Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.Constraint

Documentation

newtype CONSTRAINT Source Github #

Constructors

CNSTRNT Constraint

Instances

Instances details

Monoidal CONSTRAINT Source Github #

Products as monoidal structure.

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.Constraint type Unit = TerminalObject :: CONSTRAINT
type (a :: CONSTRAINT) ** (b :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type (a :: CONSTRAINT) ** (b :: CONSTRAINT) = a && b

Methods

withOb2 :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. (Ob a, Ob b) => (Ob (a ** b) => r) -> r Source Github #

leftUnitor :: forall (a :: CONSTRAINT). Ob a => ((Unit :: CONSTRAINT) ** a) ~> a Source Github #

leftUnitorInv :: forall (a :: CONSTRAINT). Ob a => a ~> ((Unit :: CONSTRAINT) ** a) Source Github #

rightUnitor :: forall (a :: CONSTRAINT). Ob a => (a ** (Unit :: CONSTRAINT)) ~> a Source Github #

rightUnitorInv :: forall (a :: CONSTRAINT). Ob a => a ~> (a ** (Unit :: CONSTRAINT)) Source Github #

associator :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (c :: CONSTRAINT). (Ob a, Ob b, Ob c) => ((a ** b) ** c) ~> (a ** (b ** c)) Source Github #

associatorInv :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (c :: CONSTRAINT). (Ob a, Ob b, Ob c) => (a ** (b ** c)) ~> ((a ** b) ** c) Source Github #

SymMonoidal CONSTRAINT Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

swap :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b) => (a ** b) ~> (b ** a) Source Github #

CopyDiscard CONSTRAINT Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

copy :: forall (a :: CONSTRAINT). Ob a => a ~> (a ** a) Source Github #

discard :: forall (a :: CONSTRAINT). Ob a => a ~> (Unit :: CONSTRAINT) Source Github #

CategoryOf CONSTRAINT Source Github #

The category of type class constraints. An arrow from constraint a to constraint b | means that a implies b, i.e. if a holds then b holds.

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Constraint type (~>) = (:-)
type Ob (a :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type Ob (a :: CONSTRAINT) = Is 'CNSTRNT a

HasBinaryProducts CONSTRAINT Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type ('CNSTRNT l :: CONSTRAINT) && ('CNSTRNT r :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type ('CNSTRNT l :: CONSTRAINT) && ('CNSTRNT r :: CONSTRAINT) = 'CNSTRNT (l, r)

Methods

withObProd :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. (Ob a, Ob b) => (Ob (a && b) => r) -> r Source Github #

fst :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b) => (a && b) ~> a Source Github #

snd :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b) => (a && b) ~> b Source Github #

(&&&) :: forall (a :: CONSTRAINT) (x :: CONSTRAINT) (y :: CONSTRAINT). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Github #

(***) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (x :: CONSTRAINT) (y :: CONSTRAINT). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Github #

Closed CONSTRAINT Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type (a :: CONSTRAINT) ~~> (b :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type (a :: CONSTRAINT) ~~> (b :: CONSTRAINT) = 'CNSTRNT (UN 'CNSTRNT a :=> UN 'CNSTRNT b)

Methods

withObExp :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. (Ob a, Ob b) => (Ob (a ~~> b) => r) -> r Source Github #

curry :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (c :: CONSTRAINT). (Ob a, Ob b) => ((a ** b) ~> c) -> a ~> (b ~~> c) Source Github #

apply :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b) => ((a ~~> b) ** a) ~> b Source Github #

(^^^) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (x :: CONSTRAINT) (y :: CONSTRAINT). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Github #

HasTerminalObject CONSTRAINT Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.Constraint type TerminalObject = 'CNSTRNT ()

Methods

terminate :: forall (a :: CONSTRAINT). Ob a => a ~> (TerminalObject :: CONSTRAINT) Source Github #

Promonad (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

id :: forall (a :: CONSTRAINT). Ob a => a :- a Source Github #

(.) :: forall (b :: CONSTRAINT) (c :: CONSTRAINT) (a :: CONSTRAINT). (b :- c) -> (a :- b) -> a :- c Source Github #

ThinProfunctor (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT) = UN 'CNSTRNT a :=> UN 'CNSTRNT b

Methods

arr :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b, HasArrow (:-) a b) => a :- b Source Github #

withArr :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. (a :- b) -> (HasArrow (:-) a b => r) -> r Source Github #

MonoidalProfunctor (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

par0 :: (Unit :: CONSTRAINT) :- (Unit :: CONSTRAINT) Source Github #

par :: forall (x1 :: CONSTRAINT) (x2 :: CONSTRAINT) (y1 :: CONSTRAINT) (y2 :: CONSTRAINT). (x1 :- x2) -> (y1 :- y2) -> (x1 ** y1) :- (x2 ** y2) Source Github #

Profunctor (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

dimap :: forall (c :: CONSTRAINT) (a :: CONSTRAINT) (b :: CONSTRAINT) (d :: CONSTRAINT). (c ~> a) -> (b ~> d) -> (a :- b) -> c :- d Source Github #

(\\) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. ((Ob a, Ob b) => r) -> (a :- b) -> r Source Github #

