compactable-0.1.0.4: A typeclass for structures which can be catMaybed, filtered, and partitioned.

Control.Compactable

Synopsis

# Documentation

class Compactable (f :: * -> *) where Source #

Class Compactable provides two methods which can be writen in terms of each other, compact and separate.

# Compact

is generalization of catMaybes as a new function. 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 stripping 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)

# Separate and filter

have recently elevated roles in this typeclass, and is not as well explored as compact. Here are the laws known today:

Functor identity 3
fst . separate . fmap Right = id
Functor identity 4
snd . separate . fmap Left = id
Applicative left identity 2
snd . separate . (pure Right <*>) = id
Applicative right identity 2
fst . separate . (pure Left <*>) = id
Alternative annihilation left
snd . separate . fmap (const Left) = empty
Alternative annihilation right
fst , separate . fmap (const Right) = empty

Docs for relationships between these functions and, a cleanup of laws will happen at some point.

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

separate :: f (Either l r) -> (f l, f r) Source #

separate :: Functor f => f (Either l r) -> (f l, f r) Source #

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

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

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

fmapEither :: Functor f => (a -> Either l r) -> f a -> (f l, f r) Source #

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

applyEither :: Applicative f => f (a -> Either l r) -> f a -> (f l, f r) Source #

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

bindEither :: Monad f => f a -> (a -> f (Either l r)) -> (f l, f r) Source #

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

traverseEither :: (Applicative g, Traversable f) => (a -> g (Either l r)) -> f a -> g (f l, f r) Source #

Instances

fforMaybe :: (Compactable f, Functor f) => f a -> (a -> Maybe b) -> f b Source #

fforEither :: (Compactable f, Functor f) => f a -> (a -> Either l r) -> (f l, f r) Source #

fmapMaybeM :: (Compactable f, Monad f) => (a -> MaybeT f b) -> f a -> f b Source #

fmapEitherM :: (Compactable f, Monad f) => (a -> ExceptT l f r) -> f a -> (f l, f r) Source #

fforMaybeM :: (Compactable f, Monad f) => f a -> (a -> MaybeT f b) -> f b Source #

fforEitherM :: (Compactable f, Monad f) => f a -> (a -> ExceptT l f r) -> (f l, f r) Source #

applyMaybeM :: (Compactable f, Monad f) => f (a -> MaybeT f b) -> f a -> f b Source #

bindMaybeM :: (Compactable f, Monad f) => f a -> (a -> f (MaybeT f b)) -> f b Source #

traverseMaybeM :: (Monad m, Compactable t, Traversable t) => (a -> MaybeT m b) -> t a -> m (t b) Source #

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

While more constrained, when available, this default is going to be faster than the one provided in the typeclass

altDefaultSeparate :: (Alternative f, Foldable f) => f (Either l r) -> (f l, f r) Source #

While more constrained, when available, this default is going to be faster than the one provided in the typeclass