Data.Type.Combinator

A collection of simple type combinators, such as Identity I, Constant C, Compose '(:.:)', left unnest LL, right unnest RR, the S Combinator SS, etc.

Documentation

data f :.: g :: k -> * where infixr 6

Constructors

Comp :: f (g a) -> (f :.: g) a

Fields

getComp :: f (g a)

Instances

Witness p q (f (g a)) => Witness p q ((:.:) k k f g a)

Eq (f (g a)) => Eq ((:.:) k k f g a)

Ord (f (g a)) => Ord ((:.:) k k f g a)

Show (f (g a)) => Show ((:.:) k k f g a)

type WitnessC p q ((:.:) k k1 f g a) = Witness p q (f (g a))

data f :..: g :: k -> l -> * where infixr 6

Constructors

Comp2 :: f (g a b) -> (f :..: g) a b

Instances

Witness p q (f (g a b)) => Witness p q ((:..:) k k k f g a b)

Eq (f (g a b)) => Eq ((:..:) k k k f g a b)

Ord (f (g a b)) => Ord ((:..:) k k k f g a b)

Show (f (g a b)) => Show ((:..:) k k k f g a b)

type WitnessC p q ((:..:) k k1 k2 f g a b) = Witness p q (f (g a b))

data IT :: (k -> *) -> k -> * where

Constructors

IT :: f a -> IT f a

Fields

getIT :: f a

Instances

HTraversable k k (IT k)

HFoldable k k (IT k)

HFunctor k k (IT k)

Witness p q (f a) => Witness p q (IT k f a)

Eq (f a) => Eq (IT k f a)

Num (f a) => Num (IT k f a)

Ord (f a) => Ord (IT k f a)

Show (f a) => Show (IT k f a)

type WitnessC p q (IT k f a) = Witness p q (f a)

data I :: * -> * where

Constructors

I :: a -> I a

Fields

getI :: a

Instances

Monad I

Functor I

Applicative I

Foldable I

Traversable I

Witness p q a => Witness p q (I a)

Eq a => Eq (I a)

Num a => Num (I a)

Ord a => Ord (I a)

Show a => Show (I a)

type WitnessC p q (I a) = Witness p q a

newtype LL a f g

Constructors

LL

Fields

getLL :: f (g a)

Instances

Witness p q (f (g a)) => Witness p q (LL k k a f g)

HTraversable k (k -> k) (LL k k a)

HFoldable k (k -> k) (LL k k a)

HFunctor k (k -> k) (LL k k a)

Eq (f (g a)) => Eq (LL k k a f g)

Ord (f (g a)) => Ord (LL k k a f g)

Show (f (g a)) => Show (LL k k a f g)

type WitnessC p q (LL k k1 a f g) = Witness p q (f (g a))

newtype RR g f a

Constructors

RR

Fields

getRR :: f (g a)

Instances

HTraversable k k (RR k k g)

HFoldable k k (RR k k g)

HFunctor k k (RR k k g)

Witness p q (f (g a)) => Witness p q (RR k k g f a)

Eq (f (g a)) => Eq (RR k k g f a)

Ord (f (g a)) => Ord (RR k k g f a)

Show (f (g a)) => Show (RR k k g f a)

type WitnessC p q (RR k k1 g f a) = Witness p q (f (g a))

newtype SS f g :: k -> * where

Constructors

SS :: f a (g a) -> SS f g a

Fields

getSS :: f a (g a)

Instances

Witness p q (f a (g a)) => Witness p q (SS k k f g a)

Eq (f a (g a)) => Eq (SS k k f g a)

Ord (f a (g a)) => Ord (SS k k f g a)

Show (f a (g a)) => Show (SS k k f g a)

type WitnessC p q (SS k k1 f g a) = Witness p q (f a (g a))

data CT :: * -> (k -> *) -> l -> * where

Constructors

CT :: r -> CT r f a

Fields

getCT :: r

Instances

HTraversable k k (CT k k r)

HFoldable k k (CT k k r)

HFunctor k k (CT k k r)

Witness p q r => Witness p q (CT k k r f a)

Eq r => Eq (CT k k r f a)

Num r => Num (CT k k r f a)

Ord r => Ord (CT k k r f a)

Show r => Show (CT k k r f a)

type WitnessC p q (CT k k1 r f a) = Witness p q r

data C :: * -> k -> * where

Constructors

C :: r -> C r a

Fields

getC :: r

Instances

Witness p q r => Witness p q (C k r a)

