The term "function application" in Haskell

Question

I'm currently learning Haskell, and have encountered the term "function application" a couple of times, without really understanding what is meant by it.

Could someone try to explain the meaning of the term in Haskell, or eventually in general?

Answer 1

"Function application" here just means more or less the same thing as "passing an argument to the function". For example, if you have a function f :: Int -> Int and an x :: Int then f x :: Int is an expression where the expression x is "applied" as an argument to f *.

There is no real built-in operator for doing function application in Haskell (other than the whitespace that separates a function from its argument). Prelude exports the ($) function though, which is (some unusual oddities aside) just function application: i.e. ($) f x is the same as f x (this is mostly used for some syntactic tricks, although it occasionally has other uses as well)

---

*: It's been pointed out to me that people usually think of this in terms of applying a function to an argument rather than an argument to a function, I don't think this makes much difference for understanding the meaning of application here though

Answer 2

It's mostly just standard English usage.

"Function application" is just application specifically of functions. "Application" in this context is just the noun corresponding to the verb "apply"; it means the act or process of applying something.

To "apply something" means to use it. To "apply A to B" means to do something to B using A. So "apply a function" means to use/call the function on something. In Haskell when I write the expression f x I am applying f to x.

Thus "function application" is just a term for the general concept of applying functions. In specific contexts it might be used to talk about:

1. The broad notion of applying functions in general
2. The syntax used to express "apply this function to that argument" in a programming language (e.g. "function application is by adjacency in Haskell", or "function application in Python uses C-like syntax")
3. A specific bit of code that is applying a function
4. In Haskell $ is often explained as "the function application operator", since f $ x = f x is more-or-less its definition

Or anything related.