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	Trustworthy
Language	Haskell2010

Data.Biapplicative

Contents

Biapplicative bifunctors

Description

Synopsis

class Bifunctor p => Biapplicative (p :: Type -> Type -> Type) where
- bipure :: a -> b -> p a b
- (<<*>>) :: p (a -> b) (c -> d) -> p a c -> p b d
- biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f
- (*>>) :: p a b -> p c d -> p c d
- (<<*) :: p a b -> p c d -> p a b
(<<$>>) :: (a -> b) -> a -> b
(<<**>>) :: Biapplicative p => p a c -> p (a -> b) (c -> d) -> p b d
biliftA3 :: Biapplicative w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h
traverseBia :: (Traversable t, Biapplicative p) => (a -> p b c) -> t a -> p (t b) (t c)
sequenceBia :: (Traversable t, Biapplicative p) => t (p b c) -> p (t b) (t c)
traverseBiaWith :: forall p a b c s t. Biapplicative p => (forall (f :: Type -> Type) x. Applicative f => (a -> f x) -> s -> f (t x)) -> (a -> p b c) -> s -> p (t b) (t c)
class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where
- bimap :: (a -> b) -> (c -> d) -> p a c -> p b d
- first :: (a -> b) -> p a c -> p b c
- second :: (b -> c) -> p a b -> p a c

Biapplicative bifunctors

class Bifunctor p => Biapplicative (p :: Type -> Type -> Type) where Source #

Minimal complete definition

bipure, ((<<*>>) | biliftA2)

Methods

bipure :: a -> b -> p a b Source #

(<<*>>) :: p (a -> b) (c -> d) -> p a c -> p b d infixl 4 Source #

biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> p a d -> p b e -> p c f Source #

