Data.HFunctor.Final

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

Documentation

newtype Final c f a

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)

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)

Defined in Data.HFunctor.Final

Associated Types

type C (Final c) :: (Type -> Type) -> Constraint

Methods

retract :: C (Final c) f => Final c f ~> f

interpret :: C (Final c) g => (f ~> g) -> Final c f ~> g

Inject (Final c :: (Type -> Type) -> Type -> Type)

Defined in Data.HFunctor.Final

Methods

inject :: f ~> Final c f

HFunctor (Final c :: (Type -> Type) -> Type -> Type)

Defined in Data.HFunctor.Final

Methods

hmap :: (f ~> g) -> Final c f ~> Final c g

Monad (Final Monad f)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

Defined in Data.HFunctor.Final

Methods

point :: a -> Final Pointed f a

Plus (Final Plus f)

Defined in Data.HFunctor.Final

Methods

zero :: Final Plus f a

Alt (Final Plus f)

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)

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)

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)

Defined in Data.HFunctor.Final

type C (Final c) = c

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

Concretize a Final.

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

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

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

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

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

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

Instances

FreeOf Monad Free

Defined in Data.HFunctor.Final

Methods

fromFree :: Free f ~> Final Monad f

toFree :: Functor f => Final Monad f ~> Free f

FreeOf Functor Coyoneda

Defined in Data.HFunctor.Final

Methods

fromFree :: Coyoneda f ~> Final Functor f

toFree :: Functor f => Final Functor f ~> Coyoneda f

FreeOf Applicative Ap

Defined in Data.HFunctor.Final

Methods

fromFree :: Ap f ~> Final Applicative f

toFree :: Functor f => Final Applicative f ~> Ap f

FreeOf Applicative Ap

Defined in Data.HFunctor.Final

Methods

fromFree :: Ap f ~> Final Applicative f

toFree :: Functor f => Final Applicative f ~> Ap f

FreeOf Alternative Alt

Defined in Data.HFunctor.Final

Methods

fromFree :: Alt f ~> Final Alternative f

toFree :: Functor f => Final Alternative f ~> Alt f

FreeOf Apply Ap1

Defined in Data.HFunctor.Final

Methods

fromFree :: Ap1 f ~> Final Apply f

toFree :: Functor f => Final Apply f ~> Ap1 f

FreeOf Pointed MaybeApply

Defined in Data.HFunctor.Final

Methods

fromFree :: MaybeApply f ~> Final Pointed f

toFree :: Functor f => Final Pointed f ~> MaybeApply f

FreeOf Pointed Lift

Defined in Data.HFunctor.Final

Methods

fromFree :: Lift f ~> Final Pointed f

toFree :: Functor f => Final Pointed f ~> Lift f

FreeOf Plus ListF

Defined in Data.HFunctor.Final

Methods

fromFree :: ListF f ~> Final Plus f

toFree :: Functor f => Final Plus f ~> ListF f

FreeOf Alt NonEmptyF

Defined in Data.HFunctor.Final

Methods

fromFree :: NonEmptyF f ~> Final Alt f

toFree :: Functor f => Final Alt f ~> NonEmptyF f

FreeOf Bind Free1

Defined in Data.HFunctor.Final

Methods

fromFree :: Free1 f ~> Final Bind f

toFree :: Functor f => Final Bind f ~> Free1 f

FreeOf (Unconstrained :: (Type -> Type) -> Constraint) (IdentityT :: (Type -> Type) -> Type -> Type)

Defined in Data.HFunctor.Final

Methods

fromFree :: IdentityT f ~> Final Unconstrained f

toFree :: Functor f => Final Unconstrained f ~> IdentityT f

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

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

Re-interpret the context under a Final.

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

Lift an action into a Final.

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

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

Merge two Final actions.