foldl-1.4.18: Composable, streaming, and efficient left folds

Safe Haskell | Safe-Inferred
Language | Haskell2010

Control.Foldl.NonEmpty

Contents

- Fold Types
- Folding
- Conversion between Fold and Fold1
- Folds
  - Non-empty Container Folds
- Utilities

Description

This module provides a `Fold1` type that is a "non-empty" analog of the `Fold` type, meaning that it requires at least one input element in order to produce a result

This module does not provide all of the same utilities as the Control.Foldl module. Instead, this module only provides the utilities which can make use of the non-empty input guarantee (e.g. `head`). For all other utilities you can convert them from the equivalent `Fold` using `fromFold`.

Import this module qualified to avoid clashing with the Prelude:

    >>> import qualified Control.Foldl.NonEmpty as Foldl1

Use `fold1` to apply a `Fold1` to a non-empty list:

    >>> Foldl1.fold1 Foldl1.last (1 :| [2..10])
    10

Synopsis

- data Fold1 a b where
  - Fold1 (a -> Fold a b)
  - pattern Fold1_ :: forall a b x. () => (a -> x) -> (x -> a -> x) -> (x -> b) -> Fold1 a b
- fold1 :: Foldable1 f => Fold1 a b -> f a -> b
- fromFold :: Fold a b -> Fold1 a b
- toFold :: Fold1 a b -> Fold a (Maybe b)
- sconcat :: Semigroup a => Fold1 a a
- head :: Fold1 a a
- last :: Fold1 a a
- maximum :: Ord a => Fold1 a a
- maximumBy :: (a -> a -> Ordering) -> Fold1 a a
- minimum :: Ord a => Fold1 a a
- minimumBy :: (a -> a -> Ordering) -> Fold1 a a
- nonEmpty :: Fold1 a (NonEmpty a)
- purely :: (forall x. (a -> x) -> (x -> a -> x) -> (x -> b) -> r) -> Fold1 a b -> r
- purely_ :: (forall x. (a -> x) -> (x -> a -> x) -> x) -> Fold1 a b -> b
- premap :: (a -> b) -> Fold1 b r -> Fold1 a r
- newtype FromMaybe b = FromMaybe {
  - appFromMaybe :: Maybe b -> b
  }
- type Handler1 a b = forall x. (b -> Const (Dual (FromMaybe x)) b) -> a -> Const (Dual (FromMaybe x)) a
- handles :: Handler1 a b -> Fold1 b r -> Fold1 a r
- foldOver :: Handler1 s a -> Fold1 a b -> s -> b
- folded1 :: (Contravariant f, Apply f, Foldable1 t) => (a -> f a) -> t a -> f (t a)
- nest :: Apply f => Fold1 a b -> Fold1 (f a) (f b)

# Fold Types

data Fold1 a b #

A `Fold1` is like a `Fold` except that it consumes at least one input element

Constructors

Fold1 (a -> Fold a b) |

Bundled Patterns

pattern Fold1_ :: forall a b x. () => (a -> x) -> (x -> a -> x) -> (x -> b) -> Fold1 a b | `Fold1_` is an alternative to the `Fold1` constructor if you need to explicitly work with an initial, step and extraction function. `Fold1_` is similar to the `Fold` constructor, which also works with an initial, step and extraction function. However, note that `Fold` takes the step function as the first argument and the initial accumulator as the second argument, whereas `Fold1_` takes them in swapped order: `Fold1_` `initial` `step` `extract` While `Fold` resembles `foldl`, `Fold1_` resembles `foldlMap1`.

