Type.Data.Num

Documentation

type family Negate x

Negate x evaluates to the additive inverse of (i.e., minus) x.

Instances

type Negate (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Negate (Dec x)

negate :: Proxy x -> Proxy (Negate x)

type family IsPositive x

Instances

type IsPositive (Dec x)

Defined in Type.Data.Num.Decimal.Number

type IsPositive (Dec x)

isPositive :: Proxy x -> Proxy (IsPositive x)

type family IsZero x

Instances

type IsZero (Dec x)

Defined in Type.Data.Num.Decimal.Number

type IsZero (Dec x)

isZero :: Proxy x -> Proxy (IsZero x)

type family IsNegative x

Instances

type IsNegative (Dec x)

Defined in Type.Data.Num.Decimal.Number

type IsNegative (Dec x)

isNegative :: Proxy x -> Proxy (IsNegative x)

type family IsNatural x

Instances

type IsNatural (Dec x)

Defined in Type.Data.Num.Decimal.Number

type IsNatural (Dec x)

isNatural :: Proxy x -> Proxy (IsNatural x)

type family One repr

Instances

type One Decimal

Defined in Type.Data.Num.Decimal.Number

type One Decimal

one :: Proxy repr -> Proxy (One repr)

type family Succ x

Instances

type Succ (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Succ (Dec x) = Dec (Succ x)

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

type family Pred x

Instances

type Pred (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Pred (Dec x) = Dec (Pred x)

pred :: Proxy x -> Proxy (Pred x)

type family IsEven x

Instances

type IsEven (Dec x)

Defined in Type.Data.Num.Decimal.Number

type IsEven (Dec x) = IsEven x

isEven :: Proxy x -> Proxy (IsEven x)

type family IsOdd x

Instances

type IsOdd x

Defined in Type.Data.Num

type IsOdd x = Not (IsEven x)

isOdd :: Proxy x -> Proxy (IsOdd x)

type family x :+: y

Instances

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

Defined in Type.Data.Num.Unary

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

type (Dec x) :+: (Dec y)

Defined in Type.Data.Num.Decimal.Number

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

add :: Proxy x -> Proxy y -> Proxy (x :+: y)

type family x :-: y

Instances

type (Dec x) :-: (Dec y)

Defined in Type.Data.Num.Decimal.Number

type (Dec x) :-: (Dec y) = Dec (x :-: y)

sub :: Proxy x -> Proxy y -> Proxy (x :-: y)

type family x :*: y

Instances

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

Defined in Type.Data.Num.Unary

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

type (Dec x) :*: (Dec y)

Defined in Type.Data.Num.Decimal.Number

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

mul :: Proxy x -> Proxy y -> Proxy (x :*: y)

type family Mul2 x

Instances

type Mul2 (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Mul2 (Dec x) = Dec (x :+: x)

mul2 :: Proxy x -> Proxy (Mul2 x)

type family Pow2 x

Instances

type Pow2 (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Pow2 (Dec x) = Dec (Pow2 x)

pow2 :: Proxy x -> Proxy (Pow2 x)

type family Log2Ceil x

Instances

type Log2Ceil (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Log2Ceil (Dec x) = Dec (Log2Ceil x)

log2Ceil :: Proxy x -> Proxy (Log2Ceil x)

type family DivMod x y

divMod :: Proxy x -> Proxy y -> Proxy (DivMod x y)

type family Div x y

div :: Proxy x -> Proxy y -> Proxy (Div x y)

type family Mod x y

mod :: Proxy x -> Proxy y -> Proxy (Mod x y)

type family Div2 x

Instances

type Div2 (Dec x)

Defined in Type.Data.Num.Decimal.Number

type Div2 (Dec x)

div2 :: Proxy x -> Proxy (Div2 x)

type family Fac x

Instances

type Fac x

Defined in Type.Data.Num

type Fac x

fac :: Proxy x -> Proxy (Fac x)

newtype Singleton d

Constructors

Singleton Integer

class Representation r where

Methods

reifyIntegral :: Proxy r -> Integer -> (forall s. (Integer s, Repr s ~ r) => Proxy s -> a) -> a

Instances

Representation Unary

Defined in Type.Data.Num.Unary

Methods

reifyIntegral :: Proxy Unary -> Integer -> (forall s. (Integer s, Repr s ~ Unary) => Proxy s -> a) -> a

Representation Decimal

Defined in Type.Data.Num.Decimal.Number

Methods

reifyIntegral :: Proxy Decimal -> Integer -> (forall s. (Integer s, Repr s ~ Decimal) => Proxy s -> a) -> a

class Representation (Repr x) => Integer x where

Associated Types

type Repr x

Methods

singleton :: Singleton x

Instances

Natural n => Integer (Un n)

Defined in Type.Data.Num.Unary

Associated Types

type Repr (Un n) :: Type

Methods

singleton :: Singleton (Un n)

Integer x => Integer (Dec x)

Defined in Type.Data.Num.Decimal.Number

Associated Types

type Repr (Dec x) :: Type

Methods

singleton :: Singleton (Dec x)

class Integer x => Natural x

Instances

(Integer x, IsNatural x ~ True) => Natural x

Defined in Type.Data.Num

class Integer x => Positive x

Instances

(Integer x, IsPositive x ~ True) => Positive x

Defined in Type.Data.Num

class Integer x => Negative x

Instances

(Integer x, IsNegative x ~ True) => Negative x

Defined in Type.Data.Num

integerFromSingleton :: Integer x => Singleton x -> Integer

integralFromSingleton :: (Integer x, Num y) => Singleton x -> y

singletonFromProxy :: Integer x => Proxy x -> Singleton x

integralFromProxy :: (Integer x, Num y) => Proxy x -> y

fromInteger :: (Integer x, Num y) => Proxy x -> y

synonym for integralFromProxy, kept for backward compatibility

reifyPositive :: Representation r => Proxy r -> Integer -> (forall s. (Positive s, Repr s ~ r) => Proxy s -> a) -> Maybe a

reifyNegative :: Representation r => Proxy r -> Integer -> (forall s. (Negative s, Repr s ~ r) => Proxy s -> a) -> Maybe a

reifyNatural :: Representation r => Proxy r -> Integer -> (forall s. (Natural s, Repr s ~ r) => Proxy s -> a) -> Maybe a