Control.Combine

Documentation

data Z

Constructors

Z

Instances

Nat Z

TypeCast a b => RotType Z a b

(TypeCast d a, TypeCast e b, TypeCast f c) => FlipType Z (a -> b -> c) ((d -> e -> f) -> e -> d -> f)

(TypeCast d a, TypeCast e c, TypeCast f b) => ComposeType Z (b -> c) (a -> f) (d -> e)

Apply (R a) Z (a -> a)

Apply (R (b -> a -> c)) (S Z) ((b -> a -> c) -> a -> b -> c)

(TypeCast d b, TypeCast e a, TypeCast f c) => RotType (S Z) (a -> b -> c) (d -> e -> f)

Apply (C (b -> c) (a -> b)) Z ((b -> c) -> (a -> b) -> a -> c)

data S n

Constructors

S n

Instances

Nat n => Nat (S n)

(RotType (S n) b g, FlipType (S n) a ((d -> e -> f) -> e -> d -> f), ComposeType n ((d -> e -> f) -> e -> d -> f) a b) => RotType (S (S n)) a g

FlipType n f ((a -> b -> c -> d) -> b -> a -> c -> d) => FlipType (S n) f ((b -> c -> d) -> c -> b -> d)

Apply (R (b -> a -> c)) (S Z) ((b -> a -> c) -> a -> b -> c)

(Apply (R b) (S n) (b -> f), FlipType (S n) a ((c -> d -> e) -> d -> c -> e), Compose n ((c -> d -> e) -> d -> c -> e) a b) => Apply (R a) (S (S n)) (a -> f)

(TypeCast d b, TypeCast e a, TypeCast f c) => RotType (S Z) (a -> b -> c) (d -> e -> f)

ComposeType n (b -> c) s t => ComposeType (S n) (b -> c) (a -> s) (a -> t)

Apply (C (b -> c) s) n ((b -> c) -> s -> t) => Apply (C (b -> c) (a -> s)) (S n) ((b -> c) -> (a -> s) -> a -> t)

zero :: Z

one :: S Z

two :: S (S Z)

three :: S (S (S Z))

class Nat n where

Methods

fromNat :: Enum e => n -> e

Instances

Nat Z

Nat n => Nat (S n)

class ComposeType n a b c | n a b -> c

Instances

(TypeCast d a, TypeCast e c, TypeCast f b) => ComposeType Z (b -> c) (a -> f) (d -> e)

ComposeType n (b -> c) s t => ComposeType (S n) (b -> c) (a -> s) (a -> t)

data C f g

Instances

Apply (C (b -> c) (a -> b)) Z ((b -> c) -> (a -> b) -> a -> c)

Apply (C (b -> c) s) n ((b -> c) -> s -> t) => Apply (C (b -> c) (a -> s)) (S n) ((b -> c) -> (a -> s) -> a -> t)

class Compose n a b c | n a b -> c where

Methods

compose :: n -> a -> b -> c

Instances

(ComposeType n (b -> c) (a -> f) (d -> e), Apply (C (b -> c) (a -> f)) n ((b -> c) -> (a -> f) -> d -> e)) => Compose n (b -> c) (a -> f) (d -> e)

class FlipType n a b | n a -> b

Instances

(TypeCast d a, TypeCast e b, TypeCast f c) => FlipType Z (a -> b -> c) ((d -> e -> f) -> e -> d -> f)

FlipType n f ((a -> b -> c -> d) -> b -> a -> c -> d) => FlipType (S n) f ((b -> c -> d) -> c -> b -> d)

class RotType n a b | n a -> b

Instances

TypeCast a b => RotType Z a b

(RotType (S n) b g, FlipType (S n) a ((d -> e -> f) -> e -> d -> f), ComposeType n ((d -> e -> f) -> e -> d -> f) a b) => RotType (S (S n)) a g

(TypeCast d b, TypeCast e a, TypeCast f c) => RotType (S Z) (a -> b -> c) (d -> e -> f)

data R a

Instances

Apply (R a) Z (a -> a)

Apply (R (b -> a -> c)) (S Z) ((b -> a -> c) -> a -> b -> c)

(Apply (R b) (S n) (b -> f), FlipType (S n) a ((c -> d -> e) -> d -> c -> e), Compose n ((c -> d -> e) -> d -> c -> e) a b) => Apply (R a) (S (S n)) (a -> f)

class Rot n a b | n a -> b where

Methods

rot :: n -> a -> b

Instances

(RotType n a b, Apply (R a) n (a -> b)) => Rot n a b