Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.Bool

Documentation

data BOOL Source Comments #

Constructors

FLS
TRU

Instances

Instances details

Monoidal BOOL Source Comments #

Products as monoidal structure.

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

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

Methods

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

leftUnitor :: forall (a :: BOOL). Ob a => ((Unit :: BOOL) ** a) ~> a Source Comments #

leftUnitorInv :: forall (a :: BOOL). Ob a => a ~> ((Unit :: BOOL) ** a) Source Comments #

rightUnitor :: forall (a :: BOOL). Ob a => (a ** (Unit :: BOOL)) ~> a Source Comments #

rightUnitorInv :: forall (a :: BOOL). Ob a => a ~> (a ** (Unit :: BOOL)) Source Comments #

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

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

SymMonoidal BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

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

Distributive BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

distL :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b, Ob c) => (a ** (b || c)) ~> ((a ** b) || (a ** c)) Source Comments #

distR :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b, Ob c) => ((a || b) ** c) ~> ((a ** c) || (b ** c)) Source Comments #

distL0 :: forall (a :: BOOL). Ob a => (a ** (InitialObject :: BOOL)) ~> (InitialObject :: BOOL) Source Comments #

distR0 :: forall (a :: BOOL). Ob a => ((InitialObject :: BOOL) ** a) ~> (InitialObject :: BOOL) Source Comments #

CategoryOf BOOL Source Comments #

The category of 2 objects and one arrow between them, a.k.a. the walking arrow.

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.Bool type (~>) = Booleans
type Ob (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type Ob (b :: BOOL) = IsBool b

CopyDiscard BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

copy :: forall (a :: BOOL). Ob a => a ~> (a ** a) Source Comments #

discard :: forall (a :: BOOL). Ob a => a ~> (Unit :: BOOL) Source Comments #

HasBinaryCoproducts BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type 'TRU \|\| (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type 'TRU \|\| (b :: BOOL) = 'TRU
type 'FLS \|\| (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type 'FLS \|\| (b :: BOOL) = b
type (a :: BOOL) \|\| 'TRU
Instance details Defined in Proarrow.Category.Instance.Bool type (a :: BOOL) \|\| 'TRU = 'TRU
type (a :: BOOL) \|\| 'FLS
Instance details Defined in Proarrow.Category.Instance.Bool type (a :: BOOL) \|\| 'FLS = a

Methods

withObCoprod :: forall (a :: BOOL) (b :: BOOL) r. (Ob a, Ob b) => (Ob (a || b) => r) -> r Source Comments #

lft :: forall (a :: BOOL) (b :: BOOL). (Ob a, Ob b) => a ~> (a || b) Source Comments #

rgt :: forall (a :: BOOL) (b :: BOOL). (Ob a, Ob b) => b ~> (a || b) Source Comments #

(|||) :: forall (x :: BOOL) (a :: BOOL) (y :: BOOL). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Comments #

(+++) :: forall (a :: BOOL) (b :: BOOL) (x :: BOOL) (y :: BOOL). (a ~> x) -> (b ~> y) -> (a || b) ~> (x || y) Source Comments #

HasBinaryProducts BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type 'FLS && (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type 'FLS && (b :: BOOL) = 'FLS
type 'TRU && (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type 'TRU && (b :: BOOL) = b
type (a :: BOOL) && 'FLS
Instance details Defined in Proarrow.Category.Instance.Bool type (a :: BOOL) && 'FLS = 'FLS
type (a :: BOOL) && 'TRU
Instance details Defined in Proarrow.Category.Instance.Bool type (a :: BOOL) && 'TRU = a

Methods

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

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

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

(&&&) :: forall (a :: BOOL) (x :: BOOL) (y :: BOOL). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

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

StarAutonomous BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type Dual 'TRU
Instance details Defined in Proarrow.Category.Instance.Bool type Dual 'TRU = 'FLS
type Dual 'FLS
Instance details Defined in Proarrow.Category.Instance.Bool type Dual 'FLS = 'TRU

