[Haskell-beginners] Applicative on Tree

[Imants Cekusins]

> data Tree a = Node a [Tree a]

well here is something that builds and runs. Not sure if the monad laws apply.
watch out for indents!


{-# LANGUAGE InstanceSigs #-}
module TreeApp where

import Debug.Trace
import Data.Char

data Tree a = Node a [Tree a]   deriving (Show)


instance Functor Tree where
   fmap::(a -> b) -> Tree a -> Tree b
   fmap f (Node x l0) = Node (f x) (fmap f <$> l0)


instance Applicative Tree where
   pure::a -> Tree a
   pure a =  Node a []

   (<*>)::Tree (a -> b) -> Tree a -> Tree b
   (<*>) (Node f _) tra = f <$> tra


instance Monad Tree where
   return::a -> Tree a
   return a = pure a

   (>>=)::Tree a -> (a -> Tree b) -> Tree b
   (>>=) (Node x []) amb = amb x
   (>>=) (Node x l0) amb = Node b (m1 <$> l0)
         where (Node b _) = amb x
               m1 ta = ta >>= amb


f::Char->Int
f = digitToInt

mb::Char->Tree Int
mb c = f <$> (pure c)

main::Char -> Char -> IO ()
main a b = print $ tc4 >>= mb
{-
   do
      print ti2
      print ta3
      tm4 <- tc4
-}
   where tc1 = pure a
         ti2 = f <$> tc1
         ta3 = (Node f []) <*> tc1
         tc4 = Node b [tc1]