Data.Type.Conjunction

Two type combinators for working with conjunctions: A fanout combinator '(:&:)', and a par combinator '(:*:)'.

These are analogous to '(&&&)' and '(***)' from Arrow, respectively.

Documentation

data f :&: g :: k -> * where infixr 5

Constructors

(:&:) :: !(f a) -> !(g a) -> (f :&: g) a infixr 5

Instances

Bifunctor1 k k k ((:&:) k)

Traversable1 k k ((:&:) k f)

Foldable1 k k ((:&:) k f)

Functor1 k k ((:&:) k f)

DecEquality k f => DecEquality k ((:&:) k f g)

(Show1 k f, Show1 k g) => Show1 k ((:&:) k f g)

(Ord1 k f, Ord1 k g) => Ord1 k ((:&:) k f g)

(Eq1 k f, Eq1 k g) => Eq1 k ((:&:) k f g)

(Known k f a, Known k g a) => Known k ((:&:) k f g) a

(Witness p q (f a), Witness s t (g a)) => Witness (p, s) (q, t) ((:&:) k f g a)

(Eq (f a), Eq (g a)) => Eq ((:&:) k f g a)

(Ord (f a), Ord (g a)) => Ord ((:&:) k f g a)

(Read (f a), Read (g a)) => Read ((:&:) k f g a)

(Show (f a), Show (g a)) => Show ((:&:) k f g a)

type KnownC k ((:&:) k f g) a = ØC

type WitnessC (p, s) (q, t) ((:&:) k f g a) = (Witness p q (f a), Witness s t (g a))

fanFst :: (f :&: g) a -> f a

fanSnd :: (f :&: g) a -> g a

(.&.) :: (f a -> h b) -> (g a -> i b) -> (f :&: g) a -> (h :&: i) b infixr 3

fanFirst :: (f a -> g a) -> (f :&: h) a -> (g :&: h) a

uncurryFan :: (f a -> g a -> r) -> (f :&: g) a -> r

curryFan :: ((f :&: g) a -> r) -> f a -> g a -> r

data f :*: g :: (k, l) -> * where infixr 5

Constructors

(:*:) :: !(f a) -> !(g b) -> (f :*: g) (a # b) infixr 5

Instances

Bifunctor1 k k ((,) k k) ((:*:) k k)

Traversable1 k ((,) k k) ((:*:) k k f)

Foldable1 k ((,) k k) ((:*:) k k f)

Functor1 k ((,) k k) ((:*:) k k f)

(Witness p q (f a), Witness s t (g b), (~) ((,) k k1) x ((#) k k1 a b)) => Witness (p, s) (q, t) ((:*:) k k f g x)

(DecEquality k f, DecEquality k1 g) => DecEquality ((,) k k) ((:*:) k k f g)

(Show1 k f, Show1 k1 g) => Show1 ((,) k k) ((:*:) k k f g)

(Ord1 k f, Ord1 k1 g) => Ord1 ((,) k k) ((:*:) k k f g)

(Eq1 k f, Eq1 k1 g) => Eq1 ((,) k k) ((:*:) k k f g)

((~) ((,) k k1) p ((#) k k1 a b), Known k f a, Known k1 g b) => Known ((,) k k) ((:*:) k k f g) p

(Eq (f (Fst k k1 p)), Eq (g (Snd k1 k p))) => Eq ((:*:) k k f g p)

(Ord (f (Fst k k1 p)), Ord (g (Snd k1 k p))) => Ord ((:*:) k k f g p)

((~) ((,) k k1) p ((#) k k1 a b), Read (f a), Read (g b)) => Read ((:*:) k k f g p)

(Show (f (Fst k k1 p)), Show (g (Snd k1 k p))) => Show ((:*:) k k f g p)

type WitnessC (p, s) (q, t) ((:*:) k k1 f g x) = (Witness p q (f (Fst k k1 x)), Witness s t (g (Snd k1 k x)))

type KnownC ((,) k k1) ((:*:) k k1 f g) p = ØC

parFst :: (f :*: g) p -> f (Fst p)

parSnd :: (f :*: g) p -> g (Snd p)

uncurryPar :: (forall a b. (p ~ (a # b)) => f a -> g b -> r) -> (f :*: g) p -> r

curryPar :: ((f :*: g) (a # b) -> r) -> f a -> g b -> r

_fst :: ((a # b) :~: (c # d)) -> a :~: c

_snd :: ((a # b) :~: (c # d)) -> b :~: d