle\", :color => \"tan\", :pos => \"1,0!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1\", :shape => \"circle\", :color => \"tan\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"15\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.061954935908587805,0.26293927591835253!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.08516421807581895,1.3175968447635291!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.7599599619142068,0.0476178591913291!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.2929574844314107,1.0519683238450952!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rl = Rule(id(S),id(S); expr=(Dir=[xs->left(only(xs))],))\n", "rr = Rule(id(S),id(S); expr=(Dir=[xs->right(only(xs))],));\n", "\n", "view_LV(rewrite(Coords(rl), X)) # a sheep has rotated left" ] }, { "cell_type": "code", "execution_count": 20, "id": "96436ebd", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "\n", "\n", "n1\n", "\n", "\n", "turn_left\n", "\n", "\n", "\n", "\n", "n0in1:s->n1:n\n", "\n", "\n", "S\n", "\n", "\n", "\n", "\n", "\n", "n1:s->n0out1:n\n", "\n", "\n", "S\n", "\n", "\n", "\n", "\n", "n1:s->n0out1:n\n", "\n", "\n", "S\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"dot\", Statement[Subgraph(\"\", Statement[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\")), Subgraph(\"\", Statement[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\")), Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:color => \"black\", :comment => \"turn_left\", :fillcolor => \"lightblue\", :id => \"n1\", :label => Catlab.Graphics.Graphviz.Html(\"\\n\\n\\n\\n
turn_left
\"), :style => \"filled\")), Edge(NodeID[NodeID(\"n0in1\", \"s\", \"\"), NodeID(\"n1\", \"in1\", \"n\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"S\", :id => \"e1\", :label => \"S\")), Edge(NodeID[NodeID(\"n1\", \"out1\", \"s\"), NodeID(\"n0out1\", \"n\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"S\", :id => \"e2\", :label => \"S\")), Edge(NodeID[NodeID(\"n1\", \"out2\", \"s\"), NodeID(\"n0out1\", \"n\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"S\", :id => \"e3\", :label => \"S\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :label => \"\", :labelloc => \"t\", :rankdir => \"TB\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :shape => \"none\", :width => \"0\", :height => \"0\", :margin => \"0\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:arrowsize => \"0.5\", :fontname => \"Serif\"))" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sheep_rotate_l = tryrule(RuleApp(:turn_left, rl, S))\n", "sheep_rotate_r = tryrule(RuleApp(:turn_right, rr, S))\n", "\n", "view_sched(sheep_rotate_l; names=N)" ] }, { "cell_type": "code", "execution_count": 21, "id": "3ffc417a", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "22\n", "\n", "\n", "\n", "v2\n", "\n", "1\n", "\n", "\n", "\n", "v3\n", "\n", "15\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁴\n", "\n", "\n", "\n", "s2\n", "\n", "2⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"22\", :shape => \"circle\", :color => \"tan\", :pos => \"0,0!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1\", :shape => \"circle\", :color => \"tan\", :pos => \"1,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"15\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.0338319999367087,0.2715144903507484!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.09955524312849022,1.2524208221537232!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁴\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.005154834855672,0.31898952213249837!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.3480552534673957,1.0906437076648072!