| Copyright | (C) 2011-2015 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | Edward Kmett <ekmett@gmail.com> |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Safe |
| Language | Haskell2010 |
Data.Bifunctor.Apply
Contents
Description
Synopsis
- class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where
- class Bifunctor p => Biapply (p :: Type -> Type -> Type) where
- (<<$>>) :: (a -> b) -> a -> b
- (<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d
- bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f
- bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h
Biappliable bifunctors
class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where #
A bifunctor is a type constructor that takes
two type arguments and is a functor in both arguments. That
is, unlike with Functor, a type constructor such as Either
does not need to be partially applied for a Bifunctor
instance, and the methods in this class permit mapping
functions over the Left value or the Right value,
or both at the same time.
Formally, the class Bifunctor represents a bifunctor
from Hask -> Hask.
Intuitively it is a bifunctor where both the first and second arguments are covariant.
You can define a Bifunctor by either defining bimap or by
defining both first and second. A partially applied Bifunctor
must be a Functor and the second method must agree with fmap.
From this it follows that:
secondid=id
If you supply bimap, you should ensure that:
bimapidid≡id
If you supply first and second, ensure:
firstid≡idsecondid≡id
If you supply both, you should also ensure:
bimapf g ≡firstf.secondg
These ensure by parametricity:
bimap(f.g) (h.i) ≡bimapf h.bimapg ifirst(f.g) ≡firstf.firstgsecond(f.g) ≡secondf.secondg
Since 4.18.0.0 Functor is a superclass of 'Bifunctor.
Since: base-4.8.0.0
Methods
bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #
Map over both arguments at the same time.
bimapf g ≡firstf.secondg
Examples
>>>bimap toUpper (+1) ('j', 3)('J',4)
>>>bimap toUpper (+1) (Left 'j')Left 'J'
>>>bimap toUpper (+1) (Right 3)Right 4
Instances
| Bifunctor Either | Since: base-4.8.0.0 |
| Bifunctor Arg | Since: base-4.9.0.0 |
| Bifunctor (,) | Class laws for tuples hold only up to laziness. Both
Since: base-4.8.0.0 |
| Bifunctor (Const :: Type -> Type -> Type) | Since: base-4.8.0.0 |
| Bifunctor bi => Bifunctor (Biap bi) | |
| Bifunctor (Tagged :: Type -> Type -> Type) | |
| Bifunctor (Constant :: Type -> Type -> Type) | |
| Bifunctor ((,,) x1) | Since: base-4.8.0.0 |
| Bifunctor (K1 i :: Type -> Type -> Type) | Since: base-4.9.0.0 |
| Bifunctor ((,,,) x1 x2) | Since: base-4.8.0.0 |
| Functor f => Bifunctor (Clown f :: Type -> Type -> Type) | |
| Bifunctor p => Bifunctor (Flip p) | |
| Functor g => Bifunctor (Joker g :: Type -> Type -> Type) | |
| Bifunctor p => Bifunctor (WrappedBifunctor p) | |
Defined in Data.Bifunctor.Wrapped Methods bimap :: (a -> b) -> (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d # first :: (a -> b) -> WrappedBifunctor p a c -> WrappedBifunctor p b c # second :: (b -> c) -> WrappedBifunctor p a b -> WrappedBifunctor p a c # | |
| Bifunctor ((,,,,) x1 x2 x3) | Since: base-4.8.0.0 |
| (Bifunctor f, Bifunctor g) => Bifunctor (Product f g) | |
| (Bifunctor p, Bifunctor q) => Bifunctor (Sum p q) | |
| Bifunctor ((,,,,,) x1 x2 x3 x4) | Since: base-4.8.0.0 |
| (Functor f, Bifunctor p) => Bifunctor (Tannen f p) | |
| Bifunctor ((,,,,,,) x1 x2 x3 x4 x5) | Since: base-4.8.0.0 |
| (Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g) | |
class Bifunctor p => Biapply (p :: Type -> Type -> Type) where #
Minimal complete definition
Methods
(<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d infixl 4 #
Instances
| Biapply Arg # | |
| Biapply (,) # | |
| Biapply (Const :: Type -> Type -> Type) # | |
| Biapply (Tagged :: Type -> Type -> Type) # | |
| Semigroup x => Biapply ((,,) x) # | |
| (Semigroup x, Semigroup y) => Biapply ((,,,) x y) # | |
| Apply f => Biapply (Clown f :: Type -> Type -> Type) # | |
| Biapply p => Biapply (Flip p) # | |
| Apply g => Biapply (Joker g :: Type -> Type -> Type) # | |
| Biapply p => Biapply (WrappedBifunctor p) # | |
Defined in Data.Functor.Bind.Class Methods (<<.>>) :: WrappedBifunctor p (a -> b) (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d # (.>>) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p c d # (<<.) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p a b # | |
| (Semigroup x, Semigroup y, Semigroup z) => Biapply ((,,,,) x y z) # | |
| (Biapply p, Biapply q) => Biapply (Product p q) # | |
| (Apply f, Biapply p) => Biapply (Tannen f p) # | |
| (Biapply p, Apply f, Apply g) => Biapply (Biff p f g) # | |