preservedstructure

Preservedstructure is a term used in information design and computer science to describe a property of a transformation whereby the essential structural features of an object are retained after processing. It denotes that a process maps inputs to outputs in a way that preserves relationships, hierarchy, ordering, and constraints defined by an underlying schema or algebraic structure. The term is purposefully general, applied across domains such as data models, programming languages, and linguistic representations.

Origins and usage: The phrase arises in discussions of model-driven engineering, schema-preserving migrations, and structure-preserving algorithms. While not standardized, preservedstructure typically means that the target representation is structurally equivalent to the source with respect to the specified structure, or at least isomorphic in the relevant sense.

Formal considerations: In a mathematical framing, a transformation T on a structured object S preserves structure if there is a correspondence that preserves designated operations, relations, and constraints. Depending on the domain, this can mean preserving algebraic operations, subobjects, ordering, or connectivity. In programming, it may refer to maintaining the abstract syntax tree or object graph shape.

Examples: A JSON transformer that preserves the nesting and sibling order but renames values exemplifies preservedstructure. A compiler that outputs intermediate representations with the same tree structure as the input source also illustrates the concept. In graph algorithms, a relabeling that keeps adjacency preserved without changing connectivity is another case.

Limitations: Achieving perfect preservation can conflict with other goals such as efficiency, backward compatibility, or lossy compression. Verifying preservedstructure typically requires explicit schemas or formal proofs of equivalence. See also: preservation of structure, functor, schema evolution.