Baumnotationen

Baumnotationen, or tree notations, are formal schemes for encoding hierarchical data in the form of trees. They specify how nodes and their parent‑child relationships are represented in a way that can be read by humans and processed by computers. The term is used across disciplines to describe the general idea rather than a single standardized notation.

In computer science, common tree notations include bracketed representations, s-expressions, and data formats such as JSON and XML. Bracketed notation uses nested brackets or parentheses to reflect the tree structure, for example: [root [child1] [child2 [grandchild]]]. S-expressions (as used in Lisp) encode trees as sequences within parentheses, removing extra punctuation. JSON and XML express trees as nested objects or elements, preserving the parent–child relationships of the data they represent.

In linguistics, parse trees are often shown in bracket notation or linear bracketing. Example: [S [NP the cat] [VP sat [PP on [NP the mat]]]]. The Penn Treebank style uses a similar bracketed form for syntactic structures, enabling consistent annotation and automated processing.

In mathematics and computer science, tree notation is used to represent expressions where operators form internal nodes and operands form leaves. Notations such as Polish (prefix) and Reverse Polish (postfix) notation linearize the same tree to facilitate parsing by machines or calculators, while preserving the underlying hierarchical structure.

In biology and related fields, formats like the Newick notation encode phylogenetic trees as nested parentheses with optional branch lengths, providing a compact, machine-readable way to store evolutionary relationships.

Baumnotationen emphasize readability and parsability; the choice of notation depends on the domain, tooling, and the intended audience. They provide a unifying concept for representing complex hierarchical data across disciplines.