Copyright	(c) Justin Le 2019
License	BSD3
Maintainer	[email protected]
Stability	experimental
Portability	non-portable
Safe Haskell	None
Language	Haskell2010

Data.HFunctor.Final

Description

Provides Final, which can be considered the "free Interpret over a constraint": generate a handy Interpret instance for any constraint c.

Synopsis

newtype Final c f a = Final {
- runFinal :: forall g. c g => (forall x. f x -> g x) -> g a
}
fromFinal :: (Interpret t, c (t f)) => Final c f ~> t f
toFinal :: (Interpret t, C t (Final c f)) => t f ~> Final c f
class Interpret t => FreeOf c t | t -> c where
- fromFree :: t f ~> Final c f
- toFree :: Functor f => Final c f ~> t f
finalizing :: (FreeOf c t, Functor f) => t f <~> Final c f
hoistFinalC :: (forall g x. (c g => g x) -> d g => g x) -> Final c f a -> Final d f a
liftFinal0 :: (forall g. c g => g a) -> Final c f a
liftFinal1 :: (forall g. c g => g a -> g b) -> Final c f a -> Final c f b
liftFinal2 :: (forall g. c g => g a -> g b -> g d) -> Final c f a -> Final c f b -> Final c f d

Documentation

newtype Final c f a Source #

A simple way to inject/reject into any eventual typeclass.

In a way, this is the "ultimate" multi-purpose Interpret instance. You can use this to inject an f into a free structure of any typeclass. If you want f to have a Monad instance, for example, just use

inject :: f a -> Final Monad f a

When you want to eventually interpret out the data, use:

interpret :: (f ~> g) -> Final c f a -> g a

Essentially, Final c is the "free c". Final Monad is the free Monad, etc.

Final can theoretically replace Ap, Ap1, ListF, NonEmptyF, MaybeF, Free, Identity, Coyoneda, and other instances of FreeOf, if you don't care about being able to pattern match on explicit structure.

However, it cannot replace Interpret instances that are not free structures, like Step, Steps, Backwards, etc.

Note that this doesn't have instances for all the typeclasses you could lift things into; you probably have to define your own if you want to use Final c as an instance of c (using liftFinal0, liftFinal1, liftFinal2 for help).

