Moduleprofunctors-5.6.3Haskell2010

Data.Profunctor.Strong

4 types
2 classes
8 values

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

Strength

9 declarations

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

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

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
ArrowLoop p => ArrowLoop (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
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

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

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

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

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

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

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

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

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

Costrength

5 declarations

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

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

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

cotambara . uncotambara ≡ id
uncotambara . cotambara ≡ id

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

cotambara . uncotambara ≡ id
uncotambara . cotambara ≡ id

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

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