Docs4dev
Docs
haskell / 9 / libraries / base-4.17.0.0 / ghc-typenats.html

GHC.TypeNats

Safe Haskell Trustworthy
Language Haskell2010

Description

This module is an internal GHC module. It declares the constants used in the implementation of type-level natural numbers. The programmer interface for working with type-level naturals should be defined in a separate library.

Since: base-4.10.0.0

Nat Kind

data Natural Source

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances
Instances details
Data Natural Source

Since: base-4.8.0.0
Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Natural -> c Natural Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural Source

toConstr :: Natural -> Constr Source

dataTypeOf :: Natural -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) Source

gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source
Bits Natural Source

Since: base-4.8.0
Instance details

Defined in GHC.Bits

Methods

(.&.) :: Natural -> Natural -> Natural Source

(.|.) :: Natural -> Natural -> Natural Source

xor :: Natural -> Natural -> Natural Source

complement :: Natural -> Natural Source

shift :: Natural -> Int -> Natural Source

rotate :: Natural -> Int -> Natural Source

zeroBits :: Natural Source

bit :: Int -> Natural Source

setBit :: Natural -> Int -> Natural Source

clearBit :: Natural -> Int -> Natural Source

complementBit :: Natural -> Int -> Natural Source

testBit :: Natural -> Int -> Bool Source

bitSizeMaybe :: Natural -> Maybe Int Source

bitSize :: Natural -> Int Source

isSigned :: Natural -> Bool Source

shiftL :: Natural -> Int -> Natural Source

unsafeShiftL :: Natural -> Int -> Natural Source

shiftR :: Natural -> Int -> Natural Source

unsafeShiftR :: Natural -> Int -> Natural Source

rotateL :: Natural -> Int -> Natural Source

rotateR :: Natural -> Int -> Natural Source

popCount :: Natural -> Int Source
Enum Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Enum

Methods

succ :: Natural -> Natural Source

pred :: Natural -> Natural Source

toEnum :: Int -> Natural Source

fromEnum :: Natural -> Int Source

enumFrom :: Natural -> [Natural] Source

enumFromThen :: Natural -> Natural -> [Natural] Source

enumFromTo :: Natural -> Natural -> [Natural] Source

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source
Ix Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Ix

Methods

range :: (Natural, Natural) -> [Natural] Source

index :: (Natural, Natural) -> Natural -> Int Source

unsafeIndex :: (Natural, Natural) -> Natural -> Int Source

inRange :: (Natural, Natural) -> Natural -> Bool Source

rangeSize :: (Natural, Natural) -> Int Source

unsafeRangeSize :: (Natural, Natural) -> Int Source
Num Natural Source

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0
Instance details

Defined in GHC.Num

Methods

(+) :: Natural -> Natural -> Natural Source

(-) :: Natural -> Natural -> Natural Source

(*) :: Natural -> Natural -> Natural Source

negate :: Natural -> Natural Source

abs :: Natural -> Natural Source

signum :: Natural -> Natural Source

fromInteger :: Integer -> Natural Source
Read Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS Natural Source

readList :: ReadS [Natural] Source

readPrec :: ReadPrec Natural Source

readListPrec :: ReadPrec [Natural] Source
Integral Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

Methods

quot :: Natural -> Natural -> Natural Source

rem :: Natural -> Natural -> Natural Source

div :: Natural -> Natural -> Natural Source

mod :: Natural -> Natural -> Natural Source

quotRem :: Natural -> Natural -> (Natural, Natural) Source

divMod :: Natural -> Natural -> (Natural, Natural) Source

toInteger :: Natural -> Integer Source
Real Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Real

Methods

toRational :: Natural -> Rational Source
Show Natural Source

Since: base-4.8.0.0
Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS Source

show :: Natural -> String Source

showList :: [Natural] -> ShowS Source
PrintfArg Natural Source

Since: base-4.8.0.0
Instance details

Defined in Text.Printf

Methods

formatArg :: Natural -> FieldFormatter Source

parseFormat :: Natural -> ModifierParser Source
Eq Natural
Instance details

Defined in GHC.Num.Natural

Methods

(==) :: Natural -> Natural -> Bool Source

(/=) :: Natural -> Natural -> Bool Source
Ord Natural
Instance details

Defined in GHC.Num.Natural

Methods

compare :: Natural -> Natural -> Ordering Source

(<) :: Natural -> Natural -> Bool Source

(<=) :: Natural -> Natural -> Bool Source

(>) :: Natural -> Natural -> Bool Source

(>=) :: Natural -> Natural -> Bool Source

max :: Natural -> Natural -> Natural Source

min :: Natural -> Natural -> Natural Source
KnownNat n => HasResolution (n :: Nat) Source

For example, Fixed 1000 will give you a Fixed with a resolution of 1000.
Instance details

Defined in Data.Fixed

Methods

resolution :: p n -> Integer Source
type Compare (a :: Natural) (b :: Natural) Source
Instance details

Defined in Data.Type.Ord

type Compare (a :: Natural) (b :: Natural) = CmpNat a b

type Nat = Natural Source

A type synonym for Natural.

