What is lambda expression?

Lambda functions are functions that actually have no name. Thus, mathematicians simplified to the impossibility the format of the recording function, and in general lambda calculi tried to formalize the calculations

λx.x 

λ - means that it is a lambda function. All that is after it is a list of arguments, ideally of absolutely any type, including another lambda function. After the point comes the "function body", and only then, in fact, the argument goes, which will be passed. So

 λx.x+2 2 // вернёт 4 

The example is more complicated:

 λx.x 2 λy.y+1 // результат 3 

Here, the x parameter is another lambda function λy.y + 1 , into which parameter 2 is passed. That is, any lambda function is a higher order function, it can take another function as an argument and return a function:

 λx.λy.y+x+3 2 // вернёт λy.y+5, т.к. x был равен двум. λx.λy.y+x+3 2 3 // вернёт 8. Фактически это каррирование: сначала функция принимает аргумент 2 и возвращает функцию, которая принимает ещё один аргумент и возвращает результат. 

If interested, I once wrote similar things in C #

Now let's see how all our examples will look like in C #. Here, as the lambda function, I use Func , where T is the type of the argument, and U is the type of the return value:

 1) Func<int, int> func = x=>x; 2) var result = new Func<int,int>(x=>x+2)(2); 3) var result = new Func<Func<int,int>, int>(x=>x(2))(new Func<int,int>(y=>y+1)); 4) var result = new Func<int, Func<int, int>>(x=>y=>y+x+3)(2); 5) var result = new Func<int, Func<int, int>>(x=>y=>y+x+3)(2)(3); 

The difficulty is only an explicit indication of the type of the arguments and the return value.