Methods

dual :: forall (a :: BOOL) (b :: BOOL). (a ~> b) -> Dual b ~> Dual a Source Comments #

dualInv :: forall (a :: BOOL) (b :: BOOL). (Ob a, Ob b) => (Dual a ~> Dual b) -> b ~> a Source Comments #

linDist :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b, Ob c) => ((a ** b) ~> Dual c) -> a ~> Dual (b ** c) Source Comments #

linDistInv :: forall (a :: BOOL) (b :: BOOL) (c :: BOOL). (Ob a, Ob b, Ob c) => (a ~> Dual (b ** c)) -> (a ** b) ~> Dual c Source Comments #

Closed BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type (a :: BOOL) ~~> (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type (a :: BOOL) ~~> (b :: BOOL) = ExpSA a b

Methods

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

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

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

(^^^) :: forall (a :: BOOL) (b :: BOOL) (x :: BOOL) (y :: BOOL). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Comments #

HasInitialObject BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.Bool type InitialObject = 'FLS

Methods

initiate :: forall (a :: BOOL). Ob a => (InitialObject :: BOOL) ~> a Source Comments #

HasTerminalObject BOOL Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.Bool type TerminalObject = 'TRU

Methods

terminate :: forall (a :: BOOL). Ob a => a ~> (TerminalObject :: BOOL) Source Comments #

Promonad Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

id :: forall (a :: BOOL). Ob a => Booleans a a Source Comments #

(.) :: forall (b :: BOOL) (c :: BOOL) (a :: BOOL). Booleans b c -> Booleans a b -> Booleans a c Source Comments #

Ob a => Comonoid (a :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

counit :: a ~> (Unit :: BOOL) Source Comments #

comult :: a ~> (a ** a) Source Comments #

Monoid 'TRU Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

mempty :: (Unit :: BOOL) ~> 'TRU Source Comments #

mappend :: ('TRU ** 'TRU) ~> 'TRU Source Comments #

ThinProfunctor Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type HasArrow Booleans (a :: BOOL) (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type HasArrow Booleans (a :: BOOL) (b :: BOOL) = IsBoolArr a b

Methods

arr :: forall (a :: BOOL) (b :: BOOL). (Ob a, Ob b, HasArrow Booleans a b) => Booleans a b Source Comments #

withArr :: forall (a :: BOOL) (b :: BOOL) r. Booleans a b -> (HasArrow Booleans a b => r) -> r Source Comments #

MonoidalProfunctor Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

par0 :: Booleans (Unit :: BOOL) (Unit :: BOOL) Source Comments #

par :: forall (x1 :: BOOL) (x2 :: BOOL) (y1 :: BOOL) (y2 :: BOOL). Booleans x1 x2 -> Booleans y1 y2 -> Booleans (x1 ** y1) (x2 ** y2) Source Comments #

Profunctor Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

dimap :: forall (c :: BOOL) (a :: BOOL) (b :: BOOL) (d :: BOOL). (c ~> a) -> (b ~> d) -> Booleans a b -> Booleans c d Source Comments #

(\\) :: forall (a :: BOOL) (b :: BOOL) r. ((Ob a, Ob b) => r) -> Booleans a b -> r Source Comments #

type Unit Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type Unit = TerminalObject :: BOOL

type (~>) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type (~>) = Booleans

type InitialObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type InitialObject = 'FLS

type TerminalObject Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type TerminalObject = 'TRU

type Ob (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type Ob (b :: BOOL) = IsBool b

type Dual 'FLS Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type Dual 'FLS = 'TRU

type Dual 'TRU Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type Dual 'TRU = 'FLS

type (a :: BOOL) ** (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

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

type 'FLS || (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type 'FLS || (b :: BOOL) = b

