Pandora.Pattern.Functor.Bindable

Documentation

class Covariant t => Bindable t where

When providing a new instance, you should ensure it satisfies the one law:
* Interchange: t >>= f = join (f <$> t)

Minimal complete definition

(>>=)

Methods

(>>=) :: t a -> (a -> t b) -> t b infixl 1

Infix and flipped version of bind, the dual of =>>

(=<<) :: (a -> t b) -> t a -> t b infixr 1

Flipped version of >>=, the dual of <<=

bind :: (a -> t b) -> t a -> t b

Prefix and flipped version of >>=, the dual of extend

join :: ((t :. t) := a) -> t a

Merge effects/contexts, the dual of duplicate

(>=>) :: (a -> t b) -> (b -> t c) -> a -> t c infixr 1

Left-to-right Kleisli composition

(<=<) :: (b -> t c) -> (a -> t b) -> a -> t c infixr 1

Right-to-left Kleisli composition

($>>=) :: Covariant u => ((u :. t) := a) -> (a -> t b) -> (u :. t) := b

(<>>=) :: (t b -> c) -> (a -> t b) -> t a -> c

Instances

Bindable Identity

Defined in Pandora.Paradigm.Primary.Functor.Identity

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b

(=<<) :: (a -> Identity b) -> Identity a -> Identity b

bind :: (a -> Identity b) -> Identity a -> Identity b

join :: ((Identity :. Identity) := a) -> Identity a

(>=>) :: (a -> Identity b) -> (b -> Identity c) -> a -> Identity c

(<=<) :: (b -> Identity c) -> (a -> Identity b) -> a -> Identity c

($>>=) :: Covariant u => ((u :. Identity) := a) -> (a -> Identity b) -> (u :. Identity) := b

(<>>=) :: (Identity b -> c) -> (a -> Identity b) -> Identity a -> c

Bindable Maybe

Defined in Pandora.Paradigm.Primary.Functor.Maybe

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b

(=<<) :: (a -> Maybe b) -> Maybe a -> Maybe b

bind :: (a -> Maybe b) -> Maybe a -> Maybe b

join :: ((Maybe :. Maybe) := a) -> Maybe a

(>=>) :: (a -> Maybe b) -> (b -> Maybe c) -> a -> Maybe c

(<=<) :: (b -> Maybe c) -> (a -> Maybe b) -> a -> Maybe c

($>>=) :: Covariant u => ((u :. Maybe) := a) -> (a -> Maybe b) -> (u :. Maybe) := b

(<>>=) :: (Maybe b -> c) -> (a -> Maybe b) -> Maybe a -> c

Bindable (Proxy :: Type -> Type)

Defined in Pandora.Paradigm.Primary.Functor.Proxy

Methods

(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b

(=<<) :: (a -> Proxy b) -> Proxy a -> Proxy b

bind :: (a -> Proxy b) -> Proxy a -> Proxy b

join :: ((Proxy :. Proxy) := a) -> Proxy a

(>=>) :: (a -> Proxy b) -> (b -> Proxy c) -> a -> Proxy c

(<=<) :: (b -> Proxy c) -> (a -> Proxy b) -> a -> Proxy c

($>>=) :: Covariant u => ((u :. Proxy) := a) -> (a -> Proxy b) -> (u :. Proxy) := b

(<>>=) :: (Proxy b -> c) -> (a -> Proxy b) -> Proxy a -> c

(Pointable t, Bindable t) => Bindable (Jack t)

Defined in Pandora.Paradigm.Primary.Transformer.Jack

Methods

(>>=) :: Jack t a -> (a -> Jack t b) -> Jack t b

(=<<) :: (a -> Jack t b) -> Jack t a -> Jack t b

bind :: (a -> Jack t b) -> Jack t a -> Jack t b

join :: ((Jack t :. Jack t) := a) -> Jack t a

(>=>) :: (a -> Jack t b) -> (b -> Jack t c) -> a -> Jack t c

(<=<) :: (b -> Jack t c) -> (a -> Jack t b) -> a -> Jack t c

($>>=) :: Covariant u => ((u :. Jack t) := a) -> (a -> Jack t b) -> (u :. Jack t) := b

