Safe Haskell	Safe-Inferred
Language	Haskell2010

Data.Functor.Transformer

Contents

Functor
Traversable
- Utility functions
Distributive
Applicative
- Utility functions
Monad
Constraints and instance dictionaries
- Utility functions
Support for generic derivations

Description

Functors on indexed-types.

Synopsis

class FunctorT (t :: (k -> Type) -> k' -> Type) where
- tmap :: (forall a. f a -> g a) -> t f x -> t g x
class FunctorT t => TraversableT (t :: (k -> Type) -> k' -> Type) where
- ttraverse :: Applicative e => (forall a. f a -> e (g a)) -> t f x -> e (t g x)
ttraverse_ :: (TraversableT t, Applicative e) => (forall a. f a -> e c) -> t f x -> e ()
tfoldMap :: (TraversableT t, Monoid m) => (forall a. f a -> m) -> t f x -> m
tsequence :: (Applicative e, TraversableT t) => t (Compose e f) x -> e (t f x)
tsequence' :: (Applicative e, TraversableT t) => t e x -> e (t Identity x)
class FunctorT t => DistributiveT (t :: (Type -> Type) -> i -> Type) where
- tdistribute :: Functor f => f (t g x) -> t (Compose f g) x
tdistribute' :: (DistributiveT t, Functor f) => f (t Identity x) -> t f x
tcotraverse :: (DistributiveT t, Functor f) => (forall a. f (g a) -> f a) -> f (t g x) -> t f x
tdecompose :: DistributiveT t => (a -> t Identity x) -> t ((->) a) x
trecompose :: FunctorT t => t ((->) a) x -> a -> t Identity x
class FunctorT t => ApplicativeT (t :: (k -> Type) -> k' -> Type) where
- tpure :: (forall a. f a) -> t f x
- tprod :: t f x -> t g x -> t (f `Product` g) x
tzip :: ApplicativeT t => t f x -> t g x -> t (f `Product` g) x
tunzip :: ApplicativeT t => t (f `Product` g) x -> (t f x, t g x)
tzipWith :: ApplicativeT t => (forall a. f a -> g a -> h a) -> t f x -> t g x -> t h x
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
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
class FunctorT t => MonadT t where
- tlift :: f a -> t f a
- tjoin :: t (t f) a -> t f a
- tembed :: MonadT t => (forall x. f x -> t g x) -> t f a -> t g a
class FunctorT t => ConstraintsT (t :: (kl -> Type) -> kr -> Type) where
- type AllT (c :: k -> Constraint) t :: Constraint
- taddDicts :: forall c f x. AllT c t => t f x -> t (Dict c `Product` f) x
type AllTF c f t = AllT (ClassF c f) t
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
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)
newtype Rec (p :: Type) a x = Rec {
- unRec :: K1 R a x
}

Functor

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

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) -> t f x -> t g x Source #

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

Instances

Instances details

FunctorT Lift Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> Lift f x -> Lift g x Source #
FunctorT MaybeT Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> MaybeT f x -> MaybeT g x Source #
FunctorT (AccumT w :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> AccumT w f x -> AccumT w g x Source #
FunctorT (ExceptT e :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> ExceptT e f x -> ExceptT e g x Source #
FunctorT (ReaderT r :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> ReaderT r f x -> ReaderT r g x Source #
FunctorT (StateT s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> StateT s f x -> StateT s g x Source #
FunctorT (StateT s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> StateT s f x -> StateT s g x Source #
FunctorT (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> WriterT w f x -> WriterT w g x Source #
FunctorT (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> WriterT w f x -> WriterT w g x Source #
FunctorT (Backwards :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'0). (forall (a :: k). f a -> g a) -> Backwards f x -> Backwards g x Source #
FunctorT (IdentityT :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'0). (forall (a :: k). f a -> g a) -> IdentityT f x -> IdentityT g x Source #
FunctorT (Reverse :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'0). (forall (a :: k). f a -> g a) -> Reverse f x -> Reverse g x Source #
FunctorT (Product f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f0 g (x :: k'0). (forall (a :: k). f0 a -> g a) -> Product f f0 x -> Product f g x Source #
FunctorT (Sum f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f0 g (x :: k'0). (forall (a :: k). f0 a -> g a) -> Sum f f0 x -> Sum f g x Source #
FunctorT (RWST r w s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> RWST r w s f x -> RWST r w s g x Source #
FunctorT (RWST r w s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f g (x :: k'). (forall (a :: k). f a -> g a) -> RWST r w s f x -> RWST r w s g x Source #
(forall (f :: k'). FunctorB (b f)) => FunctorT (Flip b :: (k -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Bi Methods tmap :: forall f g (x :: k'0). (forall (a :: k0). f a -> g a) -> Flip b f x -> Flip b g x Source #
Functor f => FunctorT (Compose f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.FunctorT Methods tmap :: forall f0 g (x :: k'0). (forall (a :: k). f0 a -> g a) -> Compose f f0 x -> Compose f g x Source #

