Why this recursion example in ocaml doesn't work for negative number?

In the Think Ocaml book the author gave this example:

let rec countdown n = 
    if n <= 0 then 
      ( print_string "Blastoff!"; 
        print_newline()) 
    else ( print_int n; print_newline(); 
       countdown (n-1); ());;

The function takes an int and returns a unit. However, the code suppose to work on negative numbers as mentioned in the book but it doesn't. The logic of the code seems fine and nothing wrong with it. I thought I would share it with people who know Ocaml to see what is wrong here.

Writing

countdown -1

doesn't mean what you expect it to mean. The problem is that - is an infix operator with the following signature:

# (-);;
- : int -> int -> int = <fun>

As you can see it is a function taking 2 integer arguments and returning an integer. It's the subtraction "a - b". The above statement will be parsed as:

(countdown) - (1)

And countdown has type int -> unit instead of the expected type int.

What you want instead is the unary minus that negates a number. The ocaml grammar is written so that an expression starting with - uses the unary minus but any minus in the middle of an expression is the binary minus. So you have to write one of the following:

countdown (-1)
countdown ~-1