This is not intended to be an in-depth introduction to functions, but rather show how a few features works together that allows us to build larger functionality based on smaller building blocks.

I'll use F# to show the concepts here. Not all languages works the same way, but a lot should easily transfer to your functional language of choice. F# is a functional-first, multi-paradigm, programming language for the .NET platform.

The syntax highlighted blocks in this post might be immediately followed by a block with non-highlighted evaluation of the preceding example. This is the same result you would get if you typed the block in the read-eval-print-loop (repl) manually. You can follow there examples by using fsi.exe on Windows or fsharpi on *nix operating systems.

A block of source code like the following:

let i = 1

Might be immediately followed by a block like the following, which shows the result of evaluating the code block.

val i : int = 1

Let's dive in with a small example. We'll implement the following pseudo-C# function in F#:

public static int Add(int x, int y) { return x + y; }
Add(2, 3);

let add x y = x + y
add 2 3

val add : x:int -> y:int -> int
val it : int = 5

let will bind a symbol to a value or function. Here we bind the name add to a function taking two parameters. The syntax for functions is a lot terser than C#. Parameters and arguments are separated by space rather than comma, and we don't wrap them in parenthesis. The types are also inferred in many cases so you don't have to specify them when it doesn't improve the program. The last expression is also returned from the function automatically.

The type of the function is int -> int -> int, which means it takes two ints and returns an int. A function taking int and string, returning float, would be int -> string -> float.

You might have seen lambdas (nameless functions) in various other languages, and in F#, it's called fun

(fun x y -> x + y) 2 3

val it : int = 5

We can also bind anonymous functions, thus giving it a name.

A function has parameters. The value we "pass in" for a parameter is called an argument. We say that we apply a function to arguments. For the above example, x and y are parameters. 2 and 3 are arguments. We apply the anonymous function to these arguments, thus binding the parameters x to 2 and y to 3. When the last parameter is bound, the function is evaluated.

let add = fun x y -> x + y
add 2 3

val add : x:int -> y:int -> int
val it : int = 5

Notice that this is exactly the same as our first version of add! let add x y = x + y is just a shorthand for let add = fun x y -> x + y.

But I've been lying about this function; It isn't a function taking two parameters at all! It's a function taking a single argument, returning a function that takes a single argument!

let add =
    fun x ->
        fun y ->
            x + y
add 2 3

val add : x:int -> y:int -> int
val it : int = 5

This also means that -> is right associative. The type int -> int -> int should read (int -> (int -> int)); takes a single int, returns a function which takes an int and returns an int.

Notice that the innermost lambda fun y refers to the variable x which defined as a parameter or in the body of the lambda. This means x is a free variable, which must be evaluated from the surrounding environment.

But.. If add takes a single parameter, what happens if we call it with a single argument?

let add =
  fun x ->
    fun y ->
      x + y

let add2 = add 2

// alsoAdd2 has bound x to 2, thus becoming
let alsoAdd2 =
  fun y ->
    2 + y

add2 3

val add : x:int -> y:int -> int
val add2 : (int -> int)
val alsoAdd2 : y:int -> int
val it : int = 5

This is called Partial Function Application. We're applying the function add to 2, thus binding x to 2 in the environment of fun y. In the fun y lambda, x is no longer free, and it's the same as alsoAdd2 . We say that a function with free variables such as fun y is a closure (closes over its environment).

The process of translating a function from many parameters to nested functions taking only a single parameter is called currying. In languages such as F# and Haskell, this is automatic; all functions takes just a single parameter, and functions taking multiple parameters are just syntactic sugar.

Currying and closures are the main features we need to start creating more complex functions by combining more primitive functions.

