Lambda. From a branch a leaf grows. From a trunk a branch grows. A single function could make each leaf, each branch—what makes one makes many. An earthworm crawls among the tree’s roots.
A lambda expression describes a pattern. From mathematics, the lambda calculus describes the world in patterns. In C# a lambda is a function that uses clear and short syntax.
An example. A common place to use lambdas is with List. Here we use FindIndex, which receives a Predicate method. We specify this as a lambda expression.Left, right:To the left, we have arguments. The “x” is just a name—we can use any valid name. The result is on the right.
Often:We pass lambda expressions as arguments, for sorting or for searching. We use them in queries. 


Based on: .NET 4.7 (2017)
C# program that uses lambda, List
using System;
using System.Collections.Generic;
class Program
{
    static void Main()
    {
        List<int> elements = new List<int>() { 10, 20, 31, 40 };
        // ... Find index of first odd element.
        int oddIndex = elements.FindIndex(x => x % 2 != 0);
        Console.WriteLine(oddIndex);
    }
}
Output
2
Lambda details
x          The argument name.
=>         Separates argument list from result expression.
x % 2 !=0  Returns true if x is not even.
Detailed examples. We take a closer look at lambdas and anonymous functions. The => operator separates the parameters to a method from its statements in the method’s body.Tip:Lambda expressions use the token => in an expression context. In this context, the token is not a comparison operator.
Goes to:The => operator can be read as “goes to.” It is always used when declaring a lambda expression.
Invoke:With Invoke, a method on Func and Action, we execute the methods in the lambdas. 
C# program that uses lambda expressions
using System;
class Program
{
    static void Main()
    {
        //
        // Use implicitly-typed lambda expression.
        // ... Assign it to a Func instance.
        //
        Func<int, int> func1 = x => x + 1;
        //
        // Use lambda expression with statement body.
        //
        Func<int, int> func2 = x => { return x + 1; };
        //
        // Use formal parameters with expression body.
        //
        Func<int, int> func3 = (int x) => x + 1;
        //
        // Use parameters with a statement body.
        //
        Func<int, int> func4 = (int x) => { return x + 1; };
        //
        // Use multiple parameters.
        //
        Func<int, int, int> func5 = (x, y) => x * y;
        //
        // Use no parameters in a lambda expression.
        //
        Action func6 = () => Console.WriteLine();
        //
        // Use delegate method expression.
        //
        Func<int, int> func7 = delegate(int x) { return x + 1; };
        //
        // Use delegate expression with no parameter list.
        //
        Func<int> func8 = delegate { return 1 + 1; };
        //
        // Invoke each of the lambda expressions and delegates we created.
        // ... The methods above are executed.
        //
        Console.WriteLine(func1.Invoke(1));
        Console.WriteLine(func2.Invoke(1));
        Console.WriteLine(func3.Invoke(1));
        Console.WriteLine(func4.Invoke(1));
        Console.WriteLine(func5.Invoke(2, 2));
        func6.Invoke();
        Console.WriteLine(func7.Invoke(1));
        Console.WriteLine(func8.Invoke());
    }
}
Output
2
2
2
2
4
2
2
A syntax review. Above we see many usages of lambda expressions. Sorry for the long example. The => operator separates arguments from methods. It does not compare numbers.Left side:This is the parameters. It can be empty. Sometimes it can be implicit (derived from the right).
Right side:This is a statement list inside curly brackets with a return statement, or an expression.
Func1 through func8. Above, func1 through func8 denote anonymous function instances. The C# compiler often turns different syntax forms into the same code.
Func. The key part of Func is that it returns a value. It can have zero, or many, arguments. But its invariant is a return value, indicated by the TResult parametric type.Func
Func examples
Func<TResult>              Has one result value, no parameter.
Func<T, TResult>           Has one result value, one parameter.
Func<T1, T2, TResult>      Has one result value, two parameters.
Func<T1, T2, T3, TResult>  ....
Action. This class indicates a function that receives no parameter and returns no value. It matches a void method with no arguments. This guy is a solitary character.Action
Delegate. The delegate keyword denotes an anonymous function. After this keyword, we use a formal parameter list. We can omit the list if there are no parameters.Delegate
Anonymous functions. This term includes both delegates and lambda syntaxes. An anonymous function has no name. Perhaps it is running from the law.Anonymous FunctionsOverloading:Because it has no name, method overloading is not possible for anonymous functions.
OverloadNote:Many developers regard lambda expressions as a complete improvement over (and replacement for) the delegate syntax.
Predicate. Here we use this type with an int parameter. With a lambda expression, we specify that the function returns true if the argument is equal to 5.PredicateInvoke:In this program, the Invoke method is used to show that the Predicate works as expected. 
C# program that uses Predicate
using System;
class Program
{
    static void Main()
    {
        Predicate<int> predicate = value => value == 5;
        Console.WriteLine(predicate.Invoke(4));
        Console.WriteLine(predicate.Invoke(5));
    }
}
Output
False
True
Comparison. This type is specifically used to compare objects. It is useful when calling the List.Sort or Array.Sort methods. It can be used with any object type.ComparisonPerformance:Using methods such as List.Sort or Array.Sort (with a Comparison) is often faster than using LINQ to sort on a property.
Events. Like any other method, events can be specified as lambda expressions. With events, many event handlers are called when a certain thing happens. This can simplify some programs.Event
Performance. I benchmarked a lambda against an anonymous method, one using the delegate keyword. I used the functions as arguments to the Count() extension.Result:I found no differences. The lambda expression performed the same as the explicit Func instance.
Thus:Lambda expressions cause no excess performance hit beyond other delegate syntaxes. 
Locals used in benchmark: C#
int[] array = { 1 };
Func<int, bool> f = delegate(int x)
{
    return x == 1;
};
Lambda expression tested: C#
int c = array.Count(element => element == 1);
Delegate tested: C#
int c = array.Count(f);
Expression-bodied methods. A method can be specified with lambda expression syntax. We provide a method name, and the method is compiled like a lambda. A “return” statement is implicit.Return: Expression-Bodied
C# program that uses lambda syntax, method
class Program
{
    static int TreeBranches(int branches, int trunks) => (branches * trunks);
    static void Main()
    {
        // Call the expression-bodied method.
        System.Console.WriteLine(TreeBranches(10, 2));
    }
}
Output
20
Expressive power. Lambdas advance a language. We can achieve the same thing with regular, non-lambda methods. But they make a language easier to use, more “expressive.”Higher-order procedures can serve as powerful abstraction mechanisms, vastly increasing the expressive power of our language.
Structure and Interpretation of Computer Programs: MIT
Specification. The C# language specification describes anonymous function types. The annotated edition of The C# Programming Language (3rd Edition) covers all syntaxes available.Tip:We can find more detail on this topic using the precise technical terminology on page 314 of this book.
Boring:This is pretty boring. Proceed at your own risk. Unless you are thinking about making a C# website, it may not be worth the effort.
Some help. Lambdas have unique syntactic rules. We had some help from the C# specification itself. We used lambdas with zero, one or many arguments, and with a return value.
Anonymous functions. These have no names, but we learned lots of their details. With the delegate keyword, we also specify method objects.



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