I'm working through the wonderful Haskell Book. At the end of the Traversable chapter (21), I need to write an instance for the following Tree: data Tree a = Empty | Leaf a | Node (Tree a) a (Tr...

Despite the jargon filled title I don't think this question is very complex. Introducing the characters There are two important Functor combinators at play here. Flip equivalent to the haskell func...

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, ...

While looking at the definition of Monoid I noticed that mconcat has the following definition (source): mconcat :: Monoid a => [a] -> a mconcat = foldr mappend mempty Why would the signatu...

I have just started learning Haskell. As I know maximum gives the max value for a list of integers. So, maximum [2,5,7,1] gives 7. But why by giving a tuple input does maximum always give the...

Can someone explain what the type mean and how to implement this? class Foldable f where foldMap :: (Monoid m) => (a -> m) -> f a -> m Based on https://hackage.haskell.org/package/b...

I sum a list of matrices with foldl1 (+) because I noticed that sum actually returns the sum of the top left elements as a 1x1 matrix. $ stack exec --resolver lts-12.5 --package matrix -- ghci GH...

I recently read about recursion schemes where catamorphisms are described as analogous to generalized foldr. Is is possible to write an instance of Foldable (via either foldr or foldMap) in terms...

class (Functor t, Foldable t) => Traversable t where traverse :: Applicative f => (a -> f b) -> t a -> f (t b) traverse g = sequenceA . fmap g sequenceA :: Applicative f => t...

I am trying to understand Traversable with the help of https://namc.in/2018-02-05-foldables-traversals. Somewhere the author mentioned the following sentence: Traversable is to Applicative con...

I would like to express the following Haskell code, using only functor algebra (i.e. - not relying on any specific container type, such as List): ys = zipWith (+) (head xs : repeat 0) (tail xs ++...

For me, an integer set seems to be a foldable data structure. Why is Data.IntSet not an instance of Foldable? My actual intention is to use find on an IntSet. How can I implement find for Data.Int...

The following typechecks: instance (Applicative f, Alternative f, Foldable f) => Monad f where (>>=) = flip $ \f -> foldr (<|>) empty . fmap f -- Or equivalently a >>= ...

We know fmap is fmap :: Functor f => (a -> b) -> f a -> f b and sum is sum :: (Num a, Foldable t) => t a -> a, but the code below confuse me. > :t (fmap sum Just) (fmap sum Ju...

first question here and completely a noob on haskell, so please be kind with me :) I was playing with the question number 6 of this haskell exercises and in the end came to the solution (or somet...

Consider the following signature of foldMap foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m This is very similar to "bind", just with the arguments swapped: (>>=) ::...

MonoFoldable in the mono-traversable package seems to be able to implement all of the usual Foldable containers and more, for example, things like Bytestring and homogeneous tuples can be made Mono...

I am looking at the Foldable class in Haskell. Two of the methods fold, foldMap requires a Monoid instance. But foldr or foldl don't have any such constraint. fold :: Monoid m => t m -> m fo...

While studying Applicative deeper, I came to Traversable. Although I already knew Foldable from LYHGG, I haven't seen the former yet, so I started reading the Haskell wiki about Traversable. While...

data Tree t = Empty | Node t (Tree t) (Tree t) We can create Functor instance and use fmap :: (t -> a) -> Tree t -> Tree a But what if instead of (t -> a) I want (Tree t -> a) so I co...

I'm playing around with type-aligned sequences, and in particular I'm messing around with the idea of folding them. A foldable type-aligned sequence looks something like this: class FoldableTA fm ...

I am a beginner at Haskell and learning from "Learn You a Haskell". There's something I don't understand about the Tree implementation of Foldable. instance F.Foldable Tree where foldMap f Empt...