Safe Haskell | Trustworthy |
---|---|

Language | Haskell2010 |

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: 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 = 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

# 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: 4.7.0.0*

natSing

This type represents unknown type-level natural numbers.

*Since: 4.10.0.0*

someNatVal :: Natural -> SomeNat Source #

Convert an integer into an unknown type-level natural.

*Since: 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: 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: 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: 4.7.0.0*

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

Multiplication of type-level naturals.

*Since: 4.7.0.0*

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

Exponentiation of type-level naturals.

*Since: 4.7.0.0*

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

Subtraction of type-level naturals.

*Since: 4.7.0.0*

type family CmpNat (m :: Nat) (n :: Nat) :: Ordering Source #

Comparison of type-level naturals, as a function.

*Since: 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: 4.11.0.0*