How does DPO rewriting work here?

It uses the Double Pushout pattern (L ← K → R) to define graph transformations, specifying what to find (L), what to keep (K), and what to replace (R) within a host graph or ACSet instance.

Which software ecosystem does this skill support?

This skill is deeply integrated with the AlgebraicJulia ecosystem, specifically utilizing Catlab.jl, ACSets.jl, and AlgebraicRewriting.jl for implementation.

What are ACSets in the context of this skill?

ACSets (Attributed C-Sets) are functors that treat database schemas as small categories and instances as sets, allowing for mathematically rigorous data manipulation and transformation.

What is the Self-Play Loop?

The Self-Play Loop is a self-refinement monad that iteratively executes queries, evaluates results, and mines new patterns to converge toward stable and optimized data structures.

What is GF(3) conservation in this skill?

GF(3) conservation is a method of triadic skill composition that ensures structural stability by balancing different computational behaviors (represented as trits) within a synergistic triad.

ACSets Relational Thinking

Name: ACSets Relational Thinking
Author: plurigrid

byplurigrid

•

Database Management

Applies category-theoretic principles and Attributed C-Sets to automate database schema modeling and graph transformation workflows.

About

This skill integrates the Topos Institute's RelationalThinking approach with the AlgebraicJulia ecosystem to enable advanced data modeling through Attributed C-Sets (ACSets). It allows Claude to treat databases as functors, enabling sophisticated Double Pushout (DPO) rewriting for complex graph transformations and structural state evolution. By implementing a self-play loop for query refinement and ensuring GF(3) conservation, it provides a mathematically rigorous framework for pattern mining, structural validation, and automated knowledge-based planning in technical computing environments.

Key Features

Double Pushout (DPO) rewriting for rule-based graph and database transformations
Automated self-play loops for iterative query execution, evaluation, and pattern mining
Visualization commands for schema diagrams, instance elements, and homomorphisms
Schema definition and Attributed C-Set (ACSet) instance management using Catlab.jl
2 GitHub stars
GF(3) triadic skill composition for structural stability and conservation checking

Use Cases

Automating knowledge-based planning and state transitions via graph rewriting rules
Modeling complex entity-subtype hierarchies and relational schemas using category theory
Validating structural integrity and data consistency in technical computing workflows

About

Key Features

Double Pushout (DPO) rewriting for rule-based graph and database transformations
Automated self-play loops for iterative query execution, evaluation, and pattern mining
Visualization commands for schema diagrams, instance elements, and homomorphisms
Schema definition and Attributed C-Set (ACSet) instance management using Catlab.jl
2 GitHub stars
GF(3) triadic skill composition for structural stability and conservation checking

Use Cases

Automating knowledge-based planning and state transitions via graph rewriting rules
Modeling complex entity-subtype hierarchies and relational schemas using category theory
Validating structural integrity and data consistency in technical computing workflows