Safe Haskell	None
Language	Haskell2010

Proarrow.Object.BinaryProduct

Contents

Orphan instances

Documentation

class CategoryOf k => HasBinaryProducts k where Source Comments #

Minimal complete definition

(fst | fst'), (snd | snd'), (&&&)

Associated Types

type (a :: k) && (b :: k) :: k infixl 5 Source Comments #

Methods

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

fst' :: forall (a :: k) (a' :: k) (b :: k). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: k) (b :: k) (b' :: k). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: k) (x :: k) (y :: k). (a ~> x) -> (a ~> y) -> a ~> (x && y) infixl 5 Source Comments #

(***) :: forall (a :: k) (b :: k) (x :: k) (y :: k). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) infixl 5 Source Comments #

Instances

Instances details

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

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

fst' :: forall (a :: BOOL) (a' :: BOOL) (b :: BOOL). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: BOOL) (b :: BOOL) (b' :: BOOL). Obj a -> (b ~> 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 #

HasBinaryProducts KIND Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Cat

Associated Types

type (l :: KIND) && (r :: KIND)
Instance details Defined in Proarrow.Category.Instance.Cat type (l :: KIND) && (r :: KIND) = 'K (UN 'K l, UN 'K r)

Methods

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

fst' :: forall (a :: KIND) (a' :: KIND) (b :: KIND). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: KIND) (b :: KIND) (b' :: KIND). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts CONSTRAINT Source Comments #

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

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

fst' :: forall (a :: CONSTRAINT) (a' :: CONSTRAINT) (b :: CONSTRAINT). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: CONSTRAINT) (b :: CONSTRAINT) (b' :: CONSTRAINT). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts LINEAR Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Linear

Associated Types

type ('L a :: LINEAR) && ('L b :: LINEAR)
Instance details Defined in Proarrow.Category.Instance.Linear type ('L a :: LINEAR) && ('L b :: LINEAR) = 'L (With a b)

Methods

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

fst' :: forall (a :: LINEAR) (a' :: LINEAR) (b :: LINEAR). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: LINEAR) (b :: LINEAR) (b' :: LINEAR). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts POINTED Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type ('P a :: POINTED) && ('P b :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type ('P a :: POINTED) && ('P b :: POINTED) = 'P (These a b)

Methods

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

fst' :: forall (a :: POINTED) (a' :: POINTED) (b :: POINTED). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: POINTED) (b :: POINTED) (b' :: POINTED). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts () Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type '() && '()
Instance details Defined in Proarrow.Object.BinaryProduct type '() && '() = '()

Methods

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

fst' :: forall (a :: ()) (a' :: ()) (b :: ()). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: ()) (b :: ()) (b' :: ()). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts Type Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type (a :: Type) && (b :: Type)
Instance details Defined in Proarrow.Object.BinaryProduct type (a :: Type) && (b :: Type) = (a, b)

Methods

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

fst' :: (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts (FIN ('S n)) => HasBinaryProducts (FIN ('S ('S n))) Source Comments #

Minimum

Instance details

Defined in Proarrow.Category.Instance.Fin

Methods

fst :: forall (a :: FIN ('S ('S n))) (b :: FIN ('S ('S n))). (Ob a, Ob b) => (a && b) ~> a Source Comments #

fst' :: forall (a :: FIN ('S ('S n))) (a' :: FIN ('S ('S n))) (b :: FIN ('S ('S n))). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

snd :: forall (a :: FIN ('S ('S n))) (b :: FIN ('S ('S n))). (Ob a, Ob b) => (a && b) ~> b Source Comments #

snd' :: forall (a :: FIN ('S ('S n))) (b :: FIN ('S ('S n))) (b' :: FIN ('S ('S n))). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: FIN ('S ('S n))) (x :: FIN ('S ('S n))) (y :: FIN ('S ('S n))). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: FIN ('S ('S n))) (b :: FIN ('S ('S n))) (x :: FIN ('S ('S n))) (y :: FIN ('S ('S n))). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

HasBinaryProducts (FIN ('S 'Z)) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Fin

