Safe Haskell	Safe
Language	Haskell2010

Type.Data.Num.Decimal.Number

Synopsis

Documentation

data Decimal #

Representation name for decimal type level numbers.

Instances

Representation Decimal #
Methods reifyIntegral :: Proxy Decimal -> Integer -> (forall s. (Integer s, (* ~ Repr s) Decimal) => Proxy s -> a) -> a #
type One Decimal #
type One Decimal

decimal :: Proxy n -> Proxy (Dec n) #

data Dec x #

The wrapper type for decimal type level numbers.

Instances

Integer x => Integer (Dec x) #
Associated Types type Repr (Dec x) :: * # Methods singleton :: Singleton (Dec x) #
(:/=:) x y => (Dec x) :/=: (Dec y) #

(:==:) x y => (Dec x) :==: (Dec y) #

(:>:) x y => (Dec x) :>: (Dec y) #

(:>=:) x y => (Dec x) :>=: (Dec y) #

(:<=:) x y => (Dec x) :<=: (Dec y) #

(:<:) x y => (Dec x) :<: (Dec y) #

type Repr (Dec x) #
type Repr (Dec x) = Decimal
type Log2Ceil (Dec x) #
type Log2Ceil (Dec x) = Dec (Log2Ceil x)
type Pow2 (Dec x) #
type Pow2 (Dec x) = Dec (Pow2 x)
type Div2 (Dec x) #
type Div2 (Dec x)
type Mul2 (Dec x) #
type Mul2 (Dec x) = Dec ((:+:) x x)
type IsEven (Dec x) #
type IsEven (Dec x) = IsEven x
type Pred (Dec x) #
type Pred (Dec x) = Dec (Pred x)
type Succ (Dec x) #
type Succ (Dec x) = Dec (Succ x)
type IsNatural (Dec x) #
type IsNatural (Dec x)
type IsNegative (Dec x) #
type IsNegative (Dec x)
type IsZero (Dec x) #
type IsZero (Dec x)
type IsPositive (Dec x) #
type IsPositive (Dec x)
type Negate (Dec x) #
type Negate (Dec x)
type (Dec x) :*: (Dec y) #
type (Dec x) :: (Dec y) = Dec ((::) x y)
type (Dec x) :-: (Dec y) #
type (Dec x) :-: (Dec y) = Dec ((:-:) x y)
type (Dec x) :+: (Dec y) #
type (Dec x) :+: (Dec y) = Dec ((:+:) x y)
type Compare (Dec x) (Dec y) #
type Compare (Dec x) (Dec y) = Compare x y

data Zero #

Instances

Natural Zero #
Methods switchNat :: f Zero -> (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f Zero #
Integer Zero #
Methods switch :: f Zero -> (forall x xs. (Pos x, Digits xs) => f (Neg x xs)) -> (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f Zero #
Zero :==: Zero #

