Control.Algebra.Handler

Documentation

type Handler (ctx :: Type -> Type) (m :: Type -> Type) (n :: Type -> Type) = forall x. ctx (m x) -> n (ctx x)

Handlers take an action in m bundled up with some state in some context functor ctx, and return an action in n producing a derived state in ctx.

These are expected to be well-behaved distributive laws, and are required to adhere to the following laws:

handler . fmap pure = pure

handler . fmap (k =<<) = handler . fmap k <=< handler

respectively expressing that the handler does not alter the context of pure computations, and that the handler distributes over monadic composition.

Handlers compose with handlers, using e.g. Data.Functor.Compose.Compose to ensure that the result is itself well-typed as a Handler:

fmap Compose . handler1 . fmap handler2 . getCompose

and with monad homomorphisms on the left and right:

hom . handler

handler . fmap hom

Since: 1.1.0.0

(~<~) :: forall (n :: Type -> Type) (ctx1 :: Type -> Type) (m :: Type -> Type) (ctx2 :: Type -> Type) (l :: Type -> Type). (Functor n, Functor ctx1) => Handler ctx1 m n -> Handler ctx2 l m -> Handler (Compose ctx1 ctx2) l n infixr 1

Composition of handlers.

Since: 1.1.0.0