# Haskell Quiz/Verbal Arithmetic/Solution Jethr0

From HaskellWiki

I'm using a StateT monad inside a list monad for backtracking. The State monad keeps track of the digits associated with characters and also a carry state, that remembers the carried number from prior additions.

Several constraints are already implemented (like leading digits not being zero, all associations being unique), but of course there could be lot added (checking for zero, even/odd-ness, ...)

Solution should be far quicker than generic brute-force/backtracking since it tries to fail as early as possible and with more elaborate constraints it should become even faster!

I couldn't be bothered to write yet another regexp/parser, as that didn't really interest me.

```
module Main where
import qualified Data.Map as Map
import qualified Data.List as List
import Data.Char (intToDigit)
import Control.Monad
import Control.Monad.State
import Data.Maybe (fromJust)
type Carry = Integer
type Assocs = Map.Map Char Integer
type St = (Assocs, Carry)
parts = ["forty", "ten", "ten"]
result = "sixty"
solve :: [String] -> String -> StateT St [] ()
solve parts' res' = do
let constraints = makeConstraints parts' res'
mapM_ (setDigitPairs constraints) digitPairs
(_, carry) <- get
guard $ carry == 0
where digitPairs = zip ps' (reverse res')
ps' = (List.transpose . map reverse $ parts) ++ repeat ""
{- construct constraints from actual data
TODO: a+b=a => b=0
a+a=c => c even
-}
makeConstraints :: [String] -> String -> [StateT St [] ()]
makeConstraints parts' res' =
-- leading digits shouldn't be zero
map (constraintCheck (guard . (0/=))) firsts
where firsts = map head (res' : parts)
constraintCheck cstr c = do
(s,_) <- get
case Map.lookup c s of
Nothing -> return ()
Just i -> cstr i
-- set digits, make per-digit check with carry and apply constraints
setDigitPairs cstrs (ds,res) = do
ls <- mapM placer ds
r <- placer res
(_,carry) <- get
let r' = sum ls + carry
guard $ r' `mod` 10 == r
let carry' = r' `div` 10
modify (\(a,_) -> (a,carry'))
sequence cstrs
-- place number if not yet set and check for uniqueness,
-- otherwise return already set value
placer :: Char -> StateT St [] Integer
placer l = do
(assoc,_) <- get
case Map.lookup l assoc of
Just i -> return i
Nothing -> do
a <- lift [0..9]
guard $ a `notElem` (Map.elems assoc)
modify (\(ass,c) -> (Map.insert l a ass, c))
return a
main = mapM_ print . Map.toList . fst . head $
execStateT (solve parts result) (Map.empty :: Assocs, 0)
```