Ways of Defining Functions/Relation To Type Theory
- Composite function: is formed by the composition of two functions f and g, by mapping x to f(g(x)).
- Inverse function: is declared by "doing the reverse" of a given function (e.g. arcsine is the inverse of sine).
- Piecewise function: is defined by different expressions at different intervals.
In general, functions are often defined by specifying the name of a dependent variable, and a way of calculating what it should map to. For this purpose, the symbol or Church's is often used. Also, sometimes mathematicians notate a function's domain and codomain by writing e.g. . These notions extend directly to lambda calculus and type theory, respectively.
Read more about this topic: List Of Types Of Functions
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