Safe Haskell	None
Language	GHC2024

Proarrow.Promonad.Writer

Synopsis

data Writer (w :: k) (a :: k) (b :: k) where
- Writer :: forall {k} (b :: k) (a :: k) (w :: k). Ob b => (a ~> (w ** b)) -> Writer w a b
traverseWriter :: forall {k} (p :: k +-> k) (w :: k). (Strong (Tensor :: k -> (k, k) -> Type) p, Ob w) => (Writer w :.: p) :~> (p :.: Writer w)
writerComp :: forall {k} (r :: k) (s :: k). (SymMonoidal k, Ob r, Ob s) => (Writer r :.: Writer s) ~> Writer (r ** s)
writerDay :: forall {k} (r :: k) (s :: k). (SymMonoidal k, Ob r, Ob s) => Day (Writer r) (Writer s) ~> Writer (r ** s)
newtype WriterT (w :: k) (p :: k +-> k) (a :: k) (b :: k) where
- WriterT :: forall {k} (p :: k +-> k) (w :: k) (a :: k) (b :: k). (p :.: Writer w) a b -> WriterT w p a b
runWriterT :: forall {k} p (w :: k) (a :: k) (b :: k). Profunctor p => WriterT w p a b -> p a (w ** b)
tell :: forall k (p :: k +-> k) (w :: k). (Promonad p, Monoidal k, Ob w) => WriterT w p w (Unit :: k)
listen :: forall {k} (p :: k +-> k) (w :: k) (a :: k) (b :: k). (Promonad p, Monoidal k, Comonoid w) => WriterT w p a b -> WriterT w p a (w ** b)
censor :: forall {k} (p :: k +-> k) (w :: k) (a :: k) (b :: k). (Monoidal k, Ob w) => (w ~> w) -> WriterT w p a b -> WriterT w p a b

Documentation

data Writer (w :: k) (a :: k) (b :: k) where Source Github #

Constructors

Writer :: forall {k} (b :: k) (a :: k) (w :: k). Ob b => (a ~> (w ** b)) -> Writer w a b

Instances

Instances details

(Ob w, SymMonoidal k) => Strong (Tensor :: k -> (k, k) -> Type) (Writer w :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

Methods

act :: forall (a :: k) (x :: k) (y :: k). Ob a => Writer w x y -> Writer w (Act (Tensor :: k -> (k, k) -> Type) a x) (Act (Tensor :: k -> (k, k) -> Type) a y) Source Github #

(Monoid w, SymMonoidal k) => MonoidalProfunctor (Writer w :: k -> k -> Type) Source Github #

Note: This is only premonoidal, not monoidal, unless the monoid is commutative.

Instance details

Defined in Proarrow.Promonad.Writer

Methods

one :: Writer w (Unit :: k) (Unit :: k) Source Github #

(**) :: forall (x1 :: k) (x2 :: k) (y1 :: k) (y2 :: k). Writer w x1 x2 -> Writer w y1 y2 -> Writer w (x1 ** y1) (x2 ** y2) Source Github #

(Ob w, Monoidal k) => Profunctor (Writer w :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

Methods

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

lmap :: forall (c :: k) (a :: k) (b :: k). (c ~> a) -> Writer w a b -> Writer w c b Source Github #

rmap :: forall (b :: k) (d :: k) (a :: k). (b ~> d) -> Writer w a b -> Writer w a d Source Github #

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

(Ob w, CompactClosed k) => Corepresentable (Writer w :: k -> k -> Type) Source Github #

The cowriter comonad given the Promonad instance.

Instance details

Defined in Proarrow.Promonad.Writer

Methods

coindex :: forall (a :: k) (b :: k). Writer w a b -> (Writer w %% a) ~> b Source Github #

cotabulate :: forall (a :: k) (b :: k). Ob a => ((Writer w %% a) ~> b) -> Writer w a b Source Github #

corepMap :: forall (a :: k) (b :: k). (a ~> b) -> (Writer w %% a) ~> (Writer w %% b) Source Github #

corepUniv :: forall (a :: k). Ob a => Writer w a (Writer w %% a) Source Github #

(Ob w, Monoidal k) => Representable (Writer w :: k -> k -> Type) Source Github #

The writer monad given the Promonad instance.

