Data.Functor.Transformer

Functors on indexed-types.

Functor

class FunctorT (t :: (k -> Type) -> k' -> Type) where

Functor from indexed-types to indexed-types. Instances of FunctorT should satisfy the following laws:

tmap id = id
tmap f . tmap g = tmap (f . g)

There is a default tmap implementation for Generic types, so instances can derived automatically.

Minimal complete definition

Nothing

Methods

tmap :: (forall a. f a -> g a) -> forall x. t f x -> t g x

tmap :: forall f g x. CanDeriveFunctorT t f g x => (forall a. f a -> g a) -> t f x -> t g x

Instances

FunctorT (IdentityT :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'0). IdentityT f x -> IdentityT g x

FunctorT (Reverse :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'0). Reverse f x -> Reverse g x

FunctorT (Backwards :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'0). Backwards f x -> Backwards g x

FunctorT (ReaderT r :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'0). ReaderT r f x -> ReaderT r g x

FunctorT (Sum f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f0 a -> g a) -> forall (x :: k'0). Sum f f0 x -> Sum f g x

FunctorT (Product f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f0 a -> g a) -> forall (x :: k'0). Product f f0 x -> Product f g x

Functor f => FunctorT (Compose f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f0 a -> g a) -> forall (x :: k'0). Compose f f0 x -> Compose f g x

(forall (f :: k'). FunctorB (b f)) => FunctorT (Flip b :: (k -> Type) -> k' -> Type)

Defined in Barbies.Bi

Methods

tmap :: (forall (a :: k0). f a -> g a) -> forall (x :: k'0). Flip b f x -> Flip b g x

FunctorT Lift

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). Lift f x -> Lift g x

FunctorT MaybeT

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). MaybeT f x -> MaybeT g x

FunctorT (WriterT w :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). WriterT w f x -> WriterT w g x

FunctorT (WriterT w :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). WriterT w f x -> WriterT w g x

FunctorT (StateT s :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). StateT s f x -> StateT s g x

FunctorT (StateT s :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). StateT s f x -> StateT s g x

FunctorT (ExceptT e :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). ExceptT e f x -> ExceptT e g x

FunctorT (RWST r w s :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). RWST r w s f x -> RWST r w s g x

FunctorT (RWST r w s :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.FunctorT

Methods

tmap :: (forall (a :: k). f a -> g a) -> forall (x :: k'). RWST r w s f x -> RWST r w s g x

Traversable

class FunctorT t => TraversableT (t :: (k -> Type) -> k' -> Type) where

Indexed-functors that can be traversed from left to right. Instances should satisfy the following laws:

 t . ttraverse f   = ttraverse (t . f)  -- naturality
ttraverse Identity = Identity           -- identity
ttraverse (Compose . fmap g . f) = Compose . fmap (ttraverse g) . ttraverse f -- composition

There is a default ttraverse implementation for Generic types, so instances can derived automatically.

Minimal complete definition

Nothing

Methods

ttraverse :: Applicative e => (forall a. f a -> e (g a)) -> forall x. t f x -> e (t g x)

ttraverse :: (Applicative e, CanDeriveTraversableT t f g x) => (forall a. f a -> e (g a)) -> t f x -> e (t g x)

Instances

TraversableT (IdentityT :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'0). IdentityT f x -> e (IdentityT g x)

TraversableT (Reverse :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'0). Reverse f x -> e (Reverse g x)

TraversableT (Backwards :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'0). Backwards f x -> e (Backwards g x)

TraversableT (Sum f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f0 a -> e (g a)) -> forall (x :: k'0). Sum f f0 x -> e (Sum f g x)

TraversableT (Product f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f0 a -> e (g a)) -> forall (x :: k'0). Product f f0 x -> e (Product f g x)

Traversable f => TraversableT (Compose f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f0 a -> e (g a)) -> forall (x :: k'0). Compose f f0 x -> e (Compose f g x)

(forall (f :: k'). TraversableB (b f)) => TraversableT (Flip b :: (k -> Type) -> k' -> Type)

Defined in Barbies.Bi

Methods

ttraverse :: Applicative e => (forall (a :: k0). f a -> e (g a)) -> forall (x :: k'0). Flip b f x -> e (Flip b g x)

TraversableT Lift

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'). Lift f x -> e (Lift g x)

TraversableT MaybeT

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'). MaybeT f x -> e (MaybeT g x)

