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Use migrations from Catlab.jl #81

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14 changes: 8 additions & 6 deletions benchmark/Agents.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -207,12 +207,14 @@ const WS = WS_Generic{Int}
@acset_type WS′_Generic(TheoryWS′, part_type=BitSetParts) <: HasGraph
const WS′ = WS′_Generic{Int,Tuple{Int,Int}}

F = Migrate(
Dict(:Sheep => :Wolf, :Wolf => :Sheep),
Dict([:sheep_loc => :wolf_loc, :wolf_loc => :sheep_loc,
:sheep_eng => :wolf_eng, :wolf_eng => :sheep_eng,
:countdown => :countdown]), TheoryWS, WS)
F2 = Migrate(TheoryWS, WS, TheoryWS′, WS′; delta=false)
F = ΔMigration(FinFunctor(
Dict(:V=>:V, :E=>:E, :Eng=>:Eng, :Dir=>:Dir, :Sheep => :Wolf, :Wolf => :Sheep, :Time=>:Time),
Dict(:src=>:src, :tgt=>:tgt, :dir=>:dir,
:sheep_loc => :wolf_loc, :wolf_loc => :sheep_loc,
:sheep_eng => :wolf_eng, :wolf_eng => :sheep_eng, :countdown => :countdown,
:sheep_dir => :wolf_dir, :wolf_dir => :sheep_dir), SchLV, SchLV), LV);

F2 = ΣMigration(FinFunctor(SchLV, SchLV′), LV′);

#=
Create an n × n grid with periodic boundary conditions. Edges in each cardinal
Expand Down
3 changes: 1 addition & 2 deletions docs/literate/game_of_life.jl
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Expand Up @@ -80,8 +80,7 @@ and obtain a state of the world with coordinates (the canonical way to do this
is to assign "variables" for the values of the coordinates).
=#

F = Migrate(SchLifeCoords, LifeCoords; delta=false); # adds coordinates
# F⁻¹ = DeltaMigration(FinFunctor(idₒ, idₘ, SchLife, SchLifeCoords)); # removes coordinates
F = ΣMigration(FinFunctor(SchLife, SchLifeCoords), LifeCoords); # adds coordinates

# # Helper functions

Expand Down
16 changes: 8 additions & 8 deletions docs/literate/lotka_volterra.jl
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Expand Up @@ -124,19 +124,20 @@ migration, we can define them in terms of sheep and then migrate along `F` to
obtain the analogous actions for wolves.
=#

F = Migrate(
Dict(:Sheep => :Wolf, :Wolf => :Sheep, :Time=>:Time),
Dict([:sheep_loc => :wolf_loc, :wolf_loc => :sheep_loc,
:sheep_eng => :wolf_eng, :wolf_eng => :sheep_eng, :countdown => :countdown,
:sheep_dir => :wolf_dir, :wolf_dir => :sheep_dir,]), SchLV, LV);
F = ΔMigration(FinFunctor(
Dict(:V=>:V, :E=>:E, :Eng=>:Eng, :Dir=>:Dir, :Sheep => :Wolf, :Wolf => :Sheep, :Time=>:Time),
Dict(:src=>:src, :tgt=>:tgt, :dir=>:dir,
:sheep_loc => :wolf_loc, :wolf_loc => :sheep_loc,
:sheep_eng => :wolf_eng, :wolf_eng => :sheep_eng, :countdown => :countdown,
:sheep_dir => :wolf_dir, :wolf_dir => :sheep_dir), SchLV, SchLV), LV);

#=
We ought to be able to take a state of the world (with no coordinate information)
and obtain a state of the world with coordinates (the canonical way to do this
is to assign "variables" for the values of the coordinates).
=#

F2 = Migrate(SchLV, LV, SchLV′, LV′; delta=false);
F2 = ΣMigration(FinFunctor(SchLV, SchLV′), LV′);

# # Initializing and visualizing world states

Expand Down Expand Up @@ -479,8 +480,7 @@ s_die_l = @acset_colim yLV begin s::Sheep; sheep_eng(s) == 0 end;
sheep_die_rule = Rule(hom(G, s_die_l), id(G))
sheep_starve = (RuleApp(:starve, sheep_die_rule,
hom(S, s_die_l), create(G))
⋅
(id([I]) ⊗ Weaken(create(S))) ⋅ merge_wires(I));
⋅ (id([I]) ⊗ Weaken(create(S))) ⋅ merge_wires(I));

# #### Sheep starvation test

Expand Down
2 changes: 1 addition & 1 deletion docs/literate/ptg_simple.jl
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Expand Up @@ -131,4 +131,4 @@ matches = get_matches(moveBreadRule, state)
match = matches[1]

