Control.PFunctor

This module defines functors in the category of proxies

Functors over Proxies

class PFunctor t where

A functor in the category of proxies

hoistP f . hoistP g = hoistP (f . g)

hoistP id = id

If f is a proxy morphism, then hoistP f is a proxy morphism, meaning that hoistPK f = (hoistP f .) defines a functor between five categories.

Functor between Kleisli categories:

hoistPK f p1 >=> hoistPK f p2 = hoistPK f (p1 >=> p2)

hoistPK f return = return

Functor between Proxy categories:

hoistPK f p1 >-> hoistPK f p2 = hoistPK f (p1 >-> p2)

hoistPK f idT = idT

hoistPK f p1 >~> hoistPK f p2 = hoistPK f (p1 >~> p2)

hoistPK f coidT = coidT

Functor between "request" categories:

hoistPK f p1 \>\ hoistPK f p2 = hoistPK f (p2 \>\ p2)

hoistPK f request = request

Functor between "respond" categories:

hoistPK f p1 />/ hoistPK f p2 = hoistPK f (p2 />/ p2)

hoistPK f respond = respond

Minimal complete definition

hoistP

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> t p1 a' a b' b m r2 -> t p2 a' a b' b n r2

Lift a proxy morphism from p1 to p2 into a proxy morphism from (t p1) to (t p2)

Instances

PFunctor IdentityP

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> IdentityP p1 a' a b' b m r2 -> IdentityP p2 a' a b' b n r2

PFunctor MaybeP

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> MaybeP p1 a' a b' b m r2 -> MaybeP p2 a' a b' b n r2

PFunctor (EitherP e)

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> EitherP e p1 a' a b' b m r2 -> EitherP e p2 a' a b' b n r2

PFunctor (ReaderP i)

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> ReaderP i p1 a' a b' b m r2 -> ReaderP i p2 a' a b' b n r2

PFunctor (StateP s)

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> StateP s p1 a' a b' b m r2 -> StateP s p2 a' a b' b n r2

PFunctor (WriterP w)

Methods

hoistP :: (Monad m, Proxy p1) => (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1) -> WriterP w p1 a' a b' b m r2 -> WriterP w p2 a' a b' b n r2

hoistPK

Arguments

:: (Monad m, Proxy p1, PFunctor t)

=> (forall r1. p1 a' a b' b m r1 -> p2 a' a b' b n r1)

Proxy morphism

-> (q -> t p1 a' a b' b m r2)

Proxy Kleisli arrow

-> q -> t p2 a' a b' b n r2

Convenience function equivalent to (hoistP f .)

raiseP

Arguments

:: (Monad m, Proxy p, PFunctor t1, ProxyTrans t2)

=> t1 p a' a b' b m r

Proxy

-> t1 (t2 p) a' a b' b m r

Lift the base proxy

raiseP = hoistP liftP

raisePK

Arguments

:: (Monad m, Proxy p, PFunctor t1, ProxyTrans t2)

=> (q -> t1 p a' a b' b m r)

Proxy Kleisli arrow

-> q -> t1 (t2 p) a' a b' b m r

Lift the base proxy of a 'K'leisli arrow

raisePK = hoistPK liftP