Data.Variation

Variation

data Variation f a

the variation type contains

_nominal

: a nominal value that will always exist

_variations

: alternative values which are held inside a container of type f

it is strict in both arguments.

the Applicative instance uses the Unit1 instance of f to define pure

pure x = Variation x empty1

and the Bind and Append1 instances of f to define <*>

Variation f fs <*> Variation x xs =
  Variation
    (f x)
    ((fs <.> xs) `append1` (f <$> xs) `append1` (($ x) <$> fs))

the Monad instance uses the Bind instance of f (join) to collapse collections of type f (f a)

joinV :: (Bind f, Monoid1 f) => Variation f (Variation f a) -> Variation f a
joinV (Variation (Variation nn nv) v) =
  let vv = _variations <$> v
      vn = _nominal <$> v
  in Variation nn $ join vv `append1` vn `append1` nv

other useful instances:

instance Append1 f => Semigroup (Variation f a) where
  (<>) = append1

instance (Monoid a, Monoid1 f) => Monoid (Variation f a) where
  mempty = Variation mempty empty1
  mappend = (<>)

Constructors

Variation

Fields

• _nominal :: !a
• _variations :: !(f a)

Instances

(Bind f, Monoid1 f) => Monad (Variation f)

Methods

(>>=) :: Variation f a -> (a -> Variation f b) -> Variation f b

(>>) :: Variation f a -> Variation f b -> Variation f b

return :: a -> Variation f a

fail :: String -> Variation f a

Functor f => Functor (Variation f)

Methods

fmap :: (a -> b) -> Variation f a -> Variation f b

(<$) :: a -> Variation f b -> Variation f a

(Apply f, Monoid1 f) => Applicative (Variation f)

Methods

pure :: a -> Variation f a

(<*>) :: Variation f (a -> b) -> Variation f a -> Variation f b

(*>) :: Variation f a -> Variation f b -> Variation f b

(<*) :: Variation f a -> Variation f b -> Variation f a

Foldable f => Foldable (Variation f)

Methods

fold :: Monoid m => Variation f m -> m

foldMap :: Monoid m => (a -> m) -> Variation f a -> m

foldr :: (a -> b -> b) -> b -> Variation f a -> b

foldr' :: (a -> b -> b) -> b -> Variation f a -> b

foldl :: (b -> a -> b) -> b -> Variation f a -> b

foldl' :: (b -> a -> b) -> b -> Variation f a -> b

foldr1 :: (a -> a -> a) -> Variation f a -> a

foldl1 :: (a -> a -> a) -> Variation f a -> a

toList :: Variation f a -> [a]

null :: Variation f a -> Bool

length :: Variation f a -> Int

elem :: Eq a => a -> Variation f a -> Bool

maximum :: Ord a => Variation f a -> a

minimum :: Ord a => Variation f a -> a

sum :: Num a => Variation f a -> a

product :: Num a => Variation f a -> a

Traversable f => Traversable (Variation f)

Methods

traverse :: Applicative f => (a -> f b) -> Variation f a -> f (Variation f b)

sequenceA :: Applicative f => Variation f (f a) -> f (Variation f a)

mapM :: Monad m => (a -> m b) -> Variation f a -> m (Variation f b)

sequence :: Monad m => Variation f (m a) -> m (Variation f a)

Show1 f => Show1 (Variation f)

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Variation f a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Variation f a] -> ShowS

Append1 f => Append1 (Variation f)

Methods

append1 :: Variation f a -> Variation f a -> Variation f a

(Show1 f, Show a) => Show (Variation f a)

Methods

showsPrec :: Int -> Variation f a -> ShowS

show :: Variation f a -> String

showList :: [Variation f a] -> ShowS

Generic (Variation f a)

Associated Types

type Rep (Variation f a) :: * -> *

Methods

from :: Variation f a -> Rep (Variation f a) x

to :: Rep (Variation f a) x -> Variation f a

Append1 f => Semigroup (Variation f a)

Methods

(<>) :: Variation f a -> Variation f a -> Variation f a

sconcat :: NonEmpty (Variation f a) -> Variation f a

stimes :: Integral b => b -> Variation f a -> Variation f a

(Monoid a, Monoid1 f) => Monoid (Variation f a)

Methods

mempty :: Variation f a

mappend :: Variation f a -> Variation f a -> Variation f a

mconcat :: [Variation f a] -> Variation f a

(Serialize a, Serialize (f a)) => Serialize (Variation f a)

Methods

put :: Putter (Variation f a)

get :: Get (Variation f a)

(NFData a, NFData (f a)) => NFData (Variation f a)

Methods

rnf :: Variation f a -> ()

type Rep (Variation f a)

type Rep (Variation f a) = D1 (MetaData "Variation" "Data.Variation" "variation-0.1.1.0-LQFmCGwOHr1FHYkVMaNdtJ" False) (C1 (MetaCons "Variation" PrefixI True) ((:*:) (S1 (MetaSel (Just Symbol "_nominal") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a)) (S1 (MetaSel (Just Symbol "_variations") NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (f a)))))

Lenses

nominal :: Functor f => (a -> f a) -> Variation t a -> f (Variation t a)

variations :: Functor f => (t a -> f (t a)) -> Variation t a -> f (Variation t a)