Zero :>=: Zero #

Zero :<=: Zero #

Zero :/=: (Pos y ys) #

Zero :/=: (Neg y ys) #

Zero :>: (Neg y ys) #

Zero :>=: (Neg y ys) #

Zero :<=: (Pos y ys) #

Zero :<: (Pos y ys) #

(Pos x xs) :/=: Zero #

(Neg x xs) :/=: Zero #

(Pos x xs) :>: Zero #

(Pos x xs) :>=: Zero #

(Neg x xs) :<=: Zero #

(Neg x xs) :<: Zero #

type ToUnary Zero #
type ToUnary Zero = Zero
type Pow2 Zero #
type Pow2 Zero
type IsEven Zero #
type IsEven Zero = True
type Pred Zero #
type Pred Zero = Neg Dec1 EndDesc
type Succ Zero #
type Succ Zero
type Compare Zero Zero #
type Compare Zero Zero = EQ
type Zero :*: _y #
type Zero :*: _y = Zero
type Zero :+: y #
type Zero :+: y = y
type Compare Zero (Pos _y _ys) #
type Compare Zero (Pos _y _ys) = LT
type Compare Zero (Neg _y _ys) #
type Compare Zero (Neg _y _ys) = GT
type Compare (Pos _x _xs) Zero #
type Compare (Pos _x _xs) Zero = GT
type Compare (Neg _x _xs) Zero #
type Compare (Neg _x _xs) Zero = LT
type (Pos _x _xs) :*: Zero #
type (Pos _x _xs) :*: Zero = Zero
type (Neg _x _xs) :*: Zero #
type (Neg _x _xs) :*: Zero = Zero
type (Pos x xs) :+: Zero #
type (Pos x xs) :+: Zero = Pos x xs
type (Neg x xs) :+: Zero #
type (Neg x xs) :+: Zero = Neg x xs

data Pos x xs #

Instances

Zero :/=: (Pos y ys) #

Zero :<=: (Pos y ys) #

Zero :<: (Pos y ys) #

(Pos x, Digits xs) => Positive (Pos x xs) #
Methods switchPos :: (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Pos x xs) #
(Pos x, Digits xs) => Natural (Pos x xs) #
Methods switchNat :: f Zero -> (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Pos x xs) #
(Pos x, Digits xs) => Integer (Pos x xs) #
Methods switch :: f Zero -> (forall a xs0. (Pos a, Digits xs0) => f (Neg a xs0)) -> (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Pos x xs) #
(Pos x xs) :/=: Zero #

(Pos x xs) :>: Zero #

(Pos x xs) :>=: Zero #

(~) * (IsEQ (ComparePos x xs y ys)) False => (Pos x xs) :/=: (Pos y ys) #

(Pos x xs) :/=: (Neg y ys) #

(Neg x xs) :/=: (Pos y ys) #

(~) * (ComparePos x xs y ys) EQ => (Pos x xs) :==: (Pos y ys) #

(~) * (ComparePos x xs y ys) GT => (Pos x xs) :>: (Pos y ys) #

(Pos x xs) :>: (Neg y ys) #

(~) * (GreaterPos y ys x xs) False => (Pos x xs) :>=: (Pos y ys) #

(Pos x xs) :>=: (Neg y ys) #

(~) * (GreaterPos x xs y ys) False => (Pos x xs) :<=: (Pos y ys) #

(Neg x xs) :<=: (Pos y ys) #

(~) * (ComparePos x xs y ys) LT => (Pos x xs) :<: (Pos y ys) #

(Neg x xs) :<: (Pos y ys) #

type Compare Zero (Pos _y _ys) #
type Compare Zero (Pos _y _ys) = LT
type ToUnary (Pos x xs) #
type ToUnary (Pos x xs) = ToUnaryAcc (ToUnary x) xs
type Log2Ceil (Pos x xs) #
type Log2Ceil (Pos x xs)
type Pow2 (Pos x xs) #
type Pow2 (Pos x xs)
type IsEven (Pos x xs) #
type IsEven (Pos x xs)
type Pred (Pos x xs) #
type Pred (Pos x xs)
type Succ (Pos x xs) #
type Succ (Pos x xs)
type Compare (Pos _x _xs) Zero #
type Compare (Pos _x _xs) Zero = GT
type (Pos _x _xs) :*: Zero #
type (Pos _x _xs) :*: Zero = Zero
type (Pos x xs) :+: Zero #
type (Pos x xs) :+: Zero = Pos x xs
type Compare (Pos _x _xs) (Neg _y _ys) #
type Compare (Pos _x _xs) (Neg _y _ys) = GT
type Compare (Pos x xs) (Pos y ys) #
type Compare (Pos x xs) (Pos y ys)
type Compare (Neg _x _xs) (Pos _y _ys) #
type Compare (Neg _x _xs) (Pos _y _ys) = LT
type (Pos x xs) :*: (Neg y ys) #
type (Pos x xs) :*: (Neg y ys)
type (Pos x xs) :*: (Pos y ys) #
type (Pos x xs) :*: (Pos y ys)
type (Neg x xs) :*: (Pos y ys) #
type (Neg x xs) :*: (Pos y ys)
type (Pos x xs) :+: (Pos y ys) #
type (Pos x xs) :+: (Pos y ys)
type (Pos x xs) :+: (Neg y ys) #
type (Pos x xs) :+: (Neg y ys)
type (Neg x xs) :+: (Pos y ys) #
type (Neg x xs) :+: (Pos y ys)

