these-0.7.3: An either-or-both data type & a generalized 'zip with padding' typeclass

Data.Align

Description

These-based zipping and unzipping of functors with non-uniform shapes, plus traversal of (bi)foldable (bi)functors through said functors.

Synopsis

# Documentation

class Functor f => Align f where Source #

Functors supporting a zip operation that takes the union of non-uniform shapes.

If your functor is actually a functor from Kleisli Maybe to Hask (so it supports maybeMap :: (a -> Maybe b) -> f a -> f b), then an Align instance is making your functor lax monoidal w.r.t. the cartesian monoidal structure on Kleisli Maybe, because These is the cartesian product in that category (a -> Maybe (These b c) ~ (a -> Maybe b, a -> Maybe c)). This insight is due to rwbarton.

Minimal definition: nil and either align or alignWith.

Laws:

(align nil) = fmap This
(nil align) = fmap That
join align = fmap (join These)
align (f <$> x) (g <$> y) = bimap f g <> align x y alignWith f a b = f <> align a b


Minimal complete definition

nil, (align | alignWith)

Methods

nil :: f a Source #

An empty strucutre. aligning with nil will produce a structure with the same shape and elements as the other input, modulo This or That.

align :: f a -> f b -> f (These a b) Source #

Analogous to zip, combines two structures by taking the union of their shapes and using These to hold the elements.

alignWith :: (These a b -> c) -> f a -> f b -> f c Source #

Analogous to zipWith, combines two structures by taking the union of their shapes and combining the elements with the given function.

Instances

 Align [] Source # Methodsnil :: [a] Source #align :: [a] -> [b] -> [These a b] Source #alignWith :: (These a b -> c) -> [a] -> [b] -> [c] Source # Source # Methodsalign :: Maybe a -> Maybe b -> Maybe (These a b) Source #alignWith :: (These a b -> c) -> Maybe a -> Maybe b -> Maybe c Source # Source # Methodsalign :: ZipList a -> ZipList b -> ZipList (These a b) Source #alignWith :: (These a b -> c) -> ZipList a -> ZipList b -> ZipList c Source # Source # Methodsalign :: IntMap a -> IntMap b -> IntMap (These a b) Source #alignWith :: (These a b -> c) -> IntMap a -> IntMap b -> IntMap c Source # Source # Methodsalign :: Seq a -> Seq b -> Seq (These a b) Source #alignWith :: (These a b -> c) -> Seq a -> Seq b -> Seq c Source # Source # Methodsalign :: Vector a -> Vector b -> Vector (These a b) Source #alignWith :: (These a b -> c) -> Vector a -> Vector b -> Vector c Source # (Eq k, Hashable k) => Align (HashMap k) Source # Methodsnil :: HashMap k a Source #align :: HashMap k a -> HashMap k b -> HashMap k (These a b) Source #alignWith :: (These a b -> c) -> HashMap k a -> HashMap k b -> HashMap k c Source # Ord k => Align (Map k) Source # Methodsnil :: Map k a Source #align :: Map k a -> Map k b -> Map k (These a b) Source #alignWith :: (These a b -> c) -> Map k a -> Map k b -> Map k c Source # Monad m => Align (Stream m) Source # Methodsnil :: Stream m a Source #align :: Stream m a -> Stream m b -> Stream m (These a b) Source #alignWith :: (These a b -> c) -> Stream m a -> Stream m b -> Stream m c Source # Monad m => Align (Bundle m v) Source # Methodsnil :: Bundle m v a Source #align :: Bundle m v a -> Bundle m v b -> Bundle m v (These a b) Source #alignWith :: (These a b -> c) -> Bundle m v a -> Bundle m v b -> Bundle m v c Source # (Align f, Align g) => Align (Product * f g) Source # Methodsnil :: Product * f g a Source #align :: Product * f g a -> Product * f g b -> Product * f g (These a b) Source #alignWith :: (These a b -> c) -> Product * f g a -> Product * f g b -> Product * f g c Source #

# Specialized aligns

malign :: (Align f, Monoid a) => f a -> f a -> f a Source #

Align two structures and combine with mappend.

