Programming

I'm not an OCaml person but I do know other functional languages. I looked into Alcotest and it looks like the function after "`Quick" has to be unit -> unit. Because OCaml has currying, and I think test_increment already returns unit, all you should have to do is add an extra parameter of type unit. I believe that would be done like this:

let test_increment (new_value, original_value) () =

Now the expression test_increment (1, 0) returns a function that must be passed a unit to run its body. That means you can change the lambdas to e.g. this:

test_case "blah" `Quick (test_increment (1, 0))

I don't know OCaml precedence rules so the enclosing parentheses here may not be necessary.

I'd also note that taking new_value and original_value as a tuple would probably be considered not idiomatic unless it makes sense for the structure of the rest of your code, especially because it limits currying like we did with the unit being able to be passed later. Partial application/currying is a big part of the flexibility of functional languages.

Edit: if you're getting into functional programming you may also consider calling increment_by_one "succ" or "successor" which is the typical terminology in functional land.