TraversableT (WriterT w :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'). WriterT w f x -> e (WriterT w g x)

TraversableT (WriterT w :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e => (forall (a :: k). f a -> e (g a)) -> forall (x :: k'). WriterT w f x -> e (WriterT w g x)

TraversableT (ExceptT e :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.TraversableT

Methods

ttraverse :: Applicative e0 => (forall (a :: k). f a -> e0 (g a)) -> forall (x :: k'). ExceptT e f x -> e0 (ExceptT e g x)

Utility functions

ttraverse_ :: (TraversableT t, Applicative e) => (forall a. f a -> e c) -> t f x -> e ()

Map each element to an action, evaluate these actions from left to right, and ignore the results.

tfoldMap :: (TraversableT t, Monoid m) => (forall a. f a -> m) -> t f x -> m

Map each element to a monoid, and combine the results.

tsequence :: (Applicative e, TraversableT t) => t (Compose e f) x -> e (t f x)

Evaluate each action in the structure from left to right, and collect the results.

tsequence' :: (Applicative e, TraversableT t) => t e x -> e (t Identity x)

A version of tsequence with f specialized to Identity.

Applicative

class FunctorT t => ApplicativeT (t :: (k -> Type) -> k' -> Type) where

A FunctorT with application, providing operations to:

• embed an "empty" value (tpure)
• align and combine values (tprod)

It should satisfy the following laws:

Naturality of tprod

tmap ((Pair a b) -> Pair (f a) (g b)) (u `tprod' v) = tmap f u `tprod' tmap g v

Left and right identity

tmap ((Pair _ b) -> b) (tpure e `tprod' v) = v
tmap ((Pair a _) -> a) (u `tprod' tpure e) = u

Associativity

tmap ((Pair a (Pair b c)) -> Pair (Pair a b) c) (u `tprod' (v `tprod' w)) = (u `tprod' v) `tprod' w

It is to FunctorT in the same way is Applicative relates to Functor. For a presentation of Applicative as a monoidal functor, see Section 7 of Applicative Programming with Effects.

There is a default implementation of tprod and tpure based on Generic. Intuitively, it works on types where the value of tpure is uniquely defined. This corresponds rougly to record types (in the presence of sums, there would be several candidates for tpure), where every field is either a Monoid or covered by the argument f.

Minimal complete definition

Nothing

Methods

tpure :: (forall a. f a) -> forall x. t f x

tprod :: t f x -> t g x -> t (f `Product` g) x

tpure :: CanDeriveApplicativeT t f f x => (forall a. f a) -> t f x

tprod :: CanDeriveApplicativeT t f g x => t f x -> t g x -> t (f `Product` g) x

Instances

ApplicativeT (Reverse :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.ApplicativeT

Methods

tpure :: (forall (a :: k). f a) -> forall (x :: k'0). Reverse f x

tprod :: Reverse f x -> Reverse g x -> Reverse (Product f g) x

Applicative f => ApplicativeT (Compose f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.ApplicativeT

Methods

tpure :: (forall (a :: k). f0 a) -> forall (x :: k'0). Compose f f0 x

tprod :: Compose f f0 x -> Compose f g x -> Compose f (Product f0 g) x

(forall (f :: k'). ApplicativeB (b f)) => ApplicativeT (Flip b :: (k -> Type) -> k' -> Type)

Defined in Barbies.Bi

Methods

tpure :: (forall (a :: k0). f a) -> forall (x :: k'0). Flip b f x

tprod :: Flip b f x -> Flip b g x -> Flip b (Product f g) x

Alternative f => ApplicativeT (Product f :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.ApplicativeT

Methods

tpure :: (forall (a :: k). f0 a) -> forall (x :: k'). Product f f0 x

tprod :: Product f f0 x -> Product f g x -> Product f (Product f0 g) x

Alternative f => ApplicativeT (Sum f :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.ApplicativeT

Methods

tpure :: (forall (a :: k). f0 a) -> forall (x :: k'). Sum f f0 x

tprod :: Sum f f0 x -> Sum f g x -> Sum f (Product f0 g) x

Utility functions

tzip :: ApplicativeT t => t f x -> t g x -> t (f `Product` g) x

An alias of tprod.

tunzip :: ApplicativeT t => t (f `Product` g) x -> (t f x, t g x)

An equivalent of unzip.

tzipWith :: ApplicativeT t => (forall a. f a -> g a -> h a) -> t f x -> t g x -> t h x

An equivalent of zipWith.

tzipWith3 :: ApplicativeT t => (forall a. f a -> g a -> h a -> i a) -> t f x -> t g x -> t h x -> t i x

An equivalent of zipWith3.

tzipWith4 :: ApplicativeT t => (forall a. f a -> g a -> h a -> i a -> j a) -> t f x -> t g x -> t h x -> t i x -> t j x

An equivalent of zipWith4.