Associated Types

type ('FZ :: FIN ('S 'Z)) && ('FZ :: FIN ('S 'Z))
Instance details Defined in Proarrow.Category.Instance.Fin type ('FZ :: FIN ('S 'Z)) && ('FZ :: FIN ('S 'Z)) = 'FZ :: FIN ('S 'Z)

Methods

fst :: forall (a :: FIN ('S 'Z)) (b :: FIN ('S 'Z)). (Ob a, Ob b) => (a && b) ~> a Source Comments #

fst' :: forall (a :: FIN ('S 'Z)) (a' :: FIN ('S 'Z)) (b :: FIN ('S 'Z)). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

snd :: forall (a :: FIN ('S 'Z)) (b :: FIN ('S 'Z)). (Ob a, Ob b) => (a && b) ~> b Source Comments #

snd' :: forall (a :: FIN ('S 'Z)) (b :: FIN ('S 'Z)) (b' :: FIN ('S 'Z)). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: FIN ('S 'Z)) (x :: FIN ('S 'Z)) (y :: FIN ('S 'Z)). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: FIN ('S 'Z)) (b :: FIN ('S 'Z)) (x :: FIN ('S 'Z)) (y :: FIN ('S 'Z)). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

HasBinaryProducts (FIN 'Z) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Fin

Associated Types

type (a :: FIN 'Z) && (b :: FIN 'Z)
Instance details Defined in Proarrow.Category.Instance.Fin type (a :: FIN 'Z) && (b :: FIN 'Z) = a

Methods

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

fst' :: forall (a :: FIN 'Z) (a' :: FIN 'Z) (b :: FIN 'Z). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: FIN 'Z) (b :: FIN 'Z) (b' :: FIN 'Z). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: FIN 'Z) (x :: FIN 'Z) (y :: FIN 'Z). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

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

Num a => HasBinaryProducts (MatK a) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Mat

Methods

fst :: forall (a0 :: MatK a) (b :: MatK a). (Ob a0, Ob b) => (a0 && b) ~> a0 Source Comments #

fst' :: forall (a0 :: MatK a) (a' :: MatK a) (b :: MatK a). (a0 ~> a') -> Obj b -> (a0 && b) ~> a' Source Comments #

snd :: forall (a0 :: MatK a) (b :: MatK a). (Ob a0, Ob b) => (a0 && b) ~> b Source Comments #

snd' :: forall (a0 :: MatK a) (b :: MatK a) (b' :: MatK a). Obj a0 -> (b ~> b') -> (a0 && b) ~> b' Source Comments #

(&&&) :: forall (a0 :: MatK a) (x :: MatK a) (y :: MatK a). (a0 ~> x) -> (a0 ~> y) -> a0 ~> (x && y) Source Comments #

(***) :: forall (a0 :: MatK a) (b :: MatK a) (x :: MatK a) (y :: MatK a). (a0 ~> x) -> (b ~> y) -> (a0 && b) ~> (x && y) Source Comments #

HasBinaryProducts (POCATK Constraint) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.PreorderAsCategory

Associated Types

type (l :: POCATK Constraint) && (r :: POCATK Constraint)
Instance details Defined in Proarrow.Category.Instance.PreorderAsCategory type (l :: POCATK Constraint) && (r :: POCATK Constraint) = 'PC (UN ('PC :: Constraint -> POCATK Constraint) l, UN ('PC :: Constraint -> POCATK Constraint) r)

Methods

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

fst' :: forall (a :: POCATK Constraint) (a' :: POCATK Constraint) (b :: POCATK Constraint). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: POCATK Constraint) (b :: POCATK Constraint) (b' :: POCATK Constraint). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryCoproducts k => HasBinaryProducts (OPPOSITE k) Source Comments #

Instance details

Defined in Proarrow.Category.Opposite

Methods

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

fst' :: forall (a :: OPPOSITE k) (a' :: OPPOSITE k) (b :: OPPOSITE k). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: OPPOSITE k) (b :: OPPOSITE k) (b' :: OPPOSITE k). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

