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 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

Instances details

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) Source #
Bifoldable bi => Bifoldable ( Biap bi) Source #
Instance details Defined in Data.Bifunctor.Biap Methods bifold :: Monoid m => Biap bi m m -> m Source # bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Biap bi a b -> m Source # bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Biap bi a b -> c Source # bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Biap bi a b -> c Source #
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 Source # first :: (a -> b) -> Biap bi a c -> Biap bi b c Source # second :: (b -> c) -> Biap bi a b -> Biap bi a c Source #
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 Source #
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 Source #
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 Source # Methods from1 :: forall (a0 :: k). Biap bi a a0 -> Rep1 ( Biap bi a) a0 Source # to1 :: forall (a0 :: k). Rep1 ( Biap bi a) a0 -> Biap bi a a0 Source #
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 Source # (>>) :: Biap bi a a0 -> Biap bi a b -> Biap bi a b Source # return :: a0 -> Biap bi a a0 Source #
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 Source # (<$) :: a0 -> Biap bi a b -> Biap bi a a0 Source #
MonadFail (bi a) => MonadFail ( Biap bi a) Source #
Instance details Defined in Data.Bifunctor.Biap Methods fail :: String -> Biap bi a a0 Source #
Applicative (bi a) => Applicative ( Biap bi a) Source #
Instance details Defined in Data.Bifunctor.Biap Methods pure :: a0 -> Biap bi a a0 Source # (<>) :: Biap bi a (a0 -> b) -> Biap bi a a0 -> Biap bi a b Source # liftA2 :: (a0 -> b -> c) -> Biap bi a a0 -> Biap bi a b -> Biap bi a c Source # (>) :: Biap bi a a0 -> Biap bi a b -> Biap bi a b Source # (<*) :: Biap bi a a0 -> Biap bi a b -> Biap bi a a0 Source #
Foldable (bi a) => Foldable ( Biap bi a) Source #
Instance details Defined in Data.Bifunctor.Biap Methods fold :: Monoid m => Biap bi a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Biap bi a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Biap bi a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Biap bi a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Biap bi a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Biap bi a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Biap bi a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Biap bi a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Biap bi a a0 -> a0 Source # toList :: Biap bi a a0 -> [a0] Source # null :: Biap bi a a0 -> Bool Source # length :: Biap bi a a0 -> Int Source # elem :: Eq a0 => a0 -> Biap bi a a0 -> Bool Source # maximum :: Ord a0 => Biap bi a a0 -> a0 Source # minimum :: Ord a0 => Biap bi a a0 -> a0 Source # sum :: Num a0 => Biap bi a a0 -> a0 Source # product :: Num a0 => Biap bi a a0 -> a0 Source #
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) Source # sequenceA :: Applicative f => Biap bi a (f a0) -> f ( Biap bi a a0) Source # mapM :: Monad m => (a0 -> m b) -> Biap bi a a0 -> m ( Biap bi a b) Source # sequence :: Monad m => Biap bi a (m a0) -> m ( Biap bi a a0) Source #
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 Source #
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 Source #
Alternative (bi a) => Alternative ( Biap bi a) Source #
Instance details Defined in Data.Bifunctor.Biap Methods empty :: Biap bi a a0 Source # (<\|>) :: Biap bi a a0 -> Biap bi a a0 -> Biap bi a a0 Source # some :: Biap bi a a0 -> Biap bi a [a0] Source # many :: Biap bi a a0 -> Biap bi a [a0] Source #
MonadPlus (bi a) => MonadPlus ( Biap bi a) Source #
Instance details Defined in Data.Bifunctor.Biap Methods mzero :: Biap bi a a0 Source # mplus :: Biap bi a a0 -> Biap bi a a0 -> Biap bi a a0 Source #
( 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 Source # maxBound :: Biap bi a b Source #
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 Source # pred :: Biap bi a b -> Biap bi a b Source # toEnum :: Int -> Biap bi a b Source # fromEnum :: Biap bi a b -> Int Source # enumFrom :: Biap bi a b -> [ Biap bi a b] Source # enumFromThen :: Biap bi a b -> Biap bi a b -> [ Biap bi a b] Source # enumFromTo :: Biap bi a b -> Biap bi a b -> [ Biap bi a b] Source # enumFromThenTo :: Biap bi a b -> Biap bi a b -> Biap bi a b -> [ Biap bi a b] Source #
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 Source # (/=) :: Biap bi a b -> Biap bi a b -> Bool Source #
( 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 Source # (-) :: Biap bi a b -> Biap bi a b -> Biap bi a b Source # (*) :: Biap bi a b -> Biap bi a b -> Biap bi a b Source # negate :: Biap bi a b -> Biap bi a b Source # abs :: Biap bi a b -> Biap bi a b Source # signum :: Biap bi a b -> Biap bi a b Source # fromInteger :: Integer -> Biap bi a b Source #
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 Source # (<) :: Biap bi a b -> Biap bi a b -> Bool Source # (<=) :: Biap bi a b -> Biap bi a b -> Bool Source # (>) :: Biap bi a b -> Biap bi a b -> Bool Source # (>=) :: Biap bi a b -> Biap bi a b -> Bool Source # max :: Biap bi a b -> Biap bi a b -> Biap bi a b Source # min :: Biap bi a b -> Biap bi a b -> Biap bi a b Source #
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) Source # readList :: ReadS [ Biap bi a b] Source # readPrec :: ReadPrec ( Biap bi a b) Source # readListPrec :: ReadPrec [ Biap bi a b] Source #
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 Source # show :: Biap bi a b -> String Source # showList :: [ Biap bi a b] -> ShowS Source #
Generic ( Biap bi a b) Source #
Instance details Defined in Data.Bifunctor.Biap Associated Types type Rep ( Biap bi a b) :: Type -> Type Source # Methods from :: Biap bi a b -> Rep ( Biap bi a b) x Source # to :: Rep ( Biap bi a b) x -> Biap bi a b Source #
( 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 Source # sconcat :: NonEmpty ( Biap bi a b) -> Biap bi a b Source # stimes :: Integral b0 => b0 -> Biap bi a b -> Biap bi a b Source #
( 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 Source # mappend :: Biap bi a b -> Biap bi a b -> Biap bi a b Source # mconcat :: [ Biap bi a b] -> Biap bi a b Source #
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-5.5.14-4o2vxpA6iYN8K0rfLgtyzm" ' 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-5.5.14-4o2vxpA6iYN8K0rfLgtyzm" ' True ) ( C1 (' MetaCons "Biap" ' PrefixI ' True ) ( S1 (' MetaSel (' Just "getBiap") ' NoSourceUnpackedness ' NoSourceStrictness ' DecidedLazy ) ( Rec0 (bi a b))))