Safe Haskell	None
Language	Haskell2010

Data.Polynomial.Functor.Deriving

Synopsis

newtype ViaPolynomial (e :: Poly -> Type -> Type) (f :: Type -> Type) a = ViaPolynomial {
- unwrapViaPolynomial :: f a
}
newtype Zippy (p :: Poly) x = Zippy {
- runZippy :: Ev p x
}
newtype Aligney (p :: Poly) x = Aligney {
- runAligney :: Ev p x
}

Documentation

newtype ViaPolynomial (e :: Poly -> Type -> Type) (f :: Type -> Type) a Source #

Generic Deriving

Constructors

ViaPolynomial
Fields unwrapViaPolynomial :: f a

Instances

Instances details

(PolynomialFunctor f, p ~ PolyRep f, Coercible e Ev, Applicative (e p)) => Applicative (ViaPolynomial e f) Source #

Instance details

Defined in Data.Polynomial.Functor.Deriving

Methods

pure :: a -> ViaPolynomial e f a #

(<*>) :: ViaPolynomial e f (a -> b) -> ViaPolynomial e f a -> ViaPolynomial e f b #

liftA2 :: (a -> b -> c) -> ViaPolynomial e f a -> ViaPolynomial e f b -> ViaPolynomial e f c #

(*>) :: ViaPolynomial e f a -> ViaPolynomial e f b -> ViaPolynomial e f b #

(<*) :: ViaPolynomial e f a -> ViaPolynomial e f b -> ViaPolynomial e f a #

Functor f => Functor (ViaPolynomial e f) Source #

Instance details

Defined in Data.Polynomial.Functor.Deriving

Methods

fmap :: (a -> b) -> ViaPolynomial e f a -> ViaPolynomial e f b #

(<$) :: a -> ViaPolynomial e f b -> ViaPolynomial e f a #

(PolynomialFunctor f, p ~ PolyRep f, Coercible e Ev, Monad (e p)) => Monad (ViaPolynomial e f) Source #

Instance details

Defined in Data.Polynomial.Functor.Deriving

Methods

(>>=) :: ViaPolynomial e f a -> (a -> ViaPolynomial e f b) -> ViaPolynomial e f b #

(>>) :: ViaPolynomial e f a -> ViaPolynomial e f b -> ViaPolynomial e f b #

return :: a -> ViaPolynomial e f a #

PolynomialFunctor f => PolynomialFunctor (ViaPolynomial e f) Source #

Instance details

Defined in Data.Polynomial.Functor.Deriving

Associated Types

type PolyRep (ViaPolynomial e f)
Instance details Defined in Data.Polynomial.Functor.Deriving type PolyRep (ViaPolynomial e f) = PolyRep f

Methods

sPolyRep :: Sing (PolyRep (ViaPolynomial e f)) Source #

toPoly :: ViaPolynomial e f x -> Ev (PolyRep (ViaPolynomial e f)) x Source #

fromPoly :: Ev (PolyRep (ViaPolynomial e f)) x -> ViaPolynomial e f x Source #

type PolyRep (ViaPolynomial e f) Source #

Instance details

Defined in Data.Polynomial.Functor.Deriving

type PolyRep (ViaPolynomial e f) = PolyRep f

newtype Zippy (p :: Poly) x Source #

Any polynomial functor Ev p can have a "zippy" applicative instance.