BiCCC k => HasBinaryProducts (FK k) Source Comments #

Instance details

Defined in Proarrow.Helper.CCC

Methods

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

fst' :: forall (a :: FK k) (a' :: FK k) (b :: FK k). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: FK k) (b :: FK k) (b' :: FK k). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

HasBinaryProducts k => HasBinaryProducts (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

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

fst' :: forall (a :: PROD k) (a' :: PROD k) (b :: PROD k). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: PROD k) (b :: PROD k) (b' :: PROD k). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

(CategoryOf j, CategoryOf k) => HasBinaryProducts (PRO j k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

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

fst' :: forall (a :: PRO j k) (a' :: PRO j k) (b :: PRO j k). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: PRO j k) (b :: PRO j k) (b' :: PRO j k). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: PRO j k) (x :: PRO j k) (y :: PRO j k). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

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

(HasBinaryProducts j, HasBinaryProducts k) => HasBinaryProducts (j, k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

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

fst' :: forall (a :: (j, k)) (a' :: (j, k)) (b :: (j, k)). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: (j, k)) (b :: (j, k)) (b' :: (j, k)). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: (j, k)) (x :: (j, k)) (y :: (j, k)). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

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

HasBinaryProducts (k1 -> Type) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Methods

fst :: forall (a :: k1 -> Type) (b :: k1 -> Type). (Ob a, Ob b) => (a && b) ~> a Source Comments #

fst' :: forall (a :: k1 -> Type) (a' :: k1 -> Type) (b :: k1 -> Type). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

snd :: forall (a :: k1 -> Type) (b :: k1 -> Type). (Ob a, Ob b) => (a && b) ~> b Source Comments #

snd' :: forall (a :: k1 -> Type) (b :: k1 -> Type) (b' :: k1 -> Type). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

(&&&) :: forall (a :: k1 -> Type) (x :: k1 -> Type) (y :: k1 -> Type). (a ~> x) -> (a ~> y) -> a ~> (x && y) Source Comments #

(***) :: forall (a :: k1 -> Type) (b :: k1 -> Type) (x :: k1 -> Type) (y :: k1 -> Type). (a ~> x) -> (b ~> y) -> (a && b) ~> (x && y) Source Comments #

first :: forall {k} (c :: k) (a :: k) (b :: k). (HasBinaryProducts k, Ob c) => (a ~> b) -> (a && c) ~> (b && c) Source Comments #

second :: forall {k} (c :: k) (a :: k) (b :: k). (HasBinaryProducts k, Ob c) => (a ~> b) -> (c && a) ~> (c && b) Source Comments #

diag :: forall {k} (a :: k). (HasBinaryProducts k, Ob a) => a ~> (a && a) Source Comments #

type HasProducts k = (HasTerminalObject k, HasBinaryProducts k) Source Comments #

class (a ** b) ~ (a && b) => TensorIsProduct (a :: k) (b :: k) Source Comments #

Instances

Instances details

(a ** b) ~ (a && b) => TensorIsProduct (a :: k) (b :: k) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct

class (HasProducts k, Monoidal k, (Unit :: k) ~ (TerminalObject :: k), forall (a :: k) (b :: k). TensorIsProduct a b) => Cartesian k Source Comments #

Instances

Instances details

(HasProducts k, Monoidal k, (Unit :: k) ~ (TerminalObject :: k), forall (a :: k) (b :: k). TensorIsProduct a b) => Cartesian k Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct

leftUnitorProd :: forall {k} (a :: k). (HasProducts k, Ob a) => ((TerminalObject :: k) && a) ~> a Source Comments #

leftUnitorProdInv :: forall {k} (a :: k). (HasProducts k, Ob a) => a ~> ((TerminalObject :: k) && a) Source Comments #

rightUnitorProd :: forall {k} (a :: k). (HasProducts k, Ob a) => (a && (TerminalObject :: k)) ~> a Source Comments #

rightUnitorProdInv :: forall {k} (a :: k). (HasProducts k, Ob a) => a ~> (a && (TerminalObject :: k)) Source Comments #

