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Category-theoretic graph rewriting with DPO, SPO, and SqPO pushouts for C-Sets. Declarative transformation of acset data structures.
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Attributed C-Sets as algebraic databases. Category-theoretic data structures generalizing graphs and dataframes with Gay.jl color integration.
ACSets (Attributed C-Sets): Algebraic databases with Specter-style bidirectional
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| name | algebraic-rewriting |
| description | Category-theoretic graph rewriting with DPO, SPO, and SqPO pushouts for C-Sets. Declarative transformation of acset data structures. |
| metadata | {"trit":-1,"color":"#0BAD20"} |
AlgebraicRewriting.jl is a Julia library for performing category-theoretic rewrites over C-Sets and other Catlab.jl data structures.
| Type | Description | Use Case |
|---|---|---|
| DPO | Double Pushout | Safe deletion (no dangling edges) |
| SPO | Single Pushout | Greedy deletion |
| SqPO | Sesqui-Pushout | Cloning + deletion |
A rewrite rule consists of:
using AlgebraicRewriting
# Define a rule: merge two vertices
L = @acset Graph begin V=2; E=1; src=[1]; tgt=[2] end
K = @acset Graph begin V=1 end
R = @acset Graph begin V=1 end
rule = Rule(L, K, R)
G = @acset Graph begin
V = 4
E = 3
src = [1, 2, 3]
tgt = [2, 3, 4]
end
# Find matches and rewrite
matches = homomorphisms(L, G)
G′ = rewrite(rule, G, matches[1])
L ←─ K ─→ R
↓ ↓ ↓
G ←─ D ─→ H
The context D ensures no "dangling edges" after deletion.
Supports cloning via the final pullback complement:
# Clone a vertex
L = @acset Graph begin V=1 end
K = @acset Graph begin V=1 end
R = @acset Graph begin V=2 end
clone_rule = Rule(L, K, R; type=:SqPO)
# sRGB boundary learning with rewriting seed
gay_seed!(0xabfca37b6b4bc699)
# Forward mode autodiff
∂params = Enzyme.gradient(Forward, loss, params, seed)
0xabfca37b6b4bc699algebraic-rewriting (-1) ⊗ acsets-hatchery (0) ⊗ gay-monte-carlo (+1) = 0 ✓
acsets-hatchery - ACSet data structurestopos-adhesive-rewriting - Adhesive categoriesdpo-rewriting - Graph transformationworld-a - AlgebraicJulia ecosystemPart of: para-mensch-commons.