How to make a nullary data constructor in Haskell return True for null -

i have algebraic data type, say

data tree = node (tree a) (tree a) | empty

i want null return true empty node; false otherwise.

for example,

> tree = empty > null tree  

right now, gives following error.

<interactive>:261:1: error:     • no instance (foldable tree) arising use of ‘null’     • in expression: null tree       in equation ‘it’: = null tree 

note null return true nothing.

> null nothing true 

null requires instance of foldable: null :: foldable t => t -> bool

the easiest way create instance of foldable tree a is:

{-# language derivefoldable #-}  data tree = node (tree a) (tree a) | empty deriving foldable 

or in ghci:

λ > :set -xderivefoldable λ > data tree = node (tree a) (tree a) | empty deriving foldable λ > null empty true λ > null (node 1 empty empty) false 

note: reason null return true nothing because maybe has instance of foldable.

the long way:

instead of taking shortcut using haskell's magical extensions can write foldable instance manually explained here, it's boils down to:

data tree = node (tree a) (tree a) | empty  instance foldable tree   -- minimal definition "foldmap" or "foldr", i'm choosing "foldr"   -- foldr :: (a -> b -> b) -> b -> tree -> b   foldr _ b empty               = b   foldr f b (node left right) = f (foldr f (foldr f b right) left)