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	None
Language	Haskell98

Data.Bifunctor.Biap

Description

Synopsis

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

Documentation

newtype Biap bi a b Source #

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

Bitraversable bi => Bitraversable (Biap bi) Source #
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) #
Bifoldable bi => Bifoldable (Biap bi) Source #
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) Source #
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 #
Eq2 bi => Eq2 (Biap bi) Source #
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) Source #
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) Source #
Instance details Defined in Data.Bifunctor.Biap Methods bipure :: a -> b -> Biap bi a b Source # (<<>>) :: Biap bi (a -> b) (c -> d) -> Biap bi a c -> Biap bi b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Biap bi a d -> Biap bi b e -> Biap bi c f Source # (>>) :: Biap bi a b -> Biap bi c d -> Biap bi c d Source # (<<*) :: Biap bi a b -> Biap bi c d -> Biap bi a b Source #
Generic1 (Biap bi a :: Type -> Type) Source #
Instance details Defined in Data.Bifunctor.Biap Associated Types type Rep1 (Biap bi a) :: k -> Type # Methods from1 :: Biap bi a a0 -> Rep1 (Biap bi a) a0 # to1 :: Rep1 (Biap bi a) a0 -> Biap bi a a0 #
Monad (bi a) => Monad (Biap bi a) Source #
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 # fail :: String -> Biap bi a a0 #
Functor (bi a) => Functor (Biap bi a) Source #
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 #
MonadFail (bi a) => MonadFail (Biap bi a) Source #
Instance details Defined in Data.Bifunctor.Biap Methods fail :: String -> Biap bi a a0 #
Applicative (bi a) => Applicative (Biap bi a) Source #
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 #
Foldable (bi a) => Foldable (Biap bi a) Source #
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 # 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 #
Traversable (bi a) => Traversable (Biap bi a) Source #
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) #
Eq1 (bi a) => Eq1 (Biap bi a) Source #
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) Source #
Instance details Defined in Data.Bifunctor.Biap Methods liftCompare :: (a0 -> b -> Ordering) -> Biap bi a a0 -> Biap bi a b -> Ordering #
Alternative (bi a) => Alternative (Biap bi a) Source #
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] #
MonadPlus (bi a) => MonadPlus (Biap bi a) Source #
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, Bounded a, Bounded b) => Bounded (Biap bi a b) Source #
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) Source #
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] #
Eq (bi a b) => Eq (Biap bi a b) Source #
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 #
(Biapplicative bi, Num a, Num b) => Num (Biap bi a b) Source #
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 #
Ord (bi a b) => Ord (Biap bi a b) Source #
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 #
Read (bi a b) => Read (Biap bi a b) Source #
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) Source #
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 #
Generic (Biap bi a b) Source #
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, Semigroup a, Semigroup b) => Semigroup (Biap bi a b) Source #
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, Monoid a, Monoid b) => Monoid (Biap bi a b) Source #
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 #
type Rep1 (Biap bi a :: Type -> Type) Source #
Instance details Defined in Data.Bifunctor.Biap type Rep1 (Biap bi a :: Type -> Type) = D1 (MetaData "Biap" "Data.Bifunctor.Biap" "bifunctors-5.5.7-3rob4s8r3e0FTYp3z4EUrK" True) (C1 (MetaCons "Biap" PrefixI True) (S1 (MetaSel (Just "getBiap") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 (bi a))))
type Rep (Biap bi a b) Source #
Instance details Defined in Data.Bifunctor.Biap type Rep (Biap bi a b) = D1 (MetaData "Biap" "Data.Bifunctor.Biap" "bifunctors-5.5.7-3rob4s8r3e0FTYp3z4EUrK" True) (C1 (MetaCons "Biap" PrefixI True) (S1 (MetaSel (Just "getBiap") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (bi a b))))