Safe Haskell	Trustworthy
Language	Haskell2010

GHC.TypeNats

Contents

Nat Kind
Linking type and value level
Functions on type literals

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

Synopsis

data Nat
class KnownNat (n :: Nat)
natVal :: forall n proxy. KnownNat n => proxy n -> Natural
natVal' :: forall n. KnownNat n => Proxy# n -> Natural
data SomeNat = forall n.KnownNat n => SomeNat (Proxy n)
someNatVal :: Natural -> SomeNat
sameNat :: (KnownNat a, KnownNat b) => Proxy a -> Proxy b -> Maybe (a :~: b)
type (<=) x y = (x <=? y) ~ 'True
type family (m :: Nat) <=? (n :: Nat) :: Bool
type family (m :: Nat) + (n :: Nat) :: Nat
type family (m :: Nat) * (n :: Nat) :: Nat
type family (m :: Nat) ^ (n :: Nat) :: Nat
type family (m :: Nat) - (n :: Nat) :: Nat
type family CmpNat (m :: Nat) (n :: Nat) :: Ordering
type family Div (m :: Nat) (n :: Nat) :: Nat
type family Mod (m :: Nat) (n :: Nat) :: Nat
type family Log2 (m :: Nat) :: Nat

Nat Kind

data Nat Source #

(Kind) This is the kind of type-level natural numbers.

Instances

Instances details

KnownNat n => HasResolution (n :: Nat) #	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 #

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

Eq SomeNat #	Since: base-4.7.0.0
Instance details Defined in GHC.TypeNats Methods (==) :: SomeNat -> SomeNat -> Bool Source # (/=) :: SomeNat -> SomeNat -> Bool Source #
Ord SomeNat #	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 #
Read SomeNat #	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 #	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 #

someNatVal :: Natural -> SomeNat Source #

Convert an integer into an unknown type-level natural.

Since: base-4.10.0.0

sameNat :: (KnownNat a, KnownNat b) => Proxy a -> Proxy 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 = (x <=? y) ~ 'True infix 4 Source #

Comparison of type-level naturals, as a constraint.

Since: base-4.7.0.0

type family (m :: Nat) <=? (n :: Nat) :: Bool infix 4 Source #

Comparison of type-level naturals, as a function. NOTE: The functionality for this function should be subsumed by CmpNat, so this might go away in the future. Please let us know, if you encounter discrepancies between the two.

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 :: Nat) (n :: Nat) :: Ordering Source #

Comparison of type-level naturals, as a function.

Since: base-4.7.0.0

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