associatorProd :: forall {k} (a :: k) (b :: k) (c :: k). (HasProducts k, Ob a, Ob b, Ob c) => ((a && b) && c) ~> (a && (b && c)) Source Comments #

associatorProdInv :: forall {k} (a :: k) (b :: k) (c :: k). (HasProducts k, Ob a, Ob b, Ob c) => (a && (b && c)) ~> ((a && b) && c) Source Comments #

swapProd' :: forall k (a :: k) (a' :: k) (b :: k) (b' :: k). HasBinaryProducts k => (a ~> a') -> (b ~> b') -> (a && b) ~> (b' && a') Source Comments #

swapProd :: forall k (a :: k) (b :: k). (HasBinaryProducts k, Ob a, Ob b) => (a && b) ~> (b && a) Source Comments #

newtype PROD k Source Comments #

Constructors

PR k

Instances

Instances details

HasProducts k => Monoidal (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type Unit
Instance details Defined in Proarrow.Object.BinaryProduct type Unit = TerminalObject :: PROD k

Methods

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

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

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

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

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

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

HasProducts k => SymMonoidal (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

swap' :: forall (a :: PROD k) (a' :: PROD k) (b :: PROD k) (b' :: PROD k). (a ~> a') -> (b ~> b') -> (a ** b) ~> (b' ** a') Source Comments #

BiCCC k => Distributive (PROD k) Source Comments #

Instance details

Defined in Proarrow.Category.Monoidal.Distributive

Methods

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

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

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

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

CategoryOf k => CategoryOf (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type (~>)
Instance details Defined in Proarrow.Object.BinaryProduct type (~>) = Prod ((~>) :: CAT k)

HasBinaryCoproducts k => HasBinaryCoproducts (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryCoproduct

Methods

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

lft' :: forall (a :: PROD k) (a' :: PROD k) (b :: PROD k). (a ~> a') -> Obj b -> a ~> (a' || b) Source Comments #

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

rgt' :: forall (a :: PROD k) (b :: PROD k) (b' :: PROD k). Obj a -> (b ~> b') -> b ~> (a || b') Source Comments #

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

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

HasBinaryProducts k => HasBinaryProducts (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

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

fst' :: forall (a :: PROD k) (a' :: PROD k) (b :: PROD k). (a ~> a') -> Obj b -> (a && b) ~> a' Source Comments #

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

snd' :: forall (a :: PROD k) (b :: PROD k) (b' :: PROD k). Obj a -> (b ~> b') -> (a && b) ~> b' Source Comments #

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

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

(CategoryOf j, CategoryOf k) => Closed (PROD (PRO j k)) Source Comments #

Instance details

Defined in Proarrow.Object.Exponential

Methods

curry' :: forall (a :: PROD (PRO j k)) (b :: PROD (PRO j k)) (c :: PROD (PRO j k)). Obj a -> Obj b -> ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

uncurry' :: forall (b :: PROD (PRO j k)) (c :: PROD (PRO j k)) (a :: PROD (PRO j k)). Obj b -> Obj c -> (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

(^^^) :: forall (b :: PROD (PRO j k)) (y :: PROD (PRO j k)) (x :: PROD (PRO j k)) (a :: PROD (PRO j k)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Comments #

CategoryOf k1 => Closed (PROD (k1 -> Type)) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

Methods

curry' :: forall (a :: PROD (k1 -> Type)) (b :: PROD (k1 -> Type)) (c :: PROD (k1 -> Type)). Obj a -> Obj b -> ((a ** b) ~> c) -> a ~> (b ~~> c) Source Comments #

uncurry' :: forall (b :: PROD (k1 -> Type)) (c :: PROD (k1 -> Type)) (a :: PROD (k1 -> Type)). Obj b -> Obj c -> (a ~> (b ~~> c)) -> (a ** b) ~> c Source Comments #

(^^^) :: forall (b :: PROD (k1 -> Type)) (y :: PROD (k1 -> Type)) (x :: PROD (k1 -> Type)) (a :: PROD (k1 -> Type)). (b ~> y) -> (x ~> a) -> (a ~~> b) ~> (x ~~> y) Source Comments #

