Contrast With Partial Function Application
Currying and partial function application are often conflated. The difference between the two is clearest for functions taking more than two arguments.
Given a function of type, currying produces . That is, while an evaluation of the first function might be represented as, evaluation of the curried function would be represented as, applying each argument in turn to a single-argument function returned by the previous invocation. Note that after calling, we are left with a function that takes a single argument and returns another function, not a function that takes two arguments.
In contrast, partial function application refers to the process of fixing a number of arguments to a function, producing another function of smaller arity. Given the definition of above, we might fix (or 'bind') the first argument, producing a function of type . Evaluation of this function might be represented as . Note that the result of partial function application in this case is a function that takes two arguments.
Intuitively, partial function application says "if you fix the first arguments of the function, you get a function of the remaining arguments". For example, if function div stands for the division operation x/y, then div with the parameter x fixed at 1 (i.e., div 1) is another function: the same as the function inv that returns the multiplicative inverse of its argument, defined by inv(y) = 1/y.
The practical motivation for partial application is that very often the functions obtained by supplying some but not all of the arguments to a function are useful; for example, many languages have a function or operator similar to plus_one. Partial application makes it easy to define these functions, for example by creating a function that represents the addition operator with 1 bound as its first argument.
Read more about this topic: Currying
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