sigma action on morphisms

working draft for SimpleMigrations

src/categorical_algebra/CSets.jl

@@ -211,15 +211,25 @@ hasvar(X::ACSetFunctor) = hasvar(X.acset)
 dom(F::ACSetFunctor) = FinCat(Presentation(ACSet(F)))
 
 #not clear this couldn't just always give the Vars
-function codom(F::ACSetFunctor)
-  hasvar(F) ? TypeCat{Union{SetOb,VarSet},Union{FinDomFunction{Int},VarFunction}}() :
-    TypeCat{SetOb,FinDomFunction{Int}}()
-end
-
-Categories.do_ob_map(F::ACSetFunctor, x) = 
-  (hasvar(F,functor_key(x)) ? VarSet : SetOb)(F.acset, functor_key(x))
-Categories.do_hom_map(F::ACSetFunctor, f) =  
-  (hasvar(F,functor_key(f)) ? VarFunction : FinFunction)(F.acset, functor_key(f))
+function codom(::ACSetFunctor)
+  TypeCat{Union{SetOb,VarSet},Union{FinDomFunction{Int},VarFunction}}()
+  # hasvar(F) ? TypeCat{Union{SetOb,VarSet},Union{FinDomFunction{Int},VarFunction}}() :
+  #   TypeCat{SetOb,FinDomFunction{Int}}()
+end
+
+function Categories.do_ob_map(F::ACSetFunctor, x)
+  S = acset_schema(F.acset)
+  Symbol(x) ∈ ob(S) && return SetOb(F.acset, functor_key(x))
+  Symbol(x) ∈ attrtypes(S) && return VarSet(F.acset, functor_key(x))
+  error("Bad object $S $x")
+end
+function Categories.do_hom_map(F::ACSetFunctor, x)
+  S = acset_schema(F.acset)
+  kx = functor_key(x)
+  Symbol(kx) ∈ homs(S; just_names=true) && return FinFunction(F.acset, kx)
+  Symbol(kx) ∈ attrs(S; just_names=true) && return VarFunction(F.acset, kx)
+  error("Bad hom $S $x")
+end 
 
 functor_key(x) = x
 functor_key(expr::GATExpr{:generator}) = first(expr)
@@ -442,11 +452,11 @@ function coerce_components(S, components, X::ACSet{<:PT}, Y) where PT
   end)
   ocomps = NamedTuple(map(objects(S)) do c
     c => coerce_component(c, get(components, c, 1:0), 
-                          nparts(X,c), nparts(Y,c); kw[c]...)
+                          maxpart(X,c), maxpart(Y,c); kw[c]...)
   end)
   acomps = NamedTuple(map(attrtypes(S)) do c
     c => coerce_attrvar_component(c, get(components, c, 1:0), 
-          TypeSet(X, c), TypeSet(Y, c), nparts(X,c), nparts(Y,c); kw[c]...)
+          TypeSet(X, c), TypeSet(Y, c), maxpart(X,c), maxpart(Y,c); kw[c]...)
   end)
   return merge(ocomps, acomps)
 end 
@@ -1353,7 +1363,7 @@ abstract_attributes(f::ACSetTransformation) = abstract_attributes(dom(f)) ⋅ f
 
 """
 Find some part + attr that refers to an AttrVar. 
-Throw error if none exists (i.e. `i` is a wandering variable).
+Return `nothing` if none exists (i.e. `i` is a wandering variable).
 """
 function var_reference(X::ACSet, at::Symbol, i::Int)
   S = acset_schema(X)
@@ -1363,9 +1373,50 @@ function var_reference(X::ACSet, at::Symbol, i::Int)
       return (f, c, first(inc))
     end
   end
-  error("Wandering variable $at#$p")
 end
 
+
+"""
+Given a value for each variable, create a morphism X → X′ which applies the 
+substitution. We do this via pushout.
+
+  O --> X    where C has AttrVars for `merge` equivalence classes 
+  ↓          and O has only AttrVars (sent to concrete values or eq classes 
+  C          in the map to C.
+
+`subs` and `merge` are dictionaries keyed by attrtype names
+
+`subs` values are int-keyed dictionaries indicating binding, e.g. 
+`; subs = (Weight = Dict(1 => 3.20, 5 => 2.32), ...)`
+
+`merge` values are vectors of vectors indicating equivalence classes, e.g.
+`; merge = (Weight = [[2,3], [4,6]], ...)`
+"""
+function sub_vars(X::ACSet, subs::AbstractDict=Dict(), merge::AbstractDict=Dict()) 
+  S = acset_schema(X)
+  O, C = [constructor(X)() for _ in 1:2]
+  ox_, oc_ = Dict{Symbol, Any}(), Dict{Symbol,Any}()
+  for at in attrtypes(S)
+    d = get(subs, at, Dict())
+    ox_[at] = AttrVar.(filter(p->p ∈ keys(d) && !(d[p] isa AttrVar), parts(X,at)))
+    oc_[at] = Any[d[p.val] for p in ox_[at]]
+    add_parts!(O, at, length(oc_[at]))
+
+    for eq in get(merge, at, [])
+      isempty(eq) && error("Cannot have empty eq class")
+      c = AttrVar(add_part!(C, at))
+      for var in eq
+        add_part!(O, at)
+        push!(ox_[at], AttrVar(var))
+        push!(oc_[at], c)
+      end
+    end
+  end
+  ox = ACSetTransformation(O,X; ox_...)
+  oc = ACSetTransformation(O,C; oc_...)
+  return first(legs(pushout(ox, oc)))
+end 
+
 # Mark as deleted
 #################
 

