Safe Haskell	Safe-Inferred
Language	Haskell2010

DeferredFolds.Unfoldl

Synopsis

newtype Unfoldl a = Unfoldl (forall x. (x -> a -> x) -> x -> x)
fold :: Fold input output -> Unfoldl input -> output
filter :: (a -> Bool) -> Unfoldl a -> Unfoldl a
foldable :: Foldable foldable => foldable a -> Unfoldl a
intsInRange :: Int -> Int -> Unfoldl Int
byteStringBytes :: ByteString -> Unfoldl Word8
shortByteStringBytes :: ShortByteString -> Unfoldl Word8
primArray :: Prim prim => PrimArray prim -> Unfoldl prim
primArrayWithIndices :: Prim prim => PrimArray prim -> Unfoldl (Int, prim)
unfoldlM :: UnfoldlM Identity input -> Unfoldl input
mapFoldInput :: (forall x. Fold b x -> Fold a x) -> Unfoldl a -> Unfoldl b
mapAssocs :: Map key value -> Unfoldl (key, value)
intMapAssocs :: IntMap value -> Unfoldl (Int, value)

Documentation

newtype Unfoldl a #

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 for this abstraction can be derived from lists.

Let's consider the foldl' function for lists:

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

If we rearrange 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 Unfoldl a = Unfoldl (forall b. (b -> a -> b) -> b -> b)

Then we get to this simple morphism:

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

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

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

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

abcdef :: Unfoldl 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

Constructors

Unfoldl (forall x. (x -> a -> x) -> x -> x)

Instances

Instances details

Foldable Unfoldl #
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods fold :: Monoid m => Unfoldl m -> m foldMap :: Monoid m => (a -> m) -> Unfoldl a -> m foldMap' :: Monoid m => (a -> m) -> Unfoldl a -> m foldr :: (a -> b -> b) -> b -> Unfoldl a -> b foldr' :: (a -> b -> b) -> b -> Unfoldl a -> b foldl :: (b -> a -> b) -> b -> Unfoldl a -> b foldl' :: (b -> a -> b) -> b -> Unfoldl a -> b foldr1 :: (a -> a -> a) -> Unfoldl a -> a foldl1 :: (a -> a -> a) -> Unfoldl a -> a toList :: Unfoldl a -> [a] null :: Unfoldl a -> Bool length :: Unfoldl a -> Int elem :: Eq a => a -> Unfoldl a -> Bool maximum :: Ord a => Unfoldl a -> a minimum :: Ord a => Unfoldl a -> a sum :: Num a => Unfoldl a -> a product :: Num a => Unfoldl a -> a
Alternative Unfoldl
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods empty :: Unfoldl a (<\|>) :: Unfoldl a -> Unfoldl a -> Unfoldl a some :: Unfoldl a -> Unfoldl [a] many :: Unfoldl a -> Unfoldl [a]
Applicative Unfoldl
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods pure :: a -> Unfoldl a # (<>) :: Unfoldl (a -> b) -> Unfoldl a -> Unfoldl b liftA2 :: (a -> b -> c) -> Unfoldl a -> Unfoldl b -> Unfoldl c (>) :: Unfoldl a -> Unfoldl b -> Unfoldl b (<*) :: Unfoldl a -> Unfoldl b -> Unfoldl a
Functor Unfoldl #
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods fmap :: (a -> b) -> Unfoldl a -> Unfoldl b # (<$) :: a -> Unfoldl b -> Unfoldl a #
Monad Unfoldl
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods (>>=) :: Unfoldl a -> (a -> Unfoldl b) -> Unfoldl b (>>) :: Unfoldl a -> Unfoldl b -> Unfoldl b return :: a -> Unfoldl a #
MonadPlus Unfoldl
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods mzero :: Unfoldl a mplus :: Unfoldl a -> Unfoldl a -> Unfoldl a
Monoid (Unfoldl a)
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods mempty :: Unfoldl a mappend :: Unfoldl a -> Unfoldl a -> Unfoldl a mconcat :: [Unfoldl a] -> Unfoldl a
Semigroup (Unfoldl a)
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods (<>) :: Unfoldl a -> Unfoldl a -> Unfoldl a sconcat :: NonEmpty (Unfoldl a) -> Unfoldl a stimes :: Integral b => b -> Unfoldl a -> Unfoldl a
IsList (Unfoldl a)
Instance details Defined in DeferredFolds.Defs.Unfoldl Associated Types type Item (Unfoldl a) Methods fromList :: [Item (Unfoldl a)] -> Unfoldl a fromListN :: Int -> [Item (Unfoldl a)] -> Unfoldl a toList :: Unfoldl a -> [Item (Unfoldl a)]
Show a => Show (Unfoldl a)
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods showsPrec :: Int -> Unfoldl a -> ShowS show :: Unfoldl a -> String showList :: [Unfoldl a] -> ShowS
Eq a => Eq (Unfoldl a)
Instance details Defined in DeferredFolds.Defs.Unfoldl Methods (==) :: Unfoldl a -> Unfoldl a -> Bool (/=) :: Unfoldl a -> Unfoldl a -> Bool
type Item (Unfoldl a)
Instance details Defined in DeferredFolds.Defs.Unfoldl type Item (Unfoldl a) = a