ACSets Hatchery

Overview

ACSets.jl provides acsets ("attributed C-sets") - data structures generalizing both graphs and data frames. They are an efficient in-memory implementation of category-theoretic relational databases.

Core Features

• Acset schemas - Category-theoretic data structure definitions
• Acsets - Instances of schemas (like database rows)
• Tabular columns - Efficient columnar storage
• Serialization - JSON/binary format support

What Are ACSets?

An ACSet is a functor from a category C to Set, with attributes. This means:

• Objects become tables
• Morphisms become foreign keys
• Attributes add data types to objects

Usage

using ACSets

# Define a schema
@present SchGraph(FreeSchema) begin
    V::Ob
    E::Ob
    src::Hom(E, V)
    tgt::Hom(E, V)
end

# Create an acset
g = @acset Graph begin
    V = 3
    E = 2
    src = [1, 2]
    tgt = [2, 3]
end

Extensions

• Catlab.jl - Homomorphisms, limits/colimits, functorial data migration
• AlgebraicRewriting.jl - DPO/SPO/SqPO rewriting for acsets

Learning Resources

1. Graphs and C-sets I - What is a graph?
2. Graphs and C-sets II - Half-edges and rotation systems
3. Graphs and C-sets III - Reflexive graphs and homomorphisms
4. Graphs and C-sets IV - Propositional logic of subgraphs

Gay.jl Integration

# Rec2020 wide gamut with acset seed
gay_seed!(0xb4545686b9115a09)

# Mixed mode checkpointing
params = OkhslParameters()
∂params = Enzyme.gradient(Reverse, loss, params, seed)

Citation

Patterson, Lynch, Fairbanks. Categorical data structures for technical computing. Compositionality 4, 5 (2022). arXiv:2106.04703

Repository

• Source: plurigrid/ACSets.jl (fork of AlgebraicJulia/ACSets.jl)
• Seed:

  0xb4545686b9115a09

• Index: 494/1055
• Color: #204677

GF(3) Triads

algebraic-rewriting (-1) ⊗ acsets-hatchery (0) ⊗ gay-monte-carlo (+1) = 0 ✓
catcolab-ologs (-1) ⊗ acsets-hatchery (0) ⊗ catcolab-schemas (+1) = 0 ✓
catcolab-decapodes (-1) ⊗ acsets-hatchery (0) ⊗ catcolab-petri-nets (+1) = 0 ✓
tasks-acset (-1) ⊗ acsets-hatchery (0) ⊗ calendar-acset (+1) = 0 ✓

Mixing-Optimal Cross-Layer Bridges

catcolab-stock-flow (+1) [MIXING]

# Stock-flow models as ACSet instances
@acset StockFlow(SchStockFlow) begin
  Stock = [:S, :I, :R]; Flow = 2
end

catcolab-petri-nets (+1) [MIXING]

# Petri nets via AlgebraicPetri.jl
@acset LabelledPetriNet(SchPetri) begin
  S = [:idle, :active]; T = [:start, :stop]
end

gmail-anima (0) [MIXING]

# Email threads as ACSet graph
@acset ThreadGraph(SchThread) begin
  Message = 5; reply_to = [nothing, 1, 1, 2, 3]
end

catcolab-ologs (-1) [MIXING]

# Ologs as the conceptual foundation
# Every ACSet schema IS an olog instance

Related Skills

• acsets-algebraic-databases

  - Full ACSet guide

• specter-acset

  - Bidirectional navigation

• world-a

  - AlgebraicJulia ecosystem

Forward Reference

• unified-reafference (ACSet schema consumer)

Patterns That Work

• Schema-first database design
• Morphism-based foreign keys
• Integration with unified-reafference

Patterns to Avoid

• Ad-hoc schema changes
• Missing attribute type annotations