typsystem

A type system is a formal framework in a programming language that assigns types to expressions, variables, functions, and modules, and defines how these types can be combined. The primary goal is to prevent certain kinds of errors by ensuring that operations are applied to values of appropriate kinds, such as not applying a number as a function.

Type checking can occur at compile time (static typing) or at run time (dynamic typing). Some languages emphasize safety with strict type rules, while others favor flexibility through implicit conversions or dynamic checks. The notion of typability contributes to error detection, optimization opportunities, and clearer program documentation.

Type systems can be nominal, where types are identified by names and declarations, or structural, where type compatibility is determined by the shape of values. Subtyping and inheritance enable polymorphism, allowing code to operate on values of related types. This shapes how programs are organized and how interchangeable components are composed.

Common features include type inference, where the compiler deduces types without explicit annotations; generics or parametric polymorphism, enabling code to work for any type; and advanced forms such as dependent types or effect systems used in specialized languages. These features affect expressiveness, safety guarantees, and the ease of reasoning about code.

Examples illustrate the variety of designs. ML and Haskell use static, strong type systems with type inference; Java and C# use static, nominal typing with generics; TypeScript provides static-like typing with structural subtyping and type inference; Python and Ruby are dynamically typed. Type systems relate to logic through ideas like the Curry-Howard correspondence and strive for soundness, though some languages embrace gradual typing to blend static and dynamic checking.