Above is a lambda calculus interpreter. Enter a lambda expression then click evaluate. The expression currently in the interpreter is the factorial function along with an argument of 5 (signified by the last 5 f's in the expression). Upon clicking evaluate, after a bit of waiting, the result of 5! = 120 will by displayed, this time in the form of 120 f's. For a bit more explanation, here's the main parts of the above expression:

Y-Combinator

This acts as a loop for the following expression.

Factorial function body

Notice that the first argument is a function called fact. This is another function identical to this one. Unlike regular programming languages that support recursion out of the box, in lambda calculus functions don't have assigned names, so a function can't call itself. Instead to make a recursive call, a function must take a copy of itself as an argument. The preceding expression, the Y-combinator takes this loop body and passes it into itself as many times as necessary.

Number 5

In lambda calculus an integer N is represented by a function that takes another function and apply it N times. You can think of it as a loop with a counter variable of N.