Basic nauty integration

Project.toml

@@ -35,13 +35,15 @@ Graphviz_jll = "3c863552-8265-54e4-a6dc-903eb78fde85"
 MetaGraphs = "626554b9-1ddb-594c-aa3c-2596fe9399a5"
 SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
 TikzPictures = "37f6aa50-8035-52d0-81c2-5a1d08754b2d"
+nauty_jll = "55c6dc9b-343a-50ca-8ff2-b71adb3733d5"
 
 [extensions]
 CatlabConvexExt = "Convex"
 CatlabDataFramesExt = "DataFrames"
 CatlabGraphsExt = "Graphs"
 CatlabGraphvizExt = "Graphviz_jll"
 CatlabMetaGraphsExt = "MetaGraphs"
+CatlabNautyExt = "nauty_jll"
 CatlabSCSExt = "SCS"
 CatlabTikzPicturesExt = "TikzPictures"
 

ext/CatlabNautyExt.jl

@@ -0,0 +1,92 @@
+module CatlabNautyExt
+
+using nauty_jll
+import Catlab.CategoricalAlgebra.CSets: ACSetTransformation, Multispan, 
+  Multicospan, apex, legs
+using Catlab.Theories: ⋅
+using ACSets
+import ACSets: call_nauty, strhsh, orbits, ngroup, canon, dom, codom
+using StructEquality
+
+# Morphisms up to isomorphism
+#----------------------------
+
+"""
+Given an ACSet X and a canonical element of the iso class, [X], obtain either
+a map X -> [X] or (if `inv=true`) [X]->X
+"""
+function ACSetTransformation(start::ACSet, n::CSetNautyRes; inv::Bool=false) 
+  comps = Dict([k => (inv ? invperm(v) : v) for (k, v) in pairs(canonmap(n))])
+  args = (inv ? reverse : identity)([start, canon(n)])
+  ACSetTransformation(args...; comps...)
+end
+
+"""
+Given an ACSetTransformation A -> B (and canonical isos A→A' and B→B′), we 
+construct a canonical ACSetTransformation A′→B′.
+"""
+@struct_hash_equal struct ACSetTransformationNautyRes <: NautyRes 
+  dom::CSetNautyRes
+  codom::CSetNautyRes
+  canon::ACSetTransformation # Cache the computation of this
+end
+
+"""Optionally pass in the CSetNautyRes for (co)dom if known"""
+function call_nauty(f::ACSetTransformation; dom_canon=nothing, codom_canon=nothing) 
+  d, cd = map([dom=>dom_canon, codom=>codom_canon]) do (get, canon)
+    isnothing(canon) ? call_nauty(get(f)) : canon
+  end
+  d′ = ACSetTransformation(dom(f), d; inv=true)
+  cd′ = ACSetTransformation(codom(f), cd)
+  ACSetTransformationNautyRes(d, cd, d′⋅f⋅cd′)
+end
+
+dom(n::ACSetTransformationNautyRes) = n.dom
+codom(n::ACSetTransformationNautyRes) = n.codom
+
+strhsh(n::ACSetTransformationNautyRes) = strhsh(n.dom) * strhsh(n.codom) 
+orbits(n::ACSetTransformationNautyRes) = orbits(dom(n)) => orbits(codom(n))
+generators(n::ACSetTransformationNautyRes) = generators(dom(n)) => generators(codom(n))
+ngroup(n::ACSetTransformationNautyRes) = ngroup(dom(n)) => ngroup(codom(n))
+canon(n::ACSetTransformationNautyRes) = n.canon
+
+# (Co)spans up to isomorphism
+#----------------------------
+
+abstract type SpanCospanNautyRes <: NautyRes end
+
+@struct_hash_equal struct MultispanNautyRes <: SpanCospanNautyRes 
+  apex::CSetNautyRes
+  legs::AbstractVector{ACSetTransformationNautyRes}
+end
+
+@struct_hash_equal struct MulticospanNautyRes <: SpanCospanNautyRes 
+  apex::CSetNautyRes
+  legs::AbstractVector{ACSetTransformationNautyRes}
+end
+
+apex(s::SpanCospanNautyRes) = s.apex
+legs(s::SpanCospanNautyRes) = s.legs
+Base.length(s::SpanCospanNautyRes) = length(s.legs)
+
+function call_nauty(f::Multispan)
+  ap = call_nauty(apex(f))
+  MultispanNautyRes(ap, call_nauty.(f; dom_canon=ap))
+end
+
+function call_nauty(f::Multicospan)
+  ap = call_nauty(apex(f))
+  MulticospanNautyRes(ap, call_nauty.(f; codom_canon=ap))
+end
+
+
+strhsh(n::SpanCospanNautyRes) = join(strhsh.(legs(n)))
+orbits(n::SpanCospanNautyRes) = [orbits(apex(n)), orbits.(codom.(legs(n)))...]
+generators(n::SpanCospanNautyRes) = [generators(apex(n)), generators.(codom.(legs(n)))...]
+ngroup(n::SpanCospanNautyRes) = [ngroup(apex(n)), ngroup.(codom.(legs(n)))...]
+canon(n::SpanCospanNautyRes) = Multispan(canon.(legs(n)))
+
+# C-Set diagrams up to isomorphism - TODO
+#----------------------------------------
+
+end # module

