Data.Bifunctor.Apply

semigroupoids-5.3.7: Semigroupoids: Category sans id

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

- Biappliable bifunctors

Description

Synopsis

- class 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
- class Bifunctor p => Biapply p where
  - (<<.>>) :: p (a -> b) (c -> d) -> p a c -> p b d
  - (.>>) :: p a b -> p c d -> p c d
  - (<<.) :: p a b -> p c d -> p a b
- (<<$>>) :: (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 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 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 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 (,) |
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 (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) |
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) |
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) |
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) |
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) |
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 ((,,,,,) 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) |
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) |
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 #

class Bifunctor p => Biapply p where #

Minimal complete definition

(<<.>>)

Methods

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

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

    a .> b ≡ const id <$> a <.> b

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

    a <. b ≡ const <$> a <.> b

#### Instances

Instances details

Biapply Arg # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Arg (a -> b) (c -> d) -> Arg a c -> Arg b d # (.>>) :: Arg a b -> Arg c d -> Arg c d # (<<.) :: Arg a b -> Arg c d -> Arg a b #
Biapply (,) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: (a -> b, c -> d) -> (a, c) -> (b, d) # (.>>) :: (a, b) -> (c, d) -> (c, d) # (<<.) :: (a, b) -> (c, d) -> (a, b) #
Biapply (Const :: Type -> Type -> Type) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Const (a -> b) (c -> d) -> Const a c -> Const b d # (.>>) :: Const a b -> Const c d -> Const c d # (<<.) :: Const a b -> Const c d -> Const a b #
Biapply (Tagged :: Type -> Type -> Type) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Tagged (a -> b) (c -> d) -> Tagged a c -> Tagged b d # (.>>) :: Tagged a b -> Tagged c d -> Tagged c d # (<<.) :: Tagged a b -> Tagged c d -> Tagged a b #
Semigroup x => Biapply ((,,) x) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: (x, a -> b, c -> d) -> (x, a, c) -> (x, b, d) # (.>>) :: (x, a, b) -> (x, c, d) -> (x, c, d) # (<<.) :: (x, a, b) -> (x, c, d) -> (x, a, b) #
(Semigroup x, Semigroup y) => Biapply ((,,,) x y) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: (x, y, a -> b, c -> d) -> (x, y, a, c) -> (x, y, b, d) # (.>>) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, c, d) # (<<.) :: (x, y, a, b) -> (x, y, c, d) -> (x, y, a, b) #
Apply f => Biapply (Clown f :: Type -> Type -> Type) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Clown f (a -> b) (c -> d) -> Clown f a c -> Clown f b d # (.>>) :: Clown f a b -> Clown f c d -> Clown f c d # (<<.) :: Clown f a b -> Clown f c d -> Clown f a b #
Biapply p => Biapply (Flip p) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Flip p (a -> b) (c -> d) -> Flip p a c -> Flip p b d # (.>>) :: Flip p a b -> Flip p c d -> Flip p c d # (<<.) :: Flip p a b -> Flip p c d -> Flip p a b #
Apply g => Biapply (Joker g :: Type -> Type -> Type) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Joker g (a -> b) (c -> d) -> Joker g a c -> Joker g b d # (.>>) :: Joker g a b -> Joker g c d -> Joker g c d # (<<.) :: Joker g a b -> Joker g c d -> Joker g a b #
Biapply p => Biapply (WrappedBifunctor p) # |
Instance details 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) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: (x, y, z, a -> b, c -> d) -> (x, y, z, a, c) -> (x, y, z, b, d) # (.>>) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, c, d) # (<<.) :: (x, y, z, a, b) -> (x, y, z, c, d) -> (x, y, z, a, b) #
(Biapply p, Biapply q) => Biapply (Product p q) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Product p q (a -> b) (c -> d) -> Product p q a c -> Product p q b d # (.>>) :: Product p q a b -> Product p q c d -> Product p q c d # (<<.) :: Product p q a b -> Product p q c d -> Product p q a b #
(Apply f, Biapply p) => Biapply (Tannen f p) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Tannen f p (a -> b) (c -> d) -> Tannen f p a c -> Tannen f p b d # (.>>) :: Tannen f p a b -> Tannen f p c d -> Tannen f p c d # (<<.) :: Tannen f p a b -> Tannen f p c d -> Tannen f p a b #
(Biapply p, Apply f, Apply g) => Biapply (Biff p f g) # |
Instance details Defined in Data.Functor.Bind.Class Methods (<<.>>) :: Biff p f g (a -> b) (c -> d) -> Biff p f g a c -> Biff p f g b d # (.>>) :: Biff p f g a b -> Biff p f g c d -> Biff p f g c d # (<<.) :: Biff p f g a b -> Biff p f g c d -> Biff p f g a b #

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

(<<..>>) :: Biapply p => p a c -> p (a -> b) (c -> d) -> p b d infixl 4 #

bilift2 :: Biapply w => (a -> b -> c) -> (d -> e -> f) -> w a d -> w b e -> w c f #

Lift binary functions

bilift3 :: Biapply w => (a -> b -> c -> d) -> (e -> f -> g -> h) -> w a e -> w b f -> w c g -> w d h #

Lift ternary functions