bifunctors-5.6.1: Bifunctors

Copyright | (C) 2008-2016 Edward Kmett
License | BSD-style (see the file LICENSE)
Maintainer | Edward Kmett <ekmett@gmail.com>
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Bifunctor.Biap

Description

Synopsis

- newtype Biap bi a b = Biap {
  - getBiap :: bi a b
  }

# Documentation

newtype Biap bi a b #

Pointwise lifting of a class over two arguments, using `Biapplicative`.

Classes that can be lifted include `Monoid`, `Num` and `Bounded`. Each method of those classes can be defined as lifting themselves over each argument of `Biapplicative`.

    mempty        = bipure mempty          mempty
    minBound      = bipure minBound        minBound
    maxBound      = bipure maxBound        maxBound
    fromInteger n = bipure (fromInteger n) (fromInteger n)

    negate = bimap negate negate

    (+)  = biliftA2 (+)  (+)
    (<>) = biliftA2 (<>) (<>)

`Biap` is to `Biapplicative` as `Ap` is to `Applicative`.

`Biap` can be used with `DerivingVia` to derive a numeric instance for pairs:

    newtype Numpair a = Np (a, a)
     deriving (S.Semigroup, Monoid, Num, Bounded)
     via Biap (,) a a

Constructors

Biap |
Fields getBiap :: bi a b

#### Instances

Instances details

Generic1 (Biap bi a :: Type -> Type) # |
Instance details Defined in Data.Bifunctor.Biap Associated Types type Rep1 (Biap bi a) :: k -> Type Methods from1 :: forall (a0 :: k). Biap bi a a0 -> Rep1 (Biap bi a) a0 to1 :: forall (a0 :: k). Rep1 (Biap bi a) a0 -> Biap bi a a0
Bifoldable bi => Bifoldable (Biap bi) # |
Instance details Defined in Data.Bifunctor.Biap Methods bifold :: Monoid m => Biap bi m m -> m bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Biap bi a b -> m bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c
Bifunctor bi => Bifunctor (Biap bi) # |
Instance details Defined in Data.Bifunctor.Biap Methods bimap :: (a -> b) -> (c -> d) -> Biap bi a c -> Biap bi b d first :: (a -> b) -> Biap bi a c -> Biap bi b c second :: (b -> c) -> Biap bi a b -> Biap bi a c
Bitraversable bi => Bitraversable (Biap bi) # |
Instance details Defined in Data.Bifunctor.Biap Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Biap bi a b -> f (Biap bi c d)
Eq2 bi => Eq2 (Biap bi) # |
Instance details Defined in Data.Bifunctor.Biap Methods liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Biap bi a c -> Biap bi b d -> Bool
Ord2 bi => Ord2 (Biap bi) # |
Instance details Defined in Data.Bifunctor.Biap Methods liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Biap bi a c -> Biap bi b d -> Ordering
Biapplicative bi => Biapplicative (Biap bi) # |
Instance details Defined in Data.Bifunctor.Biap Methods bipure :: a -> b -> Biap bi a b # (<<*>>) :: Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f # (*>>) :: Biap bi a b -> Biap bi c d -> Biap bi c d # (<<*) :: Biap bi a b -> Biap bi c d -> Biap bi a b #
MonadFail (bi a) => MonadFail (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods fail :: String -> Biap bi a a0
Foldable (bi a) => Foldable (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods fold :: Monoid m => Biap bi a m -> m foldMap :: Monoid m => (a0 -> m) -> Biap bi a a0 -> m foldMap' :: Monoid m => (a0 -> m) -> Biap bi a a0 -> m foldr :: (a0 -> b -> b) -> b -> Biap bi a a0 -> b foldr' :: (a0 -> b -> b) -> b -> Biap bi a a0 -> b foldl :: (b -> a0 -> b) -> b -> Biap bi a a0 -> b foldl' :: (b -> a0 -> b) -> b -> Biap bi a a0 -> b foldr1 :: (a0 -> a0 -> a0) -> Biap bi a a0 -> a0 foldl1 :: (a0 -> a0 -> a0) -> Biap bi a a0 -> a0 toList :: Biap bi a a0 -> [a0] null :: Biap bi a a0 -> Bool length :: Biap bi a a0 -> Int elem :: Eq a0 => a0 -> Biap bi a a0 -> Bool maximum :: Ord a0 => Biap bi a a0 -> a0 minimum :: Ord a0 => Biap bi a a0 -> a0 sum :: Num a0 => Biap bi a a0 -> a0 product :: Num a0 => Biap bi a a0 -> a0
Eq1 (bi a) => Eq1 (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods liftEq :: (a0 -> b -> Bool) -> Biap bi a a0 -> Biap bi a b -> Bool
Ord1 (bi a) => Ord1 (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods liftCompare :: (a0 -> b -> Ordering) -> Biap bi a a0 -> Biap bi a b -> Ordering
Traversable (bi a) => Traversable (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods traverse :: Applicative f => (a0 -> f b) -> Biap bi a a0 -> f (Biap bi a b) sequenceA :: Applicative f => Biap bi a (f a0) -> f (Biap bi a a0) mapM :: Monad m => (a0 -> m b) -> Biap bi a a0 -> m (Biap bi a b) sequence :: Monad m => Biap bi a (m a0) -> m (Biap bi a a0)