(<>>=) :: (Jack t b -> c) -> (a -> Jack t b) -> Jack t a -> c

Covariant t => Bindable (Instruction t)

Defined in Pandora.Paradigm.Primary.Transformer.Instruction

Methods

(>>=) :: Instruction t a -> (a -> Instruction t b) -> Instruction t b

(=<<) :: (a -> Instruction t b) -> Instruction t a -> Instruction t b

bind :: (a -> Instruction t b) -> Instruction t a -> Instruction t b

join :: ((Instruction t :. Instruction t) := a) -> Instruction t a

(>=>) :: (a -> Instruction t b) -> (b -> Instruction t c) -> a -> Instruction t c

(<=<) :: (b -> Instruction t c) -> (a -> Instruction t b) -> a -> Instruction t c

($>>=) :: Covariant u => ((u :. Instruction t) := a) -> (a -> Instruction t b) -> (u :. Instruction t) := b

(<>>=) :: (Instruction t b -> c) -> (a -> Instruction t b) -> Instruction t a -> c

(Extractable t, Alternative t, Bindable t) => Bindable (Tap t)

Defined in Pandora.Paradigm.Primary.Transformer.Tap

Methods

(>>=) :: Tap t a -> (a -> Tap t b) -> Tap t b

(=<<) :: (a -> Tap t b) -> Tap t a -> Tap t b

bind :: (a -> Tap t b) -> Tap t a -> Tap t b

join :: ((Tap t :. Tap t) := a) -> Tap t a

(>=>) :: (a -> Tap t b) -> (b -> Tap t c) -> a -> Tap t c

(<=<) :: (b -> Tap t c) -> (a -> Tap t b) -> a -> Tap t c

($>>=) :: Covariant u => ((u :. Tap t) := a) -> (a -> Tap t b) -> (u :. Tap t) := b

(<>>=) :: (Tap t b -> c) -> (a -> Tap t b) -> Tap t a -> c

Alternative t => Bindable (Construction t)

Defined in Pandora.Paradigm.Primary.Transformer.Construction

Methods

(>>=) :: Construction t a -> (a -> Construction t b) -> Construction t b

(=<<) :: (a -> Construction t b) -> Construction t a -> Construction t b

bind :: (a -> Construction t b) -> Construction t a -> Construction t b

join :: ((Construction t :. Construction t) := a) -> Construction t a

(>=>) :: (a -> Construction t b) -> (b -> Construction t c) -> a -> Construction t c

(<=<) :: (b -> Construction t c) -> (a -> Construction t b) -> a -> Construction t c

($>>=) :: Covariant u => ((u :. Construction t) := a) -> (a -> Construction t b) -> (u :. Construction t) := b

(<>>=) :: (Construction t b -> c) -> (a -> Construction t b) -> Construction t a -> c

(forall a. Semigroup ((t <:.> Construction t) := a), Bindable t) => Bindable (Comprehension t)

Defined in Pandora.Paradigm.Structure.Ability.Comprehension

Methods

(>>=) :: Comprehension t a -> (a -> Comprehension t b) -> Comprehension t b

(=<<) :: (a -> Comprehension t b) -> Comprehension t a -> Comprehension t b

bind :: (a -> Comprehension t b) -> Comprehension t a -> Comprehension t b

join :: ((Comprehension t :. Comprehension t) := a) -> Comprehension t a

(>=>) :: (a -> Comprehension t b) -> (b -> Comprehension t c) -> a -> Comprehension t c

(<=<) :: (b -> Comprehension t c) -> (a -> Comprehension t b) -> a -> Comprehension t c

($>>=) :: Covariant u => ((u :. Comprehension t) := a) -> (a -> Comprehension t b) -> (u :. Comprehension t) := b

(<>>=) :: (Comprehension t b -> c) -> (a -> Comprehension t b) -> Comprehension t a -> c

Bindable (Conclusion e)

