Safe Haskell	Trustworthy
Language	Haskell2010

Data.Align

Contents

Specialized aligns

Description

These-based aligning and unaligning of functors with non-uniform shapes.

For a traversals traversal of (bi)foldable (bi)functors through said functors see Data.Crosswalk.

Synopsis

class Functor f => Semialign (f :: Type -> Type) where
- align :: f a -> f b -> f (These a b)
- alignWith :: (These a b -> c) -> f a -> f b -> f c
class Semialign f => Align (f :: Type -> Type) where
- nil :: f a
class Semialign f => Unalign (f :: Type -> Type) where
- unalign :: f (These a b) -> (f a, f b)
- unalignWith :: (c -> These a b) -> f c -> (f a, f b)
salign :: (Semialign f, Semigroup a) => f a -> f a -> f a
padZip :: Semialign f => f a -> f b -> f (Maybe a, Maybe b)
padZipWith :: Semialign f => (Maybe a -> Maybe b -> c) -> f a -> f b -> f c
lpadZip :: [a] -> [b] -> [(Maybe a, b)]
lpadZipWith :: (Maybe a -> b -> c) -> [a] -> [b] -> [c]
rpadZip :: [a] -> [b] -> [(a, Maybe b)]
rpadZipWith :: (a -> Maybe b -> c) -> [a] -> [b] -> [c]
alignVectorWith :: (Vector v a, Vector v b, Vector v c) => (These a b -> c) -> v a -> v b -> v c

Documentation

class Functor f => Semialign (f :: Type -> Type) where #

Functors supporting an align operation that takes the union of non-uniform shapes.

Minimal definition: either align or alignWith.

Laws

The laws of align and zip resemble lattice laws. There is a plenty of laws, but they are simply satisfied.

And an addition property if f is Foldable, which tries to enforce align-feel: neither values are duplicated nor lost.

Note: join f x = f x x

Idempotency

join align ≡ fmap (join These)

Commutativity

align x y ≡ swap <$> align y x

Associativity

align x (align y z) ≡ assoc <$> align (align x y) z

With

alignWith f a b ≡ f <$> align a b

Functoriality

align (f <$> x) (g <$> y) ≡ bimap f g <$> align x y

Alignedness, if f is Foldable

toList x ≡ toListOf (folded . here) (align x y)
         ≡ mapMaybe justHere (toList (align x y))

And an addition property if f is Foldable, which tries to enforce align-feel: neither values are duplicated nor lost.

toList x = toListOf (folded . here) (align x y)
         = mapMaybe justHere (toList (align x y))

Minimal complete definition

(align | alignWith)

Methods

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

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 #

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

Instances

Instances details

Semialign ZipList #	`zipWith = liftA2` .
Instance details Defined in Data.Semialign.Internal Methods align :: ZipList a -> ZipList b -> ZipList (These a b) # alignWith :: (These a b -> c) -> ZipList a -> ZipList b -> ZipList c #
Semialign Identity #
Instance details Defined in Data.Semialign.Internal Methods align :: Identity a -> Identity b -> Identity (These a b) # alignWith :: (These a b -> c) -> Identity a -> Identity b -> Identity c #
Semialign NonEmpty #
Instance details Defined in Data.Semialign.Internal Methods align :: NonEmpty a -> NonEmpty b -> NonEmpty (These a b) # alignWith :: (These a b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c #
Semialign IntMap #
Instance details Defined in Data.Semialign.Internal Methods align :: IntMap a -> IntMap b -> IntMap (These a b) # alignWith :: (These a b -> c) -> IntMap a -> IntMap b -> IntMap c #
Semialign Seq #
Instance details Defined in Data.Semialign.Internal Methods align :: Seq a -> Seq b -> Seq (These a b) # alignWith :: (These a b -> c) -> Seq a -> Seq b -> Seq c #
Semialign Tree #
Instance details Defined in Data.Semialign.Internal Methods align :: Tree a -> Tree b -> Tree (These a b) # alignWith :: (These a b -> c) -> Tree a -> Tree b -> Tree c #
Semialign Vector #
Instance details Defined in Data.Semialign.Internal Methods align :: Vector a -> Vector b -> Vector (These a b) # alignWith :: (These a b -> c) -> Vector a -> Vector b -> Vector c #
Semialign Maybe #
Instance details Defined in Data.Semialign.Internal Methods align :: Maybe a -> Maybe b -> Maybe (These a b) # alignWith :: (These a b -> c) -> Maybe a -> Maybe b -> Maybe c #
Semialign [] #
Instance details Defined in Data.Semialign.Internal Methods align :: [a] -> [b] -> [These a b] # alignWith :: (These a b -> c) -> [a] -> [b] -> [c] #
Semialign (Proxy :: Type -> Type) #
Instance details Defined in Data.Semialign.Internal Methods align :: Proxy a -> Proxy b -> Proxy (These a b) # alignWith :: (These a b -> c) -> Proxy a -> Proxy b -> Proxy c #
Ord k => Semialign (Map k) #
Instance details Defined in Data.Semialign.Internal Methods align :: Map k a -> Map k b -> Map k (These a b) # alignWith :: (These a b -> c) -> Map k a -> Map k b -> Map k c #
(Eq k, Hashable k) => Semialign (HashMap k) #
Instance details Defined in Data.Semialign.Internal Methods align :: HashMap k a -> HashMap k b -> HashMap k (These a b) # alignWith :: (These a b -> c) -> HashMap k a -> HashMap k b -> HashMap k c #
Monad m => Semialign (Stream m) #
Instance details Defined in Data.Semialign.Internal Methods align :: Stream m a -> Stream m b -> Stream m (These a b) # alignWith :: (These a b -> c) -> Stream m a -> Stream m b -> Stream m c #
Semialign (Tagged b) #
Instance details Defined in Data.Semialign.Internal Methods align :: Tagged b a -> Tagged b b0 -> Tagged b (These a b0) # alignWith :: (These a b0 -> c) -> Tagged b a -> Tagged b b0 -> Tagged b c #
Monad m => Semialign (Bundle m v) #
Instance details Defined in Data.Semialign.Internal Methods align :: Bundle m v a -> Bundle m v b -> Bundle m v (These a b) # alignWith :: (These a b -> c) -> Bundle m v a -> Bundle m v b -> Bundle m v c #
(Semialign f, Semialign g) => Semialign (Product f g) #
Instance details Defined in Data.Semialign.Internal Methods align :: Product f g a -> Product f g b -> Product f g (These a b) # alignWith :: (These a b -> c) -> Product f g a -> Product f g b -> Product f g c #
Semialign ((->) e) #
Instance details Defined in Data.Semialign.Internal Methods align :: (e -> a) -> (e -> b) -> e -> These a b # alignWith :: (These a b -> c) -> (e -> a) -> (e -> b) -> e -> c #
(Semialign f, Semialign g) => Semialign (Compose f g) #
Instance details Defined in Data.Semialign.Internal Methods align :: Compose f g a -> Compose f g b -> Compose f g (These a b) # alignWith :: (These a b -> c) -> Compose f g a -> Compose f g b -> Compose f g c #

