compactable-0.1.0.1: A generalization for containers that can be stripped of Nothings.

Control.Compactable

Synopsis

# Documentation

class Compactable f where Source #

This is a generalization of catMaybes as a new function compact. Compact has relations with Functor, Applicative, Monad, Alternative, and Traversable. In that we can use these class to provide the ability to operate on a data type by throwing away intermediate Nothings. This is useful for representing striping out 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:

Kleisli composition
fmapMaybe (l <=< r) = fmapMaybe l . fmapMaybe r
Functor identity 1
compact . fmap Just = id
Functor identity 2
fmapMaybe Just = id
Functor relation
compact = fmapMaybe id

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

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

Applicative left identity
compact . (pure Just *) = id
Applicative right identity
applyMaybe (pure Just) = id
Applicative relation
compact = applyMaybe (pure id)

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

flip bindMaybe (return . Just) = id
compact . (return . Just =<<) = id
compact = flip bindMaybe return

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

Alternative identity
compact empty = empty
Alternative annihilation
compact (const Nothing <\$> xs) = empty

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

Traversable Applicative relation
traverseMaybe (pure . Just) = pure
Traversable composition
Compose . fmap (traverseMaybe f) . traverseMaybe g = traverseMaybe (Compose . fmap (traverseMaybe f) . g)
Traversable Functor relation
traverse f = traverseMaybe (fmap Just . f)
Traversable naturality
t . traverseMaybe f = traverseMaybe (t . f)

If you know of more useful laws, or have better names for the ones above (especially those marked "name me"). Please let me know.

Methods

compact :: f (Maybe a) -> f a Source #

compact :: (Monad f, Alternative f) => f (Maybe a) -> f a Source #

fmapMaybe :: Functor f => (a -> Maybe b) -> f a -> f b Source #

applyMaybe :: Applicative f => f (a -> Maybe b) -> f a -> f b Source #

bindMaybe :: Monad f => f a -> (a -> f (Maybe b)) -> f b Source #

traverseMaybe :: (Applicative g, Traversable f) => (a -> g (Maybe b)) -> f a -> g (f b) Source #

filter :: Functor f => (a -> Bool) -> f a -> f a Source #

Instances