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s_fwd_l = @acset_colim yLV begin e::E; s::Sheep; sheep_loc(s)==src(e) end \n", "s_fwd_i = @acset_colim yLV begin e::E end\n", "s_fwd_r = @acset_colim yLV begin e::E; s::Sheep; sheep_loc(s)==tgt(e) end \n", "s_n = @acset_colim yLV begin \n", " e::E; s::Sheep; sheep_loc(s)==src(e); sheep_eng(s)==0 \n", "end\n", "\n", "\n", "sheep_fwd_rule = Rule(\n", " homomorphism(s_fwd_i, s_fwd_l; monic=true),\n", " homomorphism(s_fwd_i, s_fwd_r; monic=true),\n", " ac=[AppCond(homomorphism(s_fwd_l, s_n), false)],\n", " expr=(Eng=Dict(3=>vs->vs[3]-1), Dir=Dict(2=>vs->vs[2]))\n", ")\n", "\n", "sheep_fwd = tryrule(RuleApp(:move_fwd, sheep_fwd_rule, \n", " homomorphism(S,s_fwd_l), homomorphism(S,s_fwd_r)))\n", "\n", "view_LV(rewrite(Coords(sheep_fwd_rule), X))" ] }, { "cell_type": "code", "execution_count": 22, "id": "8b39bd6d", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "30\n", "\n", "\n", "\n", "v2\n", "\n", "1\n", "\n", "\n", "\n", "v3\n", "\n", "15\n", "\n", "\n", "\n", "v4\n", "\n", "22\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁹\n", "\n", "\n", "\n", "s2\n", "\n", "2⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"30\", :shape => \"circle\", :color => \"tan\", :pos => \"1,1!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1\", :shape => \"circle\", :color => \"tan\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"15\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"22\", :shape => \"circle\", :color => \"tan\", :pos => \"1,0!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.07036570973503435,0.3213120282469349!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.08407644091544102,1.263405607784062!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁹\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.2857788074006897,1.0433429055016346!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.062613408317212,0.33590339061194174!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Eat grass + 4eng\n", "#-----------------\n", "# Grass is at 0 - meaning it's ready to be eaten\n", "s_eat_pac = @acset_colim yLV begin s::Sheep; grass_eng(sheep_loc(s))==0 end\n", "\n", "se_rule = Rule(id(S), id(S); expr=(Eng=[vs->vs[1]+4,vs->30],), \n", " ac=[AppCond(homomorphism(S,s_eat_pac))])\n", "sheep_eat = tryrule(RuleApp(:Sheep_eat, se_rule, S))\n", "sheep_eat = tryrule(RuleApp(:Sheep_eat, se_rule, S))\n", "view_LV(rewrite(Coords(se_rule), X))" ] }, { "cell_type": "code", "execution_count": 32, "id": "94b57963", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Rule{:DPO}(ACSetTransformation((V = FinFunction([1], 1, 1), E = FinFunction(Int64[], 0, 0), Sheep = FinFunction(Int64[], 0, 1), Wolf = FinFunction([1], 1, 1), Dir = VarFunction{Symbol}(FinDomFunction(Union{AttrVar, Symbol}[AttrVar(2)], FinSet(1), TypeSet(Union{AttrVar, Symbol})), FinSet(2)), Eng = VarFunction{Int64}(FinDomFunction(Union{AttrVar, Int64}[AttrVar(3), AttrVar(1)], FinSet(2), TypeSet(Union{AttrVar, Int64})), FinSet(3))), LV {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2}, LV {V:1, E:0, Sheep:1, Wolf:1, Dir:2, Eng:3}), ACSetTransformation((V = id(FinSet(1)), E = id(FinSet(0)), Sheep = id(FinSet(0)), Wolf = id(FinSet(1)), Dir = VarFunction{Symbol}(FinDomFunction(Union{AttrVar, Symbol}[AttrVar(1)], FinSet(1), TypeSet(Union{AttrVar, Symbol})), FinSet(1)), Eng = VarFunction{Int64}(FinDomFunction(Union{AttrVar, Int64}[AttrVar(1), AttrVar(2)], FinSet(2), TypeSet(Union{AttrVar, Int64})), FinSet(2))), LV {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2}, LV {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2}), Constraint[], false, Dict{Symbol, Dict{Int64, Union{Nothing, Function}}}(:Eng => Dict(2 => var\"#47#49\"(), 1 => var\"#46#48\"()), :Dir => Dict(1 => AlgebraicRewriting.Rewrite.Utils.var\"#4#8\"{Vector{AttrVar}}(AttrVar[AttrVar(2)]))))" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "w_eat_l = @acset_colim yLV begin s::Sheep; w::Wolf; sheep_loc(s)==wolf_loc(w) end\n", "\n", "we_rule = Rule(homomorphism(W, w_eat_l), id(W); expr=(Eng=[vs->vs[3]+20,vs->vs[1]],))" ] }, { "cell_type": "code", "execution_count": 26, "id": "7107be80", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "Rule{:DPO}(ACSetTransformation((V = FinFunction([1], 1, 1), E = FinFunction(Int64[], 0, 0), Sheep = FinFunction(Int64[], 0, 1), Wolf = FinFunction([1], 1, 1), Dir = VarFunction{Symbol}(FinDomFunction(Union{AttrVar, Symbol}[AttrVar(2)], FinSet(1), TypeSet(Union{AttrVar, Symbol})), FinSet(2)), Eng = VarFunction{Int64}(FinDomFunction(Union{AttrVar, Int64}[AttrVar(3), AttrVar(1)], FinSet(2), TypeSet(Union{AttrVar, Int64})), FinSet(3)), Coord = VarFunction{Tuple{Int64, Int64}}(FinDomFunction(Union{AttrVar, Tuple{Int64, Int64}}[AttrVar(1)], FinSet(1), TypeSet(Union{AttrVar, Tuple{Int64, Int64}})), FinSet(1))), LV′ {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2, Coord:1}, LV′ {V:1, E:0, Sheep:1, Wolf:1, Dir:2, Eng:3, Coord:1}), ACSetTransformation((V = FinFunction([1], 1, 1), E = FinFunction(Int64[], 0, 0), Sheep = FinFunction(Int64[], 0, 0), Wolf = FinFunction([1], 1, 1), Dir = VarFunction{Symbol}(FinDomFunction(Union{AttrVar, Symbol}[AttrVar(1)], FinSet(1), TypeSet(Union{AttrVar, Symbol})), FinSet(1)), Eng = VarFunction{Int64}(FinDomFunction(Union{AttrVar, Int64}[AttrVar(1), AttrVar(2)], FinSet(2), TypeSet(Union{AttrVar, Int64})), FinSet(2)), Coord = VarFunction{Tuple{Int64, Int64}}(FinDomFunction(Union{AttrVar, Tuple{Int64, Int64}}[AttrVar(1)], FinSet(1), TypeSet(Union{AttrVar, Tuple{Int64, Int64}})), FinSet(1))), LV′ {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2, Coord:1}, LV′ {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2, Coord:1}), Constraint[], false, Dict{Symbol, Dict{Int64, Union{Nothing, Function}}}(:Eng => Dict(2 => var\"#43#45\"(), 1 => var\"#42#44\"()), :Coord => Dict(1 => AlgebraicRewriting.Rewrite.Utils.var\"#4#8\"{Vector{AttrVar}}(AttrVar[AttrVar(1)])), :Dir => Dict(1 => AlgebraicRewriting.Rewrite.Utils.var\"#4#8\"{Vector{AttrVar}}(AttrVar[AttrVar(2)]))))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Coords(we_rule)" ] }, { "cell_type": "code", "execution_count": 33, "id": "39023520", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Schedule(WiringDiagram{AlgebraicRewriting.Schedules.Theories.ThTracedMonoidalWithBidiagonals}([LV {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2}], [LV {V:1, E:0, Sheep:0, Wolf:1, Dir:1, Eng:2}], \n", "[ -2 => {inputs},\n", " -1 => {outputs},\n", " 1 => Box(\"Wolf_eat\", [LV:\n", " V = 1:1\n", " E = 1:0\n", " Sheep = 1:0\n", " Wolf = 1:1\n", " Dir = 1:1\n", " Eng = 1:2\n", " src : E → V = Int64[]\n", " tgt : E → V = Int64[]\n", " sheep_loc : Sheep → V = Int64[]\n", " wolf_loc : Wolf → V = [1]\n", " grass_eng : V → Eng = AttrVar[AttrVar(2)]\n", " sheep_eng : Sheep → Eng = Int64[]\n", " wolf_eng : Wolf → Eng = AttrVar[AttrVar(1)]\n", " sheep_dir : Sheep → Dir = Symbol[]\n", " wolf_dir : Wolf → Dir = AttrVar[AttrVar(1)]\n", " dir : E → Dir = Symbol[]], [LV:\n", " V = 1:1\n", " E = 1:0\n", " Sheep = 1:0\n", " Wolf = 1:1\n", " Dir = 1:1\n", " Eng = 1:2\n", " src : E → V = Int64[]\n", " tgt : E → V = Int64[]\n", " sheep_loc : Sheep → V = Int64[]\n", " wolf_loc : Wolf → V = [1]\n", " grass_eng : V → Eng = AttrVar[AttrVar(2)]\n", " sheep_eng : Sheep → Eng = Int64[]\n", " wolf_eng : Wolf → Eng = AttrVar[AttrVar(1)]\n", " sheep_dir : Sheep → Dir = Symbol[]\n", " wolf_dir : Wolf → Dir = AttrVar[AttrVar(1)]\n", " dir : E → Dir = Symbol[],LV:\n", " V = 1:1\n", " E = 1:0\n", " Sheep = 1:0\n", " Wolf = 1:1\n", " Dir = 1:1\n", " Eng = 1:2\n", " src : E → V = Int64[]\n", " tgt : E → V = Int64[]\n", " sheep_loc : Sheep → V = Int64[]\n", " wolf_loc : Wolf → V = [1]\n", " grass_eng : V → Eng = AttrVar[AttrVar(2)]\n", " sheep_eng : Sheep → Eng = Int64[]\n", " wolf_eng : Wolf → Eng = AttrVar[AttrVar(1)]\n", " sheep_dir : Sheep → Dir = Symbol[]\n", " wolf_dir : Wolf → Dir = AttrVar[AttrVar(1)]\n", " dir : E → Dir = Symbol[]]) ],\n", "[ Wire((-2,1) => (1,1)),\n", " Wire((1,1) => (-1,1)),\n", " Wire((1,2) => (-1,1)) ]), compose(Wolf_eat,mmerge(LV:\n", " V = 1:1\n", " E = 1:0\n", " Sheep = 1:0\n", " Wolf = 1:1\n", " Dir = 1:1\n", " Eng = 1:2\n", " src : E → V = Int64[]\n", " tgt : E → V = Int64[]\n", " sheep_loc : Sheep → V = Int64[]\n", " wolf_loc : Wolf → V = [1]\n", " grass_eng : V → Eng = AttrVar[AttrVar(2)]\n", " sheep_eng : Sheep → Eng = Int64[]\n", " wolf_eng : Wolf → Eng = AttrVar[AttrVar(1)]\n", " sheep_dir : Sheep → Dir = Symbol[]\n", " wolf_dir : Wolf → Dir = AttrVar[AttrVar(1)]\n", " dir : E → Dir = Symbol[])))" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "wolf_eat = tryrule(RuleApp(:Wolf_eat, we_rule, W))" ] }, { "cell_type": "code", "execution_count": 30, "id": "4d4f1add", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "\n", "\n", "n1\n", "\n", "\n", "Wolf_eat\n", "\n", "\n", "\n", "\n", "n0in1:s->n1:n\n", "\n", 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Vgrass_engcoord
10(0, 0)
212(0, 1)
30(1, 0)
40(1, 1)
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Esrctgtdir
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Sheepsheep_locsheep_engsheep_dir
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Wolfwolf_locwolf_engwolf_dir
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\n" ], "text/plain": [ "LV′ {V:4, E:16, Sheep:2, Wolf:2, Dir:0, Eng:0, Coord:0}\n", "┌───┬───────────┬────────┐\n", "│\u001b[1m V \u001b[0m│\u001b[1m grass_eng \u001b[0m│\u001b[1m coord \u001b[0m│\n", "├───┼───────────┼────────┤\n", "│\u001b[1m 1 \u001b[0m│ 0 │ (0, 0) │\n", "│\u001b[1m 2 \u001b[0m│ 12 │ (0, 1) │\n", "│\u001b[1m 3 \u001b[0m│ 0 │ (1, 0) │\n", "│\u001b[1m 4 \u001b[0m│ 0 │ (1, 1) │\n", "└───┴───────────┴────────┘\n", "┌────┬─────┬─────┬─────┐\n", "│\u001b[1m E \u001b[0m│\u001b[1m src \u001b[0m│\u001b[1m tgt \u001b[0m│\u001b[1m dir \u001b[0m│\n", "├────┼─────┼─────┼─────┤\n", "│\u001b[1m 1 \u001b[0m│ 1 │ 3 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 3 │ W │\n", "│\u001b[1m 3 \u001b[0m│ 1 │ 2 │ N │\n", "│\u001b[1m 4 \u001b[0m│ 1 │ 2 │ S │\n", "│\u001b[1m 5 \u001b[0m│ 2 │ 4 │ E │\n", "│\u001b[1m 6 \u001b[0m│ 2 │ 4 │ W │\n", "│\u001b[1m 7 \u001b[0m│ 2 │ 1 │ N │\n", "│\u001b[1m 8 \u001b[0m│ 2 │ 1 │ S │\n", "│\u001b[1m 9 \u001b[0m│ 3 │ 1 │ E │\n", "│\u001b[1m 10 \u001b[0m│ 3 │ 1 │ W │\n", "│\u001b[1m 11 \u001b[0m│ 3 │ 4 │ N │\n", "│\u001b[1m 12 \u001b[0m│ 3 │ 4 │ S │\n", "│\u001b[1m 13 \u001b[0m│ 4 │ 2 │ E │\n", "│\u001b[1m 14 \u001b[0m│ 4 │ 2 │ W │\n", "│\u001b[1m 15 \u001b[0m│ 4 │ 3 │ N │\n", "│\u001b[1m 16 \u001b[0m│ 4 │ 3 │ S │\n", "└────┴─────┴─────┴─────┘\n", "┌───────┬───────────┬───────────┬───────────┐\n", "│\u001b[1m Sheep \u001b[0m│\u001b[1m sheep_loc \u001b[0m│\u001b[1m sheep_eng \u001b[0m│\u001b[1m sheep_dir \u001b[0m│\n", "├───────┼───────────┼───────────┼───────────┤\n", "│\u001b[1m 1 \u001b[0m│ 4 │ 5 │ W │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 5 │ N │\n", "└───────┴───────────┴───────────┴───────────┘\n", "┌──────┬──────────┬──────────┬──────────┐\n", "│\u001b[1m Wolf \u001b[0m│\u001b[1m wolf_loc \u001b[0m│\u001b[1m wolf_eng \u001b[0m│\u001b[1m wolf_dir \u001b[0m│\n", "├──────┼──────────┼──────────┼──────────┤\n", "│\u001b[1m 1 \u001b[0m│ 2 │ 5 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 3 │ 5 │ N │\n", "└──────┴──────────┴──────────┴──────────┘\n" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X" ] }, { "cell_type": "code", "execution_count": null, "id": "bf0d9b47", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 34, "id": "63ffb56c", "metadata": { "scrolled": true }, "outputs": [ { "ename": "LoadError", "evalue": "MethodError: no method matching view_LV(::Nothing)\n\n\u001b[0mClosest candidates are:\n\u001b[0m view_LV(\u001b[91m::ACSetTransformation\u001b[39m; name, title)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[35mMain\u001b[39m \u001b[90m\u001b[4mIn[18]:5\u001b[24m\u001b[39m\n\u001b[0m view_LV(\u001b[91m::LV′\u001b[39m; name, title, star)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[35mMain\u001b[39m \u001b[90m\u001b[4mIn[15]:22\u001b[24m\u001b[39m\n", "output_type": "error", "traceback": [ "MethodError: no method matching