An Introduction to Functional Programming Through Lambda Calculus

- 18 -As we will see, normal order is more powerful than applicative order but may be less efficient. For the moment, allfunction applications will be evaluated in normal order.The syntax allows a single name as a λ expression but in general we will restrict single names to the bodies offunctions. This is so that we can avoid having to consider names as objects in their own right, like LISP or Prologliterals for example, as it complicates the presentation. We will discuss this further later on.We will now look at a variety of simple λ functions.2.6. Identity functionConsider the function:λx.xThis is the identity function which returns whatever argument it is applied to. Its bound variable is:xand its body expression is the name:xWhen it is used as the function expression in a function application the bound variable x will be replaced by theargument expression in the body expression x giving the original argument expression.Suppose the identity function is applied to itself:(λx.x λx.x)This is a function application with:λx.xas the function expression and:λx.xas the argument expression.When this application is evaluated, the bound variable:xfor the function expression:λx.xis replaced by the argument expression:λx.xin the body expression:x