deferred-folds-0.9.17: Abstractions over deferred folds

DeferredFolds.Unfoldl

Synopsis

# Documentation

newtype Unfoldl a Source #

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 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 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
 Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methods(>>=) :: Unfoldl a -> (a -> Unfoldl b) -> Unfoldl b Source #(>>) :: Unfoldl a -> Unfoldl b -> Unfoldl b Source #return :: a -> Unfoldl a Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methodsfmap :: (a -> b) -> Unfoldl a -> Unfoldl b Source #(<\$) :: a -> Unfoldl b -> Unfoldl a Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methodspure :: a -> Unfoldl a Source #(<*>) :: Unfoldl (a -> b) -> Unfoldl a -> Unfoldl b Source #liftA2 :: (a -> b -> c) -> Unfoldl a -> Unfoldl b -> Unfoldl c Source #(*>) :: Unfoldl a -> Unfoldl b -> Unfoldl b Source #(<*) :: Unfoldl a -> Unfoldl b -> Unfoldl a Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methodsfold :: Monoid m => Unfoldl m -> m Source #foldMap :: Monoid m => (a -> m) -> Unfoldl a -> m Source #foldMap' :: Monoid m => (a -> m) -> Unfoldl a -> m Source #foldr :: (a -> b -> b) -> b -> Unfoldl a -> b Source #foldr' :: (a -> b -> b) -> b -> Unfoldl a -> b Source #foldl :: (b -> a -> b) -> b -> Unfoldl a -> b Source #foldl' :: (b -> a -> b) -> b -> Unfoldl a -> b Source #foldr1 :: (a -> a -> a) -> Unfoldl a -> a Source #foldl1 :: (a -> a -> a) -> Unfoldl a -> a Source #toList :: Unfoldl a -> [a] Source #null :: Unfoldl a -> Bool Source #length :: Unfoldl a -> Int Source #elem :: Eq a => a -> Unfoldl a -> Bool Source #maximum :: Ord a => Unfoldl a -> a Source #minimum :: Ord a => Unfoldl a -> a Source #sum :: Num a => Unfoldl a -> a Source #product :: Num a => Unfoldl a -> a Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methods(<|>) :: Unfoldl a -> Unfoldl a -> Unfoldl a Source #some :: Unfoldl a -> Unfoldl [a] Source #many :: Unfoldl a -> Unfoldl [a] Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methodsmplus :: Unfoldl a -> Unfoldl a -> Unfoldl a Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Associated Typestype Item (Unfoldl a) Source # MethodsfromList :: [Item (Unfoldl a)] -> Unfoldl a Source #fromListN :: Int -> [Item (Unfoldl a)] -> Unfoldl a Source #toList :: Unfoldl a -> [Item (Unfoldl a)] Source # Eq a => Eq (Unfoldl a) Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methods(==) :: Unfoldl a -> Unfoldl a -> Bool Source #(/=) :: Unfoldl a -> Unfoldl a -> Bool Source # Show a => Show (Unfoldl a) Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl MethodsshowsPrec :: Int -> Unfoldl a -> ShowS Source #show :: Unfoldl a -> String Source #showList :: [Unfoldl a] -> ShowS Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methods(<>) :: Unfoldl a -> Unfoldl a -> Unfoldl a Source #sconcat :: NonEmpty (Unfoldl a) -> Unfoldl a Source #stimes :: Integral b => b -> Unfoldl a -> Unfoldl a Source # Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl Methodsmappend :: Unfoldl a -> Unfoldl a -> Unfoldl a Source #mconcat :: [Unfoldl a] -> Unfoldl a Source # type Item (Unfoldl a) Source # Instance detailsDefined in DeferredFolds.Defs.Unfoldl type Item (Unfoldl a) = a

fold :: Fold input output -> Unfoldl input -> output Source #

Apply a Gonzalez fold

unfoldlM :: UnfoldlM Identity input -> Unfoldl input Source #

mapFoldInput :: (forall x. Fold b x -> Fold a x) -> Unfoldl a -> Unfoldl b Source #

Lift a fold input mapping function into a mapping of unfolds

foldable :: Foldable foldable => foldable a -> Unfoldl a Source #

Construct from any foldable

filter :: (a -> Bool) -> Unfoldl a -> Unfoldl a Source #

Filter the values given a predicate

Ints in the specified inclusive range

mapAssocs :: Map key value -> Unfoldl (key, value) Source #

Associations of a map

intMapAssocs :: IntMap value -> Unfoldl (Int, value) Source #

Associations of an intmap

Bytes of a bytestring

Bytes of a short bytestring

primArray :: Prim prim => PrimArray prim -> Unfoldl prim Source #

Elements of a prim array

primArrayWithIndices :: Prim prim => PrimArray prim -> Unfoldl (Int, prim) Source #

Elements of a prim array coming paired with indices