#### Instances

Instances details

Arrow Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods arr :: (b -> c) -> Fold1 b c # first :: Fold1 b c -> Fold1 (b, d) (c, d) # second :: Fold1 b c -> Fold1 (d, b) (d, c) # (***) :: Fold1 b c -> Fold1 b' c' -> Fold1 (b, b') (c, c') # (&&&) :: Fold1 b c -> Fold1 b c' -> Fold1 b (c, c') #
ArrowChoice Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods left :: Fold1 b c -> Fold1 (Either b d) (Either c d) # right :: Fold1 b c -> Fold1 (Either d b) (Either d c) # (+++) :: Fold1 b c -> Fold1 b' c' -> Fold1 (Either b b') (Either c c') # (|||) :: Fold1 b d -> Fold1 c d -> Fold1 (Either b c) d #
Choice Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods left' :: Fold1 a b -> Fold1 (Either a c) (Either b c) # right' :: Fold1 a b -> Fold1 (Either c a) (Either c b) #
Closed Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods closed :: Fold1 a b -> Fold1 (x -> a) (x -> b) #
Strong Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods first' :: Fold1 a b -> Fold1 (a, c) (b, c) # second' :: Fold1 a b -> Fold1 (c, a) (c, b) #
Profunctor Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods dimap :: (a -> b) -> (c -> d) -> Fold1 b c -> Fold1 a d # lmap :: (a -> b) -> Fold1 b c -> Fold1 a c # rmap :: (b -> c) -> Fold1 a b -> Fold1 a c # (#.) :: forall a b c q. Coercible c b => q b c -> Fold1 a b -> Fold1 a c # (.#) :: forall a b c q. Coercible b a => Fold1 b c -> q a b -> Fold1 a c #
Category Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods id :: Fold1 a a # (.) :: Fold1 b c -> Fold1 a b -> Fold1 a c #
Cosieve Fold1 NonEmpty # |
Instance details Defined in Control.Foldl.NonEmpty Methods cosieve :: Fold1 a b -> NonEmpty a -> b #
Semigroupoid Fold1 # |
Instance details Defined in Control.Foldl.NonEmpty Methods o :: Fold1 j k1 -> Fold1 i j -> Fold1 i k1 #
Applicative (Fold1 a) # |
Instance details Defined in Control.Foldl.NonEmpty Methods pure :: a0 -> Fold1 a a0 # (<*>) :: Fold1 a (a0 -> b) -> Fold1 a a0 -> Fold1 a b # liftA2 :: (a0 -> b -> c) -> Fold1 a a0 -> Fold1 a b -> Fold1 a c # (*>) :: Fold1 a a0 -> Fold1 a b -> Fold1 a b # (<*) :: Fold1 a a0 -> Fold1 a b -> Fold1 a a0 #
Functor (Fold1 a) # |
Instance details Defined in Control.Foldl.NonEmpty Methods fmap :: (a0 -> b) -> Fold1 a a0 -> Fold1 a b # (<$) :: a0 -> Fold1 a b -> Fold1 a a0 #
Extend (Fold1 a) # |
Instance details Defined in Control.Foldl.NonEmpty Methods duplicated :: Fold1 a a0 -> Fold1 a (Fold1 a a0) # extended :: (Fold1 a a0 -> b) -> Fold1 a a0 -> Fold1 a b #
Monoid b => Monoid (Fold1 a b) # |
Instance details Defined in Control.Foldl.NonEmpty Methods mempty :: Fold1 a b # mappend :: Fold1 a b -> Fold1 a b -> Fold1 a b # mconcat :: [Fold1 a b] -> Fold1 a b #
Semigroup b => Semigroup (Fold1 a b) # |
Instance details Defined in Control.Foldl.NonEmpty Methods (<>) :: Fold1 a b -> Fold1 a b -> Fold1 a b # sconcat :: NonEmpty (Fold1 a b) -> Fold1 a b # stimes :: Integral b0 => b0 -> Fold1 a b -> Fold1 a b #
Floating b => Floating (Fold1 a b) # |
Instance details Defined in Control.Foldl.NonEmpty Methods pi :: Fold1 a b # exp :: Fold1 a b -> Fold1 a b # log :: Fold1 a b -> Fold1 a b # sqrt :: Fold1 a b -> Fold1 a b # (**) :: Fold1 a b -> Fold1 a b -> Fold1 a b # logBase :: Fold1 a b -> Fold1 a b -> Fold1 a b # sin :: Fold1 a b -> Fold1 a b # cos :: Fold1 a b -> Fold1 a b # tan :: Fold1 a b -> Fold1 a b # asin :: Fold1 a b -> Fold1 a b # acos :: Fold1 a b -> Fold1 a b # atan :: Fold1 a b -> Fold1 a b # sinh :: Fold1 a b -> Fold1 a b # cosh :: Fold1 a b -> Fold1 a b # tanh :: Fold1 a b -> Fold1 a b # asinh :: Fold1 a b -> Fold1 a b # acosh :: Fold1 a b -> Fold1 a b # atanh :: Fold1 a b -> Fold1 a b # log1p :: Fold1 a b -> Fold1 a b # expm1 :: Fold1 a b -> Fold1 a b # log1pexp :: Fold1 a b -> Fold1 a b # log1mexp :: Fold1 a b -> Fold1 a b #
Num b => Num (Fold1 a b) # |
Instance details Defined in Control.Foldl.NonEmpty Methods (+) :: Fold1 a b -> Fold1 a b -> Fold1 a b # (-) :: Fold1 a b -> Fold1 a b -> Fold1 a b # (*) :: Fold1 a b -> Fold1 a b -> Fold1 a b # negate :: Fold1 a b -> Fold1 a b # abs :: Fold1 a b -> Fold1 a b # signum :: Fold1 a b -> Fold1 a b # fromInteger :: Integer -> Fold1 a b #
Fractional b => Fractional (Fold1 a b) # |
Instance details Defined in Control.Foldl.NonEmpty Methods (/) :: Fold1 a b -> Fold1 a b -> Fold1 a b # recip :: Fold1 a b -> Fold1 a b # fromRational :: Rational -> Fold1 a b #