HasInitialObject k => HasInitialObject (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type InitialObject
Instance details Defined in Proarrow.Object.BinaryProduct type InitialObject = 'PR (InitialObject :: k)

Methods

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

initiate' :: forall (a' :: PROD k) (a :: PROD k). (a' ~> a) -> (InitialObject :: PROD k) ~> a Source Comments #

HasTerminalObject k => HasTerminalObject (PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Object.BinaryProduct type TerminalObject = 'PR (TerminalObject :: k)

Methods

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

terminate' :: forall (a :: PROD k) (a' :: PROD k). (a ~> a') -> a ~> (TerminalObject :: PROD k) Source Comments #

(HasProducts k, Category cat) => MonoidalProfunctor (Prod cat :: PROD k -> PROD k -> Type) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

par0 :: Prod cat (Unit :: PROD k) (Unit :: PROD k) Source Comments #

par :: forall (x1 :: PROD k) (x2 :: PROD k) (y1 :: PROD k) (y2 :: PROD k). Prod cat x1 x2 -> Prod cat y1 y2 -> Prod cat (x1 ** y1) (x2 ** y2) Source Comments #

Profunctor p => Profunctor (Prod p :: PROD k -> PROD j -> Type) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

dimap :: forall (c :: PROD k) (a :: PROD k) (b :: PROD j) (d :: PROD j). (c ~> a) -> (b ~> d) -> Prod p a b -> Prod p c d Source Comments #

(\\) :: forall (a :: PROD k) (b :: PROD j) r. ((Ob a, Ob b) => r) -> Prod p a b -> r Source Comments #

(HasProducts k, Ob a) => Comonoid ('PR a :: PROD k) Source Comments #

Instance details

Defined in Proarrow.Monoid

Methods

counit :: 'PR a ~> (Unit :: PROD k) Source Comments #

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

Profunctor p => Monoid ('PR (FreeMonoid p) :: PROD (k -> k -> Type)) Source Comments #

Instance details

Defined in Proarrow.Profunctor.Free

Methods

mempty :: (Unit :: PROD (k +-> k)) ~> 'PR (FreeMonoid p) Source Comments #

mappend :: ('PR (FreeMonoid p) ** 'PR (FreeMonoid p)) ~> 'PR (FreeMonoid p) Source Comments #

Promonad p => Promonad (Prod p :: PROD j -> PROD j -> Type) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

Methods

id :: forall (a :: PROD j). Ob a => Prod p a a Source Comments #

(.) :: forall (b :: PROD j) (c :: PROD j) (a :: PROD j). Prod p b c -> Prod p a b -> Prod p a c Source Comments #

type UN ('PR :: j -> PROD j) ('PR k :: PROD j) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type UN ('PR :: j -> PROD j) ('PR k :: PROD j) = k

type Unit Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type Unit = TerminalObject :: PROD k

type (~>) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type (~>) = Prod ((~>) :: CAT k)

type InitialObject Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type InitialObject = 'PR (InitialObject :: k)

type TerminalObject Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type TerminalObject = 'PR (TerminalObject :: k)

type Ob (a :: PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type Ob (a :: PROD k) = (Is ('PR :: k -> PROD k) a, Ob (UN ('PR :: k -> PROD k) a))

type (a :: PROD k) ** (b :: PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type (a :: PROD k) ** (b :: PROD k) = a && b

type (a :: PROD k) && (b :: PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryProduct

type (a :: PROD k) && (b :: PROD k) = 'PR (UN ('PR :: k -> PROD k) a && UN ('PR :: k -> PROD k) b)

type (p :: PROD (j -> k -> Type)) ~~> (q :: PROD (j -> k -> Type)) Source Comments #

