Bijective.hs

import Data.List
import Data.Maybe
import Control.Monad

alphabet = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
base = length alphabet

encode :: Int -> String
encode 0 = "a"
encode id = map $ ((!!) alphabet) (reverse . tail) (map snd options)
    where
        options = takeWhile (/= (0,0)) (iterate (\x -> ((fst x `div` 62), (fst x `mod` 62))) (id,0))

decode :: String -> Maybe Int
decode encoded = do
    elems <- sequence $ map (\x -> elemIndex x alphabet) encoded
    return $ foldl (\x y -> x * base + y) 0 elems

-- encode 125
-- decode "cb"
-- encode 19158
-- decode "e9a"

Prelude> :load bijective.hs
[1 of 1] Compiling Main ( bijective.hs, interpreted )

bijective.hs:10:25:
Couldn't match expected type t0 -> a0 -> b0' with actual typeChar'
Expected type: [t0 -> a0 -> b0]
Actual type: [Char]
In the first argument of (!!)', namelyalphabet'
In the second argument of ($)', namely ((!!) alphabet) (reverse . tail) (map snd options)'
Failed, modules loaded: none.

After parens update

Prelude> :load bijective
[1 of 1] Compiling Main             ( bijective.hs, interpreted )

bijective.hs:10:25:
    Couldn't match expected type `a0 -> b0' with actual type `Char'
    Expected type: [a0 -> b0]
      Actual type: [Char]
    In the first argument of `(!!)', namely `alphabet'
    In the second argument of `($)', namely
      `((!!) alphabet) ((reverse . tail) (map snd options))'
Failed, modules loaded: none.