I'm experimenting with the Foldable
typeclass in Haskell, using the following data type as an example:
data Tree a = Empty
| Node (Tree a) a (Tree a)
If I use the DeriveFoldable
GHC extension, it seems to derive a Foldable
instance along the lines of
instance Foldable Tree where
foldMap _ Empty = mempty
foldMap f (Node l n r) = (foldMap f l) <> (f n) <> (foldMap f r)
i.e., an inorder traversal of the tree. However, I don't see anything obvious preventing a different Foldable
instance, such as a preorder traversal:
instance Foldable Tree where
foldMap _ Empty = mempty
foldMap f (Node l n r) = (f n) <> (foldMap f l) <> (foldMap f r)
Are there laws for the Foldable
typeclass that would make the preorder traversal instance unlawful?
Foldable
has no laws guiding the order of traversal. In fact, we can think of the act of writing a Foldable
instance as choosing a specific order of traversal. If DeriveFoldable
is used, the choice will be to follow the order of the fields in the definition of the type (see also Daniel Wagner's answer); the details are documented in the relevant section of the GHC User's Guide.
(Side note: As discussed in dfeuer's answer, Traversable
has richer laws that, among other things, limit the range of acceptable foldMap
implementations. Still, both inorder and preorder traversals for your Tree
give out lawful implementations of Traversable
.)