src/categorical_algebra/Chase.jl

@@ -95,7 +95,7 @@ function pres_to_eds(S::Presentation; types=Dict(), name="")
     eds["$(f_)_total"] = tot
   end
 
-  return Dict([Symbol(k) => v for (k,v) in collect(eds)])
+  return Dict{Symbol, ACSetTransformation}(Symbol(k) => v for (k,v) in eds)
 end
 
 """
@@ -226,17 +226,15 @@ this occured).
 function from_c_rel(J::ACSet,cset::ACSet) 
     S = acset_schema(cset)
     res = typeof(cset)()
-    for o in ob(S)
+    for o in types(S)
       add_parts!(res, o, nparts(J, o))
     end
     total = true
-    for (m, s, _) in homs(S)
+    for (m, s, _) in arrows(S)
       msrc, mtgt = add_srctgt(m)
       length(J[msrc]) == length(Set(J[msrc])) || error("non-unique $J")
-      total &= length(J[msrc]) != nparts(J, s)
-      for (domval, codomval) in zip(J[msrc], J[mtgt])
-        set_subpart!(res, domval, m, codomval)
-      end
+      total &= length(J[msrc]) == nparts(J, s)
+      res[J[msrc], m] = J[mtgt]
     end
     return res => total
 end

src/categorical_algebra/FinCats.jl

@@ -469,12 +469,19 @@ end
 """
 const FinFunctor{Dom<:FinCat,Codom<:FinCat} = FinDomFunctor{Dom,Codom}
 
+
 FinFunctor(maps, dom::FinCat, codom::FinCat) = FinDomFunctor(maps, dom, codom)
 FinFunctor(ob_map, hom_map, dom::FinCat, codom::FinCat) =
   FinDomFunctor(ob_map, hom_map, dom, codom)
 FinFunctor(ob_map, hom_map, dom::Presentation, codom::Presentation) =
   FinDomFunctor(ob_map, hom_map, FinCat(dom), FinCat(codom))
 
+"""Assume that dom ⊆ codom"""
+FinFunctor(dom::Presentation, codom::Presentation) = FinFunctor(
+  Dict(x=>x for x in ob_generators(FinCat(dom))), 
+  Dict(x=>x for x in hom_generators(FinCat(dom))), 
+  dom, codom)
+
 Categories.show_type_constructor(io::IO, ::Type{<:FinFunctor}) =
   print(io, "FinFunctor")
 
@@ -615,15 +622,32 @@ See also: [`is_functorial`](@ref).
 function is_natural(α::FinTransformation; check_equations::Bool=true)
   F, G = dom(α), codom(α)
   C, D = dom(F), codom(F) # == dom(G), codom(G)
+  # @show typeof(F)
+  # @show typeof(G)
+  # println("F"); show(stdout,"text/plain", force(F))
+  # println("\nG"); show(stdout,"text/plain", force(G))
+  # println("\nC"); show(stdout,"text/plain", C)
+  # println("\nD"); show(stdout,"text/plain", D)
   all(ob_generators(C)) do c
     α_c = α[c]
+    # println("")
+    # @show (α_c, c) 
+    # @show (dom(D, α_c), ob_map(F,c))
+    # @show dom(D, α_c) == ob_map(F,c) 
+    # @show (codom(D, α_c) , ob_map(G,c))
+    # @show (codom(D, α_c) == ob_map(G,c))
     dom(D, α_c) == ob_map(F,c) && codom(D, α_c) == ob_map(G,c)
   end || return false
 
   if check_equations
     all(hom_generators(C)) do f
       Ff, Gf = hom_map(F,f), hom_map(G,f)
       α_c, α_d = α[dom(C,f)], α[codom(C,f)]
+      # @show (f, Ff, Gf)
+      # @show (α_c, α_d)
+      # @show compose(D, α_c, Gf)
+      # @show compose(D, Ff, α_d)
+      # @show is_hom_equal(D, compose(D, α_c, Gf), compose(D, Ff, α_d))
       is_hom_equal(D, compose(D, α_c, Gf), compose(D, Ff, α_d))
     end || return false
   end