[clomduww] Foldable with metadata

The Foldable instances of Array and Map in Haskell do not provide access to the index or key respectively. It is possible to provide such access, but doing so requires defining Foldable differently, making it a multiparameter type class and explicitly specifying an intermediate type that packages up the element and metadata, e.g., index or key.

GHC 7.10.1, array-0.5.1.0, base-4.8.0.0, containers-0.5.6.2

{-# LANGUAGE MultiParamTypeClasses, FlexibleInstances, ScopedTypeVariables #-}
module FoldableWithKey where {
import Data.Array.IArray;
import qualified Data.Map as Map;

-- similar to Foldable, except the intermediate type can be different from the element type.
class FoldableWithKey collection intermediate where {
foldWithKey :: (intermediate -> b -> b) -> b -> collection -> b;
};

-- unclear why OVERLAPPABLE is needed here, as Map is clearly not an IArray
instance {-# OVERLAPPABLE #-} (IArray a e, Ix i) => FoldableWithKey (a i e) (i,e) where {
foldWithKey f z = foldr f z . assocs ;
};

instance FoldableWithKey (Map.Map k a) (k,a) where {
foldWithKey f = Map.foldWithKey $ \xk xa xb -> f (xk,xa) xb;
};

-- Overlapping Instance
-- Allows foldWithKey to be a drop-in replacement for foldr.
instance {-# OVERLAPPABLE #-} (Foldable t) => FoldableWithKey (t a) a where {
foldWithKey = foldr;
};

test1 :: [Int] -> Int;
test1 = foldWithKey (+) 0;

test2 :: Map.Map String Int -> Int;
test2 = foldWithKey (+) 0;

test3 :: Map.Map String Int -> (String,Int);
test3 = foldWithKey (\(s,i) (sold,iold) -> (s ++ sold, i + iold)) ("",0);

test4 :: Map.Map String Int -> Int;
-- explicit type signature weirdly needed on s
test4 = foldWithKey (\(s :: String, i) iold -> length s + i + iold) 0;

test5 :: Array Int Double -> Double;
-- explicit type signature weirdly needed on i
test5 = foldWithKey (\(i :: Int , d) dold -> d + dold + fromIntegral i) 0;
}