Constructors

Final
Fields runFinal :: forall g. c g => (forall x. f x -> g x) -> g a

Instances

MonadReader r (Final (MonadReader r) f) Source #
Instance details Defined in Data.HFunctor.Final Methods ask :: Final (MonadReader r) f r # local :: (r -> r) -> Final (MonadReader r) f a -> Final (MonadReader r) f a # reader :: (r -> a) -> Final (MonadReader r) f a #
Interpret (Final c) Source #
Instance details Defined in Data.HFunctor.Final Associated Types type C (Final c) :: (Type -> Type) -> Constraint Source # Methods retract :: C (Final c) f => Final c f ~> f Source # interpret :: C (Final c) g => (f ~> g) -> Final c f ~> g Source #
Inject (Final c :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Data.HFunctor.Final Methods inject :: f ~> Final c f Source #
HFunctor (Final c :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Data.HFunctor.Final Methods hmap :: (f ~> g) -> Final c f ~> Final c g Source #
Monad (Final Monad f) Source #
Instance details Defined in Data.HFunctor.Final Methods (>>=) :: Final Monad f a -> (a -> Final Monad f b) -> Final Monad f b # (>>) :: Final Monad f a -> Final Monad f b -> Final Monad f b # return :: a -> Final Monad f a # fail :: String -> Final Monad f a #
Monad (Final (MonadReader r) f) Source #
Instance details Defined in Data.HFunctor.Final Methods (>>=) :: Final (MonadReader r) f a -> (a -> Final (MonadReader r) f b) -> Final (MonadReader r) f b # (>>) :: Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f b # return :: a -> Final (MonadReader r) f a # fail :: String -> Final (MonadReader r) f a #
Monad (Final MonadPlus f) Source #
Instance details Defined in Data.HFunctor.Final Methods (>>=) :: Final MonadPlus f a -> (a -> Final MonadPlus f b) -> Final MonadPlus f b # (>>) :: Final MonadPlus f a -> Final MonadPlus f b -> Final MonadPlus f b # return :: a -> Final MonadPlus f a # fail :: String -> Final MonadPlus f a #
Functor (Final Monad f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Monad f a -> Final Monad f b # (<$) :: a -> Final Monad f b -> Final Monad f a #
Functor (Final Functor f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Functor f a -> Final Functor f b # (<$) :: a -> Final Functor f b -> Final Functor f a #
Functor (Final Applicative f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Applicative f a -> Final Applicative f b # (<$) :: a -> Final Applicative f b -> Final Applicative f a #
Functor (Final (MonadReader r) f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final (MonadReader r) f a -> Final (MonadReader r) f b # (<$) :: a -> Final (MonadReader r) f b -> Final (MonadReader r) f a #
Functor (Final Alternative f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Alternative f a -> Final Alternative f b # (<$) :: a -> Final Alternative f b -> Final Alternative f a #
Functor (Final MonadPlus f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final MonadPlus f a -> Final MonadPlus f b # (<$) :: a -> Final MonadPlus f b -> Final MonadPlus f a #
Functor (Final Apply f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Apply f a -> Final Apply f b # (<$) :: a -> Final Apply f b -> Final Apply f a #
Functor (Final Plus f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Plus f a -> Final Plus f b # (<$) :: a -> Final Plus f b -> Final Plus f a #
Functor (Final Alt f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Alt f a -> Final Alt f b # (<$) :: a -> Final Alt f b -> Final Alt f a #
Functor (Final Bind f) Source #
Instance details Defined in Data.HFunctor.Final Methods fmap :: (a -> b) -> Final Bind f a -> Final Bind f b # (<$) :: a -> Final Bind f b -> Final Bind f a #
Applicative (Final Monad f) Source #
Instance details Defined in Data.HFunctor.Final Methods pure :: a -> Final Monad f a # (<>) :: Final Monad f (a -> b) -> Final Monad f a -> Final Monad f b # liftA2 :: (a -> b -> c) -> Final Monad f a -> Final Monad f b -> Final Monad f c # (>) :: Final Monad f a -> Final Monad f b -> Final Monad f b # (<*) :: Final Monad f a -> Final Monad f b -> Final Monad f a #
Applicative (Final Applicative f) Source #
Instance details Defined in Data.HFunctor.Final Methods pure :: a -> Final Applicative f a # (<>) :: Final Applicative f (a -> b) -> Final Applicative f a -> Final Applicative f b # liftA2 :: (a -> b -> c) -> Final Applicative f a -> Final Applicative f b -> Final Applicative f c # (>) :: Final Applicative f a -> Final Applicative f b -> Final Applicative f b # (<*) :: Final Applicative f a -> Final Applicative f b -> Final Applicative f a #
Applicative (Final (MonadReader r) f) Source #
Instance details Defined in Data.HFunctor.Final Methods pure :: a -> Final (MonadReader r) f a # (<>) :: Final (MonadReader r) f (a -> b) -> Final (MonadReader r) f a -> Final (MonadReader r) f b # liftA2 :: (a -> b -> c) -> Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f c # (>) :: Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f b # (<*) :: Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f a #
Applicative (Final Alternative f) Source #
