Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Strong

Contents

Strength
Costrength

Synopsis

class Strong
value uncurry'
value strong
newtype Tambara
value tambara
value untambara
data Pastro
value pastro
value unpastro
class Costrong
data Cotambara
value cotambara
value uncotambara
newtype Copastro

Packageprofunctors-5.6.3
Exports14
LanguageHaskell2010
LicenceBSD-3-Clause
SourceStrong.hs

Strength

classclass Profunctor p => Strong (p :: Type -> Type -> Type) where

Source#

Generalizing Star of a strong Functor

Note: Every Functor in Haskell is strong with respect to (,).

This describes profunctor strength with respect to the product structure of Hask.

http://www.riec.tohoku.ac.jp/~asada/papers/arrStrMnd.pdf

Methods

first' :: p a b -> p (a, c) (b, c)

Laws:

first' ≡ dimap swap swap . second'
lmap fst ≡ rmap fst . first'
lmap (second' f) . first' ≡ rmap (second' f) . first'
first' . first' ≡ dimap assoc unassoc . first' where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

second' :: p a b -> p (c, a) (c, b)

Laws:

second' ≡ dimap swap swap . first'
lmap snd ≡ rmap snd . second'
lmap (first' f) . second' ≡ rmap (first' f) . second'
second' . second' ≡ dimap unassoc assoc . second' where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

Instances20Strong, …

Monad m => Strong (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (FreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Strong (Pastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (FreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Strong p => Strong (Closure p)Defined in profunctors-5.6.3 · Data.Profunctor.Closed
Strong p => Strong (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Strong p => Strong (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Profunctor p => Strong (CofreeMapping p)Defined in profunctors-5.6.3 · Data.Profunctor.Mapping
Profunctor p => Strong (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor p => Strong (CofreeTraversing p)Defined in profunctors-5.6.3 · Data.Profunctor.Traversing
Functor m => Strong (Star m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (->)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (Forget r)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Contravariant f => Strong (Clown f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow p => Strong (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow is Strong Category
(Strong p, Strong q) => Strong (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Strong p, Strong q) => Strong (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Strong p) => Strong (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Strong p) => Strong (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Strong p, Strong q) => Strong (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

valueuncurry' :: Strong p => p a (b -> c) -> p (a, b) c

valuestrong :: Strong p => (a -> b -> c) -> p a b -> p a c

newtypenewtype Tambara (p :: Type -> Type -> Type) a b

Source#

Tambara cofreely makes any Profunctor Strong.

Constructors

Tambara
- runTambara :: forall c. p (a, c) (b, c)

Instances18ProfunctorComonad, ProfunctorAdjunction, ProfunctorFunctor, Category, Arrow, ArrowApply, …

ProfunctorComonad TambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorAdjunction Pastro TambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorFunctor TambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
Category p => Category (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Arrow p => Arrow (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowApply p => ArrowApply (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowChoice p => ArrowChoice (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowPlus p => ArrowPlus (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowZero p => ArrowZero (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowLoop p => ArrowLoop (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Choice p => Choice (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Choice
Profunctor p => Strong (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor p => Profunctor (Tambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor p => Functor (Tambara p a)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Profunctor p, Arrow p) => Applicative (Tambara p a)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Profunctor p, ArrowPlus p) => Alternative (Tambara p a)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowPlus p => Semigroup (Tambara p a b)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowPlus p => Monoid (Tambara p a b)Defined in profunctors-5.6.3 · Data.Profunctor.Strong

valuetambara :: Strong p => p :-> q -> p :-> Tambara q

Source#

tambara (untambara f) ≡ f
untambara (tambara f) ≡ f

valueuntambara :: Profunctor q => p :-> Tambara q -> p :-> q

Source#

tambara (untambara f) ≡ f
untambara (tambara f) ≡ f

datadata Pastro (p :: Type -> Type -> Type) a b where

Source#

Pastro -| Tambara

Pastro p ~ exists z. Costar ((,)z) Procompose p Procompose Star ((,)z)

Pastro freely makes any Profunctor Strong.