Lift binary functions

(*>>) :: p a b -> p c d -> p c d infixl 4 Source #

a *>> b ≡ bimap (const id) (const id) <<$>> a <<*>> b

(<<*) :: p a b -> p c d -> p a b infixl 4 Source #

a <<* b ≡ bimap const const <<$>> a <<*>> b

Instances

Instances details

Biapplicative Arg Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> Arg a b Source # (<<>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Arg a d -> Arg b e -> Arg c f Source # (>>) :: Arg a b -> Arg c d -> Arg c d Source # (<<*) :: Arg a b -> Arg c d -> Arg a b Source #
Biapplicative (,) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> (a, b) Source # (<<>>) :: (a -> b, c -> d) -> (a, c) -> (b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (a, d) -> (b, e) -> (c, f) Source # (>>) :: (a, b) -> (c, d) -> (c, d) Source # (<<*) :: (a, b) -> (c, d) -> (a, b) 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 #
Biapplicative (Const :: Type -> Type -> Type) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> Const a b Source # (<<>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Const a d -> Const b e -> Const c f Source # (>>) :: Const a b -> Const c d -> Const c d Source # (<<*) :: Const a b -> Const c d -> Const a b Source #
Biapplicative (Tagged :: Type -> Type -> Type) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> Tagged a b Source # (<<>>) :: Tagged (a -> b) (c -> d) -> Tagged a c -> Tagged b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Tagged a d -> Tagged b e -> Tagged c f Source # (>>) :: Tagged a b -> Tagged c d -> Tagged c d Source # (<<*) :: Tagged a b -> Tagged c d -> Tagged a b Source #
Monoid x => Biapplicative ((,,) x) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> (x, a, b) Source # (<<>>) :: (x, a -> b, c -> d) -> (x, a, c) -> (x, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, a, d) -> (x, b, e) -> (x, c, f) Source # (>>) :: (x, a, b) -> (x, c, d) -> (x, c, d) Source # (<<*) :: (x, a, b) -> (x, c, d) -> (x, a, b) Source #
(Monoid x, Monoid y) => Biapplicative ((,,,) x y) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> (x, y, a, b) Source # (<<>>) :: (x, y, a -> b, c -> d) -> (x, y, a, c) -> (x, y, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, a, d) -> (x, y, b, e) -> (x, y, c, f) Source # (>>) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, c, d) Source # (<<*) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, a, b) Source #
Applicative f => Biapplicative (Clown f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Bifunctor.Clown Methods bipure :: a -> b -> Clown f a b Source # (<<>>) :: Clown f (a -> b) (c -> d) -> Clown f a c -> Clown f b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Clown f a d -> Clown f b e -> Clown f c f0 Source # (>>) :: Clown f a b -> Clown f c d -> Clown f c d Source # (<<*) :: Clown f a b -> Clown f c d -> Clown f a b Source #
Biapplicative p => Biapplicative (Flip p) Source #
Instance details Defined in Data.Bifunctor.Flip Methods bipure :: a -> b -> Flip p a b Source # (<<>>) :: Flip p (a -> b) (c -> d) -> Flip p a c -> Flip p b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Flip p a d -> Flip p b e -> Flip p c f Source # (>>) :: Flip p a b -> Flip p c d -> Flip p c d Source # (<<*) :: Flip p a b -> Flip p c d -> Flip p a b Source #
Applicative g => Biapplicative (Joker g :: Type -> Type -> Type) Source #
Instance details Defined in Data.Bifunctor.Joker Methods bipure :: a -> b -> Joker g a b Source # (<<>>) :: Joker g (a -> b) (c -> d) -> Joker g a c -> Joker g b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> Joker g a d -> Joker g b e -> Joker g c f Source # (>>) :: Joker g a b -> Joker g c d -> Joker g c d Source # (<<*) :: Joker g a b -> Joker g c d -> Joker g a b Source #
Biapplicative p => Biapplicative (WrappedBifunctor p) Source #
Instance details Defined in Data.Bifunctor.Wrapped Methods bipure :: a -> b -> WrappedBifunctor p a b Source # (<<>>) :: WrappedBifunctor p (a -> b) (c -> d) -> WrappedBifunctor p a c -> WrappedBifunctor p b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> WrappedBifunctor p a d -> WrappedBifunctor p b e -> WrappedBifunctor p c f Source # (>>) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p c d Source # (<<*) :: WrappedBifunctor p a b -> WrappedBifunctor p c d -> WrappedBifunctor p a b Source #
(Monoid x, Monoid y, Monoid z) => Biapplicative ((,,,,) x y z) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> (x, y, z, a, b) Source # (<<>>) :: (x, y, z, a -> b, c -> d) -> (x, y, z, a, c) -> (x, y, z, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, a, d) -> (x, y, z, b, e) -> (x, y, z, c, f) Source # (>>) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, c, d) Source # (<<*) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, a, b) Source #
(Biapplicative f, Biapplicative g) => Biapplicative (Product f g) Source #
Instance details Defined in Data.Bifunctor.Product Methods bipure :: a -> b -> Product f g a b Source # (<<>>) :: Product f g (a -> b) (c -> d) -> Product f g a c -> Product f g b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Product f g a d -> Product f g b e -> Product f g c f0 Source # (>>) :: Product f g a b -> Product f g c d -> Product f g c d Source # (<<*) :: Product f g a b -> Product f g c d -> Product f g a b Source #
(Monoid x, Monoid y, Monoid z, Monoid w) => Biapplicative ((,,,,,) x y z w) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> (x, y, z, w, a, b) Source # (<<>>) :: (x, y, z, w, a -> b, c -> d) -> (x, y, z, w, a, c) -> (x, y, z, w, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, w, a, d) -> (x, y, z, w, b, e) -> (x, y, z, w, c, f) Source # (>>) :: (x, y, z, w, a, b) -> (x, y, z, w, c, d) -> (x, y, z, w, c, d) Source # (<<*) :: (x, y, z, w, a, b) -> (x, y, z, w, c, d) -> (x, y, z, w, a, b) Source #
(Applicative f, Biapplicative p) => Biapplicative (Tannen f p) Source #
Instance details Defined in Data.Bifunctor.Tannen Methods bipure :: a -> b -> Tannen f p a b Source # (<<>>) :: Tannen f p (a -> b) (c -> d) -> Tannen f p a c -> Tannen f p b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Tannen f p a d -> Tannen f p b e -> Tannen f p c f0 Source # (>>) :: Tannen f p a b -> Tannen f p c d -> Tannen f p c d Source # (<<*) :: Tannen f p a b -> Tannen f p c d -> Tannen f p a b Source #
(Monoid x, Monoid y, Monoid z, Monoid w, Monoid v) => Biapplicative ((,,,,,,) x y z w v) Source #
Instance details Defined in Data.Biapplicative Methods bipure :: a -> b -> (x, y, z, w, v, a, b) Source # (<<>>) :: (x, y, z, w, v, a -> b, c -> d) -> (x, y, z, w, v, a, c) -> (x, y, z, w, v, b, d) Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f) -> (x, y, z, w, v, a, d) -> (x, y, z, w, v, b, e) -> (x, y, z, w, v, c, f) Source # (>>) :: (x, y, z, w, v, a, b) -> (x, y, z, w, v, c, d) -> (x, y, z, w, v, c, d) Source # (<<*) :: (x, y, z, w, v, a, b) -> (x, y, z, w, v, c, d) -> (x, y, z, w, v, a, b) Source #
(Biapplicative p, Applicative f, Applicative g) => Biapplicative (Biff p f g) Source #
Instance details Defined in Data.Bifunctor.Biff Methods bipure :: a -> b -> Biff p f g a b Source # (<<>>) :: Biff p f g (a -> b) (c -> d) -> Biff p f g a c -> Biff p f g b d Source # biliftA2 :: (a -> b -> c) -> (d -> e -> f0) -> Biff p f g a d -> Biff p f g b e -> Biff p f g c f0 Source # (>>) :: Biff p f g a b -> Biff p f g c d -> Biff p f g c d Source # (<<*) :: Biff p f g a b -> Biff p f g c d -> Biff p f g a b Source #

