What is a lambda (function)?

Question

For a person without a comp-sci background, what is a lambda in the world of Computer Science?

Answer 1

I got it too. I`ve tried it in JS with this one:

var addAndMult = function(x) {
        return (function(y) {
            return (function(z) {
                return (x+y)*z; 
                });
            });
        };

It adds 2 to 4 then mults the result by 6. However I find it sometimes hard to read :(

Also I`ve made an interesting forEach function:

var forEach = function(arr) {
            return (function(x) {
            for (var i=0; arr[i]; i++) {
                 x(arr[i]);
             }
        });
    }

forEach([1,2,3,4,5])(console.log);

This method will iterate an array and performs an action - in the case printing to the console. Now I too get why labmdas are powerful.

Answer 2

An example of a lambda in Ruby is as follows:

hello = lambda do
    puts('Hello')
    puts('I am inside a proc')
end

hello.call

Will genereate the following output:

Hello
I am inside a proc

Answer 3

The lambda calculus is a consistent mathematical theory of substitution. In school mathematics one sees for example x+y=5 paired with x−y=1. Along with ways to manipulate individual equations it's also possible to put the information from these two together, provided cross-equation substitutions are done logically. Lambda calculus codifies the correct way to do these substitutions.

Given that y = x−1 is a valid rearrangement of the second equation, this: λ y = x−1 means a function substituting the symbols x−1 for the symbol y. Now imagine applying λ y to each term in the first equation. If a term is y then perform the substitution; otherwise do nothing. If you do this out on paper you'll see how applying that λ y will make the first equation solvable.

That's an answer without any computer science or programming.

The simplest programming example I can think of comes from http://en.wikipedia.org/wiki/Joy_(programming_language)#How_it_works:

here is how the square function might be defined in an imperative programming language (C):

int square(int x)
{
    return x * x;
}

The variable x is a formal parameter which is replaced by the actual value to be squared when the function is called. In a functional language (Scheme) the same function would be defined:

(define square
  (lambda (x) 
    (* x x)))

This is different in many ways, but it still uses the formal parameter x in the same way.

---

Added: http://imgur.com/a/XBHub

Answer 4

The name "lambda" is just a historical artifact. All we're talking about is an expression whose value is a function.

A simple example (using Scala for the next line) is:

args.foreach(arg => println(arg))

where the argument to the foreach method is an expression for an anonymous function. The above line is more or less the same as writing something like this (not quite real code, but you'll get the idea):

void printThat(Object that) {
  println(that)
}
...
args.foreach(printThat)

except that you don't need to bother with:

1. Declaring the function somewhere else (and having to look for it when you revisit the code later).
2. Naming something that you're only using once.

Once you're used to function values, having to do without them seems as silly as being required to name every expression, such as:

int tempVar = 2 * a + b
...
println(tempVar)

instead of just writing the expression where you need it:

println(2 * a + b)

The exact notation varies from language to language; Greek isn't always required! ;-)

Answer 5

Slightly oversimplified: a lambda function is one that can be passed round to other functions and it's logic accessed.

In C# lambda syntax is often compiled to simple methods in the same way as anonymous delegates, but it can also be broken down and its logic read.

For instance (in C#3):

LinqToSqlContext.Where( 
    row => row.FieldName > 15 );

LinqToSql can read that function (x > 15) and convert it to the actual SQL to execute using expression trees.

The statement above becomes:

select ... from [tablename] 
where [FieldName] > 15      --this line was 'read' from the lambda function

This is different from normal methods or anonymous delegates (which are just compiler magic really) because they cannot be read.

Not all methods in C# that use lambda syntax can be compiled to expression trees (i.e. actual lambda functions). For instance:

LinqToSqlContext.Where( 
    row => SomeComplexCheck( row.FieldName ) );

Now the expression tree cannot be read - SomeComplexCheck cannot be broken down. The SQL statement will execute without the where, and every row in the data will be put through SomeComplexCheck.

Lambda functions should not be confused with anonymous methods. For instance:

LinqToSqlContext.Where( 
    delegate ( DataRow row ) { 
        return row.FieldName > 15; 
    } );

This also has an 'inline' function, but this time it's just compiler magic - the C# compiler will split this out to a new instance method with an autogenerated name.

Anonymous methods can't be read, and so the logic can't be translated out as it can for lambda functions.

Answer 6

It is a function that has no name. For e.g. in c# you can use

numberCollection.GetMatchingItems<int>(number => number > 5);

to return the numbers that are greater than 5.

number => number > 5

is the lambda part here. It represents a function which takes a parameter (number) and returns a boolean value (number > 5). GetMatchingItems method uses this lambda on all the items in the collection and returns the matching items.