Type.Data.Num.Unary

Documentation

data Unary

Representation name for unary type level numbers.

Instances

Representation Unary

data Un x

Instances

Natural n => Integer (Un n)

type Repr (Un n) = Unary

type (Un x) :*: (Un y) = Un ((:*:) x y)

type (Un x) :+: (Un y) = Un ((:+:) x y)

data Zero

Instances

Natural Zero

type FromUnary Zero = Zero

type x :*: Zero = Zero

type x :+: Zero = x

data Succ x

Instances

Natural n => Positive (Succ n)

Natural n => Natural (Succ n)

type x :*: (Succ y) = (:+:) x ((:*:) x y)

type x :+: (Succ y) = Succ ((:+:) x y)

type FromUnary (Succ n) = Succ (FromUnary n)

zero :: Proxy Zero

succ :: Proxy n -> Proxy (Succ n)

newtype Singleton n

Constructors

Singleton Integer

singleton :: Natural n => Singleton n

singletonFromProxy :: Natural n => Proxy n -> Singleton n

integerFromSingleton :: Natural n => Singleton n -> Integer

integralFromSingleton :: (Natural n, Num a) => Singleton n -> a

class Natural n where

Methods

switchNat :: f Zero -> (forall m. Natural m => f (Succ m)) -> f n

Instances

Natural Zero

Natural n => Natural (Succ n)

class Natural n => Positive n where

Methods

switchPos :: (forall m. Natural m => f (Succ m)) -> f n

Instances

Natural n => Positive (Succ n)

type family x :+: y

Instances

type x :+: Zero = x

type x :+: (Succ y) = Succ ((:+:) x y)

type family x :*: y

Instances

type x :*: Zero = Zero

type x :*: (Succ y) = (:+:) x ((:*:) x y)