Traversable

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

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)) -> t f x -> e (t g x) Source #

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

Instances

Instances details

TraversableT Lift Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'). Applicative e => (forall (a :: k). f a -> e (g a)) -> Lift f x -> e (Lift g x) Source #
TraversableT MaybeT Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'). Applicative e => (forall (a :: k). f a -> e (g a)) -> MaybeT f x -> e (MaybeT g x) Source #
TraversableT (ExceptT e :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e0 f g (x :: k'). Applicative e0 => (forall (a :: k). f a -> e0 (g a)) -> ExceptT e f x -> e0 (ExceptT e g x) Source #
TraversableT (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'). Applicative e => (forall (a :: k). f a -> e (g a)) -> WriterT w f x -> e (WriterT w g x) Source #
TraversableT (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'). Applicative e => (forall (a :: k). f a -> e (g a)) -> WriterT w f x -> e (WriterT w g x) Source #
TraversableT (Backwards :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'0). Applicative e => (forall (a :: k). f a -> e (g a)) -> Backwards f x -> e (Backwards g x) Source #
TraversableT (IdentityT :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'0). Applicative e => (forall (a :: k). f a -> e (g a)) -> IdentityT f x -> e (IdentityT g x) Source #
TraversableT (Reverse :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f g (x :: k'0). Applicative e => (forall (a :: k). f a -> e (g a)) -> Reverse f x -> e (Reverse g x) Source #
TraversableT (Product f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f0 g (x :: k'0). Applicative e => (forall (a :: k). f0 a -> e (g a)) -> Product f f0 x -> e (Product f g x) Source #
TraversableT (Sum f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f0 g (x :: k'0). Applicative e => (forall (a :: k). f0 a -> e (g a)) -> Sum f f0 x -> e (Sum f g x) Source #
(forall (f :: k'). TraversableB (b f)) => TraversableT (Flip b :: (k -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Bi Methods ttraverse :: forall e f g (x :: k'0). Applicative e => (forall (a :: k0). f a -> e (g a)) -> Flip b f x -> e (Flip b g x) Source #
Traversable f => TraversableT (Compose f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.TraversableT Methods ttraverse :: forall e f0 g (x :: k'0). Applicative e => (forall (a :: k). f0 a -> e (g a)) -> Compose f f0 x -> e (Compose f g x) Source #

Utility functions

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

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 Source #

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

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

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) Source #

A version of tsequence with f specialized to Identity.

Distributive

class FunctorT t => DistributiveT (t :: (Type -> Type) -> i -> Type) where Source #

A FunctorT where the effects can be distributed to the fields: tdistribute turns an effectful way of building a transformer-type into a pure transformer-type with effectful ways of computing the values of its fields.

