Haskell Defining a Binary Tree

Question

I want to define an infinite tree in Haskell using infinitree :: Tree, but want to set a pattern up for each node, defining what each node should be. The pattern is 1 more then then its parent. I am struggling on how to set up a tree to begin with, and how and where to define the pattern of each node?

Thank you

Answer 1

Infinite data structures can generally be defined by functions which call themselves but have no base case. Usually these functions don't need to pattern match on their arguments. For example, a list equal to [1..] can be written as

infiniteList :: [Int]
infiniteList = go 1 where 
  go n = n : go (n+1) 

You can use the exact same technique for a tree:

data Tree a = Node (Tree a) a (Tree a) | Nil deriving (Show)

infiniteTree :: Tree Int 
infiniteTree = go 1 where 
  go n = Node (go (2*n)) n (go (2*n+1))

This defines the infinite tree

   1 
 /   \
 2   3 
/ \ / \
4 5 6 7
...

Answer 2

A type for infinite binary trees with no leaves:

data Tree a = Tree (Tree a) a (Tree a)

One general pattern for doing this sort of thing is called unfold . For this particular type:

unfold :: (a -> (a,b,a)) -> a -> Tree b

Can you see how to define this function and use it for your purpose?