semigroupoids-5.2.1: Semigroupoids: Category sans id

Copyright (C) 2011-2015 Edward Kmett BSD-style (see the file LICENSE) Edward Kmett provisional portable Safe Haskell98

Data.Bifunctor.Apply

Contents

Description

Synopsis

# Biappliable bifunctors

class Bifunctor p where #

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: 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

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

Map covariantly over the first argument.

first f ≡ bimap f id

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

Map covariantly over the second argument.

second ≡ bimap id

Instances

 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 # Methodsbimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d) #first :: (a -> b) -> (a, c) -> (b, c) #second :: (b -> c) -> (a, b) -> (a, c) # 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 (K1 i) 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) 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) # 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 # 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 # 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 ((,,,) x1 x2) 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) 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) # 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) 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) 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) 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) 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) 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) 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) 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) 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 #

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

 # Methods(<<.>>) :: (a -> b, c -> d) -> (a, c) -> (b, d) #(.>>) :: (a, b) -> (c, d) -> (c, d) #(<<.) :: (a, b) -> (c, d) -> (a, b) # # 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 # Semigroup x => Biapply ((,,) x) # 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) # # 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 # # 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, Semigroup y) => Biapply ((,,,) x y) # 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) # (Semigroup x, Semigroup y, Semigroup z) => Biapply ((,,,,) x y z) # 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) # # 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 # Apply g => Biapply (Joker * * g) # 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 (Flip * * p) # 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 f => Biapply (Clown * * f) # 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 q) => Biapply (Product * * p q) # 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) # 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) # 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