A Function-Theoretic Definition of Data
Abstract — The term data is among the most frequently used and least precisely defined concepts in computing. Standard references converge on an informal characterization of data as "raw facts," but none specify the formal structure that makes a collection of facts addressable, comparable, or processable by a machine. This representational ambiguity propagates into system design as schema drift, serialization defects, and a class of type-confusion vulnerabilities that arise when a fixed byte sequence is silently reinterpreted under an unstated indexing or typing assumption. This paper makes the case for treating data formally as a function from an index set to a value set, sharpens this definition with explicit well-definedness conditions, and positions it against three existing frameworks: Floridi's General Definition of Information, Zins' faceted classification, and the DIKW hierarchy. We derive four corollaries connecting this definition directly to recurring failure modes in software engineering — implicit schema coupling, byte-level reinterpretation, unsound equality checks, and ambiguous serialization contracts — with worked examples for each.