Prevously, this was an opaque data type, but it was changed to a type synonym.

Since: base-4.16.0.0

Linking type and value level

class KnownNat (n :: Nat) Source

This class gives the integer associated with a type-level natural. There are instances of the class for every concrete literal: 0, 1, 2, etc.

Since: base-4.7.0.0

Minimal complete definition

natSing

natVal :: forall n proxy. KnownNat n => proxy n -> Natural Source

Since: base-4.10.0.0

natVal' :: forall n. KnownNat n => Proxy# n -> Natural Source

Since: base-4.10.0.0

data SomeNat Source

This type represents unknown type-level natural numbers.

Since: base-4.10.0.0

Constructors

forall n.KnownNat n => SomeNat (Proxy n)
Instances
Instances details
Read SomeNat Source

Since: base-4.7.0.0
Instance details

Defined in GHC.TypeNats

Methods

readsPrec :: Int -> ReadS SomeNat Source

readList :: ReadS [SomeNat] Source

readPrec :: ReadPrec SomeNat Source

readListPrec :: ReadPrec [SomeNat] Source
Show SomeNat Source

Since: base-4.7.0.0
Instance details

Defined in GHC.TypeNats

Methods

showsPrec :: Int -> SomeNat -> ShowS Source

show :: SomeNat -> String Source

showList :: [SomeNat] -> ShowS Source
Eq SomeNat Source

Since: base-4.7.0.0
Instance details

Defined in GHC.TypeNats

Methods

(==) :: SomeNat -> SomeNat -> Bool Source

(/=) :: SomeNat -> SomeNat -> Bool Source
Ord SomeNat Source

Since: base-4.7.0.0
Instance details

Defined in GHC.TypeNats

Methods

compare :: SomeNat -> SomeNat -> Ordering Source

(<) :: SomeNat -> SomeNat -> Bool Source

(<=) :: SomeNat -> SomeNat -> Bool Source

(>) :: SomeNat -> SomeNat -> Bool Source

(>=) :: SomeNat -> SomeNat -> Bool Source

max :: SomeNat -> SomeNat -> SomeNat Source

min :: SomeNat -> SomeNat -> SomeNat Source

someNatVal :: Natural -> SomeNat Source

Convert an integer into an unknown type-level natural.

Since: base-4.10.0.0

sameNat :: (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> Maybe (a :~: b) Source

We either get evidence that this function was instantiated with the same type-level numbers, or Nothing.

Since: base-4.7.0.0

Functions on type literals

type (<=) x y = Assert (x <=? y) (LeErrMsg x y) infix 4 Source

Comparison (<=) of comparable types, as a constraint.

Since: base-4.16.0.0

type (<=?) m n = OrdCond (Compare m n) 'True 'True 'False infix 4 Source

Comparison (<=) of comparable types, as a function.

Since: base-4.16.0.0

type family (m :: Nat) + (n :: Nat) :: Nat infixl 6 Source

Addition of type-level naturals.

Since: base-4.7.0.0

type family (m :: Nat) * (n :: Nat) :: Nat infixl 7 Source

Multiplication of type-level naturals.

Since: base-4.7.0.0

type family (m :: Nat) ^ (n :: Nat) :: Nat infixr 8 Source

Exponentiation of type-level naturals.

Since: base-4.7.0.0

type family (m :: Nat) - (n :: Nat) :: Nat infixl 6 Source

Subtraction of type-level naturals.

Since: base-4.7.0.0

type family CmpNat (m :: Natural) (n :: Natural) :: Ordering Source

Comparison of type-level naturals, as a function.

Since: base-4.7.0.0

cmpNat :: forall a b proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> OrderingI a b Source

Like sameNat, but if the numbers aren't equal, this additionally provides proof of LT or GT.

Since: base-4.16.0.0

type family Div (m :: Nat) (n :: Nat) :: Nat infixl 7 Source

Division (round down) of natural numbers. Div x 0 is undefined (i.e., it cannot be reduced).

Since: base-4.11.0.0

type family Mod (m :: Nat) (n :: Nat) :: Nat infixl 7 Source

Modulus of natural numbers. Mod x 0 is undefined (i.e., it cannot be reduced).

Since: base-4.11.0.0

type family Log2 (m :: Nat) :: Nat Source

Log base 2 (round down) of natural numbers. Log 0 is undefined (i.e., it cannot be reduced).

Since: base-4.11.0.0

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.4.2/docs/libraries/base-4.17.0.0/GHC-TypeNats.html