Question

I’m trying to teach myself OCaml through Jason Hickey notes and the following exercise got me stumped.
Question: Write a function sum that given two integer bounds m,n and a function f computes a summation.
I’m trying this:

     let rec sum m n f=
     if m>n then 0
     else if m=n then f n
     else f m + sum n m+1 f

but it doesn’t work, producing a type error.

Answer 1

You need some parentheses.

let rec sum m n f=
     if m>n then 0
     else if m=n then f n
     else f m + sum n (m+1) f

(Although for readability, I would usually parenthesize the last line as else (f m) + (sum n (m+1) f). )
What’s happening without the parentheses is that it’s treating it as (f m) + (sum n m) + (1 f) which is producing the error that sum n m doesn’t have type int, as it’s a partial function application with a more complex type.

As a general rule, when an expression is being passed as an argument to a function, it always needs to be parenthesized. On a related note, if you ever actually wanted to pass the plus function as an argument, you would put it in parentheses (for example: sum m n (+) (although that wouldn’t type check in this case, since + expects two numbers)).