functiontype

Functiontype, or function type, is a type that describes the inputs and output of a function. It identifies what argument types a function accepts and what type of value it returns. In statically typed languages, function types are often treated as first-class citizens: they can be stored in variables, passed as parameters, and returned from other functions. This enables higher-order programming, where functions manipulate other functions.

Notation for function types varies by language. A simple form is A -> B, meaning a function that takes an input of type A and yields a result of type B. For multiple parameters, some languages use tuples (A, B) -> C, while others support curried forms like A -> (B -> C). TypeScript uses function types such as (args: A, b: B) => C, and Haskell uses A -> B, with right-associative notation. In languages with structural typing, compatibility of function types depends on the shape of the inputs and outputs; in nominal type systems, compatibility may rely on declared interfaces or function wrappers.

Usage and implications: function types enable higher-order functions, generic programming, and flexible APIs (callbacks, event handlers, and functional interfaces). Variance matters in subtyping: input parameter types are typically contravariant, while output types are covariant. Implementation details vary: some languages have explicit function interfaces or delegates, while others rely on implicit function types and type inference. Runtime representations may differ, ranging from opaque closures to concrete callable objects, depending on the language.

In practice, function types are foundational for expressing and enforcing the contracts of functions within a program, supporting composability, reuse, and type-safe abstractions.