Safe Haskell	Safe-Inferred
Language	Haskell2010

Type.Data.Num.Decimal.Number

Synopsis

Documentation

data Decimal Source

Representation name for decimal type level numbers.

Instances

Representation Decimal
type One Decimal

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

data Dec x Source

The wrapper type for decimal type level numbers.

Instances

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

data Zero Source

Instances

Natural Zero
Integer 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 = Zero
type Pow2 Zero
type IsEven Zero = True
type Pred Zero = Neg Dec1 EndDesc
type Succ Zero
type Compare Zero Zero = EQ
type Zero :*: x = Zero
type Zero :+: y = y
type Compare Zero (Pos y ys) = LT
type Compare Zero (Neg y ys) = GT
type Compare (Pos x xs) Zero = GT
type Compare (Neg x xs) Zero = LT
type (Pos x xs) :*: Zero = Zero
type (Neg x xs) :*: Zero = Zero
type (Pos x xs) :+: Zero = Pos x xs
type (Neg x xs) :+: Zero = Neg x xs

data Pos x xs Source

Instances

Zero :/=: (Pos y ys)
Zero :<=: (Pos y ys)
Zero :<: (Pos y ys)
(Pos x, Digits xs) => Positive (Pos x xs)
(Pos x, Digits xs) => Natural (Pos x xs)
(Pos x, Digits xs) => Integer (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) = LT
type ToUnary (Pos x xs) = ToUnaryAcc (ToUnary x) xs
type Log2Ceil (Pos x xs)
type Pow2 (Pos x xs)
type IsEven (Pos x xs)
type Pred (Pos x xs)
type Succ (Pos x xs)
type Compare (Pos x xs) Zero = GT
type (Pos x xs) :*: Zero = Zero
type (Pos x xs) :+: Zero = Pos x xs
type Compare (Pos x xs) (Neg y ys) = GT
type Compare (Pos 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) :*: (Pos y ys)
type (Neg x xs) :*: (Pos y ys)
type (Pos x xs) :+: (Neg y ys)
type (Pos x xs) :+: (Pos y ys)
type (Neg x xs) :+: (Pos y ys)

data Neg x xs Source

Instances

Zero :/=: (Neg y ys)
Zero :>: (Neg y ys)
Zero :>=: (Neg y ys)
(Pos x, Digits xs) => Negative (Neg x xs)
(Pos x, Digits xs) => Integer (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) = GT
type IsEven (Neg x xs)
type Pred (Neg x xs)
type Succ (Neg x xs)
type Compare (Neg x xs) Zero = LT
type (Neg x xs) :*: Zero = Zero
type (Neg x xs) :+: Zero = Neg x xs
type Compare (Pos x xs) (Neg y ys) = GT
type Compare (Neg x xs) (Pos y ys) = LT
type Compare (Neg x xs) (Neg y ys)
type (Pos x xs) :*: (Neg y ys)
type (Neg x xs) :*: (Pos y ys)
type (Neg x xs) :*: (Neg y ys)
type (Pos x xs) :+: (Neg y ys)
type (Neg x xs) :+: (Pos y ys)
type (Neg x xs) :+: (Neg y ys)

data EndAsc Source

The terminator type for ascending decimal digit lists.

Instances

Show EndAsc

data ds :< d infixl 9 Source

data EndDesc Source

The terminator type for descending decimal digit lists.

Instances

Show EndDesc
Digits EndDesc
type ToUnaryAcc m EndDesc = m

data d :> ds infixr 9 Source

Instances

(C xh, Digits xl) => Digits ((:>) xh xl)
type ToUnaryAcc m ((:>) x xs) = ToUnaryAcc (UnaryAcc m x) xs

newtype Singleton x Source

Constructors

Singleton Integer

singleton :: Integer x => Singleton x Source

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

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

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

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

class Integer n where Source

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 Source

Instances

Integer Zero
(Pos x, Digits xs) => Integer (Pos x xs)
(Pos x, Digits xs) => Integer (Neg x xs)

class Integer n => Natural n where Source

Methods

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

Instances

Natural Zero
(Pos x, Digits xs) => Natural (Pos x xs)

class Natural n => Positive n where Source

Methods

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

Instances

(Pos x, Digits xs) => Positive (Pos x xs)

class Integer n => Negative n where Source

Methods

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

Instances

(Pos x, Digits xs) => Negative (Neg x xs)

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

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

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

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

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

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

class Digits xs where Source

Methods

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

Instances

Digits EndDesc
(C xh, Digits xl) => Digits ((:>) xh xl)

type family x :+: y Source

Instances

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

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

type family x :*: y Source

Instances

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

type family Pred x Source

Instances

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

type family Succ x Source

Instances

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

type family Compare x y Source

Instances

type Compare Zero Zero = EQ
type Compare Zero (Pos y ys) = LT
type Compare Zero (Neg y ys) = GT
type Compare (Pos x xs) Zero = GT
type Compare (Neg x xs) Zero = LT
type Compare (Pos x xs) (Neg y ys) = GT
type Compare (Pos x xs) (Pos y ys)
type Compare (Neg x xs) (Pos y ys) = LT
type Compare (Neg x xs) (Neg y ys)

type family IsEven x Source

Instances

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

type family Pow2 x Source

Instances

type Pow2 Zero
type Pow2 (Pos x xs)

type family Log2Ceil x Source

Instances

type Log2Ceil (Pos x xs)

class x :<: y Source

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 Source

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 Source

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 Source

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 Source

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 Source

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 Source

Instances

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

type family ToUnary n Source

Instances

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

type family ToUnaryAcc m n Source

Instances

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

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