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r-irber-irbe/proof-skills/skills/lean-bigraph-modeling/SKILL.md

lean-bigraph-modeling

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: Robin Milner Bigraphical Reactive Systems (BRS). DO NOT USE FOR: standard simple graphs without containment hierarchy (@lean-math-discrete). TRIGGERS: bigraph, place graph, link graph, hyperedge, containment forest.

The file

We split this skill into the rules it gives an agent

3 rules. About 0 are common, 2 are distinctive, and 1 is very specific to this project.

  • ≈0

    Common · estimate

    Many files like this have a rule of this kind.

  • ≈2

    Distinctive · estimate

    This author's own choices. Worth a look.

  • 1

    Very specific

    Tied to their project's names, files or tools. Probably skip.

  • Common
  • Distinctive
  • Very specific
  1. Distinctive:

    STOP if estimated belief that the bigraph representation satisfies structural acyclicity is below 0.90 -- ask user via HITL channel.

    line 54
  2. Very specific:

    STOP if custom axioms are proposed -- all bigraph theorems must resolve solely on propext and Quot.sound.

    line 57
  3. Distinctive:

    STOP if link rewiring leaks into place containment -- verify orthogonality by definitional reflexivity.

    line 59

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

Lean 4 Milner Bigraphical Reactive Systems Modeling

Guide to formalizing Milner Bigraphs (Place Graphs + Link Graphs), interface faces, tensor products, and categorical composition in Lean 4.

Routing

  • USE FOR: Robin Milner Bigraphical Reactive Systems (BRS), orthogonal Place Graph (containment forest) and Link Graph (relational hyperedges), tensor product, categorical composition, interface faces, and structural well-formedness proofs in Lean 4.
  • DO NOT USE FOR: standard simple graphs without containment hierarchy (delegate to @lean-math-discrete); abstract monoidal category theory without bigraphs (delegate to @lean-math-foundations).
  • TRIGGERS: bigraph, place graph, link graph, hyperedge, containment forest, milner, tensor product, categorical composition, port rewiring.

Workflow

  1. Model the Place Graph as a parent pointer function parent : NodeId -> Option NodeId with explicit acyclicity invariants.
  2. Model the Link Graph as hyperedges connecting sets of ports linkMap : Port -> Option EdgeId with typed relation kinds.
  3. Formulate interface boundaries as faces <width, names>, where width represents sites/regions and names represent inner/outer link endpoints.
  4. Prove orthogonality: demonstrate that rewiring link hyperedges leaves parent containment invariant (rfl).
  5. Prove composition properties: prove tensor product commutativity (place_tensor_count_comm) and depth monotonicity under categorical grafting.
  6. Verify against templates/Template_Bigraph.md.

Recovery & STOP

  • STOP if estimated belief that the bigraph representation satisfies structural acyclicity is below 0.90 -- ask user via HITL channel.
  • STOP if custom axioms are proposed -- all bigraph theorems must resolve solely on propext and Quot.sound.
  • STOP if link rewiring leaks into place containment -- verify orthogonality by definitional reflexivity.

Handoffs

  • Predecessors: agent:gateway, skill:lean-math-discrete (graph definitions), skill:lean-proof (tactics).
  • Successors: skill:lean-proof (theorem discharge), skill:lean-proof-review (axiom and invariant audit).

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/lean-bigraph-modeling-handbook.md .

See also

  • ../../references/lean-bigraph-modeling-handbook.md -- Complete lean-bigraph-modeling Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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