base-4.8.2.0: Basic libraries

Safe Haskell | Trustworthy
Language | Haskell2010

GHC.TypeLits

Contents

- Kinds
- 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: 4.6.0.0

Synopsis

- data Nat
- data Symbol
- class KnownNat n
- natVal :: forall n proxy. KnownNat n => proxy n -> Integer
- natVal' :: forall n. KnownNat n => Proxy# n -> Integer
- class KnownSymbol n
- symbolVal :: forall n proxy. KnownSymbol n => proxy n -> String
- symbolVal' :: forall n. KnownSymbol n => Proxy# n -> String
- data SomeNat = forall n . KnownNat n => SomeNat (Proxy n)
- data SomeSymbol = forall n . KnownSymbol n => SomeSymbol (Proxy n)
- someNatVal :: Integer -> Maybe SomeNat
- someSymbolVal :: String -> SomeSymbol
- sameNat :: (KnownNat a, KnownNat b) => Proxy a -> Proxy b -> Maybe (a :~: b)
- sameSymbol :: (KnownSymbol a, KnownSymbol b) => Proxy a -> Proxy b -> Maybe (a :~: b)
- type (<=) x y = (x <=? y) ~ True
- type family m <=? n :: Bool
- type family m + n :: Nat
- type family m * n :: Nat
- type family m ^ n :: Nat
- type family m - n :: Nat
- type family CmpNat m n :: Ordering
- type family CmpSymbol m n :: Ordering

# Kinds

data Nat

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

Instances

type (==) Nat a b |

data Symbol

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

Instances

type (==) Symbol a b |

# Linking type and value level

class KnownNat n

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

Minimal complete definition

natSing

natVal :: forall n proxy. KnownNat n => proxy n -> Integer

Since: 4.7.0.0

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

Since: 4.8.0.0

class KnownSymbol n

This class gives the string associated with a type-level symbol. There are instances of the class for every concrete literal: "hello", etc.

Since: 4.7.0.0

Minimal complete definition

symbolSing

symbolVal :: forall n proxy. KnownSymbol n => proxy n -> String

Since: 4.7.0.0

symbolVal' :: forall n. KnownSymbol n => Proxy# n -> String

Since: 4.8.0.0

data SomeNat

This type represents unknown type-level natural numbers.

Constructors

forall n . KnownNat n => SomeNat (Proxy n) | Since: 4.7.0.0

Instances

Eq SomeNat |
Ord SomeNat |
Read SomeNat |
Show SomeNat |

data SomeSymbol

This type represents unknown type-level symbols.

Constructors

forall n . KnownSymbol n => SomeSymbol (Proxy n) | Since: 4.7.0.0

Instances

Eq SomeSymbol |
Ord SomeSymbol |
Read SomeSymbol |
Show SomeSymbol |

someNatVal :: Integer -> Maybe SomeNat

Convert an integer into an unknown type-level natural.

Since: 4.7.0.0

someSymbolVal :: String -> SomeSymbol

Convert a string into an unknown type-level symbol.

Since: 4.7.0.0

sameNat :: (KnownNat a, KnownNat b) => Proxy a -> Proxy b -> Maybe (a :~: b)

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

Since: 4.7.0.0

sameSymbol :: (KnownSymbol a, KnownSymbol b) => Proxy a -> Proxy b -> Maybe (a :~: b)

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

Since: 4.7.0.0

# Functions on type literals

type (<=) x y = (x <=? y) ~ True infix 4

Comparison of type-level naturals, as a constraint.

type family m <=? n :: Bool infix 4

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 + n :: Nat infixl 6

Addition of type-level naturals.

type family m * n :: Nat infixl 7

Multiplication of type-level naturals.

type family m ^ n :: Nat infixr 8

Exponentiation of type-level naturals.

type family m - n :: Nat infixl 6

Subtraction of type-level naturals.

Since: 4.7.0.0

type family CmpNat m n :: Ordering

Comparison of type-level naturals, as a function.

Since: 4.7.0.0

type family CmpSymbol m n :: Ordering

Comparison of type-level symbols, as a function.

Since: 4.7.0.0