See salign. malign will be deprecated after Semigroup becomes a super class of Monoid

salign :: (Align f, Semigroup a) => f a -> f a -> f a Source #

Align two structures and combine with <>.

padZip :: Align f => f a -> f b -> f (Maybe a, Maybe b) Source #

Align two structures as in zip, but filling in blanks with Nothing.

padZipWith :: Align f => (Maybe a -> Maybe b -> c) -> f a -> f b -> f c Source #

Align two structures as in zipWith, but filling in blanks with Nothing.

lpadZip :: [a] -> [b] -> [(Maybe a, b)] Source #

Left-padded zip.

lpadZipWith :: (Maybe a -> b -> c) -> [a] -> [b] -> [c] Source #

Left-padded zipWith.

rpadZip :: [a] -> [b] -> [(a, Maybe b)] Source #

Right-padded zip.

rpadZipWith :: (a -> Maybe b -> c) -> [a] -> [b] -> [c] Source #

Right-padded zipWith.

alignVectorWith :: (Vector v a, Vector v b, Vector v c) => (These a b -> c) -> v a -> v b -> v c Source #

# Unalign

class Align f => Unalign f where Source #

Alignable functors supporting an "inverse" to align: splitting a union shape into its component parts.

Minimal definition: nothing; a default definition is provided, but it may not have the desired definition for all functors. See the source for more information.

Laws:

unalign nil                 = (nil,           nil)
unalign (This        <$> x) = (Just <$> x, Nothing <x) unalign (That <> y) = (Nothing <$y, Just <$> y)
unalign (join These  <$> x) = (Just <$> x, Just    <> x) unalign ((x These) <> y) = (Just x  <$y, Just <$> y)
unalign ((These y) <$> x) = (Just <$> x, Just y  <\$  x)


Methods

unalign :: f (These a b) -> (f (Maybe a), f (Maybe b)) Source #

Instances

 Unalign [] Source # Methodsunalign :: [These a b] -> ([Maybe a], [Maybe b]) Source # Source # Methodsunalign :: Maybe (These a b) -> (Maybe (Maybe a), Maybe (Maybe b)) Source # Source # Methodsunalign :: ZipList (These a b) -> (ZipList (Maybe a), ZipList (Maybe b)) Source # Monad m => Unalign (Stream m) Source # Methodsunalign :: Stream m (These a b) -> (Stream m (Maybe a), Stream m (Maybe b)) Source # (Unalign f, Unalign g) => Unalign (Product * f g) Source # Methodsunalign :: Product * f g (These a b) -> (Product * f g (Maybe a), Product * f g (Maybe b)) Source #

# Crosswalk

class (Functor t, Foldable t) => Crosswalk t where Source #

Foldable functors supporting traversal through an alignable functor.

Minimal definition: crosswalk or sequenceL.

Laws:

crosswalk (const nil) = const nil
crosswalk f = sequenceL . fmap f


Minimal complete definition

Methods

crosswalk :: Align f => (a -> f b) -> t a -> f (t b) Source #

sequenceL :: Align f => t (f a) -> f (t a) Source #

Instances

 Source # Methodscrosswalk :: Align f => (a -> f b) -> [a] -> f [b] Source #sequenceL :: Align f => [f a] -> f [a] Source # Source # Methodscrosswalk :: Align f => (a -> f b) -> Maybe a -> f (Maybe b) Source #sequenceL :: Align f => Maybe (f a) -> f (Maybe a) Source # Source # Methodscrosswalk :: Align f => (a -> f b) -> Identity a -> f (Identity b) Source #sequenceL :: Align f => Identity (f a) -> f (Identity a) Source # Source # Methodscrosswalk :: Align f => (a -> f b) -> Seq a -> f (Seq b) Source #sequenceL :: Align f => Seq (f a) -> f (Seq a) Source # Source # Methodscrosswalk :: Align f => (a -> f b) -> Vector a -> f (Vector b) Source #sequenceL :: Align f => Vector (f a) -> f (Vector a) Source # Source # Methodscrosswalk :: Align f => (a -> f b) -> These a a -> f (These a b) Source #sequenceL :: Align f => These a (f a) -> f (These a a) Source #

# Bicrosswalk

class (Bifunctor t, Bifoldable t) => Bicrosswalk t where Source #

Bifoldable bifunctors supporting traversal through an alignable functor.

Minimal definition: bicrosswalk or bisequenceL.

Laws:

bicrosswalk (const empty) (const empty) = const empty
bicrosswalk f g = bisequenceL . bimap f g


Minimal complete definition

Methods

bicrosswalk :: Align f => (a -> f c) -> (b -> f d) -> t a b -> f (t c d) Source #

bisequenceL :: Align f => t (f a) (f b) -> f (t a b) Source #

Instances

 Source # Methodsbicrosswalk :: Align f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source #bisequenceL :: Align f => Either (f a) (f b) -> f (Either a b) Source # Source # Methodsbicrosswalk :: Align f => (a -> f c) -> (b -> f d) -> These a b -> f (These c d) Source #bisequenceL :: Align f => These (f a) (f b) -> f (These a b) Source #