typerystem

A typerystem is a formal framework in programming languages for classifying values and expressions by types and guiding how they can be combined. It helps detect errors such as applying a function to an incompatible argument and can support optimizations and documentation through typed contracts.

A typerystem comprises a set of types and type constructors, rules for building complex types, and a mechanism for checking or inferring types. Static type checking occurs before execution, while dynamic type checking occurs at runtime. Many systems aim for type safety: well-typed programs avoid certain runtime errors.

Typing disciplines vary: static vs dynamic; strong vs weak; nominal vs structural. Static systems catch errors early; dynamic systems offer flexibility. Nominal typing relies on named declarations for compatibility, while structural typing relies on the shape of types. Type inference can reduce annotation burden.

Common features include generics (parametric polymorphism), subtyping, and advanced forms such as union or intersection types, along with type classes or interfaces that define behavior. Real languages mix these ideas to balance safety, expressiveness, and practicality.

Examples range from Java, C#, and TypeScript (static families) to Python with optional typing and to functional languages like Haskell and Rust, which emphasize strong, expressive type systems.

Origins lie in the simply typed lambda calculus and Hindley-Milner polymorphism; modern type systems extend these ideas with richer features and practical language integration.