Data.These

The These type and associated operations. Now enhanced with Control.Lens magic!

Documentation

data These a b

The These type represents values with two non-exclusive possibilities.

This can be useful to represent combinations of two values, where the combination is defined if either input is. Algebraically, the type These A B represents (A + B + AB), which doesn't factor easily into sums and products--a type like Either A (B, Maybe A) is unclear and awkward to use.

These has straightforward instances of Functor, Monad, &c., and behaves like a hybrid error/writer monad, as would be expected.

For zipping and unzipping of structures with These values, see Data.Align.

Constructors

This a

That b

These a b

Instances

Bifunctor These

Defined in Data.These

Methods

bimap :: (a -> b) -> (c -> d) -> These a c -> These b d

first :: (a -> b) -> These a c -> These b c

second :: (b -> c) -> These a b -> These a c

Swap These

Since: 0.8

Defined in Data.These

Methods

swap :: These a b -> These b a

Assoc These

Since: 0.8

Defined in Data.These

Methods

assoc :: These (These a b) c -> These a (These b c)

unassoc :: These a (These b c) -> These (These a b) c

Bitraversable These

Defined in Data.These

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> These a b -> f (These c d)

Bifoldable These

Defined in Data.These

Methods

bifold :: Monoid m => These m m -> m

bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> These a b -> m

bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> These a b -> c

bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> These a b -> c

Eq2 These

Since: 1.1.1

Defined in Data.These

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> These a c -> These b d -> Bool

Ord2 These

Since: 1.1.1

Defined in Data.These

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> These a c -> These b d -> Ordering

Read2 These

Since: 1.1.1

Defined in Data.These

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (These a b)

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [These a b]

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (These a b)

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [These a b]

Show2 These

Since: 1.1.1

Defined in Data.These

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> These a b -> ShowS

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [These a b] -> ShowS

NFData2 These

Since: 1.1.1

Defined in Data.These

Methods

liftRnf2 :: (a -> ()) -> (b -> ()) -> These a b -> ()

Hashable2 These

Since: 1.1.1

Defined in Data.These

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> These a b -> Int

Semigroup a => Monad (These a)

Defined in Data.These

Methods

(>>=) :: These a a0 -> (a0 -> These a b) -> These a b

(>>) :: These a a0 -> These a b -> These a b

return :: a0 -> These a a0

fail :: String -> These a a0

Functor (These a)

Defined in Data.These

Methods

fmap :: (a0 -> b) -> These a a0 -> These a b

(<$) :: a0 -> These a b -> These a a0

Semigroup a => Applicative (These a)

Defined in Data.These

Methods

pure :: a0 -> These a a0

(<*>) :: These a (a0 -> b) -> These a a0 -> These a b

liftA2 :: (a0 -> b -> c) -> These a a0 -> These a b -> These a c

(*>) :: These a a0 -> These a b -> These a b

(<*) :: These a a0 -> These a b -> These a a0

Foldable (These a)

Defined in Data.These

Methods

fold :: Monoid m => These a m -> m

foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m

foldr :: (a0 -> b -> b) -> b -> These a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b

foldl :: (b -> a0 -> b) -> b -> These a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0

toList :: These a a0 -> [a0]

null :: These a a0 -> Bool

length :: These a a0 -> Int

elem :: Eq a0 => a0 -> These a a0 -> Bool

maximum :: Ord a0 => These a a0 -> a0

minimum :: Ord a0 => These a a0 -> a0

sum :: Num a0 => These a a0 -> a0

product :: Num a0 => These a a0 -> a0

Traversable (These a)

Defined in Data.These

Methods

traverse :: Applicative f => (a0 -> f b) -> These a a0 -> f (These a b)

sequenceA :: Applicative f => These a (f a0) -> f (These a a0)

mapM :: Monad m => (a0 -> m b) -> These a a0 -> m (These a b)

sequence :: Monad m => These a (m a0) -> m (These a a0)

Eq a => Eq1 (These a)

Since: 1.1.1

Defined in Data.These

Methods

liftEq :: (a0 -> b -> Bool) -> These a a0 -> These a b -> Bool

Ord a => Ord1 (These a)

Since: 1.1.1

Defined in Data.These

Methods

liftCompare :: (a0 -> b -> Ordering) -> These a a0 -> These a b -> Ordering

Read a => Read1 (These a)

Since: 1.1.1

Defined in Data.These

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (These a a0)

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [These a a0]

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (These a a0)

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [These a a0]

Show a => Show1 (These a)

Since: 1.1.1

Defined in Data.These

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> These a a0 -> ShowS

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [These a a0] -> ShowS

NFData a => NFData1 (These a)

Since: 1.1.1

Defined in Data.These

Methods

liftRnf :: (a0 -> ()) -> These a a0 -> ()

Hashable a => Hashable1 (These a)

Since: 1.1.1

Defined in Data.These

Methods

liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> These a a0 -> Int

Generic1 (These a :: Type -> Type)

