Documentation

A projection on data, which only knows how to execute a strict left-fold.

It is a monad and a monoid, and is very useful for efficiently aggregating the projections on data intended for left-folding, since its concatenation (<>) has complexity of O(1).

Intuition

The intuition of what this abstraction is all about can be derived from lists.

Let's consider the foldl' function for lists:

foldl' :: (b -> a -> b) -> b -> [a] -> b

If we reverse its parameters we get

foldl' :: [a] -> (b -> a -> b) -> b -> b

Which in Haskell is essentially the same as

foldl' :: [a] -> (forall b. (b -> a -> b) -> b -> b)

We can isolate that part into an abstraction:

newtype ToBeFoldled a = ToBeFoldled (forall b. (b -> a -> b) -> b -> b)

Then we get to this simple morphism:

foldl' :: [a] -> ToBeFoldled a

Perform a strict left fold

Apply a Gonzalez fold

Construct from any foldable