(<<$>>) :: (a -> b) -> a -> b infixl 4 Source #

(<<**>>) :: Biapplicative p => p a c -> p (a -> b) (c -> d) -> p b d infixl 4 Source #

biliftA3 :: Biapplicative w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h Source #

Lift ternary functions

traverseBia :: (Traversable t, Biapplicative p) => (a -> p b c) -> t a -> p (t b) (t c) Source #

Traverse a Traversable container in a Biapplicative.

traverseBia satisfies the following properties:

Pairing

traverseBia (,) t = (t, t)

Composition

traverseBia (Biff . bimap g h . f) = Biff . bimap (traverse g) (traverse h) . traverseBia f

traverseBia (Tannen . fmap f . g) = Tannen . fmap (traverseBia f) . traverse g

Naturality

 t . traverseBia f = traverseBia (t . f)

for every biapplicative transformation t.

A biapplicative transformation from a Biapplicative P to a Biapplicative Q is a function

t :: P a b -> Q a b

preserving the Biapplicative operations. That is,

```
t (bipure x y) = bipure x y
```
```
t (x <<*>> y) = t x <<*>> t y
```

Performance note

traverseBia is fairly efficient, and uses compiler rewrite rules to be even more efficient for a few important types like []. However, if performance is critical, you might consider writing a container-specific implementation.

sequenceBia :: (Traversable t, Biapplicative p) => t (p b c) -> p (t b) (t c) Source #

Perform all the Biapplicative actions in a Traversable container and produce a container with all the results.

sequenceBia = traverseBia id

traverseBiaWith :: forall p a b c s t. Biapplicative p => (forall (f :: Type -> Type) x. Applicative f => (a -> f x) -> s -> f (t x)) -> (a -> p b c) -> s -> p (t b) (t c) Source #

A version of traverseBia that doesn't care how the traversal is done.