Instance details Defined in Data.HFunctor.Final Methods pure :: a -> Final Alternative f a # (<>) :: Final Alternative f (a -> b) -> Final Alternative f a -> Final Alternative f b # liftA2 :: (a -> b -> c) -> Final Alternative f a -> Final Alternative f b -> Final Alternative f c # (>) :: Final Alternative f a -> Final Alternative f b -> Final Alternative f b # (<*) :: Final Alternative f a -> Final Alternative f b -> Final Alternative f a #
Applicative (Final MonadPlus f) Source #
Instance details Defined in Data.HFunctor.Final Methods pure :: a -> Final MonadPlus f a # (<>) :: Final MonadPlus f (a -> b) -> Final MonadPlus f a -> Final MonadPlus f b # liftA2 :: (a -> b -> c) -> Final MonadPlus f a -> Final MonadPlus f b -> Final MonadPlus f c # (>) :: Final MonadPlus f a -> Final MonadPlus f b -> Final MonadPlus f b # (<*) :: Final MonadPlus f a -> Final MonadPlus f b -> Final MonadPlus f a #
Alternative (Final Alternative f) Source #
Instance details Defined in Data.HFunctor.Final Methods empty :: Final Alternative f a # (<\|>) :: Final Alternative f a -> Final Alternative f a -> Final Alternative f a # some :: Final Alternative f a -> Final Alternative f [a] # many :: Final Alternative f a -> Final Alternative f [a] #
Alternative (Final MonadPlus f) Source #
Instance details Defined in Data.HFunctor.Final Methods empty :: Final MonadPlus f a # (<\|>) :: Final MonadPlus f a -> Final MonadPlus f a -> Final MonadPlus f a # some :: Final MonadPlus f a -> Final MonadPlus f [a] # many :: Final MonadPlus f a -> Final MonadPlus f [a] #
MonadPlus (Final MonadPlus f) Source #
Instance details Defined in Data.HFunctor.Final Methods mzero :: Final MonadPlus f a # mplus :: Final MonadPlus f a -> Final MonadPlus f a -> Final MonadPlus f a #
Apply (Final Monad f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<.>) :: Final Monad f (a -> b) -> Final Monad f a -> Final Monad f b # (.>) :: Final Monad f a -> Final Monad f b -> Final Monad f b # (<.) :: Final Monad f a -> Final Monad f b -> Final Monad f a # liftF2 :: (a -> b -> c) -> Final Monad f a -> Final Monad f b -> Final Monad f c #
Apply (Final Applicative f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<.>) :: Final Applicative f (a -> b) -> Final Applicative f a -> Final Applicative f b # (.>) :: Final Applicative f a -> Final Applicative f b -> Final Applicative f b # (<.) :: Final Applicative f a -> Final Applicative f b -> Final Applicative f a # liftF2 :: (a -> b -> c) -> Final Applicative f a -> Final Applicative f b -> Final Applicative f c #
Apply (Final (MonadReader r) f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<.>) :: Final (MonadReader r) f (a -> b) -> Final (MonadReader r) f a -> Final (MonadReader r) f b # (.>) :: Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f b # (<.) :: Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f a # liftF2 :: (a -> b -> c) -> Final (MonadReader r) f a -> Final (MonadReader r) f b -> Final (MonadReader r) f c #
Apply (Final Alternative f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<.>) :: Final Alternative f (a -> b) -> Final Alternative f a -> Final Alternative f b # (.>) :: Final Alternative f a -> Final Alternative f b -> Final Alternative f b # (<.) :: Final Alternative f a -> Final Alternative f b -> Final Alternative f a # liftF2 :: (a -> b -> c) -> Final Alternative f a -> Final Alternative f b -> Final Alternative f c #
Apply (Final Apply f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<.>) :: Final Apply f (a -> b) -> Final Apply f a -> Final Apply f b # (.>) :: Final Apply f a -> Final Apply f b -> Final Apply f b # (<.) :: Final Apply f a -> Final Apply f b -> Final Apply f a # liftF2 :: (a -> b -> c) -> Final Apply f a -> Final Apply f b -> Final Apply f c #
Apply (Final Bind f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<.>) :: Final Bind f (a -> b) -> Final Bind f a -> Final Bind f b # (.>) :: Final Bind f a -> Final Bind f b -> Final Bind f b # (<.) :: Final Bind f a -> Final Bind f b -> Final Bind f a # liftF2 :: (a -> b -> c) -> Final Bind f a -> Final Bind f b -> Final Bind f c #
Pointed (Final Pointed f) Source #
Instance details Defined in Data.HFunctor.Final Methods point :: a -> Final Pointed f a #
Plus (Final Plus f) Source #
Instance details Defined in Data.HFunctor.Final Methods zero :: Final Plus f a #
Alt (Final Plus f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<!>) :: Final Plus f a -> Final Plus f a -> Final Plus f a # some :: Applicative (Final Plus f) => Final Plus f a -> Final Plus f [a] # many :: Applicative (Final Plus f) => Final Plus f a -> Final Plus f [a] #
Alt (Final Alt f) Source #
Instance details Defined in Data.HFunctor.Final Methods (<!>) :: Final Alt f a -> Final Alt f a -> Final Alt f a # some :: Applicative (Final Alt f) => Final Alt f a -> Final Alt f [a] # many :: Applicative (Final Alt f) => Final Alt f a -> Final Alt f [a] #
Bind (Final Bind f) Source #
Instance details Defined in Data.HFunctor.Final Methods (>>-) :: Final Bind f a -> (a -> Final Bind f b) -> Final Bind f b # join :: Final Bind f (Final Bind f a) -> Final Bind f a #
type C (Final c) Source #
Instance details Defined in Data.HFunctor.Final type C (Final c) = c