Instance details

Defined in Proarrow.Promonad.Writer

Methods

index :: forall (a :: k) (b :: k). Writer w a b -> a ~> (Writer w % b) Source Github #

tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> (Writer w % b)) -> Writer w a b Source Github #

repMap :: forall (a :: k) (b :: k). (a ~> b) -> (Writer w % a) ~> (Writer w % b) Source Github #

repUniv :: forall (a :: k). Ob a => Writer w (Writer w % a) a Source Github #

(Ob r, Monoidal k) => Proadjunction (Writer r :: k -> k -> Type) (Reader ('OP r) :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Reader

Methods

unit :: forall (a :: k). Ob a => (Reader ('OP r) :.: Writer r) a a Source Github #

counit :: (Writer r :.: Reader ('OP r)) :~> ((~>) :: CAT k) Source Github #

(SymMonoidal k, Ob a) => IsWriter (Writer a :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Equipment.Stateful

Associated Types

type WithReader (Writer a :: k -> k -> Type)
Instance details Defined in Proarrow.Category.Equipment.Stateful type WithReader (Writer a :: k -> k -> Type) = Reader ('OP a)

(Monoid w, Monoidal k) => Traversable (Writer w :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

Methods

traverse :: forall (p :: k +-> k). StrongDistributiveProfunctor p => (Writer w :.: p) :~> (p :.: Writer w) Source Github #

(Monoid w, Monoidal k) => Promonad (Writer w :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

Methods

id :: forall (a :: k). Ob a => Writer w a a Source Github #

(.) :: forall (b :: k) (c :: k) (a :: k). Writer w b c -> Writer w a b -> Writer w a c Source Github #

(Comonoid w, Monoidal k) => Procomonad (Writer w :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

Methods

proextract :: Writer w :~> ((~>) :: CAT k) Source Github #

produplicate :: Writer w :~> (Writer w :.: Writer w) Source Github #

Monoidal k => Functor (Writer :: k -> k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

Methods

map :: forall (a :: k) (b :: k). (a ~> b) -> Writer a ~> Writer b Source Github #

type (Writer w :: k -> k -> Type) %% (a :: k) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

type (Writer w :: k -> k -> Type) %% (a :: k) = ExpSA w a

type (Writer w :: k -> k -> Type) % (a :: k) Source Github #

Instance details

Defined in Proarrow.Promonad.Writer

type (Writer w :: k -> k -> Type) % (a :: k) = w ** a

type WithReader (Writer a :: k -> k -> Type) Source Github #

Instance details

Defined in Proarrow.Category.Equipment.Stateful

type WithReader (Writer a :: k -> k -> Type) = Reader ('OP a)

traverseWriter :: forall {k} (p :: k +-> k) (w :: k). (Strong (Tensor :: k -> (k, k) -> Type) p, Ob w) => (Writer w :.: p) :~> (p :.: Writer w) Source Github #

A version of traverse specialized to Writer, with fewer requirements on p.

writerComp :: forall {k} (r :: k) (s :: k). (SymMonoidal k, Ob r, Ob s) => (Writer r :.: Writer s) ~> Writer (r ** s) Source Github #

writerDay :: forall {k} (r :: k) (s :: k). (SymMonoidal k, Ob r, Ob s) => Day (Writer r) (Writer s) ~> Writer (r ** s) Source Github #

newtype WriterT (w :: k) (p :: k +-> k) (a :: k) (b :: k) where Source Github #

Constructors

WriterT :: forall {k} (p :: k +-> k) (w :: k) (a :: k) (b :: k). (p :.: Writer w) a b -> WriterT w p a b