view_LV(::Nothing)\n\n\u001b[0mClosest candidates are:\n\u001b[0m view_LV(\u001b[91m::ACSetTransformation\u001b[39m; name, title)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[35mMain\u001b[39m \u001b[90m\u001b[4mIn[18]:5\u001b[24m\u001b[39m\n\u001b[0m view_LV(\u001b[91m::LV′\u001b[39m; name, title, star)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[35mMain\u001b[39m \u001b[90m\u001b[4mIn[15]:22\u001b[24m\u001b[39m\n", "", "Stacktrace:", " [1] top-level scope", " @ In[34]:7" ] } ], "source": [ "# note that the below fails even if only one of the following \"wolf_eat\" invocations is included\n", "wolf_eat = tryrule(RuleApp(:Wolf_eat, we_rule, W))\n", "\n", "wolf_eat = tryrule(RuleApp(:Wolf_eat, we_rule, W))\n", " \n", "X[1,:wolf_loc] = 2 # put the wolf with the sheep -- NB: *** NDO found that the sheep are not at this location, and the code breaks accordingly.\n", "view_LV(rewrite(Coords(we_rule), X))" ] }, { "cell_type": "code", "execution_count": 36, "id": "b8f4d8e3", "metadata": {}, "outputs": [], "source": [ "# this confirms the source of the problem being that the rewrite rule returns you\n", "rewrite(Coords(we_rule), X)" ] }, { "cell_type": "code", "execution_count": 40, "id": "dfb2a876", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "\n", "\n", "\n", "v2\n", "\n", "\n", "\n", "\n", "v3\n", "\n", "12\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1²⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"12\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,0!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1²⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.283445016120271,1.0581242738758512!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.0983001575535452,0.2648596336526238!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.013943393323564847,0.33367715730613945!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#trying the below with the CORRECT location for the sheep\n", "X[1,:wolf_loc] = 4 # put the wolf with the sheep\n", "view_LV(rewrite(Coords(we_rule), X))" ] }, { "cell_type": "code", "execution_count": 41, "id": "d2e8b690", "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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Vgrass_engcoord
10(0, 0)
212(0, 1)
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Esrctgtdir
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213W
312N
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Sheepsheep_locsheep_engsheep_dir
145W
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Wolfwolf_locwolf_engwolf_dir
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\n" ], "text/plain": [ "LV′ {V:4, E:16, Sheep:2, Wolf:2, Dir:0, Eng:0, Coord:0}\n", "┌───┬───────────┬────────┐\n", "│\u001b[1m V \u001b[0m│\u001b[1m grass_eng \u001b[0m│\u001b[1m coord \u001b[0m│\n", "├───┼───────────┼────────┤\n", "│\u001b[1m 1 \u001b[0m│ 0 │ (0, 0) │\n", "│\u001b[1m 2 \u001b[0m│ 12 │ (0, 1) │\n", "│\u001b[1m 3 \u001b[0m│ 0 │ (1, 0) │\n", "│\u001b[1m 4 \u001b[0m│ 0 │ (1, 1) │\n", "└───┴───────────┴────────┘\n", "┌────┬─────┬─────┬─────┐\n", "│\u001b[1m E \u001b[0m│\u001b[1m src \u001b[0m│\u001b[1m tgt \u001b[0m│\u001b[1m dir \u001b[0m│\n", "├────┼─────┼─────┼─────┤\n", "│\u001b[1m 1 \u001b[0m│ 1 │ 3 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 3 │ W │\n", "│\u001b[1m 3 \u001b[0m│ 1 │ 2 │ N │\n", "│\u001b[1m 4 \u001b[0m│ 1 │ 2 │ S │\n", "│\u001b[1m 5 \u001b[0m│ 2 │ 4 │ E │\n", "│\u001b[1m 6 \u001b[0m│ 2 │ 4 │ W │\n", "│\u001b[1m 7 \u001b[0m│ 2 │ 1 │ N │\n", "│\u001b[1m 8 \u001b[0m│ 2 │ 1 │ S │\n", "│\u001b[1m 9 \u001b[0m│ 3 │ 1 │ E │\n", "│\u001b[1m 10 \u001b[0m│ 3 │ 1 │ W │\n", "│\u001b[1m 11 \u001b[0m│ 3 │ 4 │ N │\n", "│\u001b[1m 12 \u001b[0m│ 3 │ 4 │ S │\n", "│\u001b[1m 13 \u001b[0m│ 4 │ 2 │ E │\n", "│\u001b[1m 14 \u001b[0m│ 4 │ 2 │ W │\n", "│\u001b[1m 15 \u001b[0m│ 4 │ 3 │ N │\n", "│\u001b[1m 16 \u001b[0m│ 4 │ 3 │ S │\n", "└────┴─────┴─────┴─────┘\n", "┌───────┬───────────┬───────────┬───────────┐\n", "│\u001b[1m