Using ideas from the Lambda calculus and Church encoding, implement an interesting computation using only functions, such as the Fibonacci function or summing the elements of a list of natural numbers.

I suggest doing this experiment inside of a programming language with closures, like Racket, Javascript, or Python. You are NOT implementing the function in these languages, instead you are implementing them in Lambda calculus—i.e. using ONLY single argument functions. These languages allow you to write such functions, so you can pretend they are Lambda calculus.