Instance details

Defined in Proarrow.Object.Exponential

type (p :: PROD (j -> k -> Type)) ~~> (q :: PROD (j -> k -> Type)) = 'PR (UN ('PR :: (j -> k -> Type) -> PROD (j -> k -> Type)) p :~>: UN ('PR :: (j -> k -> Type) -> PROD (j -> k -> Type)) q)

type (f :: PROD (k1 -> Type)) ~~> (g :: PROD (k1 -> Type)) Source Comments #

Instance details

Defined in Proarrow.Category.Instance.Nat

type (f :: PROD (k1 -> Type)) ~~> (g :: PROD (k1 -> Type)) = 'PR (UN ('PR :: (k1 -> Type) -> PROD (k1 -> Type)) f :~>: UN ('PR :: (k1 -> Type) -> PROD (k1 -> Type)) g)

type ('PR a :: PROD k) || ('PR b :: PROD k) Source Comments #

Instance details

Defined in Proarrow.Object.BinaryCoproduct

type ('PR a :: PROD k) || ('PR b :: PROD k) = 'PR (a || b)

data Prod (p :: j +-> k) (a :: PROD k) (b :: PROD j) where Source Comments #

Constructors

Prod
Fields :: forall {j} {k} (p :: j +-> k) (a1 :: k) (b1 :: j). { unProd :: p a1 b1 } -> Prod p ('PR a1) ('PR b1)

Instances

Instances details

(HasProducts k, Category cat) => MonoidalProfunctor (Prod cat :: PROD k -> PROD k -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods par0 :: Prod cat (Unit :: PROD k) (Unit :: PROD k) Source Comments # par :: forall (x1 :: PROD k) (x2 :: PROD k) (y1 :: PROD k) (y2 :: PROD k). Prod cat x1 x2 -> Prod cat y1 y2 -> Prod cat (x1 y1) (x2 y2) Source Comments #
Profunctor p => Profunctor (Prod p :: PROD k -> PROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods dimap :: forall (c :: PROD k) (a :: PROD k) (b :: PROD j) (d :: PROD j). (c ~> a) -> (b ~> d) -> Prod p a b -> Prod p c d Source Comments # (\\) :: forall (a :: PROD k) (b :: PROD j) r. ((Ob a, Ob b) => r) -> Prod p a b -> r Source Comments #
Promonad p => Promonad (Prod p :: PROD j -> PROD j -> Type) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct Methods id :: forall (a :: PROD j). Ob a => Prod p a a Source Comments # (.) :: forall (b :: PROD j) (c :: PROD j) (a :: PROD j). Prod p b c -> Prod p a b -> Prod p a c Source Comments #

class Act a b ~ (a && b) => ActIsProd (a :: k) (b :: k) Source Comments #

Instances

Instances details

Act a b ~ (a && b) => ActIsProd (a :: k) (b :: k) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct

class (Strong ((~>) :: CAT k) p, HasProducts k, forall (a :: k) (b :: k). ActIsProd a b) => StrongProd (p :: CAT k) Source Comments #

Instances

Instances details

(Strong ((~>) :: CAT k) p, HasProducts k, forall (a :: k) (b :: k). ActIsProd a b) => StrongProd (p :: k +-> k) Source Comments #
Instance details Defined in Proarrow.Object.BinaryProduct

first' :: forall {k} p (c :: k) (a :: k) (b :: k). (StrongProd p, Ob c) => p a b -> p (a && c) (b && c) Source Comments #

second' :: forall {k} p (c :: k) (a :: k) (b :: k). (StrongProd p, Ob c) => p a b -> p (c && a) (c && b) Source Comments #

Orphan instances

Monoidal () Source Comments #

Instance details

Associated Types

type Unit
Instance details Defined in Proarrow.Object.BinaryProduct type Unit = TerminalObject :: ()
type (a :: ()) ** (b :: ())
Instance details Defined in Proarrow.Object.BinaryProduct type (a :: ()) ** (b :: ()) = a && b

Methods

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

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

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

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

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

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

Monoidal Type Source Comments #

Instance details

Associated Types

type Unit
Instance details Defined in Proarrow.Object.BinaryProduct type Unit = TerminalObject :: Type
type (a :: Type) ** (b :: Type)
Instance details Defined in Proarrow.Object.BinaryProduct type (a :: Type) ** (b :: Type) = a && b