Alternative (bi a) => Alternative (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods empty :: Biap bi a a0 (<|>) :: Biap bi a a0 -> Biap bi a a0 -> Biap bi a a0 some :: Biap bi a a0 -> Biap bi a [a0] many :: Biap bi a a0 -> Biap bi a [a0]
Applicative (bi a) => Applicative (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods pure :: a0 -> Biap bi a a0 (<*>) :: Biap bi a (a0 -> b) -> Biap bi a a0 -> Biap bi a b liftA2 :: (a0 -> b -> c) -> Biap bi a a0 -> Biap bi a b -> Biap bi a c (*>) :: Biap bi a a0 -> Biap bi a b -> Biap bi a b (<*) :: Biap bi a a0 -> Biap bi a b -> Biap bi a a0
Functor (bi a) => Functor (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods fmap :: (a0 -> b) -> Biap bi a a0 -> Biap bi a b # (<$) :: a0 -> Biap bi a b -> Biap bi a a0 #
Monad (bi a) => Monad (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods (>>=) :: Biap bi a a0 -> (a0 -> Biap bi a b) -> Biap bi a b (>>) :: Biap bi a a0 -> Biap bi a b -> Biap bi a b return :: a0 -> Biap bi a a0
MonadPlus (bi a) => MonadPlus (Biap bi a) # |
Instance details Defined in Data.Bifunctor.Biap Methods mzero :: Biap bi a a0 mplus :: Biap bi a a0 -> Biap bi a a0 -> Biap bi a a0
(Biapplicative bi, Monoid a, Monoid b) => Monoid (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods mempty :: Biap bi a b mappend :: Biap bi a b -> Biap bi a b -> Biap bi a b mconcat :: [Biap bi a b] -> Biap bi a b
(Biapplicative bi, Semigroup a, Semigroup b) => Semigroup (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods (<>) :: Biap bi a b -> Biap bi a b -> Biap bi a b sconcat :: NonEmpty (Biap bi a b) -> Biap bi a b stimes :: Integral b0 => b0 -> Biap bi a b -> Biap bi a b
(Biapplicative bi, Bounded a, Bounded b) => Bounded (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods minBound :: Biap bi a b maxBound :: Biap bi a b
Enum (bi a b) => Enum (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods succ :: Biap bi a b -> Biap bi a b pred :: Biap bi a b -> Biap bi a b toEnum :: Int -> Biap bi a b fromEnum :: Biap bi a b -> Int enumFrom :: Biap bi a b -> [Biap bi a b] enumFromThen :: Biap bi a b -> Biap bi a b -> [Biap bi a b] enumFromTo :: Biap bi a b -> Biap bi a b -> [Biap bi a b] enumFromThenTo :: Biap bi a b -> Biap bi a b -> Biap bi a b -> [Biap bi a b]
Generic (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Associated Types type Rep (Biap bi a b) :: Type -> Type Methods from :: Biap bi a b -> Rep (Biap bi a b) x to :: Rep (Biap bi a b) x -> Biap bi a b
(Biapplicative bi, Num a, Num b) => Num (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods (+) :: Biap bi a b -> Biap bi a b -> Biap bi a b (-) :: Biap bi a b -> Biap bi a b -> Biap bi a b (*) :: Biap bi a b -> Biap bi a b -> Biap bi a b negate :: Biap bi a b -> Biap bi a b abs :: Biap bi a b -> Biap bi a b signum :: Biap bi a b -> Biap bi a b fromInteger :: Integer -> Biap bi a b
Read (bi a b) => Read (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods readsPrec :: Int -> ReadS (Biap bi a b) readList :: ReadS [Biap bi a b] readPrec :: ReadPrec (Biap bi a b) readListPrec :: ReadPrec [Biap bi a b]
Show (bi a b) => Show (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods showsPrec :: Int -> Biap bi a b -> ShowS show :: Biap bi a b -> String showList :: [Biap bi a b] -> ShowS
Eq (bi a b) => Eq (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods (==) :: Biap bi a b -> Biap bi a b -> Bool (/=) :: Biap bi a b -> Biap bi a b -> Bool
Ord (bi a b) => Ord (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap Methods compare :: Biap bi a b -> Biap bi a b -> Ordering (<) :: Biap bi a b -> Biap bi a b -> Bool (<=) :: Biap bi a b -> Biap bi a b -> Bool (>) :: Biap bi a b -> Biap bi a b -> Bool (>=) :: Biap bi a b -> Biap bi a b -> Bool max :: Biap bi a b -> Biap bi a b -> Biap bi a b min :: Biap bi a b -> Biap bi a b -> Biap bi a b
type Rep1 (Biap bi a :: Type -> Type) # |
Instance details Defined in Data.Bifunctor.Biap type Rep1 (Biap bi a :: Type -> Type) = D1 ('MetaData "Biap" "Data.Bifunctor.Biap" "bifunctors-5.6.1-L69QUmtfyuCC1y2evrVacR" 'True) (C1 ('MetaCons "Biap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getBiap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 (bi a))))
type Rep (Biap bi a b) # |
Instance details Defined in Data.Bifunctor.Biap type Rep (Biap bi a b) = D1 ('MetaData "Biap" "Data.Bifunctor.Biap" "bifunctors-5.6.1-L69QUmtfyuCC1y2evrVacR" 'True) (C1 ('MetaCons "Biap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getBiap") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (bi a b))))