Example

>>> type P = 'S ('T ('S ('T 'U))) -- P(x) = 1 + x + x^2
>>> pure 0 :: Zippy P Int
Zippy {runZippy = Go (0 ::: Go (0 ::: End))}
>>> fx = Zippy $ Go ("A" ::: Go ("a" ::: End)) :: Zippy P String
>>> fy = Zippy $ Go ("B" ::: Stop) :: Zippy P String
>>> fz = Zippy $ Stop :: Zippy P String
>>> (++) <$> fx <*> fy
Zippy {runZippy = Go ("AB" ::: Stop)}
>>> (++) <$> fx <*> fz
Zippy {runZippy = Stop}
>>> (++) <$> fy <*> fz
Zippy {runZippy = Stop}

Constructors

Zippy
Fields runZippy :: Ev p x

Instances

Instances details

Foldable (Zippy p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods fold :: Monoid m => Zippy p m -> m # foldMap :: Monoid m => (a -> m) -> Zippy p a -> m # foldMap' :: Monoid m => (a -> m) -> Zippy p a -> m # foldr :: (a -> b -> b) -> b -> Zippy p a -> b # foldr' :: (a -> b -> b) -> b -> Zippy p a -> b # foldl :: (b -> a -> b) -> b -> Zippy p a -> b # foldl' :: (b -> a -> b) -> b -> Zippy p a -> b # foldr1 :: (a -> a -> a) -> Zippy p a -> a # foldl1 :: (a -> a -> a) -> Zippy p a -> a # toList :: Zippy p a -> [a] # null :: Zippy p a -> Bool # length :: Zippy p a -> Int # elem :: Eq a => a -> Zippy p a -> Bool # maximum :: Ord a => Zippy p a -> a # minimum :: Ord a => Zippy p a -> a # sum :: Num a => Zippy p a -> a # product :: Num a => Zippy p a -> a #
Traversable (Zippy p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods traverse :: Applicative f => (a -> f b) -> Zippy p a -> f (Zippy p b) # sequenceA :: Applicative f => Zippy p (f a) -> f (Zippy p a) # mapM :: Monad m => (a -> m b) -> Zippy p a -> m (Zippy p b) # sequence :: Monad m => Zippy p (m a) -> m (Zippy p a) #
SingI p => Applicative (Zippy p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods pure :: a -> Zippy p a # (<>) :: Zippy p (a -> b) -> Zippy p a -> Zippy p b # liftA2 :: (a -> b -> c) -> Zippy p a -> Zippy p b -> Zippy p c # (>) :: Zippy p a -> Zippy p b -> Zippy p b # (<*) :: Zippy p a -> Zippy p b -> Zippy p a #
Functor (Zippy p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods fmap :: (a -> b) -> Zippy p a -> Zippy p b # (<$) :: a -> Zippy p b -> Zippy p a #
Show x => Show (Zippy p x) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods showsPrec :: Int -> Zippy p x -> ShowS # show :: Zippy p x -> String # showList :: [Zippy p x] -> ShowS #
Eq x => Eq (Zippy p x) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods (==) :: Zippy p x -> Zippy p x -> Bool # (/=) :: Zippy p x -> Zippy p x -> Bool #
Ord x => Ord (Zippy p x) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods compare :: Zippy p x -> Zippy p x -> Ordering # (<) :: Zippy p x -> Zippy p x -> Bool # (<=) :: Zippy p x -> Zippy p x -> Bool # (>) :: Zippy p x -> Zippy p x -> Bool # (>=) :: Zippy p x -> Zippy p x -> Bool # max :: Zippy p x -> Zippy p x -> Zippy p x # min :: Zippy p x -> Zippy p x -> Zippy p x #

newtype Aligney (p :: Poly) x Source #

Any polynomial functor with no constant term, Ev (T p), can have an "aligney" applicative and monad instance.