Methods

leftUnitor :: Ob a => ((Unit :: Type) ** a) ~> a Source Comments #

leftUnitorInv :: Ob a => a ~> ((Unit :: Type) ** a) Source Comments #

rightUnitor :: Ob a => (a ** (Unit :: Type)) ~> a Source Comments #

rightUnitorInv :: Ob a => a ~> (a ** (Unit :: Type)) Source Comments #

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

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

SymMonoidal () Source Comments #

Instance details

Methods

swap' :: forall (a :: ()) (a' :: ()) (b :: ()) (b' :: ()). (a ~> a') -> (b ~> b') -> (a ** b) ~> (b' ** a') Source Comments #

SymMonoidal Type Source Comments #

Instance details

Methods

swap' :: (a ~> a') -> (b ~> b') -> (a ** b) ~> (b' ** a') Source Comments #

TracedMonoidalProfunctor Unit Source Comments #

Instance details

Methods

trace :: forall (u :: ()) (x :: ()) (y :: ()). (Ob x, Ob y, Ob u) => Unit (x ** u) (y ** u) -> Unit x y Source Comments #

trace' :: forall (x :: ()) (x' :: ()) (y :: ()) (y' :: ()) (u :: ()) (u' :: ()). (x ~> x') -> (y ~> y') -> (u ~> u') -> Unit (x' ** u') (y ** u) -> Unit x y' Source Comments #

MonoidalAction () () Source Comments #

Instance details

Associated Types

type Act (p :: ()) (x :: ())
Instance details Defined in Proarrow.Object.BinaryProduct type Act (p :: ()) (x :: ()) = p ** x

Methods

unitor :: forall (x :: ()). Ob x => Act (Unit :: ()) x ~> x Source Comments #

unitorInv :: forall (x :: ()). Ob x => x ~> Act (Unit :: ()) x Source Comments #

multiplicator :: forall (a :: ()) (b :: ()) (x :: ()). (Ob a, Ob b, Ob x) => Act a (Act b x) ~> Act (a ** b) x Source Comments #

multiplicatorInv :: forall (a :: ()) (b :: ()) (x :: ()). (Ob a, Ob b, Ob x) => Act (a ** b) x ~> Act a (Act b x) Source Comments #

MonoidalAction Type Type Source Comments #

Instance details

Associated Types

type Act (p :: Type) (x :: Type)
Instance details Defined in Proarrow.Object.BinaryProduct type Act (p :: Type) (x :: Type) = p ** x

Methods

unitor :: Ob x => Act (Unit :: Type) x ~> x Source Comments #

unitorInv :: Ob x => x ~> Act (Unit :: Type) x Source Comments #

multiplicator :: (Ob a, Ob b, Ob x) => Act a (Act b x) ~> Act (a ** b) x Source Comments #

multiplicatorInv :: (Ob a, Ob b, Ob x) => Act (a ** b) x ~> Act a (Act b x) Source Comments #

MonoidalProfunctor Unit Source Comments #

Instance details

Methods

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

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

Strong Unit Unit Source Comments #

Instance details

Methods

act :: forall (a :: ()) (b :: ()) (x :: ()) (y :: ()). Unit a b -> Unit x y -> Unit (Act a x) (Act b y) Source Comments #

Strong (->) (->) Source Comments #

Instance details

Methods

act :: (a -> b) -> (x -> y) -> Act a x -> Act b y Source Comments #

MonoidalProfunctor (->) Source Comments #

Instance details

Methods

par0 :: (Unit :: Type) -> (Unit :: Type) Source Comments #

par :: (x1 -> x2) -> (y1 -> y2) -> (x1 ** y1) -> (x2 ** y2) Source Comments #

TracedMonoidalProfunctor (->) Source Comments #

Instance details

Methods

trace :: forall u x y. (Ob x, Ob y, Ob u) => ((x ** u) -> (y ** u)) -> x -> y Source Comments #

trace' :: (x ~> x') -> (y ~> y') -> (u ~> u') -> ((x' ** u') -> (y ** u)) -> x -> y' Source Comments #