Copyright	(C) 2018 Brian Mckenna
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.Functor.Invariant.Day

Description

The Day convolution of two invariant functors is an invariant functor.

Synopsis

data Day (f :: Type -> Type) (g :: Type -> Type) a = Day (f b) (g c) (b -> c -> a) (a -> (b, c))
day :: f a -> g b -> Day f g (a, b)
assoc :: forall (f :: Type -> Type) (g :: Type -> Type) (h :: Type -> Type) a. Day f (Day g h) a -> Day (Day f g) h a
disassoc :: forall (f :: Type -> Type) (g :: Type -> Type) (h :: Type -> Type) a. Day (Day f g) h a -> Day f (Day g h) a
swapped :: forall (f :: Type -> Type) (g :: Type -> Type) a. Day f g a -> Day g f a
intro1 :: f a -> Day Identity f a
intro2 :: f a -> Day f Identity a
elim1 :: Invariant f => Day Identity f a -> f a
elim2 :: Invariant f => Day f Identity a -> f a
trans1 :: forall f g (h :: Type -> Type) a. (forall x. f x -> g x) -> Day f h a -> Day g h a
trans2 :: forall g h (f :: Type -> Type) a. (forall x. g x -> h x) -> Day f g a -> Day f h a
toContravariant :: forall (f :: Type -> Type) (g :: Type -> Type) a. Day f g a -> Day f g a
toCovariant :: forall (f :: Type -> Type) (g :: Type -> Type) a. Day f g a -> Day f g a

Documentation

data Day (f :: Type -> Type) (g :: Type -> Type) a Source #

The Day convolution of two invariant functors.

Constructors

Day (f b) (g c) (b -> c -> a) (a -> (b, c))

Instances details

Invariant (Day f g) Source #
Instance details Defined in Data.Functor.Invariant.Day Methods invmap :: (a -> b) -> (b -> a) -> Day f g a -> Day f g b #

day :: f a -> g b -> Day f g (a, b) Source #

Construct the Day convolution

assoc :: forall (f :: Type -> Type) (g :: Type -> Type) (h :: Type -> Type) a. Day f (Day g h) a -> Day (Day f g) h a Source #

Day convolution provides a monoidal product. The associativity of this monoid is witnessed by assoc and disassoc.

assoc . disassoc = id
disassoc . assoc = id
invmap f g . assoc = assoc . invmap f g

disassoc :: forall (f :: Type -> Type) (g :: Type -> Type) (h :: Type -> Type) a. Day (Day f g) h a -> Day f (Day g h) a Source #

Day convolution provides a monoidal product. The associativity of this monoid is witnessed by assoc and disassoc.

assoc . disassoc = id
disassoc . assoc = id
invmap f g . disassoc = disassoc . invmap f g

swapped :: forall (f :: Type -> Type) (g :: Type -> Type) a. Day f g a -> Day g f a Source #

The monoid for Day convolution on the cartesian monoidal structure is symmetric.

invmap f g . swapped = swapped . invmap f g

Identity is the unit of Day convolution

intro1 . elim1 = id
elim1 . intro1 = id

Identity is the unit of Day convolution

intro2 . elim2 = id
elim2 . intro2 = id

Identity is the unit of Day convolution

intro1 . elim1 = id
elim1 . intro1 = id

Identity is the unit of Day convolution

intro2 . elim2 = id
elim2 . intro2 = id

trans1 :: forall f g (h :: Type -> Type) a. (forall x. f x -> g x) -> Day f h a -> Day g h a Source #

Apply a natural transformation to the left-hand side of a Day convolution.

This respects the naturality of the natural transformation you supplied:

invmap f g . trans1 fg = trans1 fg . invmap f g

trans2 :: forall g h (f :: Type -> Type) a. (forall x. g x -> h x) -> Day f g a -> Day f h a Source #

Apply a natural transformation to the right-hand side of a Day convolution.

This respects the naturality of the natural transformation you supplied:

invmap f g . trans2 fg = trans2 fg . invmap f g

toContravariant :: forall (f :: Type -> Type) (g :: Type -> Type) a. Day f g a -> Day f g a Source #

Drop the covariant part of the Day convolution.

toCovariant :: forall (f :: Type -> Type) (g :: Type -> Type) a. Day f g a -> Day f g a Source #

Drop the contravariant part of the Day convolution.