An OpenLearn-style free course introducing the KRL stack: what it is, why it exists, and how to use it.
Scaffold. Directory structure is in place. Content is pending.
- Mathematicians new to computational knot theory
- Programmers curious about domain-specific query languages grounded in algebra
- Open University OpenLearn browsers looking for a worked example of formal/algebraic DSL design
Knot theory's skein relations, how resolution is the central operation, why "query" would undersell it.
Open tangles, closed tangles, ports, crossings, PD codes, composition. Introduce TangleIR as the canonical interchange object.
Stack layers: KRL surface → TanglePL → TangleIR → Skein.jl + KnotTheory.jl via KRLAdapter.jl → QuandleDB semantic fingerprints.
Walkthrough: trefoil, figure-eight. Running a KRL program through the stack.
R1, R2, R3 moves. Simplification. Isotopy invariants.
Quandle presentations. Fundamental quandle as a functor. Colouring counts.
Skein.jl as the store; query by invariant.
Octadic structure, observation functors, KRL as a resolution system.
Tropical types, Katagoria/TypeLL integration. (Requires user's notes to be written first.)
openlearn/
├── README.md (this file)
├── modules/ (module content — markdown/adoc/notebook)
├── exercises/ (interactive exercises, worksheets)
└── references/ (bibliography, links, pre-reqs)
- Basic linear algebra
- Undergraduate abstract algebra (groups, modules — not strictly required)
- Ability to read Julia or follow pseudocode
- No prior knot theory required (covered from scratch)
~8–12 hours of study (typical OpenLearn course length).
Each module should include:
- Learning outcomes (3–5 bullet points)
- Narrative explanation with diagrams (SVG preferred)
- Interactive exercises that can run in the KRL playground
- "Reflection" prompt at the end
- References to further reading
Modules 7 and 8 are blocked on the user's own notes crystallising (Verisim octadic framework, Katagoria, TypeLL, tropical types).