Constructors

Pastro :: ((y, z) -> b) -> p x y -> (a -> (x, z)) -> Pastro p a b

Instances6ProfunctorMonad, ProfunctorAdjunction, ProfunctorFunctor, Strong, Profunctor, Functor

ProfunctorMonad PastroDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorAdjunction Pastro TambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorFunctor PastroDefined in profunctors-5.6.3 · Data.Profunctor.Strong
Strong (Pastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Pastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor (Pastro p a)Defined in profunctors-5.6.3 · Data.Profunctor.Strong

valuepastro :: Strong q => p :-> q -> Pastro p :-> q

Source#

pastro (unpastro f) ≡ f
unpastro (pastro f) ≡ f

valueunpastro :: Pastro p :-> q -> p :-> q

Source#

pastro (unpastro f) ≡ f
unpastro (pastro f) ≡ f

Costrength

classclass Profunctor p => Costrong (p :: Type -> Type -> Type) where

Source#

Analogous to ArrowLoop, loop = unfirst

Methods

unfirst :: p (a, d) (b, d) -> p a b

Laws:

unfirst ≡ unsecond . dimap swap swap
lmap (,()) ≡ unfirst . rmap (,())
unfirst . lmap (second f) ≡ unfirst . rmap (second f)
unfirst . unfirst = unfirst . dimap assoc unassoc where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

unsecond :: p (d, a) (d, b) -> p a b

Laws:

unsecond ≡ unfirst . dimap swap swap
lmap ((),) ≡ unsecond . rmap ((),)
unsecond . lmap (first f) ≡ unsecond . rmap (first f)
unsecond . unsecond = unsecond . dimap unassoc assoc where
  assoc ((a,b),c) = (a,(b,c))
  unassoc (a,(b,c)) = ((a,b),c)

Instances15Costrong, …

MonadFix m => Costrong (Kleisli m)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong TaggedDefined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (Copastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (Cotambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong p => Costrong (Coyoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Costrong p => Costrong (Yoneda p)Defined in profunctors-5.6.3 · Data.Profunctor.Yoneda
Functor f => Costrong (Cokleisli f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor f => Costrong (Costar f)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (->)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
ArrowLoop p => Costrong (WrappedArrow p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Costrong p, Costrong q) => Costrong (Product p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Costrong p, Costrong q) => Costrong (Sum p q)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Costrong p) => Costrong (Tannen f p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
(Functor f, Costrong p) => Costrong (Cayley f p)Defined in profunctors-5.6.3 · Data.Profunctor.Cayley
(Corepresentable p, Corepresentable q) => Costrong (Procompose p q)Defined in profunctors-5.6.3 · Data.Profunctor.Composition

datadata Cotambara (q :: Type -> Type -> Type) a b where

Source#

Cotambara cofreely constructs costrength

Constructors

Cotambara :: Costrong r => r :-> q -> r a b -> Cotambara q a b

Instances6ProfunctorComonad, ProfunctorAdjunction, ProfunctorFunctor, Costrong, Profunctor, Functor

ProfunctorComonad CotambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorAdjunction Copastro CotambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorFunctor CotambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (Cotambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Cotambara p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor (Cotambara p a)Defined in profunctors-5.6.3 · Data.Profunctor.Strong

valuecotambara :: Costrong p => p :-> q -> p :-> Cotambara q

Source#

cotambara . uncotambara ≡ id
uncotambara . cotambara ≡ id

valueuncotambara :: Profunctor q => p :-> Cotambara q -> p :-> q

Source#

cotambara . uncotambara ≡ id
uncotambara . cotambara ≡ id

newtypenewtype Copastro (p :: Type -> Type -> Type) a b

Source#

Copastro -| Cotambara

Copastro freely constructs costrength

Constructors

Copastro
- runCopastro :: forall (r :: Type -> Type -> Type). Costrong r => (forall x y. p x y -> r x y) -> r a b

Instances6ProfunctorMonad, ProfunctorAdjunction, ProfunctorFunctor, Costrong, Profunctor, Functor

ProfunctorMonad CopastroDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorAdjunction Copastro CotambaraDefined in profunctors-5.6.3 · Data.Profunctor.Strong
ProfunctorFunctor CopastroDefined in profunctors-5.6.3 · Data.Profunctor.Strong
Costrong (Copastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Profunctor (Copastro p)Defined in profunctors-5.6.3 · Data.Profunctor.Strong
Functor (Copastro p a)Defined in profunctors-5.6.3 · Data.Profunctor.Strong