This class is the categorical dual of TraversableT, with tdistribute the dual of tsequence and tcotraverse the dual of ttraverse. As such, instances need to satisfy these laws:

tdistribute . h = tmap (Compose . h . getCompose) . tdistribute    -- naturality
tdistribute . Identity = tmap (Compose . Identity)                 -- identity
tdistribute . Compose = fmap (Compose . Compose . fmap getCompose . getCompose) . tdistribute . fmap distribute -- composition

By specializing f to ((->) a) and g to Identity, we can define a function that decomposes a function on distributive transformers into a collection of simpler functions:

tdecompose :: DistributiveT b => (a -> b Identity) -> b ((->) a)
tdecompose = tmap (fmap runIdentity . getCompose) . tdistribute

Lawful instances of the class can then be characterized as those that satisfy:

trecompose . tdecompose = id
tdecompose . trecompose = id

This means intuitively that instances need to have a fixed shape (i.e. no sum-types can be involved). Typically, this means record types, as long as they don't contain fields where the functor argument is not applied.

There is a default implementation of tdistribute based on Generic. Intuitively, it works on product types where the shape of a pure value is uniquely defined and every field is covered by the argument f.

Minimal complete definition

Nothing

Methods

tdistribute :: Functor f => f (t g x) -> t (Compose f g) x Source #

default tdistribute :: forall f g x. CanDeriveDistributiveT t f g x => f (t g x) -> t (Compose f g) x Source #

Instances

Instances details

DistributiveT MaybeT Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (MaybeT g x) -> MaybeT (Compose f g) x Source #
DistributiveT (Backwards :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (Backwards g x) -> Backwards (Compose f g) x Source #
DistributiveT (AccumT w :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (AccumT w g x) -> AccumT w (Compose f g) x Source #
DistributiveT (ExceptT e :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (ExceptT e g x) -> ExceptT e (Compose f g) x Source #
DistributiveT (IdentityT :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (IdentityT g x) -> IdentityT (Compose f g) x Source #
DistributiveT (ReaderT r :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (ReaderT r g x) -> ReaderT r (Compose f g) x Source #
DistributiveT (StateT s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (StateT s g x) -> StateT s (Compose f g) x Source #
DistributiveT (StateT s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (StateT s g x) -> StateT s (Compose f g) x Source #
DistributiveT (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (WriterT w g x) -> WriterT w (Compose f g) x Source #
DistributiveT (WriterT w :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (WriterT w g x) -> WriterT w (Compose f g) x Source #
DistributiveT (Reverse :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (Reverse g x) -> Reverse (Compose f g) x Source #
Distributive f => DistributiveT (Compose f :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f0 (g :: Type -> Type) (x :: i). Functor f0 => f0 (Compose f g x) -> Compose f (Compose f0 g) x Source #
DistributiveT (RWST r w s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (RWST r w s g x) -> RWST r w s (Compose f g) x Source #
DistributiveT (RWST r w s :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.DistributiveT Methods tdistribute :: forall f (g :: Type -> Type) (x :: i). Functor f => f (RWST r w s g x) -> RWST r w s (Compose f g) x Source #
(forall (f :: i). DistributiveB (b f)) => DistributiveT (Flip b :: (Type -> Type) -> i -> Type) Source #
Instance details Defined in Barbies.Bi Methods tdistribute :: forall f (g :: Type -> Type) (x :: i0). Functor f => f (Flip b g x) -> Flip b (Compose f g) x Source #

tdistribute' :: (DistributiveT t, Functor f) => f (t Identity x) -> t f x Source #

A version of tdistribute with g specialized to Identity.

tcotraverse :: (DistributiveT t, Functor f) => (forall a. f (g a) -> f a) -> f (t g x) -> t f x Source #

Dual of ttraverse

tdecompose :: DistributiveT t => (a -> t Identity x) -> t ((->) a) x Source #

Decompose a function returning a distributive transformer, into a collection of simpler functions.

trecompose :: FunctorT t => t ((->) a) x -> a -> t Identity x Source #

Recompose a decomposed function.