Defined in Data.These

Associated Types

type Rep1 (These a) :: k -> Type

Methods

from1 :: These a a0 -> Rep1 (These a) a0

to1 :: Rep1 (These a) a0 -> These a a0

(Eq a, Eq b) => Eq (These a b)

Defined in Data.These

Methods

(==) :: These a b -> These a b -> Bool

(/=) :: These a b -> These a b -> Bool

(Data a, Data b) => Data (These a b)

Defined in Data.These

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> These a b -> c (These a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (These a b)

toConstr :: These a b -> Constr

dataTypeOf :: These a b -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (These a b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (These a b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> These a b -> These a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> These a b -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> These a b -> r

gmapQ :: (forall d. Data d => d -> u) -> These a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> These a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> These a b -> m (These a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> These a b -> m (These a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> These a b -> m (These a b)

(Ord a, Ord b) => Ord (These a b)

Defined in Data.These

Methods

compare :: These a b -> These a b -> Ordering

(<) :: These a b -> These a b -> Bool

(<=) :: These a b -> These a b -> Bool

(>) :: These a b -> These a b -> Bool

(>=) :: These a b -> These a b -> Bool

max :: These a b -> These a b -> These a b

min :: These a b -> These a b -> These a b

(Read a, Read b) => Read (These a b)

Defined in Data.These

Methods

readsPrec :: Int -> ReadS (These a b)

readList :: ReadS [These a b]

readPrec :: ReadPrec (These a b)

readListPrec :: ReadPrec [These a b]

(Show a, Show b) => Show (These a b)

Defined in Data.These

Methods

showsPrec :: Int -> These a b -> ShowS

show :: These a b -> String

showList :: [These a b] -> ShowS

Generic (These a b)

Defined in Data.These

Associated Types

type Rep (These a b) :: Type -> Type

Methods

from :: These a b -> Rep (These a b) x

to :: Rep (These a b) x -> These a b

(Semigroup a, Semigroup b) => Semigroup (These a b)

Defined in Data.These

Methods

(<>) :: These a b -> These a b -> These a b

sconcat :: NonEmpty (These a b) -> These a b

stimes :: Integral b0 => b0 -> These a b -> These a b

(Binary a, Binary b) => Binary (These a b)

Since: 0.7.1

Defined in Data.These

Methods

put :: These a b -> Put

get :: Get (These a b)

putList :: [These a b] -> Put

(NFData a, NFData b) => NFData (These a b)

Since: 0.7.1

Defined in Data.These

Methods

rnf :: These a b -> ()

(Hashable a, Hashable b) => Hashable (These a b)

Defined in Data.These

Methods

hashWithSalt :: Int -> These a b -> Int

hash :: These a b -> Int

type Rep1 (These a :: Type -> Type)

Defined in Data.These

type Rep1 (These a :: Type -> Type) = D1 (MetaData "These" "Data.These" "these-1.1.1.1-7fp3Gb5JuCxEjNjnp6x24Y" False) (C1 (MetaCons "This" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: (C1 (MetaCons "That" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1) :+: C1 (MetaCons "These" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)))

type Rep (These a b)

Defined in Data.These

type Rep (These a b) = D1 (MetaData "These" "Data.These" "these-1.1.1.1-7fp3Gb5JuCxEjNjnp6x24Y" False) (C1 (MetaCons "This" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: (C1 (MetaCons "That" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b)) :+: C1 (MetaCons "These" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b))))

Functions to get rid of These

these :: (a -> c) -> (b -> c) -> (a -> b -> c) -> These a b -> c

Case analysis for the These type.

fromThese :: a -> b -> These a b -> (a, b)

Takes two default values and produces a tuple.

mergeThese :: (a -> a -> a) -> These a a -> a

Coalesce with the provided operation.

mergeTheseWith :: (a -> c) -> (b -> c) -> (c -> c -> c) -> These a b -> c

bimap and coalesce results with the provided operation.

Partition

partitionThese :: [These a b] -> ([a], [b], [(a, b)])

Select each constructor and partition them into separate lists.

partitionHereThere :: [These a b] -> ([a], [b])

Select here and there elements and partition them into separate lists.

Since: 0.8

partitionEithersNE :: NonEmpty (Either a b) -> These (NonEmpty a) (NonEmpty b)

Like partitionEithers but for NonEmpty types.

• either all are Left
• either all are Right
• or there is both Left and Right stuff

Note: this is not online algorithm. In the worst case it will traverse the whole list before deciding the result constructor.

>>> partitionEithersNE $ Left 'x' :| [Right 'y']
These ('x' :| "") ('y' :| "")

>>> partitionEithersNE $ Left 'x' :| map Left "yz"
This ('x' :| "yz")

Since: 1.0.1

Distributivity

This distributivity combinators aren't isomorphisms!

distrThesePair :: These (a, b) c -> (These a c, These b c)

undistrThesePair :: (These a c, These b c) -> These (a, b) c

distrPairThese :: (These a b, c) -> These (a, c) (b, c)

undistrPairThese :: These (a, c) (b, c) -> (These a b, c)