What is the difference between currying and partia

Question

I quite often see on the Internet various complaints that other peoples examples of currying are not currying, but are actually just partial application.

I've not found a decent explanation of what partial application is, or how it differs from currying. There seems to be a general confusion, with equivalent examples being described as currying in some places, and partial application in others.

Could someone provide me with a definition of both terms, and details of how they differ?

Answer 1

Note: this was taken from F# Basics an excellent introductory article for .NET developers getting into functional programming.

Currying means breaking a function with many arguments into a series of functions that each take one argument and ultimately produce the same result as the original function. Currying is probably the most challenging topic for developers new to functional programming, particularly because it is often confused with partial application. You can see both at work in this example:

let multiply x y = x * y    
let double = multiply 2
let ten = double 5

Right away, you should see behavior that is different from most imperative languages. The second statement creates a new function called double by passing one argument to a function that takes two. The result is a function that accepts one int argument and yields the same output as if you had called multiply with x equal to 2 and y equal to that argument. In terms of behavior, it’s the same as this code:

let double2 z = multiply 2 z

Often, people mistakenly say that multiply is curried to form double. But this is only somewhat true. The multiply function is curried, but that happens when it is defined because functions in F# are curried by default. When the double function is created, it’s more accurate to say that the multiply function is partially applied.

The multiply function is really a series of two functions. The first function takes one int argument and returns another function, effectively binding x to a specific value. This function also accepts an int argument that you can think of as the value to bind to y. After calling this second function, x and y are both bound, so the result is the product of x and y as defined in the body of double.

To create double, the first function in the chain of multiply functions is evaluated to partially apply multiply. The resulting function is given the name double. When double is evaluated, it uses its argument along with the partially applied value to create the result.