Data.Filterable

class (Compactable f, Functor f) <= Filterable f  where

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

Members

• partitionMap :: forall a l r. (a -> Either l r) -> f a -> { left :: f l, right :: f r }
• partition :: forall a. (a -> Boolean) -> f a -> { no :: f a, yes :: f a }
• filterMap :: forall a b. (a -> Maybe b) -> f a -> f b
• filter :: forall a. (a -> Boolean) -> f a -> f a

Instances

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

eitherBool :: forall a. (a -> Boolean) -> a -> Either a a

Upgrade a boolean-style predicate to an either-style predicate mapping.

partitionDefault :: forall f a. Filterable f => (a -> Boolean) -> f a -> { no :: f a, yes :: f a }

A default implementation of partition using partitionMap.

partitionDefaultFilter :: forall f a. Filterable f => (a -> Boolean) -> f a -> { no :: f a, yes :: f a }

A default implementation of partition using filter. Note that this is almost certainly going to be suboptimal compared to direct implementations.

partitionDefaultFilterMap :: forall f a. Filterable f => (a -> Boolean) -> f a -> { no :: f a, yes :: f a }

A default implementation of partition using filterMap. Note that this is almost certainly going to be suboptimal compared to direct implementations.

partitionMapDefault :: forall f a l r. Filterable f => (a -> Either l r) -> f a -> { left :: f l, right :: f r }

A default implementation of partitionMap using separate. Note that this is almost certainly going to be suboptimal compared to direct implementations.

maybeBool :: forall a. (a -> Boolean) -> a -> Maybe a

Upgrade a boolean-style predicate to a maybe-style predicate mapping.

filterDefault :: forall f a. Filterable f => (a -> Boolean) -> f a -> f a

A default implementation of filter using filterMap.

filterDefaultPartition :: forall f a. Filterable f => (a -> Boolean) -> f a -> f a

A default implementation of filter using partition.

filterDefaultPartitionMap :: forall f a. Filterable f => (a -> Boolean) -> f a -> f a

A default implementation of filter using partitionMap.

filterMapDefault :: forall f a b. Filterable f => (a -> Maybe b) -> f a -> f b

A default implementation of filterMap using separate. Note that this is almost certainly going to be suboptimal compared to direct implementations.

cleared :: forall f a b. Filterable f => f a -> f b

Filter out all values.

class Compactable f  where

Compactable represents data structures which can be compacted/filtered. This is a generalization of catMaybes as a new function compact. compact has relations with Functor, Applicative, Monad, Plus, and Traversable in that we can use these classes to provide the ability to operate on a data type by eliminating intermediate Nothings. This is useful for representing the filtering out of values, or failure.

To be compactable alone, no laws must be satisfied other than the type signature.

If the data type is also a Functor the following should hold:

• Functor Identity: compact <<< map Just ≡ id

According to Kmett, (Compactable f, Functor f) is a functor from the kleisli category of Maybe to the category of Hask. Kleisli Maybe -> Hask.

If the data type is also Applicative the following should hold:

• compact <<< (pure Just <*> _) ≡ id
• applyMaybe (pure Just) ≡ id
• compact ≡ applyMaybe (pure id)

If the data type is also a Monad the following should hold:

• flip bindMaybe (pure <<< Just) ≡ id
• compact <<< (pure <<< (Just (=<<))) ≡ id
• compact ≡ flip bindMaybe pure

If the data type is also Plus the following should hold:

• compact empty ≡ empty
• compact (const Nothing <$> xs) ≡ empty

Members

• compact :: forall a. f (Maybe a) -> f a
• separate :: forall l r. f (Either l r) -> { left :: f l, right :: f r }

Instances

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