Generic.Applicative.Idiom

Documentation

class (Applicative f, Applicative g) => Idiom tag f g where

An Idiom captures an "applicative homomorphism" between two applicatives, indexed by a tag.

An appliative homomorphism is a polymorphic function between two applicative functors that preserves the Applicative structure.

idiom (pure a) = pure a

idiom (liftA2 (·) as bs) = liftA2 (·) (idiom as) (idiom bs)

Based on: Abstracting with Applicatives.

Methods

idiom :: f ~> g

Instances

(Applicative f, Applicative g, IdiomDup (CheckIdiomDup g) f g) => Idiom Dup f g

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> g

(Applicative outer, Applicative f, comp ~ Compose outer f) => Idiom Outer f comp

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> comp

(Applicative f, Applicative inner, comp ~ Compose f inner) => Idiom Inner f comp

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> comp

(Identity ~ id, Applicative f) => Idiom Initial id f

Defined in Generic.Applicative.Idiom

Methods

idiom :: id ~> f

(Applicative f, f ~ g) => Idiom Id f g

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> g

(Applicative f, Monoid m) => Idiom Terminal f (Proxy :: Type -> Type)

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> Proxy

(Applicative f, Monoid m) => Idiom Terminal f (Const m :: Type -> Type)

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> Const m

(Applicative f, Applicative g) => Idiom Snd (Product f g) g

Defined in Generic.Applicative.Idiom

Methods

idiom :: Product f g ~> g

(Applicative f, Applicative g) => Idiom Fst (Product f g) f

Defined in Generic.Applicative.Idiom

Methods

idiom :: Product f g ~> f

(Idiom tag1 f g, Idiom tag2 g h) => Idiom (Comp tag1 tag2 :: Type) f h

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> h

(Idiom tag1 f g, Idiom tag2 f h) => Idiom (tag1 &&& tag2 :: Type) f (Product g h)

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> Product g h

data Id

The identity applicative morphism.

idiom :: f ~> f
idiom = id

Instances

(Applicative f, f ~ g) => Idiom Id f g

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> g

data Comp tag1 tag2

The left-to-right composition of applicative morphisms.

Instances

(Idiom tag1 f g, Idiom tag2 g h) => Idiom (Comp tag1 tag2 :: Type) f h

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> h

data Initial

The initial applicative morphism.

It turns Identity into any Applicative functor.

idiom :: Identity ~> f
idiom (Identity a) = pure a

Instances

(Identity ~ id, Applicative f) => Idiom Initial id f

Defined in Generic.Applicative.Idiom

Methods

idiom :: id ~> f

data Terminal

The terminal applicative morphism.

It turns any applicative into Const m, or Proxy

idiom :: f ~> Const m
idiom _ = Const mempty

idiom :: f ~> Proxy
idiom _ = Proxy

Instances

(Applicative f, Monoid m) => Idiom Terminal f (Proxy :: Type -> Type)

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> Proxy

(Applicative f, Monoid m) => Idiom Terminal f (Const m :: Type -> Type)

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> Const m

data Inner

This applicative morphism composes a functor on the _inside_.

idiom :: f ~> Compose f inner
idiom = Compose . fmap pure

Instances

(Applicative f, Applicative inner, comp ~ Compose f inner) => Idiom Inner f comp

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> comp

data Outer

This applicative morphism composes a functor on the _outside_.

idiom :: f ~> Compose outer f
idiom = Compose . pure

Instances

(Applicative outer, Applicative f, comp ~ Compose outer f) => Idiom Outer f comp

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> comp

type family CheckIdiomDup f where ...

Equations

CheckIdiomDup (Product _ _) = 'True

CheckIdiomDup _ = 'False

data Dup

This applicative morphism duplicates a functor any number of times.

idiom :: f ~> f
idiom = id

idiom :: f ~> Product f f
idiom as = Pair as as

idiom :: f ~> Product f (Product f f)
idiom as = Pair as (Pair as as)

Instances

(Applicative f, Applicative g, IdiomDup (CheckIdiomDup g) f g) => Idiom Dup f g

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> g

class (CheckIdiomDup g ~ tag, Applicative f, Applicative g) => IdiomDup tag f g where

Minimal complete definition

Nothing

Methods

idiomDup :: f ~> g

Instances

(Applicative f, CheckIdiomDup f ~ 'False, f ~ f') => IdiomDup 'False f f'

Defined in Generic.Applicative.Idiom

Methods

idiomDup :: f ~> f'

(f ~ g, IdiomDup (CheckIdiomDup g') g g') => IdiomDup 'True f (Product g g')

Defined in Generic.Applicative.Idiom

Methods

idiomDup :: f ~> Product g g'

data tag1 &&& tag2

An applicative functor for constructing a product.

idiom :: f ~> Product g h
idiom as = Pair (idiom as) (idiom as)

Instances

(Idiom tag1 f g, Idiom tag2 f h) => Idiom (tag1 &&& tag2 :: Type) f (Product g h)

Defined in Generic.Applicative.Idiom

Methods

idiom :: f ~> Product g h

data Fst

The applicative functor that gets the first component of a product.

idiom :: Product f g ~> f
idiom (Pair as _) = as

Instances

(Applicative f, Applicative g) => Idiom Fst (Product f g) f

Defined in Generic.Applicative.Idiom

Methods

idiom :: Product f g ~> f

data Snd

The applicative functor that gets the second component of a product.

idiom :: Product f g ~> g
idiom (Pair _ bs) = bs

Instances

(Applicative f, Applicative g) => Idiom Snd (Product f g) g

Defined in Generic.Applicative.Idiom

Methods

idiom :: Product f g ~> g