fromFinal :: (Interpret t, c (t f)) => Final c f ~> t f Source #

Concretize a Final.

toFinal :: (Interpret t, C t (Final c f)) => t f ~> Final c f Source #

Finalize an Interpret instance.

toFinal :: Coyoneda f ~> Final Functor f
toFinal :: Ap f ~> Final Applicative f
toFinal :: Alt f ~> Final Alternative f
toFinal :: Free f ~> Final Monad f
toFinal :: Lift f ~> Final Pointed f
toFinal :: ListF f ~> Final Plus f

Note that the instance of c for Final c must be defined.

This operation can potentially forget structure in t. For example, we have:

toFinal :: Steps f ~> Final Alt f

In this process, we lose the "positional" structure of Steps.

In the case where toFinal doesn't lose any information, this will form an isomorphism with fromFinal, and t is known as the "Free c". For such a situation, t will have a FreeOf instance.

class Interpret t => FreeOf c t | t -> c where Source #

A typeclass associating a free structure with the typeclass it is free on.

This essentially lists instances of Interpret where a "trip" through Final will leave it unchanged.

fromFree . toFree == id
toFree . fromFree == id

This can be useful because Final doesn't have a concrete structure that you can pattern match on and inspect, but t might. This lets you work on a concrete structure if you desire.

Minimal complete definition

Nothing

Methods

fromFree :: t f ~> Final c f Source #

toFree :: Functor f => Final c f ~> t f Source #

fromFree :: C t (Final c f) => t f ~> Final c f Source #

toFree :: c (t f) => Final c f ~> t f Source #

Instances

FreeOf Monad Free Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Free f ~> Final Monad f Source # toFree :: Functor f => Final Monad f ~> Free f Source #
FreeOf Functor Coyoneda Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Coyoneda f ~> Final Functor f Source # toFree :: Functor f => Final Functor f ~> Coyoneda f Source #
FreeOf Applicative Ap Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Ap f ~> Final Applicative f Source # toFree :: Functor f => Final Applicative f ~> Ap f Source #
FreeOf Applicative Ap Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Ap f ~> Final Applicative f Source # toFree :: Functor f => Final Applicative f ~> Ap f Source #
FreeOf Alternative Alt Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Alt f ~> Final Alternative f Source # toFree :: Functor f => Final Alternative f ~> Alt f Source #
FreeOf Apply Ap1 Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Ap1 f ~> Final Apply f Source # toFree :: Functor f => Final Apply f ~> Ap1 f Source #
FreeOf Pointed MaybeApply Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: MaybeApply f ~> Final Pointed f Source # toFree :: Functor f => Final Pointed f ~> MaybeApply f Source #
FreeOf Pointed Lift Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Lift f ~> Final Pointed f Source # toFree :: Functor f => Final Pointed f ~> Lift f Source #
FreeOf Plus ListF Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: ListF f ~> Final Plus f Source # toFree :: Functor f => Final Plus f ~> ListF f Source #
FreeOf Alt NonEmptyF Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: NonEmptyF f ~> Final Alt f Source # toFree :: Functor f => Final Alt f ~> NonEmptyF f Source #
FreeOf Bind Free1 Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: Free1 f ~> Final Bind f Source # toFree :: Functor f => Final Bind f ~> Free1 f Source #
FreeOf (Unconstrained :: (Type -> Type) -> Constraint) (IdentityT :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Data.HFunctor.Final Methods fromFree :: IdentityT f ~> Final Unconstrained f Source # toFree :: Functor f => Final Unconstrained f ~> IdentityT f Source #

finalizing :: (FreeOf c t, Functor f) => t f <~> Final c f Source #

The isomorphism between a free structure and its encoding as Final.

hoistFinalC :: (forall g x. (c g => g x) -> d g => g x) -> Final c f a -> Final d f a Source #

Re-interpret the context under a Final.

liftFinal0 :: (forall g. c g => g a) -> Final c f a Source #

Lift an action into a Final.

liftFinal1 :: (forall g. c g => g a -> g b) -> Final c f a -> Final c f b Source #

Map the action in a Final.

liftFinal2 :: (forall g. c g => g a -> g b -> g d) -> Final c f a -> Final c f b -> Final c f d Source #

Merge two Final actions.