Sheep \u001b[0m│\u001b[1m sheep_loc \u001b[0m│\u001b[1m sheep_eng \u001b[0m│\u001b[1m sheep_dir \u001b[0m│\n", "├───────┼───────────┼───────────┼───────────┤\n", "│\u001b[1m 1 \u001b[0m│ 4 │ 5 │ W │\n", "│\u001b[1m 2 \u001b[0m│ 1 │ 5 │ N │\n", "└───────┴───────────┴───────────┴───────────┘\n", "┌──────┬──────────┬──────────┬──────────┐\n", "│\u001b[1m Wolf \u001b[0m│\u001b[1m wolf_loc \u001b[0m│\u001b[1m wolf_eng \u001b[0m│\u001b[1m wolf_dir \u001b[0m│\n", "├──────┼──────────┼──────────┼──────────┤\n", "│\u001b[1m 1 \u001b[0m│ 4 │ 5 │ E │\n", "│\u001b[1m 2 \u001b[0m│ 3 │ 5 │ N │\n", "└──────┴──────────┴──────────┴──────────┘\n" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X" ] }, { "cell_type": "code", "execution_count": 42, "id": "097830c2", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "\n", "\n", "\n", "v2\n", "\n", "\n", "\n", "\n", "v3\n", "\n", "12\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1²⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"12\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,0!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1²⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.324491275926018,1.0622545939098518!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.0053740348101448,0.2549293997928652!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.061434857578459526,0.29033497733613584!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# note that the below fails even if only one of the following \"wolf_eat\" invocations is included\n", "wolf_eat = tryrule(RuleApp(:Wolf_eat, we_rule, W))\n", "\n", "wolf_eat = tryrule(RuleApp(:Wolf_eat, we_rule, W))\n", " \n", "X[1,:wolf_loc] = 4 # put the wolf with the sheep\n", "view_LV(rewrite(Coords(we_rule), X))" ] }, { "cell_type": "code", "execution_count": 43, "id": "6c5509c5", "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "\n", "\n", "\n", "v2\n", "\n", "\n", "\n", "\n", "v3\n", "\n", "12\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1²⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"12\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,0!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1²⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.2714212056247363,1.0858190750096561!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.0518431565424968,0.30839782681250255!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.09695290621242357,0.2975733146081277!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# note that the below fails even if only one of the following \"wolf_eat\" invocations is included\n", "wolf_eat = tryrule(RuleApp(:Wolf_eat, we_rule, W))\n", "\n", "X[1,:wolf_loc] = 4 # put the wolf with the sheep (correct address) \n", "view_LV(rewrite(Coords(we_rule), X))" ] }, { "cell_type": "code", "execution_count": 44, "id": "7816974b", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "\n", "\n", "n1\n", "\n", "\n", "starve\n", "\n", "\n", "\n", "\n", "n0in1:s->n1:n\n", "\n", "\n", "S\n", "\n", "\n", "\n", "\n", "n1:s->n0out1:n\n", "\n", "\n", "\n", "\n", "\n", "n2\n", "\n", "\n", "\n", "\n", "\n", "\n", "n1:s->n2:n\n", "\n", "\n", "S\n", "\n", "\n", "\n", "n2:s->n0out1:n\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"dot\", Statement[Subgraph(\"\", Statement[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\")), Subgraph(\"\", Statement[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\")), Node(\"n1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:color => \"black\", :comment => \"starve\", :fillcolor => \"lightblue\", :id => \"n1\", :label => Catlab.Graphics.Graphviz.Html(\"\\n\\n\\n\\n
starve
\"), :style => \"filled\")), Node(\"n2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:color => \"black\", :comment => \"\", :fillcolor => \"lavender\", :id => \"n2\", :label => Catlab.Graphics.Graphviz.Html(\"\\n\\n\\n\\n
