Safe Haskell	Trustworthy
Language	Haskell2010

Data.Zip

Description

Zipping and unzipping 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
class Semialign f => Zip f where
- zip :: f a -> f b -> f (a, b)
- zipWith :: (a -> b -> c) -> f a -> f b -> f c
class Zip f => Repeat f where
- repeat :: a -> f a
class Zip 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)
newtype Zippy f a = Zippy {
- getZippy :: f a
}

Documentation

class Functor f => Semialign f where Source #

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) 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

Instances details

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 #
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 #
Semialign Option Source #
Instance details Defined in Data.Semialign.Internal Methods align :: Option a -> Option b -> Option ( These a b) Source # alignWith :: ( These a b -> c) -> Option a -> Option b -> Option 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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
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 #
( 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 #
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 #
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 #
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 #
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 #
( 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 #
( 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 #

class Semialign f => Zip f where Source #

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

Minimal definition: either zip or zipWith .

Idempotency

join zip   ≡ fmap (join (,))

Commutativity

zip x y ≡ swap <$> zip y x

Associativity

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

zipWith f a b ≡ f <$> zip a b

Functoriality

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

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

( zip | zipWith )

Methods

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

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

Instances

Instances details

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

Zippable functors supporting left and right units

Unit

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

Methods

repeat :: a -> f a Source #

A repeat structure.

Instances

Instances details

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

class Zip 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

Instances details

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 Option Source #
Instance details Defined in Data.Semialign.Internal Methods unzipWith :: (c -> (a, b)) -> Option c -> ( Option a, Option b) Source # unzip :: Option (a, b) -> ( Option a, Option 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 #
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 #
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 #
( 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 #
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 #

newtype Zippy f a Source #

Constructors

Zippy
Fields getZippy :: f a

Instances

Instances details

Functor f => Functor ( Zippy f) Source #
Instance details Defined in Data.Zip Methods fmap :: (a -> b) -> Zippy f a -> Zippy f b Source # (<$) :: a -> Zippy f b -> Zippy f a Source #
Repeat f => Applicative ( Zippy f) Source #
Instance details Defined in Data.Zip Methods pure :: a -> Zippy f a Source # (<>) :: Zippy f (a -> b) -> Zippy f a -> Zippy f b Source # liftA2 :: (a -> b -> c) -> Zippy f a -> Zippy f b -> Zippy f c Source # (>) :: Zippy f a -> Zippy f b -> Zippy f b Source # (<*) :: Zippy f a -> Zippy f b -> Zippy f a Source #
Zip f => Apply ( Zippy f) Source #
Instance details Defined in Data.Zip Methods (<.>) :: Zippy f (a -> b) -> Zippy f a -> Zippy f b Source # (.>) :: Zippy f a -> Zippy f b -> Zippy f b Source # (<.) :: Zippy f a -> Zippy f b -> Zippy f a Source # liftF2 :: (a -> b -> c) -> Zippy f a -> Zippy f b -> Zippy f c Source #
Eq (f a) => Eq ( Zippy f a) Source #
Instance details Defined in Data.Zip Methods (==) :: Zippy f a -> Zippy f a -> Bool Source # (/=) :: Zippy f a -> Zippy f a -> Bool Source #
Ord (f a) => Ord ( Zippy f a) Source #
Instance details Defined in Data.Zip Methods compare :: Zippy f a -> Zippy f a -> Ordering Source # (<) :: Zippy f a -> Zippy f a -> Bool Source # (<=) :: Zippy f a -> Zippy f a -> Bool Source # (>) :: Zippy f a -> Zippy f a -> Bool Source # (>=) :: Zippy f a -> Zippy f a -> Bool Source # max :: Zippy f a -> Zippy f a -> Zippy f a Source # min :: Zippy f a -> Zippy f a -> Zippy f a Source #
Read (f a) => Read ( Zippy f a) Source #
Instance details Defined in Data.Zip Methods readsPrec :: Int -> ReadS ( Zippy f a) Source # readList :: ReadS [ Zippy f a] Source # readPrec :: ReadPrec ( Zippy f a) Source # readListPrec :: ReadPrec [ Zippy f a] Source #
Show (f a) => Show ( Zippy f a) Source #
Instance details Defined in Data.Zip Methods showsPrec :: Int -> Zippy f a -> ShowS Source # show :: Zippy f a -> String Source # showList :: [ Zippy f a] -> ShowS Source #
( Zip f, Semigroup a) => Semigroup ( Zippy f a) Source #
Instance details Defined in Data.Zip Methods (<>) :: Zippy f a -> Zippy f a -> Zippy f a Source # sconcat :: NonEmpty ( Zippy f a) -> Zippy f a Source # stimes :: Integral b => b -> Zippy f a -> Zippy f a Source #
( Repeat f, Monoid a) => Monoid ( Zippy f a) Source #
Instance details Defined in Data.Zip Methods mempty :: Zippy f a Source # mappend :: Zippy f a -> Zippy f a -> Zippy f a Source # mconcat :: [ Zippy f a] -> Zippy f a Source #