Safe Haskell	None
Language	GHC2024

Proarrow.Category.Instance.PointedHask

Synopsis

data POINTED = P Type
data Pointed (a :: POINTED) (b :: POINTED) where
- Pt :: forall a1 b1. {..} -> Pointed ('P a1) ('P b1)
toHask :: ('P a ~> 'P b) -> Maybe a -> Maybe b
data These a b
- = This a
- | That b
- | These a b
memptyDefault :: Monoid a => (Unit :: POINTED) ~> 'P a
mappendDefault :: Monoid a => ('P a ** 'P a) ~> 'P a
underlyingPt :: forall k (a :: k) (b :: k). HasZeroObject k => (a ~> b) -> (Unit :: POINTED) ~> 'P (a ~> b)
enrichedPt :: forall k (a :: k) (b :: k). (Ob a, Ob b, HasZeroObject k) => ((Unit :: POINTED) ~> 'P (a ~> b)) -> a ~> b
compPt :: forall k (a :: k) (b :: k) (c :: k). (Ob a, Ob b, Ob c, HasZeroObject k) => ('P (b ~> c) ** 'P (a ~> b)) ~> 'P (a ~> c)
data FromPointed (f :: Type -> Type) (a :: POINTED) where
- FromPointed :: forall (f :: Type -> Type) a1. {..} -> FromPointed f ('P a1)
type Filterable (f :: Type -> Type) = Functor (FromPointed f)
mapMaybe :: Filterable f => (a -> Maybe b) -> f a -> f b
type Align (f :: Type -> Type) = Applicative (FromProd (FromPointed f))
alignWith :: Align f => (These a b -> Maybe c) -> f a -> f b -> f c
nil :: Align f => f a

Documentation

data POINTED Source Github #

Constructors

P Type

Instances

Instances details

Monoidal POINTED Source Github #

The smash product of pointed sets. Monoids relative to the smash product are absorption monoids.

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type Unit
Instance details Defined in Proarrow.Category.Instance.PointedHask type Unit = 'P ()
type ('P a :: POINTED) ** ('P b :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type ('P a :: POINTED) ** ('P b :: POINTED) = 'P (a, b)

Methods

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

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

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

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

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

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

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

SymMonoidal POINTED Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

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

CopyDiscard POINTED Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

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

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

HasBinaryCoproducts POINTED Source Github #

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 (a \|\| b)

Methods

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

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

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

(|||) :: forall (x :: POINTED) (a :: POINTED) (y :: POINTED). (x ~> a) -> (y ~> a) -> (x || y) ~> a Source Github #

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

HasInitialObject POINTED Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type InitialObject
Instance details Defined in Proarrow.Category.Instance.PointedHask type InitialObject = 'P Void

Methods

initiate :: forall (a :: POINTED). Ob a => (InitialObject :: POINTED) ~> a Source Github #

CategoryOf POINTED Source Github #

The category of types with an added point and point-preserving morphisms.

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type (~>)
Instance details Defined in Proarrow.Category.Instance.PointedHask type (~>) = Pointed
type Ob (a :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type Ob (a :: POINTED) = a ~ 'P (UN 'P a)

HasBinaryProducts POINTED Source Github #

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

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

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

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

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

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

HasTerminalObject POINTED Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type TerminalObject
Instance details Defined in Proarrow.Category.Instance.PointedHask type TerminalObject = 'P Void

Methods

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

Copowered Type POINTED Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type (n :: Type) *. ('P a :: POINTED)
Instance details Defined in Proarrow.Category.Instance.PointedHask type (n :: Type) *. ('P a :: POINTED) = 'P (n, a)

Methods

withObCopower :: forall (a :: POINTED) n r. (Ob a, Ob n) => (Ob (n *. a) => r) -> r Source Github #

copower :: forall (a :: POINTED) (b :: POINTED) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> (n *. a) ~> b Source Github #

uncopower :: forall (a :: POINTED) n (b :: POINTED). (Ob a, Ob n) => ((n *. a) ~> b) -> n ~> HomObj Type a b Source Github #

Promonad Pointed Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

id :: forall (a :: POINTED). Ob a => Pointed a a Source Github #

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

Powered Type POINTED Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type ('P a :: POINTED) ^ (n :: Type)
Instance details Defined in Proarrow.Category.Instance.PointedHask type ('P a :: POINTED) ^ (n :: Type) = 'P (n -> Maybe a)

Methods

withObPower :: forall (a :: POINTED) n r. (Ob a, Ob n) => (Ob (a ^ n) => r) -> r Source Github #

power :: forall (a :: POINTED) (b :: POINTED) n. (Ob a, Ob b) => (n ~> HomObj Type a b) -> a ~> (b ^ n) Source Github #

unpower :: forall (b :: POINTED) n (a :: POINTED). (Ob b, Ob n) => (a ~> (b ^ n)) -> n ~> HomObj Type a b Source Github #