\"), :style => \"filled\")), Edge(NodeID[NodeID(\"n0in1\", \"s\", \"\"), NodeID(\"n1\", \"in1\", \"n\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"S\", :id => \"e1\", :label => \"S\")), Edge(NodeID[NodeID(\"n1\", \"out2\", \"s\"), NodeID(\"n2\", \"in1\", \"n\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"S\", :id => \"e2\", :label => \"S\")), Edge(NodeID[NodeID(\"n1\", \"out1\", \"s\"), NodeID(\"n0out1\", \"n\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"\", :id => \"e3\", :label => \"\")), Edge(NodeID[NodeID(\"n2\", \"out1\", \"s\"), NodeID(\"n0out1\", \"n\", \"\")], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:comment => \"\", :id => \"e4\", :label => \"\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :label => \"\", :labelloc => \"t\", :rankdir => \"TB\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:fontname => \"Serif\", :shape => \"none\", :width => \"0\", :height => \"0\", :margin => \"0\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:arrowsize => \"0.5\", :fontname => \"Serif\"))" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Die if 0 eng\n", "#-------------\n", "s_die_l = @acset_colim yLV begin s::Sheep; sheep_eng(s)==0 end \n", "\n", "sheep_die_rule = Rule(homomorphism(G, s_die_l), id(G))\n", "sheep_starve = (RuleApp(:starve, sheep_die_rule, \n", " homomorphism(S,s_die_l), create(G))\n", " ⋅ (id([I]) ⊗ Weaken(create(S))) ⋅ merge_wires(I))\n", "\n", "view_sched(sheep_starve; names=N)" ] }, { "cell_type": "code", "execution_count": 45, "id": "63cc3404", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "\n", "\n", "\n", "v2\n", "\n", "\n", "\n", "\n", "v3\n", "\n", "12\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1³\n", "\n", "\n", "\n", "s2\n", "\n", "2³\n", "\n", "\n", "\n", "s3\n", "\n", "3⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"12\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,0!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.281947788490046,1.0659916916178562!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.0948080890756835,0.33458180827351286!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1³\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.7702198866699627,1.0507109586669932!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2³\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.8226164017440437,1.0944824655265233!\", :color => \"lightblue\")), Node(\"s3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"3⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.01551824146469032,0.32001903312470475!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s_reprod_r = @acset_colim yLV begin (x,y)::Sheep; sheep_loc(x)==sheep_loc(y) end\n", "\n", "sheep_reprod_rule = Rule(\n", " homomorphism(G, S),\n", " homomorphism(G, s_reprod_r); \n", " expr=(Dir=[vs->vs[1],vs->vs[1]], Eng=[vs->vs[2], \n", " fill(vs->round(Int, vs[1]/2, RoundUp), 2)...],)\n", " )\n", "\n", "\n", "sheep_reprod = RuleApp(:reproduce, sheep_reprod_rule, \n", " id(S), homomorphism(S, s_reprod_r)) |> tryrule\n", "\n", "view_LV(rewrite(Coords(sheep_reprod_rule), X))\n" ] }, { "cell_type": "code", "execution_count": 46, "id": "215677dd", "metadata": {}, "outputs": [ { "data": { "image/svg+xml": [ "\n", "\n", "\n", "\n", "\n", "\n", "G\n", "\n", "\n", "\n", "v1\n", "\n", "11\n", "\n", "\n", "\n", "v2\n", "\n", "\n", "\n", "\n", "v3\n", "\n", "\n", "\n", "\n", "v4\n", "\n", "\n", "\n", "\n", "w1\n", "\n", "1⁵\n", "\n", "\n", "\n", "w2\n", "\n", "2⁵\n", "\n", "\n", "\n", "s1\n", "\n", "1⁵\n", "\n", "\n", "\n", "s2\n", "\n", "2⁵\n", "\n", "\n", "\n" ], "text/plain": [ "Catlab.Graphics.Graphviz.Graph(\"G\", true, \"neato\", Statement[Node(\"v1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"11\", :shape => \"circle\", :color => \"tan\", :pos => \"0,1!\")), Node(\"v2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"0,0!\")), Node(\"v3\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,0!\")), Node(\"v4\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :shape => \"circle\", :color => \"lightgreen\", :pos => \"1,1!