How do I get the sums of the digits of a large number in Haskell?

I'm a C++ Programmer trying to teach myself Haskell and it's proving to be challenging grasping the basics of using functions as a type of loop. I have a large number, 50!, and I need to add the sum of its digits. It's a relatively easy loop in C++ but I want to learn how to do it in Haskell.

I've read some introductory guides and am able to get 50! with

sum50fac.hs::

fac 0 = 1
fac n = n * fac (n-1)
x = fac 50
main开发者_StackOverflow社区 = print x

Unfortunately at this point I'm not entirely sure how to approach the problem. Is it possible to write a function that adds (mod) x 10 to a value and then calls the same function again on x / 10 until x / 10 is less than 10? If that's not possible how should I approach this problem?

Thanks!

---

sumd 0 = 0
sumd x = (x `mod` 10) + sumd (x `div` 10)

Then run it:

ghci> sumd 2345
14

UPDATE 1:

This one doesn't generate thunks and uses accumulator:

sumd2 0 acc = acc
sumd2 x acc = sumd2 (x `div` 10) (acc + (x `mod` 10))

Test:

ghci> sumd2 2345 0
14

UPDATE 2:

Partially applied version in pointfree style:

sumd2w = (flip sumd2) 0

Test:

ghci> sumd2w 2345
14

I used flip here because function for some reason (probably due to GHC design) didn't work with accumulator as a first parameter.

---

Why not just

sumd = sum . map Char.digitToInt . show

---

This is just a variant of @ony's, but how I'd write it:

import Data.List (unfoldr)

digits :: (Integral a) => a -> [a]
digits = unfoldr step . abs
    where step n = if n==0 then Nothing else let (q,r)=n`divMod`10 in Just (r,q)

This will product the digits from low to high, which while unnatural for reading, is generally what you want for mathematical problems involving the digits of a number. (Project Euler anyone?) Also note that 0 produces [], and negative numbers are accepted, but produce the digits of the absolute value. (I don't want partial functions!)

If, on the other hand, I need the digits of a number as they are commonly written, then I would use @newacct's method, since the problem is one of essentially orthography, not math:

import Data.Char (digitToInt)

writtenDigits :: (Integral a) => a -> [a]
writtenDigits = map (fromIntegral.digitToInt) . show . abs

Compare output:

> digits 123
[3,2,1]
> writtenDigits 123
[1,2,3]

> digits 12300
[0,0,3,2,1]
> writtenDigits 12300
[1,2,3,0,0]

> digits 0
[]
> writtenDigits 0
[0]

In doing Project Euler, I've actually found that some problems call for one, and some call for the other.

About . and "point-free" style

To make this clear for those not familiar with Haskell's . operator, and "point-free" style, these could be rewritten as:

import Data.Char (digitToInt)
import Data.List (unfoldr)

digits :: (Integral a) => a -> [a]
digits i = unfoldr step (abs i)
    where step n = if n==0 then Nothing else let (q,r)=n`divMod`10 in Just (r,q)

writtenDigits :: (Integral a) => a -> [a]
writtenDigits i = map (fromIntegral.digitToInt) (show (abs i))

These are exactly the same as the above. You should learn that these are the same:

f . g
(\a -> f (g a))

And "point-free" means that these are the same:

foo a = bar a
foo   = bar

Combining these ideas, these are the same:

foo a = bar (baz a)
foo a = (bar . baz) a
foo   = bar . baz 

The laster is idiomatic Haskell, since once you get used to reading it, you can see that it is very concise.

---

To sum up all digits of a number:

digitSum = sum . map (read . return) . show

show transforms a number to a string. map iterates over the single elements of the string (i.e. the digits), turns them into a string (e.g. character '1' becomes the string "1") and read turns them back to an integer. sum finally calculates the sum.

---

Just to make pool of solutions greater:

miterate :: (a -> Maybe (a, b)) -> a -> [b]
miterate f = go . f where
    go Nothing = []
    go (Just (x, y)) = y : (go (f x))

sumd = sum . miterate f where
    f 0 = Nothing
    f x = Just (x `divMod` 10)

---

Well, one, your Haskell function misses brackets, you need fac (n - 1). (oh, I see you fixed that now)

Two, the real answer, what you want is first make a list:

listdigits n = if n < 10 then [n] else (listdigits (n `div` 10)) ++ (listdigits (n `mod` 10))

This should just compose a list of all the digits (type: Int -> [Int]).

Then we just make a sum as in sum (listdigits n). And we should be done.

Naturally, you can generalize the example above for the list for many different radices, also, you can easily translate this to products too.

---

Although maybe not as efficient as the other examples, here is a different way of approaching it:

import Data.Char

sumDigits :: Integer -> Int
sumDigits = foldr ((+) . digitToInt) 0 . show

Edit: newacct's method is very similar, and I like it a bit better :-)