type 'TRU || (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type 'TRU || (b :: BOOL) = 'TRU

type (a :: BOOL) || 'FLS Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type (a :: BOOL) || 'FLS = a

type (a :: BOOL) || 'TRU Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type (a :: BOOL) || 'TRU = 'TRU

type 'FLS && (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type 'FLS && (b :: BOOL) = 'FLS

type 'TRU && (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type 'TRU && (b :: BOOL) = b

type (a :: BOOL) && 'FLS Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type (a :: BOOL) && 'FLS = 'FLS

type (a :: BOOL) && 'TRU Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type (a :: BOOL) && 'TRU = a

type (a :: BOOL) ~~> (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type (a :: BOOL) ~~> (b :: BOOL) = ExpSA a b

type HasArrow Booleans (a :: BOOL) (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type HasArrow Booleans (a :: BOOL) (b :: BOOL) = IsBoolArr a b

data Booleans (a :: BOOL) (b :: BOOL) where Source Comments #

Constructors

Fls :: Booleans 'FLS 'FLS
F2T :: Booleans 'FLS 'TRU
Tru :: Booleans 'TRU 'TRU

Instances

Instances details

Promonad Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

id :: forall (a :: BOOL). Ob a => Booleans a a Source Comments #

(.) :: forall (b :: BOOL) (c :: BOOL) (a :: BOOL). Booleans b c -> Booleans a b -> Booleans a c Source Comments #

ThinProfunctor Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Associated Types

type HasArrow Booleans (a :: BOOL) (b :: BOOL)
Instance details Defined in Proarrow.Category.Instance.Bool type HasArrow Booleans (a :: BOOL) (b :: BOOL) = IsBoolArr a b

Methods

arr :: forall (a :: BOOL) (b :: BOOL). (Ob a, Ob b, HasArrow Booleans a b) => Booleans a b Source Comments #

withArr :: forall (a :: BOOL) (b :: BOOL) r. Booleans a b -> (HasArrow Booleans a b => r) -> r Source Comments #

MonoidalProfunctor Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

par0 :: Booleans (Unit :: BOOL) (Unit :: BOOL) Source Comments #

par :: forall (x1 :: BOOL) (x2 :: BOOL) (y1 :: BOOL) (y2 :: BOOL). Booleans x1 x2 -> Booleans y1 y2 -> Booleans (x1 ** y1) (x2 ** y2) Source Comments #

Profunctor Booleans Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

Methods

dimap :: forall (c :: BOOL) (a :: BOOL) (b :: BOOL) (d :: BOOL). (c ~> a) -> (b ~> d) -> Booleans a b -> Booleans c d Source Comments #

(\\) :: forall (a :: BOOL) (b :: BOOL) r. ((Ob a, Ob b) => r) -> Booleans a b -> r Source Comments #

type HasArrow Booleans (a :: BOOL) (b :: BOOL) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Bool

type HasArrow Booleans (a :: BOOL) (b :: BOOL) = IsBoolArr a b

class IsBool (Dual b) => IsBool (b :: BOOL) where Source Comments #

Methods

boolId :: b ~> b Source Comments #

Instances

Instances details

IsBool 'FLS Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods boolId :: 'FLS ~> 'FLS Source Comments #
IsBool 'TRU Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods boolId :: 'TRU ~> 'TRU Source Comments #

class IsBoolArr (a :: BOOL) (b :: BOOL) where Source Comments #

Methods

boolArr :: a ~> b Source Comments #

Instances

Instances details

IsBoolArr 'FLS 'FLS Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods boolArr :: 'FLS ~> 'FLS Source Comments #
IsBoolArr 'FLS 'TRU Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods boolArr :: 'FLS ~> 'TRU Source Comments #
IsBoolArr 'TRU 'TRU Source Comments #
Instance details Defined in Proarrow.Category.Instance.Bool Methods boolArr :: 'TRU ~> 'TRU Source Comments #