Currying in the context of Function type

In mathematics and computer science, currying is the technique of translating a function that takes multiple arguments into a sequence of families of functions, each taking a single argument.

In the prototypical example, one begins with a function ${\displaystyle f:(X\times Y)\to Z}$ that takes two arguments, one from ${\displaystyle X}$ and one from ${\displaystyle Y,}$ and produces objects in ${\displaystyle Z.}$ The curried form of this function treats the first argument as a parameter, so as to create a family of functions ${\displaystyle f_{x}:Y\to Z.}$ The family is arranged so that for each object ${\displaystyle x}$ in ${\displaystyle X,}$ there is exactly one function ${\displaystyle f_{x}}$, such that for any ${\displaystyle y}$ in ${\displaystyle Y}$, ${\displaystyle f_{x}(y)=f(x,y)}$.