Eq r => Eq (C k r a)

Num r => Num (C k r a)

Ord r => Ord (C k r a)

Show r => Show (C k r a)

type WitnessC p q (C k r a) = Witness p q r

newtype Join f a

Constructors

Join

Fields

getJoin :: f a a

Instances

Witness p q (f a a) => Witness p q (Join k f a)

Known k (f a) a => Known k (Join k f) a

Eq (f a a) => Eq (Join k f a)

Ord (f a a) => Ord (Join k f a)

Show (f a a) => Show (Join k f a)

type WitnessC p q (Join k f a) = Witness p q (f a a)

type KnownC k (Join k f) a = Known k (f a) a

newtype Flip p b a

Constructors

Flip

Fields

getFlip :: p a b

Instances

Witness p q (f a b) => Witness p q (Flip k k f b a)

Known k1 (p a) b => Known k (Flip k k p b) a

Eq (p a b) => Eq (Flip k k p b a)

Ord (p a b) => Ord (Flip k k p b a)

Show (p a b) => Show (Flip k k p b a)

type WitnessC p q (Flip k k1 f b a) = Witness p q (f a b)

type KnownC k (Flip k k1 p b) a = Known k1 (p a) b

flipped :: (f a b -> g c d) -> Flip f b a -> Flip g d c

newtype Cur p :: k -> l -> * where

Constructors

Cur :: p (a # b) -> Cur p a b

Fields

getCur :: p (a # b)

Instances

Witness q r (p ((#) k k1 a b)) => Witness q r (Cur k k p a b)

Known ((,) k1 k) p ((#) k1 k a b) => Known k (Cur k k p a) b

type WitnessC q r (Cur k k1 p a b) = Witness q r (p ((#) k k1 a b))

type KnownC k (Cur k1 k p a) b = Known ((,) k1 k) p ((#) k1 k a b)

data Uncur p :: (k, l) -> * where

Constructors

Uncur :: p a b -> Uncur p (a # b)

Fields

getUncur :: p a b

Instances

(Witness r s (p a b), (~) ((,) k k1) q ((#) k k1 a b)) => Witness r s (Uncur k k p q)

(Known k1 (p a) b, (~) ((,) k k1) q ((#) k k1 a b)) => Known ((,) k k) (Uncur k k p) q

type WitnessC r s (Uncur k k1 p q) = Witness r s (p (Fst k k1 q) (Snd k1 k q))

type KnownC ((,) k k1) (Uncur k k1 p) q = Known k1 (p (Fst k k1 q)) (Snd k1 k q)

newtype Cur3 p :: k -> l -> m -> * where

Constructors

Cur3 :: p `(a, b, c)` -> Cur3 p a b c

Fields

getCur3 :: p `(a, b, c)`

Instances

Witness q r (p ((,,) k k1 k2 a b c)) => Witness q r (Cur3 k k k p a b c)

Known ((,,) k1 k2 k) p ((,,) k1 k2 k a b c) => Known k (Cur3 k k k p a b) c

type WitnessC q r (Cur3 k k1 k2 p a b c) = Witness q r (p ((,,) k k1 k2 a b c))

type KnownC k (Cur3 k1 k2 k p a b) c = Known ((,,) k1 k2 k) p ((,,) k1 k2 k a b c)

data Uncur3 p :: (k, l, m) -> * where

Constructors

Uncur3 :: p a b c -> Uncur3 p `(a, b, c)`

Fields

getUncur3 :: p a b c

Instances

(Witness r s (p a b c), (~) ((,,) k k1 k2) q ((,,) k k1 k2 a b c)) => Witness r s (Uncur3 k k k p q)

(Known k2 (p a b) c, (~) ((,,) k k1 k2) q ((,,) k k1 k2 a b c)) => Known ((,,) k k k) (Uncur3 k k k p) q

type WitnessC r s (Uncur3 k k1 k2 p q) = Witness r s (p (Fst3 k k1 k2 q) (Snd3 k1 k k2 q) (Thd3 k2 k k1 q))

type KnownC ((,,) k k1 k2) (Uncur3 k k1 k2 p) q = Known k2 (p (Fst3 k k1 k2 q) (Snd3 k1 k k2 q)) (Thd3 k2 k k1 q)