Safe Haskell	None
Language	Haskell2010

Control.Alternative.Free.Lawless

Contents

Type definitions
Universal property
Auxiliary types

Description

Free Alternative (with no laws beyond monoidal).

Free Alternative but assumes no laws relating Applicative structure and Alternative methods, just inherited Applicative laws and (empty, <|>) being monoid.

Synopsis

data Free (f :: Type -> Type) a where
- FreeLift (f a)
- FreeSumOf' (NotOne (Summand f a))
- FreeApOf' (Ap' (Factor f) a)
- pattern SumOf :: [Summand f a] -> Free f a
- pattern ApOf :: Functor f => Ap (Factor f) a -> Free f a
newtype Factor (f :: Type -> Type) a = Factor {
- runFactor :: Either (f a) (NotOne (Summand f a))
}
newtype Summand (f :: Type -> Type) a = Summand {
- runSummand :: Either (f a) (Ap' (Factor f) a)
}
viewAp :: forall (f :: Type -> Type) a. Free f a -> Ap (Factor f) a
reviewAp :: forall (f :: Type -> Type) a. Functor f => Ap (Factor f) a -> Free f a
viewSum :: forall (f :: Type -> Type) a. Free f a -> [Summand f a]
reviewSum :: forall (f :: Type -> Type) a. [Summand f a] -> Free f a
liftFree :: f a -> Free f a
hoistFree :: (forall x. f x -> g x) -> Free f a -> Free g a
foldFree :: forall f g a. Alternative g => (forall x. f x -> g x) -> Free f a -> g a
data Ap' (f :: Type -> Type) a where
- Pure' :: forall a (f :: Type -> Type). a -> Ap' f a
- ApMany' :: forall (f :: Type -> Type) a1 b a. f a1 -> f b -> Ap f (b -> a1 -> a) -> Ap' f a
toAp :: forall (f :: Type -> Type) a. Ap' f a -> Ap f a
notOneAp :: Functor f => Ap f a -> Either (f a) (Ap' f a)

Type definitions

data Free (f :: Type -> Type) a Source #

Constructors

FreeLift (f a)
FreeSumOf' (NotOne (Summand f a))
FreeApOf' (Ap' (Factor f) a)

Bundled Patterns

pattern SumOf :: [Summand f a] -> Free f a	View as a list of `Summand`s
pattern ApOf :: Functor f => Ap (Factor f) a -> Free f a	View as a `Ap`, formal chain of `*`, of `Factor`s.

Instances

Instances details

FFunctor Free Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods ffmap :: forall (g :: Type -> Type) (h :: Type -> Type) x. (Functor g, Functor h) => (g ~> h) -> Free g x -> Free h x #
FMonad Free Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods fpure :: forall (g :: Type -> Type). Functor g => g ~> Free g # fbind :: forall (g :: Type -> Type) (h :: Type -> Type) a. (Functor g, Functor h) => (g ~> Free h) -> Free g a -> Free h a #
Functor f => Alternative (Free f) Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods empty :: Free f a # (<\|>) :: Free f a -> Free f a -> Free f a # some :: Free f a -> Free f [a] # many :: Free f a -> Free f [a] #
Functor f => Applicative (Free f) Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods pure :: a -> Free f a # (<>) :: Free f (a -> b) -> Free f a -> Free f b # liftA2 :: (a -> b -> c) -> Free f a -> Free f b -> Free f c # (>) :: Free f a -> Free f b -> Free f b # (<*) :: Free f a -> Free f b -> Free f a #
Functor f => Functor (Free f) Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods fmap :: (a -> b) -> Free f a -> Free f b # (<$) :: a -> Free f b -> Free f a #

newtype Factor (f :: Type -> Type) a Source #

Subexpressions of Free f a which cannot be written as nontrivial apply x <*> y.

Constructors

Factor
Fields runFactor :: Either (f a) (NotOne (Summand f a))

Instances

Instances details

FFunctor Factor Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods ffmap :: forall (g :: Type -> Type) (h :: Type -> Type) x. (Functor g, Functor h) => (g ~> h) -> Factor g x -> Factor h x #
Functor f => Functor (Factor f) Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods fmap :: (a -> b) -> Factor f a -> Factor f b # (<$) :: a -> Factor f b -> Factor f a #

newtype Summand (f :: Type -> Type) a Source #

Subexpressions of Free f a which cannot be written as nontrivial sum x <|> y.

Constructors

Summand
Fields runSummand :: Either (f a) (Ap' (Factor f) a)

Instances

Instances details

FFunctor Summand Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods ffmap :: forall (g :: Type -> Type) (h :: Type -> Type) x. (Functor g, Functor h) => (g ~> h) -> Summand g x -> Summand h x #
Functor f => Functor (Summand f) Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods fmap :: (a -> b) -> Summand f a -> Summand f b # (<$) :: a -> Summand f b -> Summand f a #

viewAp :: forall (f :: Type -> Type) a. Free f a -> Ap (Factor f) a Source #

reviewAp :: forall (f :: Type -> Type) a. Functor f => Ap (Factor f) a -> Free f a Source #

viewSum :: forall (f :: Type -> Type) a. Free f a -> [Summand f a] Source #

reviewSum :: forall (f :: Type -> Type) a. [Summand f a] -> Free f a Source #

Universal property

liftFree :: f a -> Free f a Source #

hoistFree :: (forall x. f x -> g x) -> Free f a -> Free g a Source #

foldFree :: forall f g a. Alternative g => (forall x. f x -> g x) -> Free f a -> g a Source #

Auxiliary types

data Ap' (f :: Type -> Type) a where Source #

Free Applicative Ap f a but liftAp fa, is excluded.

Ap f a uses zero or more values of f _, but Ap' f a uses either none (Pure') or 2+ times (ApMany').

Constructors

Pure' :: forall a (f :: Type -> Type). a -> Ap' f a
ApMany' :: forall (f :: Type -> Type) a1 b a. f a1 -> f b -> Ap f (b -> a1 -> a) -> Ap' f a

Instances

Instances details

FFunctor Ap' Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods ffmap :: forall (g :: Type -> Type) (h :: Type -> Type) x. (Functor g, Functor h) => (g ~> h) -> Ap' g x -> Ap' h x #
Functor f => Functor (Ap' f) Source #
Instance details Defined in Control.Alternative.Free.Lawless Methods fmap :: (a -> b) -> Ap' f a -> Ap' f b # (<$) :: a -> Ap' f b -> Ap' f a #

toAp :: forall (f :: Type -> Type) a. Ap' f a -> Ap f a Source #

notOneAp :: Functor f => Ap f a -> Either (f a) (Ap' f a) Source #