Example

>>> type Q = 'T ('S ('T 'U)) -- Q(x) = x + x^2
>>> pure 0 :: Aligney Q Int
Aligney {runAligney = 0 ::: Stop}
>>> fx = Aligney $ "A" ::: Go ("a" ::: End) :: Aligney Q String
>>> fy = Aligney $ "B" ::: Go ("b" ::: End) :: Aligney Q String
>>> fz = Aligney $ "C" ::: Stop :: Aligney Q String
>>> (++) <$> fx <*> fy
Aligney {runAligney = "AB" ::: Go ("ab" ::: End)}
>>> (++) <$> fx <*> fz
Aligney {runAligney = "AC" ::: Go ("aC" ::: End)}
>>> (++) <$> fy <*> fz
Aligney {runAligney = "BC" ::: Go ("bC" ::: End)}
>>> fx >>= \x -> if x == "A" then fz else fy
Aligney {runAligney = "C" ::: Go ("b" ::: End)}

Constructors

Aligney
Fields runAligney :: Ev p x

Instances

Instances details

Foldable (Aligney p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods fold :: Monoid m => Aligney p m -> m # foldMap :: Monoid m => (a -> m) -> Aligney p a -> m # foldMap' :: Monoid m => (a -> m) -> Aligney p a -> m # foldr :: (a -> b -> b) -> b -> Aligney p a -> b # foldr' :: (a -> b -> b) -> b -> Aligney p a -> b # foldl :: (b -> a -> b) -> b -> Aligney p a -> b # foldl' :: (b -> a -> b) -> b -> Aligney p a -> b # foldr1 :: (a -> a -> a) -> Aligney p a -> a # foldl1 :: (a -> a -> a) -> Aligney p a -> a # toList :: Aligney p a -> [a] # null :: Aligney p a -> Bool # length :: Aligney p a -> Int # elem :: Eq a => a -> Aligney p a -> Bool # maximum :: Ord a => Aligney p a -> a # minimum :: Ord a => Aligney p a -> a # sum :: Num a => Aligney p a -> a # product :: Num a => Aligney p a -> a #
Traversable (Aligney p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods traverse :: Applicative f => (a -> f b) -> Aligney p a -> f (Aligney p b) # sequenceA :: Applicative f => Aligney p (f a) -> f (Aligney p a) # mapM :: Monad m => (a -> m b) -> Aligney p a -> m (Aligney p b) # sequence :: Monad m => Aligney p (m a) -> m (Aligney p a) #
SingI p => Applicative (Aligney ('T p)) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods pure :: a -> Aligney ('T p) a # (<>) :: Aligney ('T p) (a -> b) -> Aligney ('T p) a -> Aligney ('T p) b # liftA2 :: (a -> b -> c) -> Aligney ('T p) a -> Aligney ('T p) b -> Aligney ('T p) c # (>) :: Aligney ('T p) a -> Aligney ('T p) b -> Aligney ('T p) b # (<*) :: Aligney ('T p) a -> Aligney ('T p) b -> Aligney ('T p) a #
Functor (Aligney p) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods fmap :: (a -> b) -> Aligney p a -> Aligney p b # (<$) :: a -> Aligney p b -> Aligney p a #
SingI p => Monad (Aligney ('T p)) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods (>>=) :: Aligney ('T p) a -> (a -> Aligney ('T p) b) -> Aligney ('T p) b # (>>) :: Aligney ('T p) a -> Aligney ('T p) b -> Aligney ('T p) b # return :: a -> Aligney ('T p) a #
Show x => Show (Aligney p x) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods showsPrec :: Int -> Aligney p x -> ShowS # show :: Aligney p x -> String # showList :: [Aligney p x] -> ShowS #
Eq x => Eq (Aligney p x) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods (==) :: Aligney p x -> Aligney p x -> Bool # (/=) :: Aligney p x -> Aligney p x -> Bool #
Ord x => Ord (Aligney p x) Source #
Instance details Defined in Data.Polynomial.Functor.Deriving Methods compare :: Aligney p x -> Aligney p x -> Ordering # (<) :: Aligney p x -> Aligney p x -> Bool # (<=) :: Aligney p x -> Aligney p x -> Bool # (>) :: Aligney p x -> Aligney p x -> Bool # (>=) :: Aligney p x -> Aligney p x -> Bool # max :: Aligney p x -> Aligney p x -> Aligney p x # min :: Aligney p x -> Aligney p x -> Aligney p x #