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to Luhn in the OCaml Track

Published at Dec 14 2018 · 0 comments
Test suite


This exercise has changed since this solution was written.

Given a number determine whether or not it is valid per the Luhn formula.

The Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers and Canadian Social Insurance Numbers.

The task is to check if a given string is valid.

Validating a Number

Strings of length 1 or less are not valid. Spaces are allowed in the input, but they should be stripped before checking. All other non-digit characters are disallowed.

Example 1: valid credit card number

4539 1488 0343 6467

The first step of the Luhn algorithm is to double every second digit, starting from the right. We will be doubling

4_3_ 1_8_ 0_4_ 6_6_

If doubling the number results in a number greater than 9 then subtract 9 from the product. The results of our doubling:

8569 2478 0383 3437

Then sum all of the digits:

8+5+6+9+2+4+7+8+0+3+8+3+3+4+3+7 = 80

If the sum is evenly divisible by 10, then the number is valid. This number is valid!

Example 2: invalid credit card number

8273 1232 7352 0569

Double the second digits, starting from the right

7253 2262 5312 0539

Sum the digits

7+2+5+3+2+2+6+2+5+3+1+2+0+5+3+9 = 57

57 is not evenly divisible by 10, so this number is not valid.

Getting Started

For installation and learning resources, refer to the exercism help page.


To work on the exercises, you will need Opam and Base. Consult opam website for instructions on how to install opam for your OS. Once opam is installed open a terminal window and run the following command to install base:

opam install base

To run the tests you will need OUnit. Install it using opam:

opam install ounit

Running Tests

A Makefile is provided with a default target to compile your solution and run the tests. At the command line, type:


Interactive Shell

utop is a command line program which allows you to run Ocaml code interactively. The easiest way to install it is via opam:

opam install utop

Consult utop for more detail.

Feedback, Issues, Pull Requests

The exercism/ocaml repository on GitHub is the home for all of the Ocaml exercises.

If you have feedback about an exercise, or want to help implementing a new one, head over there and create an issue. We'll do our best to help you!


The Luhn Algorithm on Wikipedia http://en.wikipedia.org/wiki/Luhn_algorithm

Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.


open Base
open OUnit2
open Luhn

let assert_valid expected input _test_ctxt = 
  assert_equal ~printer:Bool.to_string expected (valid input)

let tests = [
  "single digit strings can not be valid" >::
    assert_valid false "1";
  "a single zero is invalid" >::
    assert_valid false "0";
  "a simple valid SIN that remains valid if reversed" >::
    assert_valid true "059";
  "a simple valid SIN that becomes invalid if reversed" >::
    assert_valid true "59";
  "a valid Canadian SIN" >::
    assert_valid true "055 444 285";
  "invalid Canadian SIN" >::
    assert_valid false "055 444 286";
  "invalid credit card" >::
    assert_valid false "8273 1232 7352 0569";
  "valid strings with a non-digit included become invalid" >::
    assert_valid false "055a 444 285";
  "valid strings with punctuation included become invalid" >::
    assert_valid false "055-444-285";
  "valid strings with symbols included become invalid" >::
    assert_valid false "055\194\163 444$ 285";
  "single zero with space is invalid" >::
    assert_valid false " 0";
  "more than a single zero is valid" >::
    assert_valid true "0000 0";
  "input digit 9 is correctly converted to output digit 9" >::
    assert_valid true "091";
  "strings with non-digits is invalid" >::
    assert_valid false ":9";

let () =
  run_test_tt_main ("luhn tests" >::: tests)
open Core

module CS = Base.Continue_or_stop

let valid (s : string) =
  String.to_list_rev s
  |> List.fold_until ~init:(false, 0, 0)
  ~f:(fun (_, len, sum) c ->
    if c = ' ' then (* skip spaces *)
      CS.Continue (false, len, sum)
    else if (Char.is_digit c) = false then (* err on non-digits *)
      CS.Stop (true, len, sum)
    else (* calculate length and sum *)
      let ival = if (Int.rem len 2) <> 0 then
        (Char.get_digit_exn c) * 2
        Char.get_digit_exn c
      let ival = if ival > 9 then ival - 9 else ival in
      CS.Continue (false, len + 1, sum + ival)
  ~finish:(fun (bad, len, sum) ->
    if bad || len < 2 || (Int.rem sum 10) <> 0 then
      (true, len, sum)
      (false, len, sum)
  |> fun (bad, _, _) -> not bad

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