data Neg x xs #

Instances

Zero :/=: (Neg y ys) #

Zero :>: (Neg y ys) #

Zero :>=: (Neg y ys) #

(Pos x, Digits xs) => Negative (Neg x xs) #
Methods switchNeg :: (forall a xs0. (Pos a, Digits xs0) => f (Neg a xs0)) -> f (Neg x xs) #
(Pos x, Digits xs) => Integer (Neg x xs) #
Methods switch :: f Zero -> (forall a xs0. (Pos a, Digits xs0) => f (Neg a xs0)) -> (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Neg x xs) #
(Neg x xs) :/=: Zero #

(Neg x xs) :<=: Zero #

(Neg x xs) :<: Zero #

(Pos x xs) :/=: (Neg y ys) #

(~) * (IsEQ (ComparePos x xs y ys)) False => (Neg x xs) :/=: (Neg y ys) #

(Neg x xs) :/=: (Pos y ys) #

(~) * (ComparePos x xs y ys) EQ => (Neg x xs) :==: (Neg y ys) #

(Pos x xs) :>: (Neg y ys) #

(~) * (ComparePos x xs y ys) LT => (Neg x xs) :>: (Neg y ys) #

(Pos x xs) :>=: (Neg y ys) #

(~) * (GreaterPos x xs y ys) False => (Neg x xs) :>=: (Neg y ys) #

(~) * (GreaterPos y ys x xs) False => (Neg x xs) :<=: (Neg y ys) #

(Neg x xs) :<=: (Pos y ys) #

(~) * (ComparePos x xs y ys) GT => (Neg x xs) :<: (Neg y ys) #

(Neg x xs) :<: (Pos y ys) #

type Compare Zero (Neg _y _ys) #
type Compare Zero (Neg _y _ys) = GT
type IsEven (Neg x xs) #
type IsEven (Neg x xs)
type Pred (Neg x xs) #
type Pred (Neg x xs)
type Succ (Neg x xs) #
type Succ (Neg x xs)
type Compare (Neg _x _xs) Zero #
type Compare (Neg _x _xs) Zero = LT
type (Neg _x _xs) :*: Zero #
type (Neg _x _xs) :*: Zero = Zero
type (Neg x xs) :+: Zero #
type (Neg x xs) :+: Zero = Neg x xs
type Compare (Pos _x _xs) (Neg _y _ys) #
type Compare (Pos _x _xs) (Neg _y _ys) = GT
type Compare (Neg _x _xs) (Pos _y _ys) #
type Compare (Neg _x _xs) (Pos _y _ys) = LT
type Compare (Neg x xs) (Neg y ys) #
type Compare (Neg x xs) (Neg y ys)
type (Pos x xs) :*: (Neg y ys) #
type (Pos x xs) :*: (Neg y ys)
type (Neg x xs) :*: (Pos y ys) #
type (Neg x xs) :*: (Pos y ys)
type (Neg x xs) :*: (Neg y ys) #
type (Neg x xs) :*: (Neg y ys)
type (Pos x xs) :+: (Neg y ys) #
type (Pos x xs) :+: (Neg y ys)
type (Neg x xs) :+: (Neg y ys) #
type (Neg x xs) :+: (Neg y ys)
type (Neg x xs) :+: (Pos y ys) #
type (Neg x xs) :+: (Pos y ys)

data EndAsc #

The terminator type for ascending decimal digit lists.

