Monad Bind, Associativity Matters
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{-# LANGUAGE DeriveFunctor #-}
import Debug.Trace (trace)
import Control.Monad ((>=>))
data Tree a = Node (Tree a) (Tree a) | Leaf a deriving Functor
instance Applicative Tree where
pure = Leaf
Leaf f <*> Leaf a = Leaf $ f a
Leaf f <*> Node a b = Node (f <$> a) (f <$> b)
Node f g <*> leaf@(Leaf x) = Node (f <*> leaf) (g <*> leaf)
Node f g <*> Node a b = Node (f <*> a) (g <*> b)
instance Monad Tree where
return = pure
(>>=) = (<-/)
(<-/) :: Tree a -> (a -> Tree b) -> Tree b
(Leaf a) <-/ f = f a
Node l r <-/ f = trace "<-/" (Node (l <-/ f) (r <-/ f))
instance Show a => Show (Tree a) where
show (Leaf a) = "Leaf " ++ show a
show (Node l r) = "Node (" ++ show l ++ ") (" ++ show r ++ ")"
x :: Tree Int
x =
Node
(Node
(Leaf 9)
(Node (Leaf 8) (Leaf 7))
)
(Leaf 2)
f x = Leaf $ x * 5
g x = Leaf $ x + 1
main = do
-- time: |x| + |(x >>= f)| steps
print $ (x >>= f) >>= g
trace (replicate 10 '-') (return ())
-- time: |x >>= f| steps
print $ x >>= (\x -> f x >>= g)
trace (replicate 10 '-') (return ())
print $ x >>= (f >=> g)
Haskell
INFO