So, just for fun, I've been playing with a CountedList type in Haskell, using Peano numbers and smart constructors.

Type-safe head and tail just seem really cool to me.

And I think I've reached the limit of what I know how to do

{-# LANGUAGE EmptyDataDecls #-}
module CountedList (
  Zero, Succ, CountedList,
  toList, ofList, 
  empty, cons, uncons, 
  head, tail, 
  fmap, map, foldl, foldr, filter
) where

import qualified List (foldr, foldl, filter)
import Prelude hiding (map, head, foldl, foldr, tail, filter)

data Zero
data Succ n
data CountedList n a = CL [a]

toList :: CountedList n a -> [a]
toList (CL as) = as

ofList :: [a] -> CountedList n a
ofList [] = empty
ofList (a:as) = cons a $ ofList as

empty :: CountedList Zero a
empty = CL []

cons :: a -> CountedList n a -> CountedList (Succ n) a
cons a = CL . (a:) . toList

uncons :: CountedList (Succ n) a -> (a, CountedList n a)
uncons (CL (a:as)) = (a, CL as)

head :: CountedList (Succ n) a -> a
head = fst . uncons

tail :: CountedList (Succ n) a -> CountedList n a
tail = snd . uncons

instance Functor (CountedList n) where
  fmap f = CL . fmap f . toList

map :: (a -> b) -> CountedList n a -> CountedList n b
map = fmap

foldl :: (a -> b -> a) -> a -> CountedList n b -> a
foldl f a = List.foldl f a . toList

foldr :: (a -> b -> b) -> b -> CountedList n a -> b
foldr f b = List.foldr f b . toList

filter :: (a -> Bool) -> CountedList n a -> CountedList m a
filter p = ofList . List.filter p . toList

(sorry for any transcription errors - the machine I originally wrote this on w/ my Haskell compiler is currently down).

Most of what I've done compiles w/o an issue, but I run into issues with ofList and filter. I think I understand why - when I say

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