Why isn't this tail-recursive?

Question

I'm working through the book Real-World Functional Programming , and I tried to come up with my own example of tail recursion before reading the book's example (listing 10.2, p. 265). The book's example works; mine causes a stack overflow.

I've found if I use a tuple argument or pre-calculate a + accum then mine will work. I want to understand why.

let rnd = new System.Random()
let test2 = List.init 1000000 (fun _ -> rnd.Next(-50, 51))

let rec sum2 list accum =
  match list with
  | [] -> accum
  | a::b -> sum2 b a + accum

let result = sum2 test2 0

printfn "%d" result

Answer 1

sum2 b a + accum

Note that this is parsed as (sum2 ba) + accum , not sum2 b (a + accum) .

So this calls sum2 ba . Then it takes the result of that call and adds accum to it. So the last expression evaluated is the addition, not the call to sum2 . Thus the call to sum2 is not a tail call.

Answer 2

Maybe the compiler is reading

a::b -> (sum2 b a) + accum

instead of

a::b -> sum2 b (a + accum)