Data types | Type theory

Function type

In computer science and mathematical logic, a function type (or arrow type or exponential) is the type of a variable or parameter to which a function has or can be assigned, or an argument or result type of a higher-order function taking or returning a function. A function type depends on the type of the parameters and the result type of the function (it, or more accurately the unapplied type constructor ยท โ†’ ยท, is a higher-kinded type). In theoretical settings and programming languages where functions are defined in curried form, such as the simply typed lambda calculus, a function type depends on exactly two types, the domain A and the range B. Here a function type is often denoted A โ†’ B, following mathematical convention, or BA, based on there existing exactly BA (exponentially many) set-theoretic functions mappings A to B in the category of sets. The class of such maps or functions is called the exponential object. The act of currying makes the function type adjoint to the product type; this is explored in detail in the article on currying. The function type can be considered to be a special case of the dependent product type, which among other properties, encompasses the idea of a polymorphic function. (Wikipedia).

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From playlist Characteristics of Functions

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๐Ÿ‘‰ Learn about the characteristics of a function. Given a function, we can determine the characteristics of the function's graph. We can determine the end behavior of the graph of the function (rises or falls left and rises or falls right). We can determine the number of zeros of the functi

From playlist Characteristics of Functions

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Related pages

Category of sets | First-class function | Parametric polymorphism | Type constructor | Domain theory | Variable (computer science) | Currying | Higher-order function | Scala (programming language) | Domain of a function | Type inference | Cardinality of the continuum | Computable function | Type signature | Exponential object | Product type | Dependent type | Natural number | Denotational semantics | Function space | Halting problem | Template (C++) | Type erasure | Mathematical logic | Cartesian closed category | Polymorphism (computer science) | Simply typed lambda calculus | Range of a function