Data.Witherable

class Witherable :: (Type -> Type) -> Constraintclass (Filterable t, Traversable t) <= Witherable t  where

Witherable represents data structures which can be partitioned with effects in some Applicative functor.

• wilt - partition a structure with effects
• wither - filter a structure with effects

Laws:

• Naturality: t <<< wither f ≡ wither (t <<< f)
• Identity: wither (pure <<< Just) ≡ pure
• Composition: Compose <<< map (wither f) <<< wither g ≡ wither (Compose <<< map (wither f) <<< g)
• Multipass partition: wilt p ≡ map separate <<< traverse p
• Multipass filter: wither p ≡ map compact <<< traverse p

Superclass equivalences:

• partitionMap p = runIdentity <<< wilt (Identity <<< p)
• filterMap p = runIdentity <<< wither (Identity <<< p)
• traverse f ≡ wither (map Just <<< f)

Default implementations are provided by the following functions:

• wiltDefault
• witherDefault
• partitionMapByWilt
• filterMapByWither
• traverseByWither

Members

• wilt :: forall m a l r. Applicative m => (a -> m (Either l r)) -> t a -> m { left :: t l, right :: t r }
• wither :: forall m a b. Applicative m => (a -> m (Maybe b)) -> t a -> m (t b)

Instances

• Witherable Array
• Witherable List
• (Ord k) => Witherable (Map k)
• Witherable Maybe
• (Monoid m) => Witherable (Either m)

partitionMapByWilt :: forall t a l r. Witherable t => (a -> Either l r) -> t a -> { left :: t l, right :: t r }

A default implementation of parititonMap given a Witherable.

filterMapByWither :: forall t a b. Witherable t => (a -> Maybe b) -> t a -> t b

A default implementation of filterMap given a Witherable.

traverseByWither :: forall t m a b. Witherable t => Applicative m => (a -> m b) -> t a -> m (t b)

A default implementation of traverse given a Witherable.

wilted :: forall t m l r. Witherable t => Applicative m => t (m (Either l r)) -> m { left :: t l, right :: t r }

Partition between Left and Right values - with effects in m.

withered :: forall t m x. Witherable t => Applicative m => t (m (Maybe x)) -> m (t x)

Filter out all the Nothing values - with effects in m.

witherDefault :: forall t m a b. Witherable t => Applicative m => (a -> m (Maybe b)) -> t a -> m (t b)

A default implementation of wither using compact.

wiltDefault :: forall t m a l r. Witherable t => Applicative m => (a -> m (Either l r)) -> t a -> m { left :: t l, right :: t r }

A default implementation of wilt using separate

class Filterable :: (Type -> Type) -> Constraintclass (Compactable f, Functor f) <= Filterable f 

Filterable represents data structures which can be partitioned/filtered.

• partitionMap - partition a data structure based on an either predicate.
• partition - partition a data structure based on boolean predicate.
• filterMap - map over a data structure and filter based on a maybe.
• filter - filter a data structure based on a boolean.

Laws:

• Functor Relation: filterMap identity ≡ compact

• Functor Identity: filterMap Just ≡ identity

• Kleisli Composition: filterMap (l <=< r) ≡ filterMap l <<< filterMap r

• filter ≡ filterMap <<< maybeBool

• filterMap p ≡ filter (isJust <<< p)

• Functor Relation: partitionMap identity ≡ separate

• Functor Identity 1: _.right <<< partitionMap Right ≡ identity

• Functor Identity 2: _.left <<< partitionMap Left ≡ identity

• f <<< partition ≡ partitionMap <<< eitherBool where f = \{ no, yes } -> { left: no, right: yes }

• f <<< partitionMap p ≡ partition (isRight <<< p) where f = \{ left, right } -> { no: left, yes: right}

Default implementations are provided by the following functions:

• partitionDefault
• partitionDefaultFilter
• partitionDefaultFilterMap
• partitionMapDefault
• filterDefault
• filterDefaultPartition
• filterDefaultPartitionMap
• filterMapDefault

Instances

• Filterable Array
• Filterable Maybe
• (Monoid m) => Filterable (Either m)
• Filterable List
• (Ord k) => Filterable (Map k)