Trying to implement "the essence of the iterator pattern"

Question

I came across the paper "https://www.cs.ox.ac.uk/jeremy.gibbons/publications/iterator.pdf" which has code examples in quite an abstract pseudo haskell syntax.

I'm struggeling to implement the example from section 6.2. in real haskell. This is how far I came:

module Iterator where
import Data.Functor.Const               -- for Const
import Data.Monoid (Sum (..), getSum)   -- for Sum
import Control.Monad.State.Lazy         -- for State
import Control.Applicative              -- for WrappedMonad


data Prod m n a = Prod {pfst:: m a, psnd:: n a} deriving (Show)

instance (Functor m, Functor n) => Functor (Prod m n) where    
fmap f (Prod m n) = Prod (fmap f m) (fmap f n)

instance (Applicative m, Applicative n) => Applicative (Prod m n) where
    pure x = Prod (pure x) (pure x)
    mf <*> mx = Prod (pfst mf <*> pfst mx) (psnd mf <*> psnd mx)

-- Functor Product
x :: (Functor m, Functor n) => (a -> m b) -> (a -> n b) -> (a -> Prod m n b)
(f `x` g) y = Prod (f y) (g y) 


type Count = Const (Sum Integer)
count :: a -> Count b
count _ = Const 1

cciBody :: Char -> Count a
cciBody = count

cci :: String -> Count [a]
cci = traverse cciBody

lciBody :: Char -> Count a
lciBody c = Const (Sum $ test (c == '\n'))

test :: Bool -> Integer
test b = if b then 1 else 0

lci :: String -> Count [a]
lci = traverse lciBody

clci :: String -> Prod Count Count [a]
clci = traverse (cciBody `x` lciBody)
-- up to here the code is working

-- can't get this to compile:
wciBody :: Char -> (WrappedMonad (Prod (State Bool) Count)) a
wciBody c =  pure $ state (updateState c) where
    updateState :: Char -> Bool -> (Integer, Bool)
    updateState c w = let s = c /= ' ' in (test (not(w && s)), s)

wci :: String -> (WrappedMonad (Prod (State Bool) Count)) [a]
wci = traverse wciBody

clwci :: String -> (Prod (Prod Count Count) (WrappedMonad (Prod (State Bool) Count))) [a]
clwci = traverse (cciBody `x` lciBody `x` wciBody)

str :: [Char]
str = "hello \n nice \t and \n busy world"

iteratorDemo = do
    print $ clci str
    print $ clwci str

The problematic spot is wciBody where I have no idea how to implement the ⇑ function from the paper. Any ideas?

Answer 1

I think you may be mis-translating between the infix type operators used in the paper with the prefix type constructors in your definitions. I say this because the paper contains

wciBody :: Char → (𝕄 (State Bool) ⊡ Count) a

You have translated this as

wciBody :: Char -> (WrappedMonad (Prod (State Bool) Count)) a

which I don't think makes sense: Prod x y has no Monad instance, so it makes no sense to wrap it in WrapMonad. Rather, you are intended to read the ⊡ character as separating its entire left half (𝕄 (State Bool)) from its right half (Count), similar to how value-level operators in Haskell parse:

wciBody :: Char -> Prod (WrappedMonad (State Bool)) Count a

This makes more sense, doesn't it? Prod now takes three arguments, the first two of which are each of kind * -> *, and WrappedMonad's argument is clearly a monad. Does this change get you back on track?