\")), Node(\"w1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.257235291686873,1.0522285128192137!\", :color => \"red\")), Node(\"w2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"1.0021286008315382,0.27952073275749506!\", :color => \"red\")), Node(\"s1\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"1⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.7916706192984608,1.0652711855236812!\", :color => \"lightblue\")), Node(\"s2\", OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"2⁵\", :shape => \"square\", :width => \"0.3px\", :height => \"0.3px\", :fixedsize => \"true\", :pos => \"0.023232632932794553,0.32032924351948766!\", :color => \"lightblue\"))], OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:label => \"\", :labelloc => \"t\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}(:shape => \"plain\", :style => \"filled\"), OrderedCollections.OrderedDict{Symbol, Union{String, Catlab.Graphics.Graphviz.Html}}())" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" } ], "source": [ "g_inc_n = deepcopy(G)\n", "set_subpart!(g_inc_n,1, :grass_eng, 0); \n", "rem_part!(g_inc_n, :Eng, 1)\n", "\n", "g_inc_rule = Rule(id(G), id(G);\n", " ac=[AppCond(homomorphism(G, g_inc_n), false)],\n", " expr=(Eng=[vs->only(vs)-1],))\n", "g_inc = RuleApp(:GrassIncrements,g_inc_rule, G) |> tryrule\n", "\n", "view_LV(rewrite(Coords(g_inc_rule), X))" ] }, { "cell_type": "code", "execution_count": 47, "id": "c1147bdb", "metadata": {}, "outputs": [ { "ename": "LoadError", "evalue": "MethodError: no method matching mk_sched(::NamedTuple{(), Tuple{}}, ::NamedTuple{(:init,), Tuple{Symbol}}, ::NamedTuple{(:S, :I, :G, :turn, :maybe, :lft, :rght, :fwd, :repro, :starve), Tuple{LV, LV, LV, Conditional, Conditional, Vararg{Schedule, 5}}}, ::Expr)\n\n\u001b[0mClosest candidates are:\n\u001b[0m mk_sched(::NamedTuple, ::NamedTuple, \u001b[91m::Names\u001b[39m, \u001b[91m::Union{AbstractDict, NamedTuple}\u001b[39m, \u001b[91m::Expr\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[36mAlgebraicRewriting\u001b[39m \u001b[90m~/.julia/packages/AlgebraicRewriting/S1Bfw/src/schedules/\u001b[39m\u001b[90m\u001b[4mWiring.jl:52\u001b[24m\u001b[39m\n", "output_type": "error", "traceback": [ "MethodError: no method matching mk_sched(::NamedTuple{(), Tuple{}}, ::NamedTuple{(:init,), Tuple{Symbol}}, ::NamedTuple{(:S, :I, :G, :turn, :maybe, :lft, :rght, :fwd, :repro, :starve), Tuple{LV, LV, LV, Conditional, Conditional, Vararg{Schedule, 5}}}, ::Expr)\n\n\u001b[0mClosest candidates are:\n\u001b[0m mk_sched(::NamedTuple, ::NamedTuple, \u001b[91m::Names\u001b[39m, \u001b[91m::Union{AbstractDict, NamedTuple}\u001b[39m, \u001b[91m::Expr\u001b[39m)\n\u001b[0m\u001b[90m @\u001b[39m \u001b[36mAlgebraicRewriting\u001b[39m \u001b[90m~/.julia/packages/AlgebraicRewriting/S1Bfw/src/schedules/\u001b[39m\u001b[90m\u001b[4mWiring.jl:52\u001b[24m\u001b[39m\n", "", "Stacktrace:", " [1] top-level scope", " @ In[47]:6" ] } ], "source": [ "# Stuff that happens once per sheep \n", "#----------------------------------\n", "\n", "# 25% chance of left turn, 25% chance of right turn, 50% stay in same direction\n", "# 50% chance of reproducing\n", "general = mk_sched((;),(init=:S,), (\n", " S = S, I = I, G = G,\n", " turn = const_cond([1.,2.,1.], S; name=:turn), \n", " maybe = uniform(2, S), \n", " lft = sheep_rotate_l, \n", " rght = sheep_rotate_r, \n", " fwd = sheep_fwd, \n", " repro = sheep_reprod, \n", " starve = sheep_starve), \n", " quote \n", " out_l, out_str, out_r = turn(init)\n", " moved = fwd([lft(out_l), out_str, rght(out_r)]) \n", " out_repro, out_no_repro = maybe(moved)\n", " return starve([repro(out_repro), out_no_repro])\n", "end)\n", "view_sched(general; names=N)" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.9.3", "language": "julia", "name": "julia-1.9" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.9.3" } }, "nbformat": 4, "nbformat_minor": 5 }