Instances

Show EndAsc #
Methods showsPrec :: Int -> EndAsc -> ShowS # show :: EndAsc -> String # showList :: [EndAsc] -> ShowS #

data ds :< d infixl 9 #

data EndDesc #

The terminator type for descending decimal digit lists.

Instances

Show EndDesc #
Methods showsPrec :: Int -> EndDesc -> ShowS # show :: EndDesc -> String # showList :: [EndDesc] -> ShowS #
Digits EndDesc #
Methods switchDigits :: f EndDesc -> (forall xh xl. (C xh, Digits xl) => f (xh :> xl)) -> f EndDesc #
type ToUnaryAcc m EndDesc #
type ToUnaryAcc m EndDesc = m

data d :> ds infixr 9 #

Instances

(C xh, Digits xl) => Digits ((:>) xh xl) #
Methods switchDigits :: f EndDesc -> (forall xh0 xl0. (C xh0, Digits xl0) => f (xh0 :> xl0)) -> f (xh :> xl) #
type ToUnaryAcc m ((:>) x xs) #
type ToUnaryAcc m ((:>) x xs) = ToUnaryAcc (UnaryAcc m x) xs

newtype Singleton x #

Constructors

Singleton Integer

singleton :: Integer x => Singleton x #

singletonFromProxy :: Integer n => Proxy n -> Singleton n #

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

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

integralFromProxy :: (Integer n, Num a) => Proxy n -> a #

class Integer n where #

Minimal complete definition

switch

Methods

switch :: f Zero -> (forall x xs. (Pos x, Digits xs) => f (Neg x xs)) -> (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f n #

Instances

Integer Zero #
Methods switch :: f Zero -> (forall x xs. (Pos x, Digits xs) => f (Neg x xs)) -> (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f Zero #
(Pos x, Digits xs) => Integer (Pos x xs) #
Methods switch :: f Zero -> (forall a xs0. (Pos a, Digits xs0) => f (Neg a xs0)) -> (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Pos x xs) #
(Pos x, Digits xs) => Integer (Neg x xs) #
Methods switch :: f Zero -> (forall a xs0. (Pos a, Digits xs0) => f (Neg a xs0)) -> (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Neg x xs) #

class Integer n => Natural n where #

Minimal complete definition

switchNat

Methods

switchNat :: f Zero -> (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f n #

Instances

Natural Zero #
Methods switchNat :: f Zero -> (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f Zero #
(Pos x, Digits xs) => Natural (Pos x xs) #
Methods switchNat :: f Zero -> (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Pos x xs) #

class Natural n => Positive n where #

Minimal complete definition

switchPos

Methods

switchPos :: (forall x xs. (Pos x, Digits xs) => f (Pos x xs)) -> f n #

Instances

(Pos x, Digits xs) => Positive (Pos x xs) #
Methods switchPos :: (forall a xs0. (Pos a, Digits xs0) => f (Pos a xs0)) -> f (Pos x xs) #

class Integer n => Negative n where #

Minimal complete definition

switchNeg

Methods

switchNeg :: (forall x xs. (Pos x, Digits xs) => f (Neg x xs)) -> f n #

Instances

(Pos x, Digits xs) => Negative (Neg x xs) #
Methods switchNeg :: (forall a xs0. (Pos a, Digits xs0) => f (Neg a xs0)) -> f (Neg x xs) #

reifyIntegral :: Integer -> (forall s. Integer s => Proxy s -> w) -> w #

reifyNatural :: Integer -> (forall s. Natural s => Proxy s -> a) -> Maybe a #

reifyPositive :: Integer -> (forall s. Positive s => Proxy s -> a) -> Maybe a #

reifyNegative :: Integer -> (forall s. Negative s => Proxy s -> a) -> Maybe a #

reifyPos :: Integer -> (forall x xs. (Pos x, Digits xs) => Proxy (Pos x xs) -> a) -> Maybe a #

reifyNeg :: Integer -> (forall x xs. (Pos x, Digits xs) => Proxy (Neg x xs) -> a) -> Maybe a #

class Digits xs where #

Minimal complete definition

switchDigits

Methods

switchDigits :: f EndDesc -> (forall xh xl. (C xh, Digits xl) => f (xh :> xl)) -> f xs #

