Data.Type.Combinator

A collection of simple type combinators, such as Identity I, Constant C, Compose '(:.:)', Currying/Uncurrying, etc.

Documentation

newtype (f :.: g) a

Constructors

Comp

Fields

getComp :: f (g a)

Instances

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

TestEquality k1 f => TestEquality k ((:.:) k k f g)

Show1 k1 f => Show1 k ((:.:) k k f g)

Ord1 k1 f => Ord1 k ((:.:) k k f g)

Eq1 k1 f => Eq1 k ((:.:) k k f g)

TestEquality k1 f => TestEquality1 (k -> k) k ((:.:) k k f)

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

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

Read (f (g a)) => Read ((:.:) l k f g a)

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

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

newtype I a

Constructors

I

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 C r a

Constructors

C

Fields

getC :: r

Instances

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

Read r => Read1 k (C k r)

Show r => Show1 k (C k r)

Ord r => Ord1 k (C k r)

Eq r => Eq1 k (C k r)

Functor (C * r)

Foldable (C * r)

Traversable (C * r)

Eq r => Eq (C k r a)

Num r => Num (C k r a)

Ord r => Ord (C k r a)

Read r => Read (C k r a)

Show r => Show (C k r a)

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

mapC :: (r -> s) -> C r a -> C s b

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)

TestEquality1 k k1 p => TestEquality k (Flip k k p b)

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)

Read (p a b) => Read (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

flipTestEquality1 :: TestEquality (p c) => Flip p a c -> Flip p b c -> Maybe (a :~: b)

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

newtype Cur p a b

Constructors

Cur

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

Eq (p ((#) k k1 a b)) => Eq (Cur k k p a b)

Ord (p ((#) k k1 a b)) => Ord (Cur k k p a b)

Read (p ((#) k k1 a b)) => Read (Cur k k p a b)

Show (p ((#) k k1 a b)) => Show (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)

mapCur :: (p `(a, b)` -> q `(c, d)`) -> Cur p a b -> Cur q c d

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)

Read2 k k1 p => Read1 ((,) k k) (Uncur k k p)

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

Eq (p (Fst k k1 x) (Snd k1 k x)) => Eq (Uncur k k p x)

Ord (p (Fst k k1 x) (Snd k1 k x)) => Ord (Uncur k k p x)

((~) ((,) k k1) x ((#) k k1 a b), Read (p a b)) => Read (Uncur k k p x)

Show (p (Fst k k1 x) (Snd k1 k x)) => Show (Uncur k k p x)

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)

mapUncur :: (p (Fst a) (Snd a) -> q b c) -> Uncur p a -> Uncur q `(b, c)`

newtype Cur3 p a b c

Constructors

Cur3

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

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

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

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

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

mapCur3 :: (p `(a, b, c)` -> q `(d, e, f)`) -> Cur3 p a b c -> Cur3 q d e f

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)

Read3 k k1 k2 p => Read1 ((,,) k k k) (Uncur3 k k k p)

(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

Eq (p (Fst3 k k1 k2 x) (Snd3 k1 k k2 x) (Thd3 k2 k k1 x)) => Eq (Uncur3 k k k p x)

Ord (p (Fst3 k k1 k2 x) (Snd3 k1 k k2 x) (Thd3 k2 k k1 x)) => Ord (Uncur3 k k k p x)

((~) ((,,) k k1 k2) x ((,,) k k1 k2 a b c), Read (p a b c)) => Read (Uncur3 k k k p x)

Show (p (Fst3 k k1 k2 x) (Snd3 k1 k k2 x) (Thd3 k2 k k1 x)) => Show (Uncur3 k k k p x)

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)

mapUncur3 :: (p (Fst3 x) (Snd3 x) (Thd3 x) -> q d e f) -> Uncur3 p x -> Uncur3 q `(d, e, f)`

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)

Show2 k k f => Show1 k (Join k f)

Ord2 k k f => Ord1 k (Join k f)

Eq2 k k f => Eq1 k (Join k f)

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)

Read (f a a) => Read (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

mapJoin :: (f a a -> g b b) -> Join f a -> Join g b