Monad

class FunctorT t => MonadT t where

Some endo-functors on indexed-types are monads. Common examples would be "functor-transformers", like Compose or ReaderT. In that sense, MonadT is similar to MonadTrans but with additional structure (see also mmorph's MMonad class).

Notice though that while lift assumes a Monad instance of the value to be lifted, tlift has no such constraint. This means we cannot have instances for most "monad transformers", since lifting typically involves an fmap.

MonadT also corresponds to the indexed-monad of Kleisli arrows of outrageous fortune.

Instances of this class should to satisfy the monad laws. They laws can stated either in terms of (tlift, tjoin) or (tlift, tembed). In the former:

tmap h . tlift = tlift . h
tmap h . tjoin = tjoin . tmap (tmap h)
tjoin . tlift  = id
tjoin . 'tmap tlift' = id
tjoin . tjoin = tjoin . tmap tjoin

In the latter:

tembed f . tlift = f
tembed tlift = id
tembed f . tembed g = tembed (tembed f . g)

Minimal complete definition

tlift, tjoin | tlift, tembed

Methods

tlift :: f a -> t f a

Lift a functor to a transformed functor.

tjoin :: t (t f) a -> t f a

The conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

tembed :: MonadT t => (forall x. f x -> t g x) -> t f a -> t g a

Analogous to (=<<).

Instances

MonadT (Reverse :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f a -> Reverse f a

tjoin :: Reverse (Reverse f) a -> Reverse f a

tembed :: MonadT Reverse => (forall (x :: k'0). f x -> Reverse g x) -> Reverse f a -> Reverse g a

MonadT (IdentityT :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f a -> IdentityT f a

tjoin :: IdentityT (IdentityT f) a -> IdentityT f a

tembed :: MonadT IdentityT => (forall (x :: k'0). f x -> IdentityT g x) -> IdentityT f a -> IdentityT g a

MonadT (Backwards :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f a -> Backwards f a

tjoin :: Backwards (Backwards f) a -> Backwards f a

tembed :: MonadT Backwards => (forall (x :: k'0). f x -> Backwards g x) -> Backwards f a -> Backwards g a

MonadT (ReaderT r :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f a -> ReaderT r f a

tjoin :: ReaderT r (ReaderT r f) a -> ReaderT r f a

tembed :: MonadT (ReaderT r) => (forall (x :: k'0). f x -> ReaderT r g x) -> ReaderT r f a -> ReaderT r g a

MonadT (Sum f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f0 a -> Sum f f0 a

tjoin :: Sum f (Sum f f0) a -> Sum f f0 a

tembed :: MonadT (Sum f) => (forall (x :: k'0). f0 x -> Sum f g x) -> Sum f f0 a -> Sum f g a

Monad f => MonadT (Compose f :: (k' -> Type) -> k' -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f0 a -> Compose f f0 a

tjoin :: Compose f (Compose f f0) a -> Compose f f0 a

tembed :: MonadT (Compose f) => (forall (x :: k'0). f0 x -> Compose f g x) -> Compose f f0 a -> Compose f g a

MonadT Lift

Defined in Barbies.Internal.MonadT

Methods

tlift :: f a -> Lift f a

tjoin :: Lift (Lift f) a -> Lift f a

tembed :: MonadT Lift => (forall (x :: k'). f x -> Lift g x) -> Lift f a -> Lift g a

Alternative f => MonadT (Product f :: (Type -> Type) -> Type -> Type)

Defined in Barbies.Internal.MonadT

Methods

tlift :: f0 a -> Product f f0 a

tjoin :: Product f (Product f f0) a -> Product f f0 a

tembed :: MonadT (Product f) => (forall (x :: k'). f0 x -> Product f g x) -> Product f f0 a -> Product f g a

Constraints and instance dictionaries

class FunctorT t => ConstraintsT (t :: (kl -> *) -> kr -> *) where

Instances of this class provide means to talk about constraints, both at compile-time, using AllT, and at run-time, in the form of Dict, via taddDicts.

