Euler 43 - is there a monad to help write this list comprehension?

Question

Here is a way to solve Euler problem 43 (please let me know if this doesn\'t give the correct answer). Is there a monad or some other syntatic sugar which could assist with

Answer 1

The UniqueSel monad suggested by Louis Wasserman is exactly StateT [Integer] [] (I'm using Integer everywhere for simplicity).

The state keeps the available digits and every computation is nondeterministic - from a given state we can select different digits to continue with. Now the choose function can be implemented as

import Control.Monad
import Control.Monad.State
import Control.Monad.Trans
import Data.List

choose :: PanM Integer
choose = do
    xs <- get
    x <- lift xs -- pick one of `xs`
    let xs' = x `delete` xs
    put xs'
    return x

And then the monad is run by evalStateT as

main = do
         let nums = evalStateT pandigitals [0..9]
         -- ...