class Semialign f => Align (f :: Type -> Type) where #

A unit of align.

Laws

(`align` nil) ≡ fmap This
(nil `align`) ≡ fmap That

Methods

nil :: f a #

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

Instances

Instances details

Align ZipList #
Instance details Defined in Data.Semialign.Internal Methods nil :: ZipList a #
Align IntMap #
Instance details Defined in Data.Semialign.Internal Methods nil :: IntMap a #
Align Seq #
Instance details Defined in Data.Semialign.Internal Methods nil :: Seq a #
Align Vector #
Instance details Defined in Data.Semialign.Internal Methods nil :: Vector a #
Align Maybe #
Instance details Defined in Data.Semialign.Internal Methods nil :: Maybe a #
Align [] #
Instance details Defined in Data.Semialign.Internal Methods nil :: [a] #
Align (Proxy :: Type -> Type) #
Instance details Defined in Data.Semialign.Internal Methods nil :: Proxy a #
Ord k => Align (Map k) #
Instance details Defined in Data.Semialign.Internal Methods nil :: Map k a #
(Eq k, Hashable k) => Align (HashMap k) #
Instance details Defined in Data.Semialign.Internal Methods nil :: HashMap k a #
Monad m => Align (Stream m) #
Instance details Defined in Data.Semialign.Internal Methods nil :: Stream m a #
Monad m => Align (Bundle m v) #
Instance details Defined in Data.Semialign.Internal Methods nil :: Bundle m v a #
(Align f, Align g) => Align (Product f g) #
Instance details Defined in Data.Semialign.Internal Methods nil :: Product f g a #
(Align f, Semialign g) => Align (Compose f g) #
Instance details Defined in Data.Semialign.Internal Methods nil :: Compose f g a #

class Semialign f => Unalign (f :: Type -> Type) where #

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

Laws

uncurry align (unalign xs) ≡ xs
unalign (align xs ys) ≡ (xs, ys)

Compatibility note

In version 1 unalign was changed to return (f a, f b) pair, instead of (f (Just a), f (Just b)). Old behaviour can be achieved with if ever needed.

>>> unzipWith (unalign . Just) [This 'a', That 'b', These 'c' 'd']
([Just 'a',Nothing,Just 'c'],[Nothing,Just 'b',Just 'd'])

Minimal complete definition

unalignWith | unalign

Methods

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

unalignWith :: (c -> These a b) -> f c -> (f a, f b) #

Instances

Instances details

Unalign IntMap #
Instance details Defined in Data.Semialign.Internal Methods unalign :: IntMap (These a b) -> (IntMap a, IntMap b) # unalignWith :: (c -> These a b) -> IntMap c -> (IntMap a, IntMap b) #
Unalign Maybe #
Instance details Defined in Data.Semialign.Internal Methods unalign :: Maybe (These a b) -> (Maybe a, Maybe b) # unalignWith :: (c -> These a b) -> Maybe c -> (Maybe a, Maybe b) #
Unalign (Proxy :: Type -> Type) #
Instance details Defined in Data.Semialign.Internal Methods unalign :: Proxy (These a b) -> (Proxy a, Proxy b) # unalignWith :: (c -> These a b) -> Proxy c -> (Proxy a, Proxy b) #
Ord k => Unalign (Map k) #
Instance details Defined in Data.Semialign.Internal Methods unalign :: Map k (These a b) -> (Map k a, Map k b) # unalignWith :: (c -> These a b) -> Map k c -> (Map k a, Map k b) #
(Eq k, Hashable k) => Unalign (HashMap k) #
Instance details Defined in Data.Semialign.Internal Methods unalign :: HashMap k (These a b) -> (HashMap k a, HashMap k b) # unalignWith :: (c -> These a b) -> HashMap k c -> (HashMap k a, HashMap k b) #
(Unalign f, Unalign g) => Unalign (Product f g) #
Instance details Defined in Data.Semialign.Internal Methods unalign :: Product f g (These a b) -> (Product f g a, Product f g b) # unalignWith :: (c -> These a b) -> Product f g c -> (Product f g a, Product f g b) #

Specialized aligns

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

Align two structures and combine with <>.

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

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

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

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

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

Left-padded zip.

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

Left-padded zipWith.

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

Right-padded zip.

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

Right-padded zipWith.

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