On Thursday 17 February 2011 22:02:58, Javier M Mora wrote:
Yes, I'm trying to learn/practice Design Patterns in Haskell making euler problems three times:
1. Non Monad
That's easy for this one. And I don't think this problem lends itself well to a monadic approach (it can be done okay enough with a State and/or Writer, but it still seems artificial to use those).
2. Ad-hoc Monad
The problem is too specialised to fit a custom Monad to it, I think. There's only one (base) type involved, so you have not enough to find out how (>>=) :: m a -> (a -> m b) -> m b should work.
3. Standard Monad
State 1: import Data.List (partition) multiples :: Integral a => a -> State [a] [a] multiples k = state (partition (\m -> m `mod` k == 0)) -- if you use mtl-1.*, replace the lowercase state with State -- could also be any Integral type euler1M :: [Integer] -> State [Integer] Integer euler1M nums = do mlists <- mapM multiples nums return (sum $ concat mlists) -- or, special and not general -- euler1 :: State [Integer] Integer -- euler1M = do -- m3 <- multiples 3 -- m5 <- multiples 5 -- return (sum m3 + sum m5) euler1 :: [Integer] -> Integer -> Integer euler1 nums limit = evalState (euler1M nums) [1 .. limit-1] answer = euler1 [3,5] 1000 State 2: import Data.List (partition) multiples :: Integral a => a -> State ([a],[a]) () multiples k = state $ \(v,c) -> let (nv,nc) = partition (\m -> m `mod` k == 0) c in ((), (nv ++ v, nc)) validSum :: Num a => State ([a],[a]) a validSum = state $ \s@(v,_) -> (sum v, s) euler1M :: Integral a => [a] -> State ([a],[a]) a euler1M nums = do mapM_ multiples nums validSum Writer: import Data.List (partition) multiples :: Integral a => [a] -> a -> Writer [a] [a] multiples candidates k = writer (partition (\m -> m `mod` k /= 0) candidates -- For mtl-1.*, that has to be Writer euler1M :: Integral a => [a] -> [a] -> Writer [a] [a] euler1M = foldM multiples euler1 :: [Integer] -> Integer -> Integer euler1 nums limit = sum . execWriter $ euler1M [1 .. limit-1] nums Really, there are problems that lend themselves better to a monadic approach.
Thank you for help me in the 3rd Stage. I was trying to solve 2nd Stage. :-(