DeferredFolds.ToBeFoldled

Documentation

newtype ToBeFoldled input

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

Constructors

ToBeFoldled (forall output. (output -> input -> output) -> output -> output)

Instances

Monad ToBeFoldled

Methods

(>>=) :: ToBeFoldled a -> (a -> ToBeFoldled b) -> ToBeFoldled b

(>>) :: ToBeFoldled a -> ToBeFoldled b -> ToBeFoldled b

return :: a -> ToBeFoldled a

fail :: String -> ToBeFoldled a

Functor ToBeFoldled

Methods

fmap :: (a -> b) -> ToBeFoldled a -> ToBeFoldled b

(<$) :: a -> ToBeFoldled b -> ToBeFoldled a

Applicative ToBeFoldled

Methods

pure :: a -> ToBeFoldled a

(<*>) :: ToBeFoldled (a -> b) -> ToBeFoldled a -> ToBeFoldled b

liftA2 :: (a -> b -> c) -> ToBeFoldled a -> ToBeFoldled b -> ToBeFoldled c

(*>) :: ToBeFoldled a -> ToBeFoldled b -> ToBeFoldled b

(<*) :: ToBeFoldled a -> ToBeFoldled b -> ToBeFoldled a

Alternative ToBeFoldled

Methods

empty :: ToBeFoldled a

(<|>) :: ToBeFoldled a -> ToBeFoldled a -> ToBeFoldled a

some :: ToBeFoldled a -> ToBeFoldled [a]

many :: ToBeFoldled a -> ToBeFoldled [a]

MonadPlus ToBeFoldled

Methods

mzero :: ToBeFoldled a

mplus :: ToBeFoldled a -> ToBeFoldled a -> ToBeFoldled a

Semigroup (ToBeFoldled a)

Methods

(<>) :: ToBeFoldled a -> ToBeFoldled a -> ToBeFoldled a

sconcat :: NonEmpty (ToBeFoldled a) -> ToBeFoldled a

stimes :: Integral b => b -> ToBeFoldled a -> ToBeFoldled a

Monoid (ToBeFoldled a)

Methods

mempty :: ToBeFoldled a

mappend :: ToBeFoldled a -> ToBeFoldled a -> ToBeFoldled a

mconcat :: [ToBeFoldled a] -> ToBeFoldled a

foldl' :: (output -> input -> output) -> output -> ToBeFoldled input -> output

Perform a strict left fold

fold :: Fold input output -> ToBeFoldled input -> output

Apply a Gonzalez fold

foldable :: Foldable foldable => foldable a -> ToBeFoldled a

Construct from any foldable