structured-decompositions-jl

name: structured-decompositions-jl description: Use when users ask about StructuredDecompositions.jl, structured decompositions, or sheaf-based decision problems (AlgebraicJulia/Catlab).

StructuredDecompositions.jl

You help with Julia tasks involving StructuredDecompositions.jl. Prefer precise, minimal examples and reuse the package's existing API rather than inventing new abstractions.

Quick start

• using StructuredDecompositions
• Build a decomposition from a graph: d = StrDecomp(graph) (optional alg and snd keywords).
• Build from a shape + diagram: d = StrDecomp(shape, diagram, Decomposition) or CoDecomposition.
• Inspect: bags(d), adhesions(d), adhesionSpans(d) (pass true for indexed pairs).
• Lift a functor: use the bold-D function (type \mathbf{D} then Tab in Julia) with signature D(f, d, t::DecompType = d.decomp_type).
• Decide a sheaf-encoded problem: ok, witness = decide_sheaf_tree_shape(f, d).

Guidelines

• decide_sheaf_tree_shape assumes FinSet-valued sheaves; if you pass a solution_space_decomp, ensure it is a CoDecomposition.
• adhesion_filter (not exported) errors on Decomposition; only use it with CoDecomposition.
• Use Catlab types (Graph, ACSetTransformation, FinDomFunctor, FinSet, FinFunction) to build diagrams.
• Prefer small, runnable snippets. If a full example is large, summarize and point to the references.
• If a task needs ACSet schema definitions or Catlab graph basics, consult references/acsets-bridge.md or load the acsets-algebraic-databases skill.

References

• references/overview.md for the API map and key behaviors.
• references/examples.md for minimal usage sketches.
• references/graph-coloring.md for an ASCII-only end-to-end coloring example.
• references/acsets-bridge.md for ACSet/Catlab basics used by this package.

Scripts

• scripts/quickstart.jl builds a simple decomposition and prints bags/adhesions.

Example triggers

• "Make a structured decomposition for this graph."
• "Lift a functor over a decomposition and decide a sheaf."
• "How do I use decide_sheaf_tree_shape for graph coloring?"