-- TODO: Characters
-- TODO: Bytes

type Optional a = Some a | None

type Words = Words (List Nat)
type Integer = Integer

Integer.zero : Integer
Integer.zero = _

shiftLeft : Nat -> Integer -> Integer
shiftLeft x y = _

(+) : Integer -> Integer -> Integer
(+) x y = _

unfoldRight : ∀ a b . (a -> Optional (a, b)) -> a -> List b
unfoldRight f z = _

foldLeft : ∀ a b . a -> (a -> b -> a) -> List b -> a
foldLeft z f s = _

toInteger : Nat -> Integer
toInteger x = _

bigEndian : Words -> Integer
bigEndian ws = case ws of
  Words.Words s -> 
    foldLeft Integer.zero (acc w -> shiftLeft 8 acc + toInteger w) s

-- TODO: Need some conversions between integers and machine integers
divmod : Integer -> Nat -> (Integer, Nat)
divmod x y = _

(|>) : ∀ a b c . (a -> b) -> (b -> c) -> a -> c
(|>) g f x = f (g x)

(==) : Integer -> Nat -> Boolean
(==) a b = _

charAt : Nat -> Text -> Text
charAt n = Text.drop n |> Text.take 1

codeString : Text
codeString = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"

base58Encode : Words -> Text
base58Encode ws = 
  x = bigEndian ws
  base58 : Integer -> Optional (Integer, Text)
  base58 a = 
    if a == 0
    then Optional.None
    else case divmod a 58 of
           (d, m) -> Optional.Some (d, charAt m codeString)
  foldLeft "" Text.concatenate (unfoldRight base58 x)

base58Decode : Text -> Words
base58Decode txt = _