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 Unfold a = Unfold (forall b. (b -> a -> b) -> b -> b)

Then we get to this simple morphism:

list :: [a] -> Unfold a
list list = Unfold (\ step init -> foldl' step init list)

We can do the same with say Data.Text.Text:

text :: Text -> Unfold Char
text text = Unfold (\ step init -> Data.Text.foldl' step init text)

And then we can use those both to concatenate with just an O(1) cost:

abcdef :: Unfold Char
abcdef = list ['a', 'b', 'c'] <> text "def"

Please notice that up until this moment no actual data materialization has happened and hence no traversals have appeared. All that we've done is just composed a function, which only specifies which parts of data structures to traverse to perform a left-fold. Only at the moment where the actual folding will happen will we actually traverse the source data. E.g., using the "fold" function:

abcdefLength :: Int
abcdefLength = fold Control.Foldl.length abcdef

Perform a strict left fold

Apply a Gonzalez fold

Construct from any foldable

Ints in the specified inclusive range