Question

Sometimes I get myself using different types of trees in Haskell and I don’t know what they are called or where to get more information on algorithms using them or class instances for them, or even some pre-existing code or library on hackage.

Examples:

Binary trees where the labels are on the leaves or the branches:

data BinTree1 a = Leaf | 
                  Branch {label :: a, leftChild :: BinTree1 a, rightChild :: BinTree1 a}

data BinTree2 a = Leaf {label :: a} | 
                  Branch {leftChild :: BinTree2 a, rightChild :: BinTree2 a}

Similarly trees with the labels for each children node or a general label for all their children:

data Tree1 a = Branch {label :: a, children :: [Tree1 a]}

data Tree2 a = Branch {labelledChildren :: [(a, Tree2 a)]}

Sometimes I start using Tree2 and somehow on the course of developing it gets refactored into Tree1, which seems simpler to deal with, but I never gave a lot of thought about it. Is there some kind of duality here?

Also, if you can post some other different kinds of trees that you think are useful, please do.

In summary: everything you can tell me about those trees will be useful! 🙂

Thanks.

EDIT:

Clarification: this is not homework. It’s just that I usually end up using those data types and creating instances (Functor, Monad, etc…) and maybe if I new their names I would find libraries with stuff implemented and more theoretical information on them.

Usually when a library on Hackage have Tree in the name, it implements BinTree2 or some version of a non-binary tree with labels only on the leaves, so it seems to me that maybe Tree2 and BinTree2 have some other name or identifier.

Also I feel that there may be some kind of duality or isomorphism, or a way of turning code that uses Tree1 into code that uses Tree2 with some transformation. Is there? May be it’s just an impression.

Answer 1

The names I’ve heard:

• BinTree1 is a binary tree
• BinTree2 don’t know a name but you can use such a tree to represent a prefix-free code like huffman coding for example
• Tree1 is a Rose tree
• Tree2 is isomoprhic to [Tree1] (a forest of Tree1) or another way to view it is a Tree1 without a label for the root.