# Folding

fold1 :: Foldable1 f => Fold1 a b -> f a -> b #

Apply a strict left `Fold1` to a `NonEmpty` list

# Conversion between Fold and Fold1

fromFold :: Fold a b -> Fold1 a b #

Promote any `Fold` to an equivalent `Fold1`

toFold :: Fold1 a b -> Fold a (Maybe b) #

Promote any `Fold1` to an equivalent `Fold`

# Folds

sconcat :: Semigroup a => Fold1 a a #

Fold all values within a non-empty container using (`<>`)

head :: Fold1 a a #

Get the first element of a non-empty container

last :: Fold1 a a #

Get the last element of a non-empty container

maximum :: Ord a => Fold1 a a #

Computes the maximum element

maximumBy :: (a -> a -> Ordering) -> Fold1 a a #

Computes the maximum element with respect to the given comparison function

minimum :: Ord a => Fold1 a a #

Computes the minimum element

minimumBy :: (a -> a -> Ordering) -> Fold1 a a #

Computes the minimum element with respect to the given comparison function

## Non-empty Container Folds

nonEmpty :: Fold1 a (NonEmpty a) #

Fold all values within a non-empty container into a `NonEmpty` list

# Utilities

purely :: (forall x. (a -> x) -> (x -> a -> x) -> (x -> b) -> r) -> Fold1 a b -> r #

Upgrade a fold to accept the `Fold1` type

purely_ :: (forall x. (a -> x) -> (x -> a -> x) -> x) -> Fold1 a b -> b #

Upgrade a more traditional fold to accept the `Fold1` type

premap :: (a -> b) -> Fold1 b r -> Fold1 a r #

`(premap f folder)` returns a new `Fold1` where f is applied at each step

    Foldl1.fold1 (premap f folder) list = Foldl1.fold1 folder (NonEmpty.map f list)

    >>> Foldl1.fold1 (premap Sum Foldl1.sconcat) (1 :| [2..10])
    Sum {getSum = 55}

    >>> Foldl1.fold1 Foldl1.sconcat $ NonEmpty.map Sum (1 :| [2..10])
    Sum {getSum = 55}

    premap id = id

    premap (f . g) = premap g . premap f

    premap k (pure r) = pure r

    premap k (f <*> x) = premap k f <*> premap k x

newtype FromMaybe b #

    instance Monad m => Semigroup (FromMaybe m a) where
        mappend (FromMaybe f) (FromMaybe g) = FromMaybeM (f . Just . g)

Constructors

FromMaybe |
Fields appFromMaybe :: Maybe b -> b

#### Instances

Instances details

Semigroup (FromMaybe b) # |
Instance details Defined in Control.Foldl.NonEmpty Methods (<>) :: FromMaybe b -> FromMaybe b -> FromMaybe b # sconcat :: NonEmpty (FromMaybe b) -> FromMaybe b # stimes :: Integral b0 => b0 -> FromMaybe b -> FromMaybe b #

type Handler1 a b = forall x. (b -> Const (Dual (FromMaybe x)) b) -> a -> Const (Dual (FromMaybe x)) a #

A handler for the upstream input of a `Fold1`

This is compatible with van Laarhoven optics as defined in the lens package. Any lens, fold1 or traversal1 will type-check as a `Handler1`.

handles :: Handler1 a b -> Fold1 b r -> Fold1 a r #

`(handles t folder)` transforms the input of a `Fold1` using a Lens, Traversal1, or Fold1 optic:

    handles _1        :: Fold1 a r -> Fold1 (a, b) r
    handles traverse1 :: Traversable1 t => Fold1 a r -> Fold1 (t a) r
    handles folded1   :: Foldable1    t => Fold1 a r -> Fold1 (t a) r

    >>> Foldl1.fold1 (handles traverse1 Foldl1.nonEmpty) $ (1 :| [2..4]) :| [ 5 :| [6,7], 8 :| [9,10] ]
    1 :| [2,3,4,5,6,7,8,9,10]

    >>> Foldl1.fold1 (handles _2 Foldl1.sconcat) $ (1,"Hello ") :| [(2,"World"),(3,"!")]
    "Hello World!"

    handles id = id

    handles (f . g) = handles f . handles g

    handles t (pure r) = pure r

    handles t (f <*> x) = handles t f <*> handles t x

foldOver :: Handler1 s a -> Fold1 a b -> s -> b #

`(foldOver f folder xs)` folds all values from a Lens, Traversal1 or Fold1 optic with the given folder

    >>> foldOver (_2 . both1) Foldl1.nonEmpty (1, (2, 3))
    2 :| [3]

    Foldl1.foldOver f folder xs == Foldl1.fold1 folder (xs ^.. f)

    Foldl1.foldOver (folded1 . f) folder == Foldl1.fold1 (Foldl1.handles f folder)

    Foldl1.foldOver folded1 == Foldl1.fold1

folded1 :: (Contravariant f, Apply f, Foldable1 t) => (a -> f a) -> t a -> f (t a) #

    handles folded1 :: Foldable1 t => Fold1 a r -> Fold1 (t a) r

nest :: Apply f => Fold1 a b -> Fold1 (f a) (f b) #

Nest a fold in an Apply.