ThinProfunctor p => EnrichedProfunctor CONSTRAINT (p :: j +-> k) Source Github #

Instance details

Defined in Proarrow.Category.Enriched

Methods

withProObj :: forall (a :: k) (b :: j) r. (Ob a, Ob b) => (Ob (ProObj CONSTRAINT p a b) => r) -> r Source Github #

underlying :: forall (a :: k) (b :: j). p a b -> (Unit :: CONSTRAINT) ~> ProObj CONSTRAINT p a b Source Github #

enriched :: forall (a :: k) (b :: j). (Ob a, Ob b) => ((Unit :: CONSTRAINT) ~> ProObj CONSTRAINT p a b) -> p a b Source Github #

rmap :: forall (a :: k) (b :: j) (c :: j). (Ob a, Ob b, Ob c) => (HomObj CONSTRAINT b c ** ProObj CONSTRAINT p a b) ~> ProObj CONSTRAINT p a c Source Github #

lmap :: forall (a :: k) (b :: j) (c :: k). (Ob a, Ob b, Ob c) => (HomObj CONSTRAINT c a ** ProObj CONSTRAINT p a b) ~> ProObj CONSTRAINT p c b Source Github #

Comonoid ('CNSTRNT a :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

counit :: 'CNSTRNT a ~> (Unit :: CONSTRAINT) Source Github #

comult :: 'CNSTRNT a ~> ('CNSTRNT a ** 'CNSTRNT a) Source Github #

Monoid ('CNSTRNT ()) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

mempty :: (Unit :: CONSTRAINT) ~> 'CNSTRNT () Source Github #

mappend :: ('CNSTRNT () ** 'CNSTRNT ()) ~> 'CNSTRNT () Source Github #

type Unit Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type Unit = TerminalObject :: CONSTRAINT

type (~>) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type (~>) = (:-)

type TerminalObject Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type TerminalObject = 'CNSTRNT ()

type Ob (a :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type Ob (a :: CONSTRAINT) = Is 'CNSTRNT a

type (a :: CONSTRAINT) ** (b :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type (a :: CONSTRAINT) ** (b :: CONSTRAINT) = a && b

type (a :: CONSTRAINT) ~~> (b :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type (a :: CONSTRAINT) ~~> (b :: CONSTRAINT) = 'CNSTRNT (UN 'CNSTRNT a :=> UN 'CNSTRNT b)

type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT) = UN 'CNSTRNT a :=> UN 'CNSTRNT b

type ProObj CONSTRAINT (p :: j +-> k) (a :: k) (b :: j) Source Github #

Instance details

Defined in Proarrow.Category.Enriched

type ProObj CONSTRAINT (p :: j +-> k) (a :: k) (b :: j) = 'CNSTRNT (HasArrow p a b)

type UN 'CNSTRNT ('CNSTRNT a :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type UN 'CNSTRNT ('CNSTRNT a :: CONSTRAINT) = a

type ('CNSTRNT l :: CONSTRAINT) && ('CNSTRNT r :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type ('CNSTRNT l :: CONSTRAINT) && ('CNSTRNT r :: CONSTRAINT) = 'CNSTRNT (l, r)

data (a :: CONSTRAINT) :- (b :: CONSTRAINT) where Source Github #

Constructors

Entails
Fields :: forall a1 b1. { unEntails :: forall r. a1 => (b1 => r) -> r } -> 'CNSTRNT a1 :- 'CNSTRNT b1

Instances

Instances details

Promonad (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

id :: forall (a :: CONSTRAINT). Ob a => a :- a Source Github #

(.) :: forall (b :: CONSTRAINT) (c :: CONSTRAINT) (a :: CONSTRAINT). (b :- c) -> (a :- b) -> a :- c Source Github #

ThinProfunctor (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Associated Types

type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT)
Instance details Defined in Proarrow.Category.Instance.Constraint type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT) = UN 'CNSTRNT a :=> UN 'CNSTRNT b

Methods

arr :: forall (a :: CONSTRAINT) (b :: CONSTRAINT). (Ob a, Ob b, HasArrow (:-) a b) => a :- b Source Github #

withArr :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. (a :- b) -> (HasArrow (:-) a b => r) -> r Source Github #

MonoidalProfunctor (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

par0 :: (Unit :: CONSTRAINT) :- (Unit :: CONSTRAINT) Source Github #

par :: forall (x1 :: CONSTRAINT) (x2 :: CONSTRAINT) (y1 :: CONSTRAINT) (y2 :: CONSTRAINT). (x1 :- x2) -> (y1 :- y2) -> (x1 ** y1) :- (x2 ** y2) Source Github #

Profunctor (:-) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

Methods

dimap :: forall (c :: CONSTRAINT) (a :: CONSTRAINT) (b :: CONSTRAINT) (d :: CONSTRAINT). (c ~> a) -> (b ~> d) -> (a :- b) -> c :- d Source Github #

(\\) :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) r. ((Ob a, Ob b) => r) -> (a :- b) -> r Source Github #

type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT) Source Github #

Instance details

Defined in Proarrow.Category.Instance.Constraint

type HasArrow (:-) (a :: CONSTRAINT) (b :: CONSTRAINT) = UN 'CNSTRNT a :=> UN 'CNSTRNT b

class b :=> c where Source Github #

Methods

entails :: 'CNSTRNT b :- 'CNSTRNT c Source Github #

Instances

Instances details

(b => c) => b :=> c Source Github #
Instance details Defined in Proarrow.Category.Instance.Constraint Methods entails :: 'CNSTRNT b :- 'CNSTRNT c Source Github #

reifyExp :: ('CNSTRNT b :- 'CNSTRNT c) -> (b :=> c => r) -> r Source Github #

eqIsSuperOrd :: 'CNSTRNT (Ord a) :- 'CNSTRNT (Eq a) Source Github #

maybeLiftsSemigroup :: 'CNSTRNT (Semigroup a) :- 'CNSTRNT (Monoid (Maybe a)) Source Github #