Instances

Instances details

(Strong (Tensor :: k -> (k, k) -> Type) p, Ob w, SymMonoidal k) => Strong (Tensor :: k -> (k, k) -> Type) (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods act :: forall (a :: k) (x :: k) (y :: k). Ob a => WriterT w p x y -> WriterT w p (Act (Tensor :: k -> (k, k) -> Type) a x) (Act (Tensor :: k -> (k, k) -> Type) a y) Source Github #
(MonoidalProfunctor p, Monoid w, SymMonoidal k) => MonoidalProfunctor (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods one :: WriterT w p (Unit :: k) (Unit :: k) Source Github # () :: forall (x1 :: k) (x2 :: k) (y1 :: k) (y2 :: k). WriterT w p x1 x2 -> WriterT w p y1 y2 -> WriterT w p (x1 y1) (x2 ** y2) Source Github #
(Profunctor p, Monoidal k, Ob w) => Profunctor (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods dimap :: forall (c :: k) (a :: k) (b :: k) (d :: k). (c ~> a) -> (b ~> d) -> WriterT w p a b -> WriterT w p c d Source Github # lmap :: forall (c :: k) (a :: k) (b :: k). (c ~> a) -> WriterT w p a b -> WriterT w p c b Source Github # rmap :: forall (b :: k) (d :: k) (a :: k). (b ~> d) -> WriterT w p a b -> WriterT w p a d Source Github # (\\) :: forall (a :: k) (b :: k) r. ((Ob a, Ob b) => r) -> WriterT w p a b -> r Source Github #
(Corepresentable p, Ob w, CompactClosed k) => Corepresentable (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods coindex :: forall (a :: k) (b :: k). WriterT w p a b -> (WriterT w p %% a) ~> b Source Github # cotabulate :: forall (a :: k) (b :: k). Ob a => ((WriterT w p %% a) ~> b) -> WriterT w p a b Source Github # corepMap :: forall (a :: k) (b :: k). (a ~> b) -> (WriterT w p %% a) ~> (WriterT w p %% b) Source Github # corepUniv :: forall (a :: k). Ob a => WriterT w p a (WriterT w p %% a) Source Github #
(Representable p, Ob w, Monoidal k) => Representable (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods index :: forall (a :: k) (b :: k). WriterT w p a b -> a ~> (WriterT w p % b) Source Github # tabulate :: forall (b :: k) (a :: k). Ob b => (a ~> (WriterT w p % b)) -> WriterT w p a b Source Github # repMap :: forall (a :: k) (b :: k). (a ~> b) -> (WriterT w p % a) ~> (WriterT w p % b) Source Github # repUniv :: forall (a :: k). Ob a => WriterT w p (WriterT w p % a) a Source Github #
(Proadjunction p q, Ob r, Monoidal k) => Proadjunction (WriterT r p :: k -> k -> Type) (ReaderT ('OP r) q :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Reader Methods unit :: forall (a :: k). Ob a => (ReaderT ('OP r) q :.: WriterT r p) a a Source Github # counit :: (WriterT r p :.: ReaderT ('OP r) q) :~> ((~>) :: CAT k) Source Github #
Monoidal k => Functor (WriterT :: k -> (k +-> k) -> k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods map :: forall (a :: k) (b :: k). (a ~> b) -> WriterT a ~> WriterT b Source Github #
(Traversable p, Monoid w) => Traversable (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods traverse :: forall (p0 :: k +-> k). StrongDistributiveProfunctor p0 => (WriterT w p :.: p0) :~> (p0 :.: WriterT w p) Source Github #
(Monoid w, Strong (Tensor :: k -> (k, k) -> Type) p, Promonad p) => Promonad (WriterT w p :: k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods id :: forall (a :: k). Ob a => WriterT w p a a Source Github # (.) :: forall (b :: k) (c :: k) (a :: k). WriterT w p b c -> WriterT w p a b -> WriterT w p a c Source Github #
(Monoidal k, Ob w) => Functor (WriterT w :: (k +-> k) -> k -> k -> Type) Source Github #
Instance details Defined in Proarrow.Promonad.Writer Methods map :: forall (a :: k +-> k) (b :: k +-> k). (a ~> b) -> WriterT w a ~> WriterT w b Source Github #
(Monoid w, Monoidal k) => Promonad (Star (WriterT w) :: (k +-> k) -> (k +-> k) -> Type) Source Github #	WriterT is a monad on profunctors, i.e. we have `p ~> WriterT p` and `WriterT (WriterT p) ~> WriterT p`.
Instance details Defined in Proarrow.Promonad.Writer Methods id :: forall (a :: k +-> k). Ob a => Star (WriterT w) a a Source Github # (.) :: forall (b :: k +-> k) (c :: k +-> k) (a :: k +-> k). Star (WriterT w) b c -> Star (WriterT w) a b -> Star (WriterT w) a c Source Github #
type (WriterT w p :: k -> k -> Type) %% (a :: k) Source Github #
Instance details Defined in Proarrow.Promonad.Writer type (WriterT w p :: k -> k -> Type) %% (a :: k) = (p :.: Writer w) %% a
type (WriterT w p :: k -> k -> Type) % (a :: k) Source Github #
Instance details Defined in Proarrow.Promonad.Writer type (WriterT w p :: k -> k -> Type) % (a :: k) = (p :.: Writer w) % a

runWriterT :: forall {k} p (w :: k) (a :: k) (b :: k). Profunctor p => WriterT w p a b -> p a (w ** b) Source Github #

tell :: forall k (p :: k +-> k) (w :: k). (Promonad p, Monoidal k, Ob w) => WriterT w p w (Unit :: k) Source Github #

listen :: forall {k} (p :: k +-> k) (w :: k) (a :: k) (b :: k). (Promonad p, Monoidal k, Comonoid w) => WriterT w p a b -> WriterT w p a (w ** b) Source Github #

censor :: forall {k} (p :: k +-> k) (w :: k) (a :: k) (b :: k). (Monoidal k, Ob w) => (w ~> w) -> WriterT w p a b -> WriterT w p a b Source Github #