Comment by lucasoshiro

I don't know if it will work for you, but I wrote a Quicksort using lambda calculus in Python, and I explained the process of writing it here:

https://lucasoshiro.github.io/software-en/2020-06-06-lambdas...

Please note that I'm not an expert in lambda calculus, just a curious nerd and it won't explain everything, like the reductions, combinators and so on. But there I explain how to implement simple types (int, boolean, pairs and lists) using Church encoding, let expressions and recursion using the Y combinator (yay, I finally used the expression "Y combinator" on HN!). Everything that we need to implement a quicksort (which is a relatively complex algorithm) using the almost nothing that we have in lambda calculus.

Another point is that it's all implemented in Python, using the Python notation instead of the lambda calculus notation, so you can run the code in your machine and play with the examples