Instances

Digits EndDesc #
Methods switchDigits :: f EndDesc -> (forall xh xl. (C xh, Digits xl) => f (xh :> xl)) -> f EndDesc #
(C xh, Digits xl) => Digits ((:>) xh xl) #
Methods switchDigits :: f EndDesc -> (forall xh0 xl0. (C xh0, Digits xl0) => f (xh0 :> xl0)) -> f (xh :> xl) #

type family x :+: y #

Instances

type Zero :+: y #
type Zero :+: y = y
type (Pos x xs) :+: Zero #
type (Pos x xs) :+: Zero = Pos x xs
type (Neg x xs) :+: Zero #
type (Neg x xs) :+: Zero = Neg x xs
type (Pos x xs) :+: (Pos y ys) #
type (Pos x xs) :+: (Pos y ys)
type (Pos x xs) :+: (Neg y ys) #
type (Pos x xs) :+: (Neg y ys)
type (Neg x xs) :+: (Neg y ys) #
type (Neg x xs) :+: (Neg y ys)
type (Neg x xs) :+: (Pos y ys) #
type (Neg x xs) :+: (Pos y ys)

type (:-:) x y = x :+: Negate y #

type family x :*: y #

Instances

type Zero :*: _y #
type Zero :*: _y = Zero
type (Pos _x _xs) :*: Zero #
type (Pos _x _xs) :*: Zero = Zero
type (Neg _x _xs) :*: Zero #
type (Neg _x _xs) :*: Zero = Zero
type (Pos x xs) :*: (Neg y ys) #
type (Pos x xs) :*: (Neg y ys)
type (Pos x xs) :*: (Pos y ys) #
type (Pos x xs) :*: (Pos y ys)
type (Neg x xs) :*: (Pos y ys) #
type (Neg x xs) :*: (Pos y ys)
type (Neg x xs) :*: (Neg y ys) #
type (Neg x xs) :*: (Neg y ys)

type family Pred x #

Instances

type Pred Zero #
type Pred Zero = Neg Dec1 EndDesc
type Pred (Pos x xs) #
type Pred (Pos x xs)
type Pred (Neg x xs) #
type Pred (Neg x xs)

type family Succ x #

Instances

type Succ Zero #
type Succ Zero
type Succ (Pos x xs) #
type Succ (Pos x xs)
type Succ (Neg x xs) #
type Succ (Neg x xs)

type family Compare x y #

Instances

type Compare Zero Zero #
type Compare Zero Zero = EQ
type Compare Zero (Pos _y _ys) #
type Compare Zero (Pos _y _ys) = LT
type Compare Zero (Neg _y _ys) #
type Compare Zero (Neg _y _ys) = GT
type Compare (Pos _x _xs) Zero #
type Compare (Pos _x _xs) Zero = GT
type Compare (Neg _x _xs) Zero #
type Compare (Neg _x _xs) Zero = LT
type Compare (Pos _x _xs) (Neg _y _ys) #
type Compare (Pos _x _xs) (Neg _y _ys) = GT
type Compare (Pos x xs) (Pos y ys) #
type Compare (Pos x xs) (Pos y ys)
type Compare (Neg _x _xs) (Pos _y _ys) #
type Compare (Neg _x _xs) (Pos _y _ys) = LT
type Compare (Neg x xs) (Neg y ys) #
type Compare (Neg x xs) (Neg y ys)

type family IsEven x #

Instances

type IsEven Zero #
type IsEven Zero = True
type IsEven (Pos x xs) #
type IsEven (Pos x xs)
type IsEven (Neg x xs) #
type IsEven (Neg x xs)

