In the previous post we saw the lexical syntax of lambda calculus. From now on we will explore lambda calculus functions starting with Identity function in this post.

### Identity function

A function which returns the argument to which it is applied is an `Identity function`

.

`λx.x`

is an identity function. If the function is applied to an argument, the function simply returns the argument.

```
(λx.x y)
y
```

In the above `function application`

the identity function `λx.x`

when applied to the argument `y`

returns `y`

, by replacing the bound variable `x`

which is also the body expression.

An identity function is like 0 in addition/subtraction or like 1 in multiplication/division.

It serves its purpose better in Category theory.