Closures can also be used to hide implementation details or state. The following example creates a counter. You can never modify the variable directly.

let mkCounter () =
  let mutable x = 0
  let get () = x
  let inc () = x <- x + 1
  (get, inc)

let (getX, incX) = mkCounter ()
let (getY, incY) = mkCounter ()

incX ()
incX ()
incX ()

incY ()

(getX (), getY ())

val mkCounter : unit -> (unit -> int) * (unit -> unit)
val incX : (unit -> unit)
val getX : (unit -> int)
val incY : (unit -> unit)
val getY : (unit -> int)
val it : int * int = (3, 1)

A common pattern in programming is to process some data in a pipeline without caring much about the intermediate steps.

X x = FetchSomething();
Y y = SomeProcessing(x);
DoSomething(y);

// And sometimes it's inlined to avoid temporary variables
DoSomething(SomeProcessing(FetchSomething()));

// Or a helper function is created
void LotsOfStuff() {
  X x = FetchSomething();
  Y y = SomeProcessing(x);
  DoSomething(y);
}

// Or even a class can be created to support method chaining
class C {
  X x;
  Y y;

  C FetchSomething() {
    this.x = ActualFetchSomething();
    return this;
  }

  C SomeProcessing() {
    this.y = ActualSomeProcessing(x);
    return this;
  }

  C DoSomething() {
    ActualDoSomething(y);
    return this;
  }
}

var c = new C();
c.FetchSomething().SomeProcessing().DoSomething();

In functional programming, we can build bigger functions by composing smaller functions.

let compose f g x = g (f x)

val compose : f:('a -> 'b) -> g:('b -> 'c) -> x:'a -> 'c

The strange 'a types are generic arguments, and they will be inferred from the functions you pass into compose. If we don't omit redundant parenthesis, it becomes clearer (a -> b) -> (b -> c) -> (a -> c). "Given a function from a to b and a function from b to c, create a new function from a to c".

compose will first run the first function, and then use the result of the first as an argument to the second function. And this can be nested so we can create arbitrary complex functions compose (compose first next) last.

let fetchSomething () = 1
let someProcessing x = x + 1
let doSomething y = ()

// Compose them in multiple operations
let fetchThenProcess = compose fetchSomething someProcessing
let fetchThenProcessThenDoSomething = compose fetchThenProcess doSomething

// Or all in one
let lotsOfStuff = compose (compose fetchSomething someProcessing) doSomething

val fetchSomething : unit -> int
val someProcessing : x:int -> int
val doSomething : y:'a -> unit
val fetchThenProcess : (unit -> int)
val fetchThenProcessThenDoSomething : (unit -> unit)
val lotsOfStuff : (unit -> unit)

While this works fine, there's a bit noise in the form of parenthesis and function names. Luckily, F# contains an infix alias for compose.

(>>)

val it : (('a -> 'b) -> ('b -> 'c) -> 'a -> 'c)

Composing a set of operations would now be op1 >> op2 >> op3 >> .. >> opN

let lotsOfStuff = fetchSomething >> someProcessing >> doSomething

val lotsOfStuff : (unit -> unit)

Another useful function is apply. It's the kind of functions that looks utterly useless, but makes "pipelines" a lot easier to read.

let apply x f = f x

val apply : x:'a -> f:('a -> 'b) -> 'b

Soooo… Instead of writing f 1 we can write apply 1 f! Profit! But when we consider partial application, apply 1 will create a function that will pass 1 as an argument to any function. This can be used to supply common parameters to functions. apply connection transaction config creates a function that will send those arguments to the functions you apply. apply also has a useful infix version, |>, which shows a common use-case for apply.

let f x = x+1
let g x = x.ToString()
let h (x : string) = x.ToLower()

1
|> f
|> g
|> h

val f : x:int -> int
val g : x:'a -> string
val h : x:string -> string
val it : string = "2"

This could also be written as

(f >> g >> h) 1

val it : string = "2"

Or even

1 |> (f >> g >> h)

val it : string = "2"

This concludes our little introduction. We've talked a bit about currying, partial function application, arguments, parameters, closures, compose and apply. There's a lot more to be said about each of these topics, and a whole lot more about functions in general. But this is enough to start exploring how to use functions for abstractions rather than classes.