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: base-4.10.0.0
Synopsis
- data Natural
- type Nat = Natural
- class KnownNat (n :: Nat) where
- 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 :: forall a b proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> Maybe (a :~: b)
- data SNat (n :: Nat)
- pattern SNat :: forall n. () => KnownNat n => SNat n
- fromSNat :: SNat n -> Natural
- withSomeSNat :: forall rep (r :: TYPE rep). Natural -> (forall n. SNat n -> r) -> r
- withKnownNat :: forall n rep (r :: TYPE rep). SNat n -> (KnownNat n => r) -> r
- type (<=) x y = Assert (x <=? y) (LeErrMsg x y)
- type (<=?) m n = OrdCond (Compare m n) 'True 'True 'False
- 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 :: Natural) (n :: Natural) :: Ordering
- cmpNat :: forall a b proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> OrderingI a b
- type family Div (m :: Nat) (n :: Nat) :: Nat
- type family Mod (m :: Nat) (n :: Nat) :: Nat
- type family Log2 (m :: Nat) :: Nat
Nat Kind
Natural number
Invariant: numbers <= 0xffffffffffffffff use the NS
constructor
Instances
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) where 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
This type represents unknown type-level natural numbers.
Since: base-4.10.0.0
Instances
Read SomeNat Source # | Since: base-4.7.0.0 |
Show SomeNat Source # | Since: base-4.7.0.0 |
Eq SomeNat Source # | Since: base-4.7.0.0 |
Ord SomeNat Source # | Since: base-4.7.0.0 |
someNatVal :: Natural -> SomeNat Source #
Convert an integer into an unknown type-level natural.
Since: base-4.10.0.0
sameNat :: forall a b proxy1 proxy2. (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
Singleton values
A value-level witness for a type-level natural number. This is commonly
referred to as a singleton type, as for each n
, there is a single value
that inhabits the type
(aside from bottom).SNat
n
The definition of SNat
is intentionally left abstract. To obtain an SNat
value, use one of the following:
- The
natSing
method ofKnownNat
. - The
SNat
pattern synonym. - The
withSomeSNat
function, which creates anSNat
from aNatural
number.
Since: base-4.18.0.0
Instances
TestCoercion SNat Source # | Since: base-4.18.0.0 |
Defined in GHC.TypeNats | |
TestEquality SNat Source # | Since: base-4.18.0.0 |
Defined in GHC.TypeNats | |
Show (SNat n) Source # | Since: base-4.18.0.0 |
pattern SNat :: forall n. () => KnownNat n => SNat n Source #
A explicitly bidirectional pattern synonym relating an SNat
to a
KnownNat
constraint.
As an expression: Constructs an explicit
value from an
implicit SNat
n
constraint:KnownNat
n
SNat @n ::KnownNat
n =>SNat
n
As a pattern: Matches on an explicit
value bringing
an implicit SNat
n
constraint into scope:KnownNat
n
f :: SNat
n -> ..
f SNat = {- SNat n in scope -}
Since: base-4.18.0.0
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