Types

Types are categories that group objects by shared properties and allowed operations. The idea functions across disciplines to organize knowledge, constrain behavior, and enable reasoning.

In philosophy and logic, type theory arranges entities into hierarchical levels to avoid paradoxes and self-reference. This formal approach underpins certain logics and foundations of mathematics.

In mathematics and computer science, a type defines the set of values and the operations that can be performed on them. In programming languages, type systems enforce correct usage of data, help prevent errors, and support abstractions such as polymorphism and generics. Types can be static or dynamic, strong or weak, and may be inferred automatically or checked explicitly. Common types include integers, real numbers, booleans, characters, and strings; more complex types include arrays, records, functions, and algebraic data types such as sum and product types. Type safety and type checking are central goals, often with casts or conversions for interoperability.

In linguistics, the type-token distinction differentiates a type (a distinct word form) from tokens (instances of that form in use). In biology, a type (or type specimen) anchors the name of a species or other taxon, providing a reference point for classification.

Beyond theory, types influence data validation, database schemas, and programming interfaces, shaping how information is stored, processed, and reasoned about. Overall, the notion of type helps distinguish kinds of things while guiding their valid use and interaction.