Defined in Pandora.Paradigm.Primary.Functor.Conclusion

Methods

(>>=) :: Conclusion e a -> (a -> Conclusion e b) -> Conclusion e b

(=<<) :: (a -> Conclusion e b) -> Conclusion e a -> Conclusion e b

bind :: (a -> Conclusion e b) -> Conclusion e a -> Conclusion e b

join :: ((Conclusion e :. Conclusion e) := a) -> Conclusion e a

(>=>) :: (a -> Conclusion e b) -> (b -> Conclusion e c) -> a -> Conclusion e c

(<=<) :: (b -> Conclusion e c) -> (a -> Conclusion e b) -> a -> Conclusion e c

($>>=) :: Covariant u => ((u :. Conclusion e) := a) -> (a -> Conclusion e b) -> (u :. Conclusion e) := b

(<>>=) :: (Conclusion e b -> c) -> (a -> Conclusion e b) -> Conclusion e a -> c

Bindable (State s)

Defined in Pandora.Paradigm.Inventory.State

Methods

(>>=) :: State s a -> (a -> State s b) -> State s b

(=<<) :: (a -> State s b) -> State s a -> State s b

bind :: (a -> State s b) -> State s a -> State s b

join :: ((State s :. State s) := a) -> State s a

(>=>) :: (a -> State s b) -> (b -> State s c) -> a -> State s c

(<=<) :: (b -> State s c) -> (a -> State s b) -> a -> State s c

($>>=) :: Covariant u => ((u :. State s) := a) -> (a -> State s b) -> (u :. State s) := b

(<>>=) :: (State s b -> c) -> (a -> State s b) -> State s a -> c

Bindable (Environment e)

Defined in Pandora.Paradigm.Inventory.Environment

Methods

(>>=) :: Environment e a -> (a -> Environment e b) -> Environment e b

(=<<) :: (a -> Environment e b) -> Environment e a -> Environment e b

bind :: (a -> Environment e b) -> Environment e a -> Environment e b

join :: ((Environment e :. Environment e) := a) -> Environment e a

(>=>) :: (a -> Environment e b) -> (b -> Environment e c) -> a -> Environment e c

(<=<) :: (b -> Environment e c) -> (a -> Environment e b) -> a -> Environment e c

($>>=) :: Covariant u => ((u :. Environment e) := a) -> (a -> Environment e b) -> (u :. Environment e) := b

(<>>=) :: (Environment e b -> c) -> (a -> Environment e b) -> Environment e a -> c

Semigroup e => Bindable (Accumulator e)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

(>>=) :: Accumulator e a -> (a -> Accumulator e b) -> Accumulator e b

(=<<) :: (a -> Accumulator e b) -> Accumulator e a -> Accumulator e b

bind :: (a -> Accumulator e b) -> Accumulator e a -> Accumulator e b

join :: ((Accumulator e :. Accumulator e) := a) -> Accumulator e a

(>=>) :: (a -> Accumulator e b) -> (b -> Accumulator e c) -> a -> Accumulator e c

(<=<) :: (b -> Accumulator e c) -> (a -> Accumulator e b) -> a -> Accumulator e c

($>>=) :: Covariant u => ((u :. Accumulator e) := a) -> (a -> Accumulator e b) -> (u :. Accumulator e) := b

(<>>=) :: (Accumulator e b -> c) -> (a -> Accumulator e b) -> Accumulator e a -> c

Bindable (Tagged tag)

Defined in Pandora.Paradigm.Primary.Functor.Tagged

Methods

(>>=) :: Tagged tag a -> (a -> Tagged tag b) -> Tagged tag b

(=<<) :: (a -> Tagged tag b) -> Tagged tag a -> Tagged tag b

bind :: (a -> Tagged tag b) -> Tagged tag a -> Tagged tag b

join :: ((Tagged tag :. Tagged tag) := a) -> Tagged tag a

(>=>) :: (a -> Tagged tag b) -> (b -> Tagged tag c) -> a -> Tagged tag c

(<=<) :: (b -> Tagged tag c) -> (a -> Tagged tag b) -> a -> Tagged tag c

($>>=) :: Covariant u => ((u :. Tagged tag) := a) -> (a -> Tagged tag b) -> (u :. Tagged tag) := b

(<>>=) :: (Tagged tag b -> c) -> (a -> Tagged tag b) -> Tagged tag a -> c

Bindable (Schematic Monad t u) => Bindable (t :> u)

Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Monadic

Methods

(>>=) :: (t :> u) a -> (a -> (t :> u) b) -> (t :> u) b

(=<<) :: (a -> (t :> u) b) -> (t :> u) a -> (t :> u) b

bind :: (a -> (t :> u) b) -> (t :> u) a -> (t :> u) b

join :: (((t :> u) :. (t :> u)) := a) -> (t :> u) a

(>=>) :: (a -> (t :> u) b) -> (b -> (t :> u) c) -> a -> (t :> u) c

(<=<) :: (b -> (t :> u) c) -> (a -> (t :> u) b) -> a -> (t :> u) c

($>>=) :: Covariant u0 => ((u0 :. (t :> u)) := a) -> (a -> (t :> u) b) -> (u0 :. (t :> u)) := b

(<>>=) :: ((t :> u) b -> c) -> (a -> (t :> u) b) -> (t :> u) a -> c

Bindable (Schematic Comonad t u) => Bindable (t :< u)

Defined in Pandora.Paradigm.Controlflow.Effect.Transformer.Comonadic

Methods

(>>=) :: (t :< u) a -> (a -> (t :< u) b) -> (t :< u) b

(=<<) :: (a -> (t :< u) b) -> (t :< u) a -> (t :< u) b

bind :: (a -> (t :< u) b) -> (t :< u) a -> (t :< u) b

join :: (((t :< u) :. (t :< u)) := a) -> (t :< u) a

(>=>) :: (a -> (t :< u) b) -> (b -> (t :< u) c) -> a -> (t :< u) c

(<=<) :: (b -> (t :< u) c) -> (a -> (t :< u) b) -> a -> (t :< u) c

($>>=) :: Covariant u0 => ((u0 :. (t :< u)) := a) -> (a -> (t :< u) b) -> (u0 :. (t :< u)) := b

(<>>=) :: ((t :< u) b -> c) -> (a -> (t :< u) b) -> (t :< u) a -> c

Bindable ((->) e :: Type -> Type)

Defined in Pandora.Pattern.Functor.Bindable

Methods

(>>=) :: (e -> a) -> (a -> e -> b) -> e -> b

(=<<) :: (a -> e -> b) -> (e -> a) -> e -> b

bind :: (a -> e -> b) -> (e -> a) -> e -> b

join :: (((->) e :. (->) e) := a) -> e -> a

(>=>) :: (a -> e -> b) -> (b -> e -> c) -> a -> e -> c

(<=<) :: (b -> e -> c) -> (a -> e -> b) -> a -> e -> c

($>>=) :: Covariant u => ((u :. (->) e) := a) -> (a -> e -> b) -> (u :. (->) e) := b

(<>>=) :: ((e -> b) -> c) -> (a -> e -> b) -> (e -> a) -> c

Covariant t => Bindable (Continuation r t)

Defined in Pandora.Paradigm.Primary.Transformer.Continuation

Methods

(>>=) :: Continuation r t a -> (a -> Continuation r t b) -> Continuation r t b

(=<<) :: (a -> Continuation r t b) -> Continuation r t a -> Continuation r t b

bind :: (a -> Continuation r t b) -> Continuation r t a -> Continuation r t b

join :: ((Continuation r t :. Continuation r t) := a) -> Continuation r t a

(>=>) :: (a -> Continuation r t b) -> (b -> Continuation r t c) -> a -> Continuation r t c

(<=<) :: (b -> Continuation r t c) -> (a -> Continuation r t b) -> a -> Continuation r t c

($>>=) :: Covariant u => ((u :. Continuation r t) := a) -> (a -> Continuation r t b) -> (u :. Continuation r t) := b

(<>>=) :: (Continuation r t b -> c) -> (a -> Continuation r t b) -> Continuation r t a -> c

(Adjoint t' t, Bindable u) => Bindable ((t <:<.>:> t') := u)

Defined in Pandora.Paradigm.Schemes.TUT

Methods

(>>=) :: ((t <:<.>:> t') := u) a -> (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) b

(=<<) :: (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

bind :: (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> ((t <:<.>:> t') := u) b

join :: ((((t <:<.>:> t') := u) :. ((t <:<.>:> t') := u)) := a) -> ((t <:<.>:> t') := u) a