src/categorical_algebra/FreeDiagrams.jl

@@ -25,7 +25,7 @@
 using GATlab
 using ...Theories, ...Graphs, ..FinCats
 import AlgebraicInterfaces: ob, hom, dom, codom
-import ..FinCats: FreeCatGraph, FinDomFunctor, collect_ob, collect_hom
+import ..FinCats: FreeCatGraph, FinDomFunctor, collect_ob, collect_hom, force
 
 # Diagram interface
 ###################
@@ -161,6 +161,8 @@
 Base.eltype(span::Multispan) = eltype(span.legs)
 Base.length(span::Multispan) = length(span.legs)
 
+force(span::Multispan) = Multispan(apex(span), force.(legs(span)))
+
 """ Multicospan of morphisms in a category.
 
 A multicospan is like a [`Cospan`](@ref) except that it may have a number of
@@ -203,6 +205,8 @@
 Base.eltype(cospan::Multicospan) = eltype(cospan.legs)
 Base.length(cospan::Multicospan) = length(cospan.legs)
 
+force(span::Multicospan) = Multicospan(apex(span), force.(legs(span)))
+
 """ Bundle together legs of a multi(co)span.
 
 For example, calling `bundle_legs(span, SVector((1,2),(3,4)))` on a multispan

test/Project.toml

@@ -17,6 +17,7 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+nauty_jll = "55c6dc9b-343a-50ca-8ff2-b71adb3733d5"
 
 [compat]
 Graphs = "^1"

test/categorical_algebra/CSets.jl

@@ -3,6 +3,8 @@ using Test
 
 using Catlab.Theories, Catlab.Graphs, Catlab.CategoricalAlgebra
 
+
+
 @present SchDDS(FreeSchema) begin
   X::Ob
   Φ::Hom(X,X)
@@ -796,4 +798,36 @@ rem_part!(p3, :E, 3)
 rem_part!(p3, :V, 4)
 @test !in_bounds(f)
 
+
+# Test nauty interface
+######################
+
+if !Sys.iswindows()
+  using nauty_jll
+
+  # G1 = 3-cycle, G2 = 3-cycle with extra vertex
+  G1 = @acset Graph begin V=3; E=3; src=[1,2,3]; tgt=[2,3,1] end;
+  G1′ = @acset Graph begin V=3; E=3; src=[3,2,1]; tgt=[2,1,3] end;
+  G2 = @acset Graph begin V=4; E=3; src=[2,3,4]; tgt=[3,4,2] end;
+  G2′ = @acset Graph begin V=4; E=3; src=[1,2,3]; tgt=[2,3,1] end;
+  h,h′ = call_nauty.(homomorphism.([G1,G1′],[G2,G2′]));
+  @test canon(h)  == canon(h′)
+
+  # Test pullback up to iso
+  G = @acset Graph begin V=3; E=3; src=[1,1,2]; tgt=[1,2,2] end
+  f = homomorphism(path_graph(Graph, 3), G; initial=(E=[1,2],))
+  g = homomorphism(path_graph(Graph, 2), G; initial=(E=[2],))
+  eq = pullback(f,g);
+  canon_eq = canon(call_nauty(cone(eq))) |> force
+
+  bkwd_path_3 = @acset Graph begin V=3; E=2; src=[3,2]; tgt=[2,1] end
+  bkwd_path_2 = @acset Graph begin V=2; E=1; src=2; tgt=1 end
+  bkwd_apex = @acset Graph begin V=3; E=1; src=1; tgt=3 end
+  L = homomorphisms(bkwd_apex, bkwd_path_3; monic=true, initial=(E=[2],)) |> only
+  R = homomorphisms(bkwd_apex, bkwd_path_2; initial=(V=[2,2,1],)) |> only
+  expected = canon(call_nauty(Span(L,R)))
+  @test expected == canon_eq
+
 end
+
+end # module