type family Pow2 x #

Instances

type Pow2 Zero #
type Pow2 Zero
type Pow2 (Pos x xs) #
type Pow2 (Pos x xs)

type family Log2Ceil x #

Instances

type Log2Ceil (Pos x xs) #
type Log2Ceil (Pos x xs)

class x :<: y #

Instances

Zero :<: (Pos y ys) #

(:<:) x y => (Dec x) :<: (Dec y) #

(Neg x xs) :<: Zero #

(~) * (ComparePos x xs y ys) LT => (Pos x xs) :<: (Pos y ys) #

(~) * (ComparePos x xs y ys) GT => (Neg x xs) :<: (Neg y ys) #

(Neg x xs) :<: (Pos y ys) #

class x :<=: y #

Instances

Zero :<=: Zero #

Zero :<=: (Pos y ys) #

(:<=:) x y => (Dec x) :<=: (Dec y) #

(Neg x xs) :<=: Zero #

(~) * (GreaterPos x xs y ys) False => (Pos x xs) :<=: (Pos y ys) #

(~) * (GreaterPos y ys x xs) False => (Neg x xs) :<=: (Neg y ys) #

(Neg x xs) :<=: (Pos y ys) #

class x :==: y #

Instances

Zero :==: Zero #

(:==:) x y => (Dec x) :==: (Dec y) #

(~) * (ComparePos x xs y ys) EQ => (Pos x xs) :==: (Pos y ys) #

(~) * (ComparePos x xs y ys) EQ => (Neg x xs) :==: (Neg y ys) #

class x :>: y #

Instances

Zero :>: (Neg y ys) #

(:>:) x y => (Dec x) :>: (Dec y) #

(Pos x xs) :>: Zero #

(~) * (ComparePos x xs y ys) GT => (Pos x xs) :>: (Pos y ys) #

(Pos x xs) :>: (Neg y ys) #

(~) * (ComparePos x xs y ys) LT => (Neg x xs) :>: (Neg y ys) #

class x :>=: y #

Instances

Zero :>=: Zero #

Zero :>=: (Neg y ys) #

(:>=:) x y => (Dec x) :>=: (Dec y) #

(Pos x xs) :>=: Zero #

(~) * (GreaterPos y ys x xs) False => (Pos x xs) :>=: (Pos y ys) #

(Pos x xs) :>=: (Neg y ys) #

(~) * (GreaterPos x xs y ys) False => (Neg x xs) :>=: (Neg y ys) #

class x :/=: y #

Instances

Zero :/=: (Pos y ys) #

Zero :/=: (Neg y ys) #

(:/=:) x y => (Dec x) :/=: (Dec y) #

(Pos x xs) :/=: Zero #

(Neg x xs) :/=: Zero #

(~) * (IsEQ (ComparePos x xs y ys)) False => (Pos x xs) :/=: (Pos y ys) #

(Pos x xs) :/=: (Neg y ys) #

(~) * (IsEQ (ComparePos x xs y ys)) False => (Neg x xs) :/=: (Neg y ys) #

(Neg x xs) :/=: (Pos y ys) #

type family FromUnary n #

Instances

type FromUnary Zero #
type FromUnary Zero = Zero
type FromUnary (Succ n) #
type FromUnary (Succ n) = Succ (FromUnary n)

type family ToUnary n #

Instances

type ToUnary Zero #
type ToUnary Zero = Zero
type ToUnary (Pos x xs) #
type ToUnary (Pos x xs) = ToUnaryAcc (ToUnary x) xs

type family ToUnaryAcc m n #

Instances

type ToUnaryAcc m EndDesc #
type ToUnaryAcc m EndDesc = m
type ToUnaryAcc m ((:>) x xs) #
type ToUnaryAcc m ((:>) x xs) = ToUnaryAcc (UnaryAcc m x) xs

type UnaryAcc m x = ToUnary x :+: (m :*: U10) #