A manual definition would look like this:

data T f a = A (f Int) (f String) | B (f Bool) (f Int)

instance ConstraintsT T where
  type AllT c T = (c Int, c String, c Bool)

  taddDicts t = case t of
    A x y -> A (Pair Dict x) (Pair Dict y)
    B z w -> B (Pair Dict z) (Pair Dict w)

Now, when we given a T f, if we need to use the Show instance of their fields, we can use:

taddDicts :: AllT Show t => t f -> t (Dict Show `Product' f)

There is a default implementation of ConstraintsT for Generic types, so in practice one will simply do:

derive instance Generic (T f a)
instance ConstraintsT T

Minimal complete definition

Nothing

Associated Types

type AllT (c :: k -> Constraint) t :: Constraint

AllT c t should contain a constraint c a for each a occurring under an f in t f.

For requiring constraints of the form c (f a), use AllTF.

Methods

taddDicts :: forall c f x. AllT c t => t f x -> t (Dict c `Product` f) x

taddDicts :: forall c f x. (CanDeriveConstraintsT c t f x, AllT c t) => t f x -> t (Dict c `Product` f) x

type AllTF c f t = AllT (ClassF c f) t

Similar to AllT but will put the functor argument f between the constraint c and the type a.

Utility functions

tmapC :: forall c t f g x. (AllT c t, ConstraintsT t) => (forall a. c a => f a -> g a) -> t f x -> t g x

Like tmap but a constraint is allowed to be required on each element of t.

ttraverseC :: forall c t f g e x. (TraversableT t, ConstraintsT t, AllT c t, Applicative e) => (forall a. c a => f a -> e (g a)) -> t f x -> e (t g x)

Like ttraverse but with a constraint on the elements of t.

Support for generic derivations

newtype Rec (p :: Type) a x

Constructors

Rec

Fields

• unRec :: K1 R a x

Instances

GTraversable (n :: k3) (f :: k2 -> Type) (g :: k2 -> Type) (Rec a a :: k1 -> Type) (Rec a a :: k1 -> Type)

Defined in Barbies.Generics.Traversable

Methods

gtraverse :: Applicative t => Proxy n -> (forall (a0 :: k). f a0 -> t (g a0)) -> Rec a a x -> t (Rec a a x)

GConstraints n (c :: k3 -> Constraint) (f :: k2) (Rec a' a :: Type -> Type) (Rec a a :: k1 -> Type) (Rec a a :: k1 -> Type)

Defined in Barbies.Generics.Constraints

Methods

gaddDicts :: GAll n c (Rec a' a) => Rec a a x -> Rec a a x

Monoid x => GApplicative (n :: k3) (f :: k2 -> Type) (g :: k2 -> Type) (Rec x x :: k1 -> Type) (Rec x x :: k1 -> Type) (Rec x x :: k1 -> Type)

Defined in Barbies.Generics.Applicative

Methods

gprod :: Proxy n -> Proxy f -> Proxy g -> Rec x x x0 -> Rec x x x0 -> Rec x x x0

gpure :: (f ~ g, Rec x x ~ Rec x x) => Proxy n -> Proxy f -> Proxy (Rec x x) -> Proxy (Rec x x) -> (forall (a :: k). f a) -> Rec x x x0

GFunctor n (f :: k2 -> Type) (g :: k2 -> Type) (Rec x x :: k1 -> Type) (Rec x x :: k1 -> Type)

Defined in Barbies.Generics.Functor

Methods

gmap :: Proxy n -> (forall (a :: k). f a -> g a) -> Rec x x x0 -> Rec x x x0

repbi ~ repbb => GBare n (Rec repbi repbi :: k -> Type) (Rec repbb repbb :: k -> Type)

Defined in Barbies.Generics.Bare

Methods

gstrip :: Proxy n -> Rec repbi repbi x -> Rec repbb repbb x

gcover :: Proxy n -> Rec repbb repbb x -> Rec repbi repbi x

type GAll n (c :: k -> Constraint) (Rec a a :: Type -> Type)

Defined in Barbies.Generics.Constraints

type GAll n (c :: k -> Constraint) (Rec a a :: Type -> Type) = ()