Question

I’ve defined a polymorphic data type called Tree a as follows:

data Tree a = Leaf | Node a (Tree a) (Tree a)

I want to define a function mapT that takes a function and applies it to every data item of type a within a tree of type Tree a. The essential purpose of this function would be to operate on trees the same way the map function operates on list so I’ve written a function based off of that idea:

mapT :: (a -> b) -> Tree a -> Tree b
mapT f Leaf = Leaf
mapT f ((Tree a) left right) = (Tree a) (mapT f left) (mapT f right)

However, when I run this, I get a Parse error in pattern: (Tree a) and I can’t figure out what’s wrong. Does anyone have any idea how to get passed this?

Answer 1

Try:

data Tree a = Leaf | Node a (Tree a) (Tree a)

mapT :: (a -> b) -> Tree a -> Tree b
mapT f Leaf = Leaf
mapT f (Node a left right) = Node (f a)  (mapT f left) (mapT f right)

Note that your Leaf constructor doesn’t have any data associated with is, so perhaps you really want:

data Tree a = Leaf a | Node ...

with the corresponding change in mapT.

Also, once you have got mapT working for you, you should read up on the Functor type class, and why you might want to create a Functor instance for Tree a:

instance Functor Tree where
  fmap (Leaf ...)  = ...
  fmap (Node x l r) = Node ...