acsets-hatchery

# 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 ```julia 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](https://blog.algebraicjulia.org/post/2020/09/cset-graphs-1/) - What is a graph? 2. [Graphs and C-sets II](https://blog.algebraicjulia.org/post/2020/09/cset-graphs-2/) - Half-edges and rotation systems 3. [Graphs and C-sets III](https://blog.algebraicjulia.org/post/2021/04/cset-graphs-3/) - Reflexive graphs and homomorphisms 4. [Graphs and C-sets IV](https://blog.algebraicjulia.org/post/2021/09/cset-graphs-4/) - Propositional logic of subgraphs ## Gay.jl Integration ```julia # 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](https://arxiv.org/abs/2106.04703) ## Repository - **Source**: plurigrid/ACSets.jl (fork of AlgebraicJulia/ACSets.jl) - **Seed**: `0xb4545686b9115a09` - **Index**: 494/1055 - **Color**: #204677 ## GF(3) Triad ``` algebraic-rewriting (-1) ⊗ acsets-hatchery (0) ⊗ gay-monte-carlo (+1) = 0 ✓ ``` ## Related Skills - `acsets-algebraic-databases` - Full ACSet guide - `specter-acset` - Bidirectional navigation - `world-a` - AlgebraicJulia ecosystem