MonoidalProfunctor Pointed Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

one :: Pointed (Unit :: POINTED) (Unit :: POINTED) Source Github #

(**) :: forall (x1 :: POINTED) (x2 :: POINTED) (y1 :: POINTED) (y2 :: POINTED). Pointed x1 x2 -> Pointed y1 y2 -> Pointed (x1 ** y1) (x2 ** y2) Source Github #

Profunctor Pointed Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

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

lmap :: forall (c :: POINTED) (a :: POINTED) (b :: POINTED). (c ~> a) -> Pointed a b -> Pointed c b Source Github #

rmap :: forall (b :: POINTED) (d :: POINTED) (a :: POINTED). (b ~> d) -> Pointed a b -> Pointed a d Source Github #

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

Functor (FromPointed (Map k) :: POINTED -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

map :: forall (a :: POINTED) (b :: POINTED). (a ~> b) -> FromPointed (Map k) a ~> FromPointed (Map k) b Source Github #

Functor (FromPointed []) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

map :: forall (a :: POINTED) (b :: POINTED). (a ~> b) -> FromPointed [] a ~> FromPointed [] b Source Github #

Comonoid ('P x :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

counit :: 'P x ~> (Unit :: POINTED) Source Github #

comult :: 'P x ~> ('P x ** 'P x) Source Github #

Monoid ('P Void) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

mempty :: (Unit :: POINTED) ~> 'P Void Source Github #

mappend :: ('P Void ** 'P Void) ~> 'P Void Source Github #

Monoid ('P ()) Source Github #

Conjunction with False = Nothing, True = Just ()

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

mempty :: (Unit :: POINTED) ~> 'P () Source Github #

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

Monoid ('P [a] :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

mempty :: (Unit :: POINTED) ~> 'P [a] Source Github #

mappend :: ('P [a] ** 'P [a]) ~> 'P [a] Source Github #

Ord k => Applicative (FromProd (FromPointed (Map k)) :: PROD POINTED -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

pure :: forall (a :: PROD POINTED). ((Unit :: PROD POINTED) ~> a) -> (Unit :: Type) ~> FromProd (FromPointed (Map k)) a Source Github #

liftA2 :: forall (a :: PROD POINTED) (b :: PROD POINTED) (c :: PROD POINTED). (Ob a, Ob b) => ((a ** b) ~> c) -> (FromProd (FromPointed (Map k)) a ** FromProd (FromPointed (Map k)) b) ~> FromProd (FromPointed (Map k)) c Source Github #

Applicative (FromProd (FromPointed [])) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

pure :: forall (a :: PROD POINTED). ((Unit :: PROD POINTED) ~> a) -> (Unit :: Type) ~> FromProd (FromPointed []) a Source Github #

liftA2 :: forall (a :: PROD POINTED) (b :: PROD POINTED) (c :: PROD POINTED). (Ob a, Ob b) => ((a ** b) ~> c) -> (FromProd (FromPointed []) a ** FromProd (FromPointed []) b) ~> FromProd (FromPointed []) c Source Github #

type Unit Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type Unit = 'P ()

type InitialObject Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type InitialObject = 'P Void

type (~>) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type (~>) = Pointed

type TerminalObject Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type TerminalObject = 'P Void

type Ob (a :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type Ob (a :: POINTED) = a ~ 'P (UN 'P a)

type (n :: Type) *. ('P a :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type (n :: Type) *. ('P a :: POINTED) = 'P (n, a)

type ('P a :: POINTED) ^ (n :: Type) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) ^ (n :: Type) = 'P (n -> Maybe a)

type ('P a :: POINTED) ** ('P b :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) ** ('P b :: POINTED) = 'P (a, b)

type ('P a :: POINTED) || ('P b :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) || ('P b :: POINTED) = 'P (a || b)

type ('P a :: POINTED) && ('P b :: POINTED) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type ('P a :: POINTED) && ('P b :: POINTED) = 'P (These a b)

data Pointed (a :: POINTED) (b :: POINTED) where Source Github #

Constructors

Pt
Fields :: forall a1 b1. { unPt :: a1 -> Maybe b1 } -> Pointed ('P a1) ('P b1)

Instances

Instances details

Promonad Pointed Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods id :: forall (a :: POINTED). Ob a => Pointed a a Source Github # (.) :: forall (b :: POINTED) (c :: POINTED) (a :: POINTED). Pointed b c -> Pointed a b -> Pointed a c Source Github #
MonoidalProfunctor Pointed Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods one :: Pointed (Unit :: POINTED) (Unit :: POINTED) Source Github # () :: forall (x1 :: POINTED) (x2 :: POINTED) (y1 :: POINTED) (y2 :: POINTED). Pointed x1 x2 -> Pointed y1 y2 -> Pointed (x1 y1) (x2 ** y2) Source Github #
Profunctor Pointed Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods dimap :: forall (c :: POINTED) (a :: POINTED) (b :: POINTED) (d :: POINTED). (c ~> a) -> (b ~> d) -> Pointed a b -> Pointed c d Source Github # lmap :: forall (c :: POINTED) (a :: POINTED) (b :: POINTED). (c ~> a) -> Pointed a b -> Pointed c b Source Github # rmap :: forall (b :: POINTED) (d :: POINTED) (a :: POINTED). (b ~> d) -> Pointed a b -> Pointed a d Source Github # (\\) :: forall (a :: POINTED) (b :: POINTED) r. ((Ob a, Ob b) => r) -> Pointed a b -> r Source Github #

toHask :: ('P a ~> 'P b) -> Maybe a -> Maybe b Source Github #

data These a b Source Github #

Constructors

This a
That b
These a b

Instances

Instances details

Generic (These a b) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Associated Types

type Rep (These a b)

