semigroupoids-5.3.1: Semigroupoids: Category sans id

Data.Bifunctor.Apply

Contents

Description

Synopsis

# Biappliable bifunctors

class Bifunctor (p :: * -> * -> *) 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.

If you supply bimap, you should ensure that:

bimap id id ≡ id

If you supply first and second, ensure:

first id ≡ id
second id ≡ id


If you supply both, you should also ensure:

bimap f g ≡ first f . second g

These ensure by parametricity:

bimap  (f . g) (h . i) ≡ bimap f h . bimap g i
first  (f . g) ≡ first  f . first  g
second (f . g) ≡ second f . second g


Since: base-4.8.0.0

Minimal complete definition

Methods

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

Map over both arguments at the same time.

bimap f g ≡ first f . second g

#### Examples

Expand
>>> bimap toUpper (+1) ('j', 3)
('J',4)

>>> bimap toUpper (+1) (Left 'j')
Left 'J'

>>> bimap toUpper (+1) (Right 3)
Right 4


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

Map covariantly over the first argument.

first f ≡ bimap f id

#### Examples

Expand
>>> first toUpper ('j', 3)
('J',3)

>>> first toUpper (Left 'j')
Left 'J'


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

Map covariantly over the second argument.

second ≡ bimap id

#### Examples

Expand
>>> second (+1) ('j', 3)
('j',4)

>>> second (+1) (Right 3)
Right 4

Instances
 Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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 # Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) #first :: (a -> b) -> (a, c) -> (b, c) #second :: (b -> c) -> (a, b) -> (a, c) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsbimap :: (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 ((,,) x1) Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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 (Const :: * -> * -> *) Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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 :: * -> * -> *) Instance detailsDefined in Data.Tagged Methodsbimap :: (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 :: * -> * -> *) Instance detailsDefined in Data.Functor.Constant Methodsbimap :: (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 (K1 i :: * -> * -> *) Since: base-4.9.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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) Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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) # Bifunctor ((,,,,) x1 x2 x3) Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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) # Instance detailsDefined in Data.Bifunctor.Wrapped Methodsbimap :: (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 # Functor g => Bifunctor (Joker g :: * -> * -> *) Instance detailsDefined in Data.Bifunctor.Joker Methodsbimap :: (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 (Flip p) Instance detailsDefined in Data.Bifunctor.Flip Methodsbimap :: (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 f => Bifunctor (Clown f :: * -> * -> *) Instance detailsDefined in Data.Bifunctor.Clown Methodsbimap :: (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 ((,,,,,) x1 x2 x3 x4) Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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) # (Bifunctor f, Bifunctor g) => Bifunctor (Product f g) Instance detailsDefined in Data.Bifunctor.Product Methodsbimap :: (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 x5) Since: base-4.8.0.0 Instance detailsDefined in Data.Bifunctor Methodsbimap :: (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) # (Functor f, Bifunctor p) => Bifunctor (Tannen f p) Instance detailsDefined in Data.Bifunctor.Tannen Methodsbimap :: (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 p, Functor f, Functor g) => Bifunctor (Biff p f g) Instance detailsDefined in Data.Bifunctor.Biff Methodsbimap :: (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 Source #

Minimal complete definition

(<<.>>)

Methods

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

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

a .> b ≡ const id <$> a <.> b  (<<.) :: p a b -> p c d -> p a b infixl 4 Source # a <. b ≡ const <$> a <.> b

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

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

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

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 Source #

Lift ternary functions