roman_numerals.elm

module RomanNumeral exposing (numeral_to_number)

type Digit = I | V | X | L | C | D | M


value : Digit -> number
value d = 
  case d of
    I ->    1
    V ->    5
    X ->   10
    L ->   50
    C ->  100
    D ->  500
    M -> 1000


-- todo parse String
parse : String -> List Digit
parse s = [M, X, M, I, V]


values : List Digit -> List number
values digits = List.map value digits


-- Chunk a list into a list of adjacent pairs
-- Tail is right padded with given value

chunk : comparable -> List comparable -> (List (comparable, comparable))
chunk padding list = 
  case list of
    [] -> 
      []

    [x] -> 
      [(x, padding)]

    (x::y::xs) -> 
      (x,y)::(chunk padding (y::xs))


-- chunk_numbers [1,2,3] == [[1,2], [2,3], [3,0]]

chunk_numbers = chunk 0


-- Accumulate (sum) a list of pairs of numbers

accumulate : List (number, number) -> number
accumulate pairs =
  List.foldr 
    (\ (a,b) acc -> if a >= b then acc + a else acc - a ) 
    0 pairs


numeral_to_number : String -> number
numeral_to_number s = 
  (parse s) 
  |> values 
  |> chunk_numbers
  |> accumulate

TODO:

1. parse String to list of Digits

We need an error type:

type DigitList = List Digit | Invalid

Solution using pattern matching:

module RomanNumeral exposing (numeral_to_number)

import String exposing (toList)

value : List Char -> number
value lc = 
  case lc of
    ('C' :: 'M' :: xs) ->
      900 + value xs

    ('C' :: 'D' :: xs) ->
      400 + value xs

    ('X' :: 'C' :: xs) ->
      90 + value xs

    ('X' :: 'L' :: xs) ->
      40 + value xs

    ('I' :: 'X' :: xs) ->
      9 + (value xs)

    ('I' :: 'V' :: xs) ->
      4 + value xs

    ('M' :: xs) ->
      1000 + value xs

    ('D' :: xs) ->
      500 + value xs

    ('C' :: xs) ->
      100 + value xs

    ('L' :: xs) ->
      50 + value xs

    ('X' :: xs) ->
      10 + value xs

    ('V' :: xs) ->
      5 + value xs

    ('I' :: xs) ->
      1 + value xs

    _ ->
      0

numeral_to_number : String -> number
numeral_to_number s =
  s
  |> toList
  |> value