algebraic-rewriting
Category-theoretic graph rewriting with DPO, SPO, and SqPO pushouts for C-Sets. Declarative transformation of acset data structures.
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- 2026年6月10日 11:55
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来源说明 · 只读预览- name
- algebraic-rewriting
- description
- Category-theoretic graph rewriting with DPO, SPO, and SqPO pushouts for C-Sets. Declarative transformation of acset data structures.
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- {"trit":-1,"color":"#0BAD20"}
# Algebraic Rewriting
## Overview
**AlgebraicRewriting.jl** is a Julia library for performing category-theoretic rewrites over C-Sets and other Catlab.jl data structures.
## Rewriting Approaches
| Type | Description | Use Case |
|------|-------------|----------|
| **DPO** | Double Pushout | Safe deletion (no dangling edges) |
| **SPO** | Single Pushout | Greedy deletion |
| **SqPO** | Sesqui-Pushout | Cloning + deletion |
## Core Concepts
### Rewrite Rules
A rewrite rule consists of:
- **L** (left) - Pattern to match
- **K** (interface) - What to preserve
- **R** (right) - Replacement pattern
```julia
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)
```
### Apply Rewriting
```julia
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])
```
## Double Pushout (DPO)
```
L ←─ K ─→ R
↓ ↓ ↓
G ←─ D ─→ H
```
The context D ensures no "dangling edges" after deletion.
## Sesqui-Pushout (SqPO)
Supports cloning via the final pullback complement:
```julia
# 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)
```
## Gay.jl Integration
```julia
# sRGB boundary learning with rewriting seed
gay_seed!(0xabfca37b6b4bc699)
# Forward mode autodiff
∂params = Enzyme.gradient(Forward, loss, params, seed)
```
## Documentation
- [Full Documentation](https://algebraicjulia.github.io/AlgebraicRewriting.jl/dev/)
- [Brown 2022](https://arxiv.org/abs/2111.03784) - Theoretical foundation
## Repository
- **Source**: plurigrid/AlgebraicRewriting.jl (fork of AlgebraicJulia)
- **Seed**: `0xabfca37b6b4bc699`
- **Index**: 496/1055
- **Color**: #c25d0b
## GF(3) Triad
```
algebraic-rewriting (-1) ⊗ acsets-hatchery (0) ⊗ gay-monte-carlo (+1) = 0 ✓
```
## Related Skills
- `acsets-hatchery` - ACSet data structures
- `topos-adhesive-rewriting` - Adhesive categories
- `dpo-rewriting` - Graph transformation
- `world-a` - AlgebraicJulia ecosystem
## Para(Optic) atlas
Part of: `para-mensch-commons`.
在 GitHub 查看