GHC.TypeNats

Safe Haskell	Trustworthy
Language	Haskell2010

Nat Kind

data Nat Source

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

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

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

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