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type Rep (These a b) = D1 ('MetaData "These" "Proarrow.Category.Instance.PointedHask" "proarrow-0-inplace" 'False) (C1 ('MetaCons "This" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 a)) :+: (C1 ('MetaCons "That" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 b)) :+: C1 ('MetaCons "These" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 b))))

Methods

from :: These a b -> Rep (These a b) x Github #

to :: Rep (These a b) x -> These a b Github #

(Show a, Show b) => Show (These a b) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

showsPrec :: Int -> These a b -> ShowS Github #

show :: These a b -> String Github #

showList :: [These a b] -> ShowS Github #

(Eq a, Eq b) => Eq (These a b) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

Methods

(==) :: These a b -> These a b -> Bool Github #

(/=) :: These a b -> These a b -> Bool Github #

type Rep (These a b) Source Github #

Instance details

Defined in Proarrow.Category.Instance.PointedHask

type Rep (These a b) = D1 ('MetaData "These" "Proarrow.Category.Instance.PointedHask" "proarrow-0-inplace" 'False) (C1 ('MetaCons "This" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 a)) :+: (C1 ('MetaCons "That" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 b)) :+: C1 ('MetaCons "These" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedStrict) (Rec0 b))))

memptyDefault :: Monoid a => (Unit :: POINTED) ~> 'P a Source Github #

Lift Hask monoids.

mappendDefault :: Monoid a => ('P a ** 'P a) ~> 'P a Source Github #

underlyingPt :: forall k (a :: k) (b :: k). HasZeroObject k => (a ~> b) -> (Unit :: POINTED) ~> 'P (a ~> b) Source Github #

Categories with a zero object can be seen as categories enriched in Pointed.

enrichedPt :: forall k (a :: k) (b :: k). (Ob a, Ob b, HasZeroObject k) => ((Unit :: POINTED) ~> 'P (a ~> b)) -> a ~> b Source Github #

compPt :: forall k (a :: k) (b :: k) (c :: k). (Ob a, Ob b, Ob c, HasZeroObject k) => ('P (b ~> c) ** 'P (a ~> b)) ~> 'P (a ~> c) Source Github #

data FromPointed (f :: Type -> Type) (a :: POINTED) where Source Github #

Constructors

FromPointed
Fields :: forall (f :: Type -> Type) a1. { unFromPointed :: f a1 } -> FromPointed f ('P a1)

Instances

Instances details

Functor (FromPointed (Map k) :: POINTED -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods map :: forall (a :: POINTED) (b :: POINTED). (a ~> b) -> FromPointed (Map k) a ~> FromPointed (Map k) b Source Github #
Functor (FromPointed []) Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods map :: forall (a :: POINTED) (b :: POINTED). (a ~> b) -> FromPointed [] a ~> FromPointed [] b Source Github #
Ord k => Applicative (FromProd (FromPointed (Map k)) :: PROD POINTED -> Type) Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods pure :: forall (a :: PROD POINTED). ((Unit :: PROD POINTED) ~> a) -> (Unit :: Type) ~> FromProd (FromPointed (Map k)) a Source Github # liftA2 :: forall (a :: PROD POINTED) (b :: PROD POINTED) (c :: PROD POINTED). (Ob a, Ob b) => ((a b) ~> c) -> (FromProd (FromPointed (Map k)) a FromProd (FromPointed (Map k)) b) ~> FromProd (FromPointed (Map k)) c Source Github #
Applicative (FromProd (FromPointed [])) Source Github #
Instance details Defined in Proarrow.Category.Instance.PointedHask Methods pure :: forall (a :: PROD POINTED). ((Unit :: PROD POINTED) ~> a) -> (Unit :: Type) ~> FromProd (FromPointed []) a Source Github # liftA2 :: forall (a :: PROD POINTED) (b :: PROD POINTED) (c :: PROD POINTED). (Ob a, Ob b) => ((a b) ~> c) -> (FromProd (FromPointed []) a FromProd (FromPointed []) b) ~> FromProd (FromPointed []) c Source Github #

type Filterable (f :: Type -> Type) = Functor (FromPointed f) Source Github #

mapMaybe :: Filterable f => (a -> Maybe b) -> f a -> f b Source Github #

type Align (f :: Type -> Type) = Applicative (FromProd (FromPointed f)) Source Github #

Not quite Align from the semialign package. This requires being able to dynamically decide per position if it is included in the result. So more like merge from Data.Map.

alignWith :: Align f => (These a b -> Maybe c) -> f a -> f b -> f c Source Github #

nil :: Align f => f a Source Github #