Safe Haskell	Trustworthy
Language	Haskell2010

Data.Semialign

Contents

Specialized aligns

Description

Zipping and aligning of functors with non-uniform shapes.

Synopsis

class Functor f => Semialign f where
- align :: f a -> f b -> f (These a b)
- alignWith :: (These a b -> c) -> f a -> f b -> f c
- zip :: f a -> f b -> f (a, b)
- zipWith :: (a -> b -> c) -> f a -> f b -> f c
class Semialign f => Align f where
- nil :: f a
class Semialign f => Unalign f where
- unalign :: f (These a b) -> (f a, f b)
- unalignWith :: (c -> These a b) -> f c -> (f a, f b)
class Semialign f => Zip f where
- full :: a -> f a
class Semialign f => Unzip f where
- unzipWith :: (c -> (a, b)) -> f c -> (f a, f b)
- unzip :: f (a, b) -> (f a, f b)
unzipDefault :: Functor f => f (a, b) -> (f a, f b)
malign :: (Semialign f, Monoid a) => f a -> f a -> f a
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 where Source #

Functors supporting a zip and align operations that takes the intersection and union of non-uniform shapes.

Minimal definition: either align or alignWith and either zip or zipWith.

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)
join zip   ≡ fmap (join (,))

Commutativity

align x y ≡ swap <$> align y x
  zip x y ≡ swap <$> zip y x

Associativity

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

Absorption

fst    <$> zip xs (align xs ys) ≡ xs
toThis <$> align xs (zip xs ys) ≡ This <$> xs
  where
    toThis (This a)    = This a
    toThis (These a _) = This a
    toThis (That b)    = That b

With

alignWith f a b ≡ f <$> align a b
  zipWith f a b ≡ f <$> zip a b

Functoriality

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

Zippyness

fmap fst (zip x x) ≡ x
fmap snd (zip x x) ≡ x
zip (fmap fst x) (fmap snd x) ≡ x

Alignedness, if f is Foldable

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

Distributivity

                   align (zip xs ys) zs ≡ undistrThesePair <$> zip (align xs zs) (align ys zs)
distrPairThese <$> zip (align xs ys) zs ≡                      align (zip xs zs) (zip ys zs)
                   zip (align xs ys) zs ≡ undistrPairThese <$> align (zip xs zs) (zip ys zs)

Note, the following doesn't hold:

distrThesePair <$> align (zip xs ys) zs ≢ zip (align xs zs) (align ys zs)

when xs = [] and ys = zs = [0], then the left hand side is "only" [(That 0, That 0)], but the right hand side is [(That 0, These 0 0)].

Minimal complete definition

(align | alignWith), (zip | zipWith)

Methods

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.

zip :: f a -> f b -> f (a, b) Source #

Combines to structures by taking the intersection of their shapes and using pair to hold the elements.

zipWith :: (a -> b -> c) -> f a -> f b -> f c Source #

Combines to structures by taking the intersection of their shapes and combining the elements with the given function.

Instances

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

class Semialign f => Align f where Source #

A unit of align.

Laws

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

Methods

nil :: f a Source #

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

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

class Semialign f => Unalign f where Source #

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) Source #

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

Instances

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

class Semialign f => Zip f where Source #

A unit of zip.

fst <$> zip xs (full y) ≡ xs
snd <$> zip (full x) ys ≡ ys

Methods

full :: a -> f a Source #

A full strucutre.

Instances

Zip [] Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> [a] Source #
Zip Maybe Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Maybe a Source #
Zip ZipList Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> ZipList a Source #
Zip Identity Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Identity a Source #
Zip NonEmpty Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> NonEmpty a Source #
Zip Tree Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Tree a Source #
Zip (Proxy :: Type -> Type) Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Proxy a Source #
Zip (Tagged b) Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Tagged b a Source #
Zip ((->) e :: Type -> Type) Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> e -> a Source #
(Zip f, Zip g) => Zip (Product f g) Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Product f g a Source #
(Zip f, Zip g) => Zip (Compose f g) Source #
Instance details Defined in Data.Semialign.Internal Methods full :: a -> Compose f g a Source #

class Semialign f => Unzip f where Source #

Right inverse of zip.

This class is definable for every Functor. See unzipDefault.

Laws

uncurry zip (unzip xs) ≡ xs
unzip (zip xs xs) ≡ (xs, xs)

Note:

unzip (zip xs ys) ≢ (xs, _) or (_, ys)

For sequence-like types this holds, but for Map-like it doesn't.

Minimal complete definition

unzipWith | unzip

Methods

unzipWith :: (c -> (a, b)) -> f c -> (f a, f b) Source #

unzip :: f (a, b) -> (f a, f b) Source #

Instances

Unzip [] Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> [c] -> ([a], [b]) Source # unzip :: [(a, b)] -> ([a], [b]) Source #
Unzip Maybe Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Maybe c -> (Maybe a, Maybe b) Source # unzip :: Maybe (a, b) -> (Maybe a, Maybe b) Source #
Unzip ZipList Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> ZipList c -> (ZipList a, ZipList b) Source # unzip :: ZipList (a, b) -> (ZipList a, ZipList b) Source #
Unzip Identity Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Identity c -> (Identity a, Identity b) Source # unzip :: Identity (a, b) -> (Identity a, Identity b) Source #
Unzip NonEmpty Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> NonEmpty c -> (NonEmpty a, NonEmpty b) Source # unzip :: NonEmpty (a, b) -> (NonEmpty a, NonEmpty b) Source #
Unzip IntMap Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> IntMap c -> (IntMap a, IntMap b) Source # unzip :: IntMap (a, b) -> (IntMap a, IntMap b) Source #
Unzip Tree Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Tree c -> (Tree a, Tree b) Source # unzip :: Tree (a, b) -> (Tree a, Tree b) Source #
Unzip Seq Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Seq c -> (Seq a, Seq b) Source # unzip :: Seq (a, b) -> (Seq a, Seq b) Source #
Unzip Vector Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Vector c -> (Vector a, Vector b) Source # unzip :: Vector (a, b) -> (Vector a, Vector b) Source #
(Eq k, Hashable k) => Unzip (HashMap k) Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> HashMap k c -> (HashMap k a, HashMap k b) Source # unzip :: HashMap k (a, b) -> (HashMap k a, HashMap k b) Source #
Ord k => Unzip (Map k) Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Map k c -> (Map k a, Map k b) Source # unzip :: Map k (a, b) -> (Map k a, Map k b) Source #
Unzip (Proxy :: Type -> Type) Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Proxy c -> (Proxy a, Proxy b) Source # unzip :: Proxy (a, b) -> (Proxy a, Proxy b) Source #
Unzip (Tagged b) Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b0)) -> Tagged b c -> (Tagged b a, Tagged b b0) Source # unzip :: Tagged b (a, b0) -> (Tagged b a, Tagged b b0) Source #
(Unzip f, Unzip g) => Unzip (Product f g) Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Product f g c -> (Product f g a, Product f g b) Source # unzip :: Product f g (a, b) -> (Product f g a, Product f g b) Source #
(Unzip f, Unzip g) => Unzip (Compose f g) Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Compose f g c -> (Compose f g a, Compose f g b) Source # unzip :: Compose f g (a, b) -> (Compose f g a, Compose f g b) Source #

unzipDefault :: Functor f => f (a, b) -> (f a, f b) Source #

Specialized aligns

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

Align two structures and combine with <>.

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

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 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 #