Lambda Calculus: Identity function

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)


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.

Rajesh PG

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