Currying functions in C#

This article will look into helper methods for currying functions in C#. The definition of Currying consists of splitting up a function with multiple arguments into multiple functions accepting one argument. But you can also have some of the arguments provided via smaller functions, so be aware also of this alternative. What is in the name currying? The name has nothing to do with cooking from India, but comes from the mathematician Haskell Brooks Curry (!)

https://en.wikipedia.org/wiki/Haskell_Curry

A reason for introducing support for currying is that you can build complex functions from simpler functions as building blocks. Currying is explained great here:
https://www.c-sharpcorner.com/UploadFile/rmcochran/functional-programming-in-C-Sharp-currying/

We will see in the examples that we can provide multiple arguments at once and the syntax will look a bit special compared to other C# code. Curryings benefits is to allow a more flexible way to call a method. You can store into variables calls to a function providing a subset of argument and use that variable to either specify an intermediate other call or get the final result. Note - The function will be called when ALL arguments are provided ONCE ! This helps a lot of avoiding surprising side effects. Let's first look at a sample set of methods we want to support currying.

int FooFourArgs(string st, float x, int j, int k)
{
	Console.WriteLine($"Inside method FooFourArgs. Got parameters: st={st}, x={x}, j={j}, k={k}");
	return 42;
}

int FooThreeArgs(string st, float x, int j)
{
	Console.WriteLine($"Inside method FooThreeArgs. Got parameters: st={st}, x={x}, j={j}");
	return 42;
}

int FooTwoArgs(string st, float x)
{
	Console.WriteLine($"Inside method FooTwoArgs. Got parameters: st={st}, x={x}");
	return 41;
}

int FooOneArgs(string st)
{
	Console.WriteLine($"Inside method FooOneArgs. Got parameters: st={st}");
	return 40;
}

We want to call the sample methods above in a more flexible way by splitting the number of arguments we provide. Let's see the extension methods to call up to four arguments to a function. Note the use of chaining the lambda operator (=>) to provide the support for currying.

public static class FunctionExtensions
{
	public static Func<T1, TResult> Curried<T1, TResult>(this Func<T1, TResult> func)
	{
		return x1 => func(x1);
	}
	
	public static Func<T1, Func<T2, TResult>> Curried<T1, T2, TResult>(this Func<T1, T2, TResult> func)
	{
		return x1 => x2 => func(x1, x2);
	}

	public static Func<T1, Func<T2, Func<T3, TResult>>> Curried<T1, T2, T3, TResult>(this Func<T1, T2, T3, TResult> func)
	{
		return x1 => x2 => x3 => func(x1, x2, x3);
	}

	public static Func<T1, Func<T2, Func<T3, Func<T4, TResult>>>> Curried<T1, T2, T3, T4, TResult>(this Func<T1, T2, T3, T4, TResult> func)
	{
		return x1 => x2 => x3 => x4 => func(x1, x2, x3,x4);
	}
}

The following main method shows how to use these curry helper methods:

void Main()
{
	var curryOneArgsDelegate = new Func<string, int>((st) => FooOneArgs(st)).Curried();
	var curryOneArgsPhaseOne = curryOneArgsDelegate("hello");

	var curryTwoArgsDelegate = new Func<string, float, int>((st, x) => FooTwoArgs(st,x)).Curried();
	var curryTwoArgsPhaseOne = curryTwoArgsDelegate("hello");
	var curryTwoArgsPhaseTwo = curryTwoArgsPhaseOne(3.14f);

	var curryThreeArgsDelegate = new Func<string, float, int, int>((st, x, j) => FooThreeArgs(st, x, j)).Curried();
	var curryThreeArgsPhaseOne = curryThreeArgsDelegate("hello");
	var curryThreeArgsPhaseTwo = curryThreeArgsPhaseOne(3.14f);
	var curryThreeArgsPhaseThree = curryThreeArgsPhaseTwo(123);	
	//Or call currying in a single call passing in two or more parametres
	var curryThreeArgsPhaseOneToThree = curryThreeArgsDelegate("hello")(3.14f)(123);

	var curryFourArgsDelegate = new Func<string, float, int, int, int>((st, x, j, k) => FooFourArgs(st, x, j, k)).Curried();
	var curryFourArgsPhaseOne = curryFourArgsDelegate("hello");
	var curryFourArgsNextPhases = curryFourArgsPhaseOne(3.14f)(123)(456); //just pass in the last arguments if they are known at this stage
	curryFourArgsDelegate("hello")(3.14f)(123)(456); //you can pass in 1-4 parameters to FooFourArgs method - all in a single call for example or one by one
}

The output we get is this. Note that we only call the methods we defined when all parameters are sent in. The function call which had partial argument list provided did not result into a function call.

Inside method FooOneArgs. Got parameters: st=hello
Inside method FooTwoArgs. Got parameters: st=hello, x=3,14
Inside method FooThreeArgs. Got parameters: st=hello, x=3,14, j=123
Inside method FooThreeArgs. Got parameters: st=hello, x=3,14, j=123
Inside method FooFourArgs. Got parameters: st=hello, x=3,14, j=123, k=456

So from a higher level, currying a function f(x,y,z) means adding support that you could call the function like this:
f(x,g(y,z)) or f(x,g(y,h(z))) - there more arguments you get there is more variations of number of parameters and methods you can pass in. Here is another example how you can build up a calculation uing simpler methods.

void Main()
{
	Func Area = (x,y) => x*y;
	Func CubicArea = (x,y,z) => Area.Curried()(Area(x,y))(z);	
	CubicArea(3,2,4); //supplying all arguments manully is okay
}

CubicArea expects THREE arguments. The implementation allows us to use the Area function and via currying we can use that method and provide the last third argument avoiding compilation error. Currying makes your functions allow more flexible ways of being called.