haskellfunctorfoldable

Haskell creating map and foldr function for new datatype


I have written a data structure,

data Bit a = Add a (Bit a) | End deriving (Show,Eq)
data Bits a = Bits (Bit a) (Bit a) deriving (Show,Eq)

but am struggling to create a map and foldr function for them.

So far I have this:

instance Functor Bit 
    where
       fmap _ (End) = End
       fmap f (Add x (y)) = Add (f x) $ (fmap f y)

instance Foldable Bit
    where 
       foldr _ z (End) = z 
       foldr f z (Add x (y)) = f x $ foldr f z y

instance Functor Bits 
    where 
       fmap _ (Bits (End) (End)) = Bits (End) (End)
       fmap f (Bits (Add x (y)) (End)) = error "dont know what to put here"

instance Foldable Bits
    where 
       foldr _ z (Bits (End) (End)) = z
       foldr f z (Bits (Add x (y)) (End) = Bits (f x $ f y) (End)
       foldr f z (Bits (Add x (y)) (Add a (b)) = error "dont know"

Any idea on how to implement them? Also not sure if I am missing anything so please let me know if that is also the case.


Solution

  • Perhaps it's easier to implement the Foldable instances via foldMap:

    import Data.Monoid
    
    data Bit a = Add a (Bit a) | End deriving (Show,Eq)
    data Bits a = Bits (Bit a) (Bit a) deriving (Show,Eq)
    
    instance Functor Bit where
      fmap _ End = End
      fmap f (Add x b) = Add (f x) $ fmap f b
    
    instance Foldable Bit where
      foldMap _ End = mempty
      foldMap f (Add x b) = f x <> foldMap f b
    
    instance Functor Bits where
      fmap f (Bits l r) = Bits (fmap f l) (fmap f r)
    
    instance Foldable Bits where
      foldMap f (Bits l r) = foldMap f l <> foldMap f r
    

    Here's some GHCi examples:

    *Q51009307> foldr (\x a -> show x ++ a) "" $ End
    ""
    *Q51009307> foldr (\x a -> show x ++ a) "" $ Add 1 $ End
    "1"
    *Q51009307> foldr (\x a -> show x ++ a) "" $ Add 1 $ Add 2 $ End
    "12"
    *Q51009307> foldr (\x a -> show x ++ a) "" $ Add 1 $ Add 2 $ Add 3 $ End
    "123"
    *Q51009307> foldMap Sum $ Bits (Add 1 $ End) End
    Sum {getSum = 1}
    *Q51009307> foldMap Sum $ Bits (Add 1 $ Add 2 $ End) (Add 1 $ End)
    Sum {getSum = 4}
    *Q51009307> foldr (+) 0 $ Bits (Add 1 $ Add 2 $ End) (Add 1 $ End)
    4