Data.Functor.ProductIsomorphic.Class

This module defines functor interfaces which morphed functions are restricted to products.

ProductIso classes

class ProductIsoFunctor f where

Restricted functor on products.

Minimal complete definition

(|$|)

Methods

(|$|) :: ProductConstructor (a -> b) => (a -> b) -> f a -> f b infixl 4

Instances

Functor f => ProductIsoFunctor (WrappedFunctor f)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

(|$|) :: ProductConstructor (a -> b) => (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b

ProductIsoFunctor (Const a :: * -> *)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

(|$|) :: ProductConstructor (a0 -> b) => (a0 -> b) -> Const a a0 -> Const a b

ProductIsoFunctor (WrappedAlter f a)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

(|$|) :: ProductConstructor (a0 -> b) => (a0 -> b) -> WrappedAlter f a a0 -> WrappedAlter f a b

class ProductIsoFunctor f => ProductIsoApplicative f where

Restricted applicative functor on products.

Minimal complete definition

pureP, (|*|)

Methods

pureP :: ProductConstructor a => a -> f a

(|*|) :: f (a -> b) -> f a -> f b infixl 4

Instances

Applicative f => ProductIsoApplicative (WrappedFunctor f)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

pureP :: ProductConstructor a => a -> WrappedFunctor f a

(|*|) :: WrappedFunctor f (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b

Monoid a => ProductIsoApplicative (Const a :: * -> *)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

pureP :: ProductConstructor a0 => a0 -> Const a a0

(|*|) :: Const a (a0 -> b) -> Const a a0 -> Const a b

Alternative f => ProductIsoApplicative (WrappedAlter f a)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

pureP :: ProductConstructor a0 => a0 -> WrappedAlter f a a0

(|*|) :: WrappedAlter f a (a0 -> b) -> WrappedAlter f a a0 -> WrappedAlter f a b

class ProductIsoApplicative f => ProductIsoAlternative f where

Restricted alternative on products.

Minimal complete definition

emptyP, (|||)

Methods

emptyP :: f a

(|||) :: f a -> f a -> f a infixl 3

Instances

Alternative f => ProductIsoAlternative (WrappedFunctor f)

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

emptyP :: WrappedFunctor f a

(|||) :: WrappedFunctor f a -> WrappedFunctor f a -> WrappedFunctor f a

Empty element

class ProductIsoApplicative f => ProductIsoEmpty f e where

Empty element of product operator

Minimal complete definition

pureE, peRight, peLeft

Methods

pureE :: f e

peRight :: f (a, e) -> f a

peLeft :: f (e, a) -> f a

Instances

Applicative f => ProductIsoEmpty (WrappedFunctor f) ()

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

pureE :: WrappedFunctor f ()

peRight :: WrappedFunctor f (a, ()) -> WrappedFunctor f a

peLeft :: WrappedFunctor f ((), a) -> WrappedFunctor f a

Monoid a => ProductIsoEmpty (Const a :: * -> *) ()

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

pureE :: Const a ()

peRight :: Const a (a0, ()) -> Const a a0

peLeft :: Const a ((), a0) -> Const a a0

Alternative f => ProductIsoEmpty (WrappedAlter f a) ()

Defined in Data.Functor.ProductIsomorphic.Instances

Methods

pureE :: WrappedAlter f a ()

peRight :: WrappedAlter f a (a0, ()) -> WrappedAlter f a a0

peLeft :: WrappedAlter f a ((), a0) -> WrappedAlter f a a0

peRightR :: ProductIsoEmpty f e => f a -> f (a, e)

peRight and peRightR should have isomorphic law. peRight . peRightR == peRightR . peRight == id

peLeftR :: ProductIsoEmpty f e => f a -> f (e, a)

peLeft and peLeftR should have isomorphic law. peLeft . peLeftR == peLeftR . peLeft == id