# Specifying acsets using Algebraic Data Types

ACSets are an extremely flexible data representation that can store anything you can put in a database. But in order to construct them, you might want something that feels more like a custom programming language. The Graphviz software comes with a custom language called dot files for specifying the data of a graph that Graphviz will draw. In order to make implementing these linguisting interfaces easier, ACSets.jl supports an Algebraic Data Types approach to specification of ACSets.

using ACSets, ACSets.ADTs
using MLStyle
using Test
import ACSets.ADTs: symb2string

Our schema will be labeled graphs. These are graphs with vertex labels.

SchLabeledGraph = BasicSchema([:E,:V], [(:src,:E,:V),(:tgt,:E,:V)],
[:L], [(:label,:V,:L)])

@acset_type LabeledGraph(SchLabeledGraph, index=[:src,:tgt])
Main.LabeledGraph

The basic principle is a nested expression syntax for specifying the ACSet.

s = Statement(:E, [Value(2), Value(3)])
  E(2,3)

You can extract information from an expression with pattern matching from MLStyle.jl

get_table(s) = @match s begin
Statement(t, e) => t
_ => nothing
end
get_arg1(s) = @match s begin
Statement(t, e) => e[1]
end

@test get_table(s) == :E
@test get_arg1(s) == Value(2)
Test Passed

These statements can be grouped together into a list an tagged with the type of ACSet you want to make.

gspec = ACSetSpec(
:(LabeledGraph{Symbol}),
[
Statement(:V, [Kwarg(:label, Value(:a))])
Statement(:V, [Kwarg(:label, Value(:b))])
Statement(:V, [Kwarg(:label, Value(:c))])
Statement(:E, [Value(1), Value(3)])
Statement(:E, [Value(2), Value(3)])
]
)
LabeledGraph{Symbol} begin
V(label=a)
V(label=b)
V(label=c)
E(1,3)
E(2,3)
end

These expressions can be serialized as strings:

sprint(show, gspec)
"LabeledGraph{Symbol} begin \n  V(label=a)\n  V(label=b)\n  V(label=c)\n  E(1,3)\n  E(2,3)\n end"

Or as Julia code:

generate_expr(gspec)
quote
X = LabeledGraph{Symbol}()
end

From the ACSetSpec you can construct the ACSet that it specifies.

gspec = ACSetSpec(
:(LabeledGraph{Symbol}),
[
Statement(:V, [Kwarg(:label, Value(:a))])
Statement(:V, [Kwarg(:label, Value(:b))])
Statement(:V, [Kwarg(:label, Value(:c))])
Statement(:E, [Kwarg(:src, Value(1)), Kwarg(:tgt, Value(3))])
Statement(:E, [Kwarg(:src, Value(2)), Kwarg(:tgt, Value(3))])
]
)
g = construct(LabeledGraph{Symbol}, gspec)
E src tgt
1 1 3
2 2 3
V label
1 a
2 b
3 c

There is an embedding of ACSetSpec into Expr:

hspec = acsetspec(:(LabeledGraph{Symbol}),quote
V(label=a)
V(label=b)
V(label=c)
E(src=1,tgt=3)
E(src=2,tgt=3)
end
)
LabeledGraph{Symbol} begin
V(label=a)
V(label=b)
V(label=c)
E(src=1,tgt=3)
E(src=2,tgt=3)
end

The acsetspec function is a good example of embedding your custom language into Julia syntax That save you the trouble of writing your own lexer and parser for your custom language.

construct(LabeledGraph{Symbol}, hspec) == construct(LabeledGraph{Symbol}, gspec)
true

You can export your specification to a dictionary and put that dictionary into a JSON document this gives you a nice way of serializing the ACSet that is machine readable and row oriented. The ACSet serialization is by column oriented which might be inconvenient for your consumers.

to_dict(gspec)
Dict{Symbol, Any} with 2 entries:
:type => "LabeledGraph{Symbol}"
:data => Dict{Symbol, Any}[Dict(:table=>:V, :fields=>Dict(:label=>:a)), Dict(…