Question

Given the type and instance declarations below, verify the functor laws for the Tree type, by induction on trees. data Tree a = Leaf a | Node (Tree a) (Tree a) instance Functor Tree where — fmap :: (a -> b) -> Tree a -> Tree b fmap g (Leaf x) = Leaf (g x) fmap g (Node l r) = Node (fmap g l) (fmap g r)

   Given the type and instance declarations below, verify the functor laws for the Tree type, by induction on trees.
data Tree a = Leaf a | Node (Tree a) (Tree a)

instance Functor Tree where
— fmap :: (a -> b) -> Tree a -> Tree b
fmap g (Leaf x) = Leaf (g x)
fmap g (Node l r) = Node (fmap g l) (fmap g
r)

Show more…

Programming in Haskell

Programming in Haskell

Graham Hutton 2nd Edition

Chapter 16, Problem 8

Instant Answer

Step 1

To verify the functor laws for the Tree type, we need to check if the following two laws hold: Show more…

Show all steps

lock

Thanks for your feedback!

Given the type and instance declarations below, verify the functor laws for the Tree type, by induction on trees. data Tree a = Leaf a | Node (Tree a) (Tree a) instance Functor Tree where — fmap :: (a -> b) -> Tree a -> Tree b fmap g (Leaf x) = Leaf (g x) fmap g (Node l r) = Node (fmap g l) (fmap g r)

Play audio

Feedback

Powered by NumerAI

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later