Currying - Motivation

Motivation

Currying is similar to the process of calculating a function of multiple variables for some given values on paper. For example, given the function f(x,y) = y / x:

To evaluate f(2,3), first replace x with 2.
Since the result is a function of y, this function g(y) can be defined as g(y) = f(2,y) = y/2.
Next, replace the y argument with 3, producing g(3) = f(2,3) = 3/2.

On paper, using classical notation, this is usually done all in one step. However, each argument can be replaced sequentially as well. Each replacement results in a function taking exactly one argument. This produces a chain of functions as in lambda calculus, and multi-argument functions are usually represented in curried form.

Some programming languages almost always use curried functions to achieve multiple arguments; notable examples are ML and Haskell, where in both cases all functions have exactly one argument.

If we let f be a function

then the function h where

is a curried version of . Here, is a function that maps an argument y to result z. In particular,

is the curried equivalent of the example above. Note, however, that currying, while similar, is not the same operation as partial function application.

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