Data.Functor.ProductIsomorphic.Class

Contents

Description

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

Synopsis

class ProductIsoFunctor f where
- (|$|) :: ProductConstructor (a -> b) => (a -> b) -> f a -> f b
class ProductIsoFunctor f => ProductIsoApplicative f where
- pureP :: ProductConstructor a => a -> f a
- (|*|) :: f (a -> b) -> f a -> f b
class ProductIsoApplicative f => ProductIsoAlternative f where
- emptyP :: f a
- (|||) :: f a -> f a -> f a
class ProductIsoApplicative f => ProductIsoEmpty f e where
- pureE :: f e
- peRight :: f (a, e) -> f a
- peLeft :: f (e, a) -> f a
peRightR :: ProductIsoEmpty f e => f a -> f (a, e)
peLeftR :: ProductIsoEmpty f e => f a -> f (e, a)

ProductIso classes

Restricted functor on products.

Methods

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

Instances details

Functor f => ProductIsoFunctor (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods (\|$\|) :: ProductConstructor (a -> b) => (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b Source #
ProductIsoFunctor (Const a :: Type -> Type) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods (\|$\|) :: ProductConstructor (a0 -> b) => (a0 -> b) -> Const a a0 -> Const a b Source #
ProductIsoFunctor (WrappedAlter f a) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods (\|$\|) :: ProductConstructor (a0 -> b) => (a0 -> b) -> WrappedAlter f a a0 -> WrappedAlter f a b Source #

Restricted applicative functor on products.

Methods

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

Instances details

Applicative f => ProductIsoApplicative (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods pureP :: ProductConstructor a => a -> WrappedFunctor f a Source # (\|*\|) :: WrappedFunctor f (a -> b) -> WrappedFunctor f a -> WrappedFunctor f b Source #
Monoid a => ProductIsoApplicative (Const a :: Type -> Type) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods pureP :: ProductConstructor a0 => a0 -> Const a a0 Source # (\|*\|) :: Const a (a0 -> b) -> Const a a0 -> Const a b Source #
Alternative f => ProductIsoApplicative (WrappedAlter f a) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods pureP :: ProductConstructor a0 => a0 -> WrappedAlter f a a0 Source # (\|*\|) :: WrappedAlter f a (a0 -> b) -> WrappedAlter f a a0 -> WrappedAlter f a b Source #

Restricted alternative on products.

Methods

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

Instances details

Alternative f => ProductIsoAlternative (WrappedFunctor f) Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods emptyP :: WrappedFunctor f a Source # (\|\|\|) :: WrappedFunctor f a -> WrappedFunctor f a -> WrappedFunctor f a Source #

Empty element

Empty element of product operator

Methods

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

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

Instances details

Applicative f => ProductIsoEmpty (WrappedFunctor f) () Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods pureE :: WrappedFunctor f () Source # peRight :: WrappedFunctor f (a, ()) -> WrappedFunctor f a Source # peLeft :: WrappedFunctor f ((), a) -> WrappedFunctor f a Source #
Monoid a => ProductIsoEmpty (Const a :: Type -> Type) () Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods pureE :: Const a () Source # peRight :: Const a (a0, ()) -> Const a a0 Source # peLeft :: Const a ((), a0) -> Const a a0 Source #
Alternative f => ProductIsoEmpty (WrappedAlter f a) () Source #
Instance details Defined in Data.Functor.ProductIsomorphic.Instances Methods pureE :: WrappedAlter f a () Source # peRight :: WrappedAlter f a (a0, ()) -> WrappedAlter f a a0 Source # peLeft :: WrappedAlter f a ((), a0) -> WrappedAlter f a a0 Source #

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

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