You said:
do you know lambda calculus
ChatGPT said:
ChatGPT

Yes, I know about lambda calculus! It’s a formal system in mathematical logic and computer science for expressing computation based on function abstraction and application. Developed by Alonzo Church in the 1930s, lambda calculus uses function definitions and applications as its fundamental operations.

In lambda calculus, functions are defined using lambda notation. For instance, a function that adds 1 to its argument can be written as:

λx.(x+1)

Here, λx denotes a function that takes an argument x and returns x + 1.

Lambda calculus is foundational for understanding functional programming languages and has been influential in the development of programming language theory. Do you have a specific question about lambda calculus or its applications?


You said:
reduce (lambda x.lambda y.y x) y to beta normal form
ChatGPT said:
ChatGPT

To reduce the lambda expression (λx.λy.y x) y to beta normal form, we need to perform beta reduction steps. Here’s the step-by-step process:

    Initial Expression:
    (λx.λy.y x) y

    Here, we have a function λx.λy.y x being applied to an argument y.

    Apply the Argument y to the Function λx.λy.y x:

    When we apply y to λx.λy.y x, we substitute y for x in the body of the function λx.λy.y x.

    (λx.λy.y x) y

    Here, we replace x with y in the body of the lambda expression λx.λy.y x. This results in:

    λy.y y

    Resulting Expression:

    The resulting expression λy.y y is in beta normal form. It is a function that takes an argument yy and applies yy to itself.

So the beta normal form of (λx.λy.y x) y is:

λy.y y