Applicative

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

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) -> t f x Source #

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

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

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

Instances

Instances details

ApplicativeT (Reverse :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.ApplicativeT Methods tpure :: forall f (x :: k'0). (forall (a :: k). f a) -> Reverse f x Source # tprod :: forall (f :: k -> Type) (x :: k'0) (g :: k -> Type). Reverse f x -> Reverse g x -> Reverse (Product f g) x Source #
Alternative f => ApplicativeT (Product f :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.ApplicativeT Methods tpure :: forall f0 (x :: k'). (forall (a :: k). f0 a) -> Product f f0 x Source # tprod :: forall (f0 :: k -> Type) (x :: k') (g :: k -> Type). Product f f0 x -> Product f g x -> Product f (Product f0 g) x Source #
Alternative f => ApplicativeT (Sum f :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.ApplicativeT Methods tpure :: forall f0 (x :: k'). (forall (a :: k). f0 a) -> Sum f f0 x Source # tprod :: forall (f0 :: k -> Type) (x :: k') (g :: k -> Type). Sum f f0 x -> Sum f g x -> Sum f (Product f0 g) x Source #
(forall (f :: k'). ApplicativeB (b f)) => ApplicativeT (Flip b :: (k -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Bi Methods tpure :: forall f (x :: k'0). (forall (a :: k0). f a) -> Flip b f x Source # tprod :: forall (f :: k0 -> Type) (x :: k'0) (g :: k0 -> Type). Flip b f x -> Flip b g x -> Flip b (Product f g) x Source #
Applicative f => ApplicativeT (Compose f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.ApplicativeT Methods tpure :: forall f0 (x :: k'0). (forall (a :: k). f0 a) -> Compose f f0 x Source # tprod :: forall (f0 :: k -> Type) (x :: k'0) (g :: k -> Type). Compose f f0 x -> Compose f g x -> Compose f (Product f0 g) x Source #

Utility functions

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

An alias of tprod.

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

An equivalent of unzip.

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

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 Source #

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 Source #

An equivalent of zipWith4.

Monad

class FunctorT t => MonadT t where Source #

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 Source #

Lift a functor to a transformed functor.

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

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 Source #

Analogous to (=<<).

Instances

Instances details

MonadT Lift Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f (a :: k'). f a -> Lift f a Source # tjoin :: forall (f :: k' -> Type) (a :: k'). Lift (Lift f) a -> Lift f a Source # tembed :: forall f (g :: k' -> Type) (a :: k'). MonadT Lift => (forall (x :: k'). f x -> Lift g x) -> Lift f a -> Lift g a Source #
MonadT (ReaderT r :: (Type -> Type) -> Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f (a :: k'). f a -> ReaderT r f a Source # tjoin :: forall (f :: k' -> Type) (a :: k'). ReaderT r (ReaderT r f) a -> ReaderT r f a Source # tembed :: forall f (g :: k' -> Type) (a :: k'). MonadT (ReaderT r) => (forall (x :: k'). f x -> ReaderT r g x) -> ReaderT r f a -> ReaderT r g a Source #
MonadT (Backwards :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f (a :: k'0). f a -> Backwards f a Source # tjoin :: forall (f :: k'0 -> Type) (a :: k'0). Backwards (Backwards f) a -> Backwards f a Source # tembed :: forall f (g :: k'0 -> Type) (a :: k'0). MonadT Backwards => (forall (x :: k'0). f x -> Backwards g x) -> Backwards f a -> Backwards g a Source #
MonadT (IdentityT :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f (a :: k'0). f a -> IdentityT f a Source # tjoin :: forall (f :: k'0 -> Type) (a :: k'0). IdentityT (IdentityT f) a -> IdentityT f a Source # tembed :: forall f (g :: k'0 -> Type) (a :: k'0). MonadT IdentityT => (forall (x :: k'0). f x -> IdentityT g x) -> IdentityT f a -> IdentityT g a Source #
MonadT (Reverse :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f (a :: k'0). f a -> Reverse f a Source # tjoin :: forall (f :: k'0 -> Type) (a :: k'0). Reverse (Reverse f) a -> Reverse f a Source # tembed :: forall f (g :: k'0 -> Type) (a :: k'0). MonadT Reverse => (forall (x :: k'0). f x -> Reverse g x) -> Reverse f a -> Reverse g a Source #
Alternative f => MonadT (Product f :: (Type -> Type) -> Type -> Type) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f0 (a :: k'). f0 a -> Product f f0 a Source # tjoin :: forall (f0 :: k' -> Type) (a :: k'). Product f (Product f f0) a -> Product f f0 a Source # tembed :: forall f0 (g :: k' -> Type) (a :: k'). MonadT (Product f) => (forall (x :: k'). f0 x -> Product f g x) -> Product f f0 a -> Product f g a Source #
MonadT (Sum f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f0 (a :: k'0). f0 a -> Sum f f0 a Source # tjoin :: forall (f0 :: k'0 -> Type) (a :: k'0). Sum f (Sum f f0) a -> Sum f f0 a Source # tembed :: forall f0 (g :: k'0 -> Type) (a :: k'0). MonadT (Sum f) => (forall (x :: k'0). f0 x -> Sum f g x) -> Sum f f0 a -> Sum f g a Source #
Monad f => MonadT (Compose f :: (k' -> Type) -> k' -> Type) Source #
Instance details Defined in Barbies.Internal.MonadT Methods tlift :: forall f0 (a :: k'0). f0 a -> Compose f f0 a Source # tjoin :: forall (f0 :: k'0 -> Type) (a :: k'0). Compose f (Compose f f0) a -> Compose f f0 a Source # tembed :: forall f0 (g :: k'0 -> Type) (a :: k'0). MonadT (Compose f) => (forall (x :: k'0). f0 x -> Compose f g x) -> Compose f f0 a -> Compose f g a Source #

