Concepts

Currying

Definition

Consists in transforming :

• a function taking N parameters Func<T1, T2, ...Tn, TReturn> in C♯

• into a chain of N functions taking 1 parameter Func<T1, Func<Tn, ...Func<Tn, TReturn>>

Partial application

Calling a function with fewer arguments than its number of parameters.

• Possible thanks to currying

• Returns a function taking the remaining number of arguments as parameters.

// Template function with 2 parameters
let insideTag (tagName: string) (content: string) =
    $"<{tagName}>{content}</{tagName}>"

// Helpers with a single parameter `content`
// `tagName` is fixed by partial application
let emphasize = insideTag "em"     // `tagName` fixed to "em"
let strong    = insideTag "strong" // `tagName` fixed to "strong"

// Equivalent less elegant but more explicit
let em content = insideTag "em" content

⚠️ Caution : partial application impacts the signature:

val insideTag: tagName: string -> content: string -> string
val emphasize: (string -> string)  // 👈 (1)(2)
val em: content: string -> string

1. Loss of parameter names (content: string becomes just string)

2. Signature of a function value, hence the parentheses ((string -> string))

Syntax of F♯ functions

Parameters separated by spaces:

• Indicates that functions are curried

• Hence the -> in the signature between parameters

let fn () = result         // unit -> TResult
let fn arg = ()            // T    -> unit
let fn arg = result        // T    -> TResult

let fn x y = (x, y)        // T1 -> T2 -> (T1 * T2)

// Equivalent, explicitly curried:
let fn x = fun y -> (x, y) // 1. With a lambda
let fn x =                 // 2. With a named sub-function
    let fn' y = (x, y)     // 👈 `x` captured from the outer scope
    fn'

IntelliSense with Ionide

💡 In VsCode with Ionide, IntelliSense provides a more readable description of functions, putting each argument in a new line:

let pair x y = (x, y)
// val pair:
//    x: 'a ->
//    y: 'b
//    -> 'a * 'b

let triplet x y z = (x, y, z)
// val triplet:
//    x: 'a ->
//    y: 'b ->
//    z: 'c
//    -> 'a * 'b * 'c

.NET compilation of a curried function

☝ A curried function is compiled differently depending on how it's called!

• Basically, it is compiled as a method with tuple-parameters → Viewed as a regular method when consumed in C♯

Example: F♯ then C♯ equivalent, based on a simplified version from SharpLab:

module A =
    let add x y = x + y
    let value = 2 |> add 1

public static class A
{
    public static int add(int x, int y) => x + y;
    public static int value => 3;
}

• When partially applied, the function is compiled as a pseudo Delegate class extending FSharpFunc<int, int> with an Invoke method that encapsulates the 1st supplied arguments.

Example: F♯ then C♯ equivalent, based on a simplified version from SharpLab:

module A =
    let add x y = x + y
    let addOne = add 1

public static class A
{
    internal sealed class addOne@3 : FSharpFunc<int, int>
    {
        internal static readonly addOne@3 @_instance = new addOne@3();

        internal addOne@3() { }

        public override int Invoke(int y) => 1 + y;
    }

    public static FSharpFunc<int, int> addOne => addOne@3.@_instance;

    public static int add(int x, int y) => x + y;
}

Unified function design

unit type and currying make it possible to design functions simply as:

• Takes a single parameter of any type

  • including unit for a “parameterless” function

  • including another (callback) function

• Returns a single value of any type

  • including unit for a “return nothing” function

  • including another function

👉 Universal signature of a function in F♯: 'T -> 'U.

Parameter order

Between C♯ and F♯, the parameter concerning the main object (the this in case of a method) is not placed in the same place:

• In a method extension C♯, the this object is the first parameter.

  • E.g. items.Select(x => x)

• In F♯, the main object is rather the last parameter: (it's called the data-last style)

  • E.g. List.map (fun x -> x) items

The data-last style favors :

• Pipeline: items |> List.map square |> List.sum

• Partial application: let sortDesc = List.sortBy (fun i -> -i)

• Composition of partially applied functions up to param “data”.

  • (List.map square) >> List.sum

⚠️ There can be some friction with .NET BCL methods because the BCL is data-first driven. The solution is to wrap the method in a new curried function having parameters sorted in an order more F♯ piping friendly.

let startsWith (prefix: string) (value: string) =
    value.StartsWith(prefix)

💡 Tips

Prefer to put 1st the most static parameters = those likely to be predefined by partial applications.

E.g.: “dependencies” that would be injected into an object in C♯.

👉 Partial application is a way to implement the dependency injection in F♯.