(>=>) :: (a -> ((t <:<.>:> t') := u) b) -> (b -> ((t <:<.>:> t') := u) c) -> a -> ((t <:<.>:> t') := u) c

(<=<) :: (b -> ((t <:<.>:> t') := u) c) -> (a -> ((t <:<.>:> t') := u) b) -> a -> ((t <:<.>:> t') := u) c

($>>=) :: Covariant u0 => ((u0 :. ((t <:<.>:> t') := u)) := a) -> (a -> ((t <:<.>:> t') := u) b) -> (u0 :. ((t <:<.>:> t') := u)) := b

(<>>=) :: (((t <:<.>:> t') := u) b -> c) -> (a -> ((t <:<.>:> t') := u) b) -> ((t <:<.>:> t') := u) a -> c

(Traversable t, Bindable t, Applicative u, Monad u) => Bindable (t <.:> u)

Defined in Pandora.Paradigm.Schemes.UT

Methods

(>>=) :: (t <.:> u) a -> (a -> (t <.:> u) b) -> (t <.:> u) b

(=<<) :: (a -> (t <.:> u) b) -> (t <.:> u) a -> (t <.:> u) b

bind :: (a -> (t <.:> u) b) -> (t <.:> u) a -> (t <.:> u) b

join :: (((t <.:> u) :. (t <.:> u)) := a) -> (t <.:> u) a

(>=>) :: (a -> (t <.:> u) b) -> (b -> (t <.:> u) c) -> a -> (t <.:> u) c

(<=<) :: (b -> (t <.:> u) c) -> (a -> (t <.:> u) b) -> a -> (t <.:> u) c

($>>=) :: Covariant u0 => ((u0 :. (t <.:> u)) := a) -> (a -> (t <.:> u) b) -> (u0 :. (t <.:> u)) := b

(<>>=) :: ((t <.:> u) b -> c) -> (a -> (t <.:> u) b) -> (t <.:> u) a -> c

(Semigroup e, Pointable u, Bindable u) => Bindable ((:*:) e <.:> u)

Defined in Pandora.Paradigm.Inventory.Accumulator

Methods

(>>=) :: ((:*:) e <.:> u) a -> (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) b

(=<<) :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

bind :: (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> ((:*:) e <.:> u) b

join :: ((((:*:) e <.:> u) :. ((:*:) e <.:> u)) := a) -> ((:*:) e <.:> u) a

(>=>) :: (a -> ((:*:) e <.:> u) b) -> (b -> ((:*:) e <.:> u) c) -> a -> ((:*:) e <.:> u) c

(<=<) :: (b -> ((:*:) e <.:> u) c) -> (a -> ((:*:) e <.:> u) b) -> a -> ((:*:) e <.:> u) c

($>>=) :: Covariant u0 => ((u0 :. ((:*:) e <.:> u)) := a) -> (a -> ((:*:) e <.:> u) b) -> (u0 :. ((:*:) e <.:> u)) := b

(<>>=) :: (((:*:) e <.:> u) b -> c) -> (a -> ((:*:) e <.:> u) b) -> ((:*:) e <.:> u) a -> c

(Bindable t, Distributive t, Bindable u) => Bindable (t <:.> u)

Defined in Pandora.Paradigm.Schemes.TU

Methods

(>>=) :: (t <:.> u) a -> (a -> (t <:.> u) b) -> (t <:.> u) b

(=<<) :: (a -> (t <:.> u) b) -> (t <:.> u) a -> (t <:.> u) b

bind :: (a -> (t <:.> u) b) -> (t <:.> u) a -> (t <:.> u) b

join :: (((t <:.> u) :. (t <:.> u)) := a) -> (t <:.> u) a

(>=>) :: (a -> (t <:.> u) b) -> (b -> (t <:.> u) c) -> a -> (t <:.> u) c

(<=<) :: (b -> (t <:.> u) c) -> (a -> (t <:.> u) b) -> a -> (t <:.> u) c

($>>=) :: Covariant u0 => ((u0 :. (t <:.> u)) := a) -> (a -> (t <:.> u) b) -> (u0 :. (t <:.> u)) := b

(<>>=) :: ((t <:.> u) b -> c) -> (a -> (t <:.> u) b) -> (t <:.> u) a -> c