Constraints and instance dictionaries

class FunctorT t => ConstraintsT (t :: (kl -> Type) -> kr -> Type) where Source #

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 Source #

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.

type AllT c t = GAll 1 c (GAllRepT t)

Methods

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

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

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

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 Source #

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) Source #

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

Support for generic derivations

newtype Rec (p :: Type) a x Source #

Constructors

Rec
Fields unRec :: K1 R a x

Instances

Instances details

GTraversable (n :: k1) (f :: k2 -> Type) (g :: k2 -> Type) (Rec a a :: k3 -> TYPE LiftedRep) (Rec a a :: k3 -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Generics.Traversable Methods gtraverse :: forall t (x :: k). Applicative t => Proxy n -> (forall (a0 :: k). f a0 -> t (g a0)) -> Rec a a x -> t (Rec a a x) Source #
Monoid x => GApplicative (n :: k1) (f :: k2 -> Type) (g :: k2 -> Type) (Rec x x :: k3 -> TYPE LiftedRep) (Rec x x :: k3 -> TYPE LiftedRep) (Rec x x :: k3 -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Generics.Applicative Methods gprod :: forall (x0 :: k). Proxy n -> Proxy f -> Proxy g -> Rec x x x0 -> Rec x x x0 -> Rec x x x0 Source # gpure :: forall (x0 :: k). (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 Source #
GConstraints n (c :: k1 -> Constraint) (f :: k2) (Rec a' a :: Type -> TYPE LiftedRep) (Rec b' b :: k3 -> TYPE LiftedRep) (Rec b' b :: k3 -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Generics.Constraints Methods gaddDicts :: forall (x :: k). GAll n c (Rec a' a) => Rec b' b x -> Rec b' b x Source #
GFunctor n (f :: k1 -> Type) (g :: k1 -> Type) (Rec x x :: k2 -> TYPE LiftedRep) (Rec x x :: k2 -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Generics.Functor Methods gmap :: forall (x0 :: k). Proxy n -> (forall (a :: k). f a -> g a) -> Rec x x x0 -> Rec x x x0 Source #
repbi ~ repbb => GBare n (Rec repbi repbi :: k -> TYPE LiftedRep) (Rec repbb repbb :: k -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Generics.Bare Methods gstrip :: forall (x :: k0). Proxy n -> Rec repbi repbi x -> Rec repbb repbb x Source # gcover :: forall (x :: k0). Proxy n -> Rec repbb repbb x -> Rec repbi repbi x Source #
type GAll n (c :: k -> Constraint) (Rec l r :: Type -> TYPE LiftedRep) Source #
Instance details Defined in Barbies.Generics.Constraints type GAll n (c :: k -> Constraint) (Rec l r :: Type -> TYPE LiftedRep)