Tools for testing Functors, Applicatives and Monads?

Question

I have created a type which implements Functor, Applicative and Monad. I wanted to verify that they follow the laws of each. But upon trying to do this manually, it turned into a daunting and quite difficult task.

So, what I am wondering is:

How can I automatically test that the laws of each class are properly implemented?

Answer 1

But upon trying to do this manually, it turned into a daunting and quite difficult task.

One way is to state your laws in a language like Coq and formally prove them. For example, John Wiegley proved pipes law in Coq.

How can I automatically test that the laws of each class are properly implemented?

You cannot get a strong guarantee unless you prove them. Maybe you can check their property using a library like Quickcheck .