# Compute the new world state after rewriting
new_state = rewrite_match(moveBreadRule, match)
new_state = rewrite_match(moveBreadRule, match)
116 changes: 3 additions & 113 deletions src/categorical_algebra/CSets.jl
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Original file line number Diff line number Diff line change
@@ -1,8 +1,7 @@
module CSets
export extend_morphism, pushout_complement,
can_pushout_complement, dangling_condition, invert_hom, check_pb,
gluing_conditions, extend_morphisms, sub_vars,
Migrate, invert_iso, deattr, var_pullback
gluing_conditions, invert_iso, deattr, var_pullback

using CompTime

Expand Down Expand Up @@ -305,53 +304,11 @@ function cascade_subobj(X::ACSet, sub)
end
return Dict([k => collect(v) for (k,v) in pairs(sub)])
end



# Variables
###########

"""
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

# TODO check if this can be replaced by pullbacks of CSetTransformations
"""
Take an ACSet pullback combinatorially and freely add variables for all
attribute subparts.
Expand Down Expand Up @@ -416,80 +373,13 @@ function homomorphisms(X::Slice,Y::Slice; kw...)
end |> collect
end

function homomorphism(X::Slice,Y::Slice; kw...)
function homomorphism(X::Slice, Y::Slice; kw...)
hs = homomorphisms(X,Y; kw...)
return isempty(hs) ? nothing : first(hs)
end

# Simple Δ migrations (or limited case Σ)
#########################################

"""TODO: check if functorial"""
@struct_hash_equal struct Migrate
obs::Dict{Symbol, Symbol}
homs::Dict{Symbol, Symbol}
P1::Presentation
T1::Type
P2::Presentation
T2::Type
delta::Bool
end

Migrate(s1::Presentation, t1::Type, s2=nothing, t2=nothing; delta=true) =
Migrate(Dict(x => x for x in Symbol.(generators(s1, :Ob))),
Dict(x => x for x in Symbol.(generators(s1, :Hom))),
s1, t1, s2, t2; delta)

Migrate(o::Dict, h::Dict, s1::Presentation, t1::Type, s2=nothing, t2=nothing;
delta::Bool=true) = Migrate(Dict(collect(pairs(o))),
Dict(collect(pairs(h))), s1, t1,
isnothing(s2) ? s1 : s2,
isnothing(t2) ? t1 : t2,
delta)


sparsify(d::Dict{V,<:ACSet}) where V = Dict([k=>sparsify(v) for (k,v) in collect(d)])
sparsify(d::Dict{<:ACSet,V}) where V = Dict([sparsify(k)=>v for (k,v) in collect(d)])
sparsify(::Nothing) = nothing

(F::Migrate)(d::Dict{V,<:ACSet}) where V = Dict([k=>F(v) for (k,v) in collect(d)])
(F::Migrate)(d::Dict{<:ACSet,V}) where V = Dict([F(k)=>v for (k,v) in collect(d)])
(m::Migrate)(::Nothing) = nothing
(m::Migrate)(s::Union{String,Symbol}) = s
function (m::Migrate)(Y::ACSet)
if m.delta
typeof(Y) <: m.T1 || error("Cannot Δ migrate a $(typeof(Y))")
end
S = acset_schema(Y)
X = m.T2()
partsX = Dict(c => add_parts!(X, c, nparts(Y, get(m.obs,c,c)))
for c in ob(S) ∪ attrtypes(S))
for (f,c,d) in homs(S)
set_subpart!(X, partsX[c], f, partsX[d][subpart(Y, get(m.homs,f,f))])
end
for (f,c,_) in attrs(S)
set_subpart!(X, partsX[c], f, subpart(Y, get(m.homs,f,f)))
end
if !m.delta
# undefined attrs (Σ migration) get replaced with free variables
for (f,c,d) in attrs(acset_schema(X))
for i in setdiff(parts(X,c), X.subparts[f].m.defined)
X[i,f] = AttrVar(add_part!(X,d))
end
end
end
return X
end

function (F::Migrate)(f::ACSetTransformation)
d = Dict(map(collect(pairs(components(f)))) do (k,v)
get(F.obs,k,k) => collect(v)
end)
only(homomorphisms(F(dom(f)), F(codom(f)), initial=d))
end

(F::Migrate)(s::Multispan) = Multispan(apex(s), F.(collect(s)))
(F::Migrate)(s::Multicospan) = Multicospan(apex(s), F.(collect(s)))
(F::Migrate)(d::AbstractDict) = Dict(get(F.obs,k, k)=>v for (k,v) in collect(d))

end # module
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