An Introduction to Functional Programming Through Lambda Calculus

- 19 -giving:λx.xAn identity operation always leaves its argument unchanged. In arithmetic, adding or subtracting 0 are identityoperations. For any number : + 0 = - 0 = Multiplying or dividing by 1 are also identity opeartions: * 1 = / 1 = The identity function is an identity operation for λ functions.We could equally well have used different names for the bound variable, for example:or:λa.aλyibble.yibbleto define other versions of the identity function. We will consider naming in more detail later but note just now that wecan consistently change names.2.7. Self application functionConsider the rather odd function:λs.(s s)which applies its argument to its argument. The bound variable is:sand the body expression is the function application:(s s)which has the name:sas function expression and the same name:sas argument expression.Let us apply the identity function to it:(λx.x λs.(s s))In this application, the function expression is: