Why is Pattern not a tree?

Pattern<V> is recursive and looks tree-like in structure, but calling it a tree leads to wrong expectations about traversal, equality, and composition.

A tree implies:

• A single root with a distinguished root position
• A clear parent-child hierarchy
• Traversal from root to leaves
• Nodes at "higher" levels are more significant than nodes at "lower" levels

None of these holds in general for Pattern<V>. A pattern can represent:

• A graph relationship, where the two element patterns are endpoints — neither is "above" the other
• A walk, where elements are traversed in order as a sequence
• A pure value with no elements at all (atomic pattern)
• A line of a poem, where the elements are words and the parent is a stanza

The decorated sequence model makes no hierarchy claim. Elements are ordered sub-parts; the value decorates them. The meaning of that relationship is determined by the context, not the structure.

Calling Pattern<V> a tree also suggests tree-specific algorithms (depth-first search, parent pointers, tree balancing) that do not apply. The correct operations are map, fold, para, combine — structure-preserving transformations, not tree traversals.