traverseBia = traverseBiaWith traverse

class (forall a. Functor (p a)) => Bifunctor (p :: Type -> Type -> Type) where #

Minimal complete definition

bimap | first, second

Methods

bimap :: (a -> b) -> (c -> d) -> p a c -> p b d #

first :: (a -> b) -> p a c -> p b c #

second :: (b -> c) -> p a b -> p a c #

Instances

Instances details

Bifunctor Arg
Instance details Defined in Data.Semigroup Methods bimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d # first :: (a -> b) -> Arg a c -> Arg b c # second :: (b -> c) -> Arg a b -> Arg a c #
Bifunctor Either
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Either a c -> Either b d # first :: (a -> b) -> Either a c -> Either b c # second :: (b -> c) -> Either a b -> Either a c #
Bifunctor (,)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) # first :: (a -> b) -> (a, c) -> (b, c) # second :: (b -> c) -> (a, b) -> (a, 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 #
Bifunctor (Const :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d # first :: (a -> b) -> Const a c -> Const b c # second :: (b -> c) -> Const a b -> Const a c #
Bifunctor (Tagged :: Type -> Type -> Type)
Instance details Defined in Data.Tagged Methods bimap :: (a -> b) -> (c -> d) -> Tagged a c -> Tagged b d # first :: (a -> b) -> Tagged a c -> Tagged b c # second :: (b -> c) -> Tagged a b -> Tagged a c #
Bifunctor (Constant :: Type -> Type -> Type)
Instance details Defined in Data.Functor.Constant Methods bimap :: (a -> b) -> (c -> d) -> Constant a c -> Constant b d # first :: (a -> b) -> Constant a c -> Constant b c # second :: (b -> c) -> Constant a b -> Constant a c #
Bifunctor ((,,) x1)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, a, c) -> (x1, b, d) # first :: (a -> b) -> (x1, a, c) -> (x1, b, c) # second :: (b -> c) -> (x1, a, b) -> (x1, a, c) #
Bifunctor (K1 i :: Type -> Type -> Type)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> K1 i a c -> K1 i b d # first :: (a -> b) -> K1 i a c -> K1 i b c # second :: (b -> c) -> K1 i a b -> K1 i a c #
Bifunctor ((,,,) x1 x2)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, a, c) -> (x1, x2, b, d) # first :: (a -> b) -> (x1, x2, a, c) -> (x1, x2, b, c) # second :: (b -> c) -> (x1, x2, a, b) -> (x1, x2, a, c) #
Functor f => Bifunctor (Clown f :: Type -> Type -> Type) Source #
Instance details Defined in Data.Bifunctor.Clown Methods bimap :: (a -> b) -> (c -> d) -> Clown f a c -> Clown f b d # first :: (a -> b) -> Clown f a c -> Clown f b c # second :: (b -> c) -> Clown f a b -> Clown f a c #
Bifunctor p => Bifunctor (Flip p) Source #
Instance details Defined in Data.Bifunctor.Flip Methods bimap :: (a -> b) -> (c -> d) -> Flip p a c -> Flip p b d # first :: (a -> b) -> Flip p a c -> Flip p b c # second :: (b -> c) -> Flip p a b -> Flip p a c #
Functor g => Bifunctor (Joker g :: Type -> Type -> Type) Source #
Instance details Defined in Data.Bifunctor.Joker Methods bimap :: (a -> b) -> (c -> d) -> Joker g a c -> Joker g b d # first :: (a -> b) -> Joker g a c -> Joker g b c # second :: (b -> c) -> Joker g a b -> Joker g a c #
Bifunctor p => Bifunctor (WrappedBifunctor p) Source #
Instance details 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)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, d) # first :: (a -> b) -> (x1, x2, x3, a, c) -> (x1, x2, x3, b, c) # second :: (b -> c) -> (x1, x2, x3, a, b) -> (x1, x2, x3, a, c) #
(Bifunctor f, Bifunctor g) => Bifunctor (Product f g) Source #
Instance details Defined in Data.Bifunctor.Product Methods bimap :: (a -> b) -> (c -> d) -> Product f g a c -> Product f g b d # first :: (a -> b) -> Product f g a c -> Product f g b c # second :: (b -> c) -> Product f g a b -> Product f g a c #
(Bifunctor p, Bifunctor q) => Bifunctor (Sum p q) Source #
Instance details Defined in Data.Bifunctor.Sum Methods bimap :: (a -> b) -> (c -> d) -> Sum p q a c -> Sum p q b d # first :: (a -> b) -> Sum p q a c -> Sum p q b c # second :: (b -> c) -> Sum p q a b -> Sum p q a c #
Bifunctor ((,,,,,) x1 x2 x3 x4)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, a, c) -> (x1, x2, x3, x4, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, a, b) -> (x1, x2, x3, x4, a, c) #
(Functor f, Bifunctor p) => Bifunctor (Tannen f p) Source #
Instance details Defined in Data.Bifunctor.Tannen Methods bimap :: (a -> b) -> (c -> d) -> Tannen f p a c -> Tannen f p b d # first :: (a -> b) -> Tannen f p a c -> Tannen f p b c # second :: (b -> c) -> Tannen f p a b -> Tannen f p a c #
Bifunctor ((,,,,,,) x1 x2 x3 x4 x5)
Instance details Defined in Data.Bifunctor Methods bimap :: (a -> b) -> (c -> d) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, d) # first :: (a -> b) -> (x1, x2, x3, x4, x5, a, c) -> (x1, x2, x3, x4, x5, b, c) # second :: (b -> c) -> (x1, x2, x3, x4, x5, a, b) -> (x1, x2, x3, x4, x5, a, c) #
(Bifunctor p, Functor f, Functor g) => Bifunctor (Biff p f g) Source #
Instance details Defined in Data.Bifunctor.Biff Methods bimap :: (a -> b) -> (c -> d) -> Biff p f g a c -> Biff p f g b d # first :: (a -> b) -> Biff p f g a c -> Biff p f g b c # second :: (b -> c) -> Biff p f g a b -> Biff p f g a c #