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?"