GHC.TypeLits

base-4.9.0.0: Basic libraries

Safe Haskell | Trustworthy
Language | Haskell2010

GHC.TypeLits

Contents

- Kinds
- Linking type and value level
- Functions on type literals
- User-defined type errors

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 :: TYPE Lifted
- data Symbol :: TYPE Lifted
- 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 = KnownNat n => SomeNat (Proxy n)
- data SomeSymbol = 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
- type family TypeError a :: b
- data ErrorMessage
  - = Text Symbol
  - | ShowType t
  - | ErrorMessage :<>: ErrorMessage
  - | ErrorMessage :$$: ErrorMessage

# Kinds

data Nat :: TYPE Lifted Source

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

Instances

type (==) Nat a b |

data Symbol :: TYPE Lifted Source

(Kind) This is the kind of type-level symbols. Declared here because class IP needs it

Instances

type (==) Symbol a b |

# Linking type and value level

class KnownNat n 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

Minimal complete definition

natSing

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

Since: 4.7.0.0

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

Since: 4.8.0.0

class KnownSymbol n Source

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 Source

Since: 4.7.0.0

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

Since: 4.8.0.0

data SomeNat Source

This type represents unknown type-level natural numbers.

Constructors

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

Instances

Eq SomeNat |
Methods (==) :: SomeNat -> SomeNat -> Bool Source (/=) :: SomeNat -> SomeNat -> Bool Source
Ord SomeNat |
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 |
Methods readsPrec :: Int -> ReadS SomeNat Source readList :: ReadS [SomeNat] Source readPrec :: ReadPrec SomeNat Source readListPrec :: ReadPrec [SomeNat] Source
Show SomeNat |
Methods showsPrec :: Int -> SomeNat -> ShowS Source show :: SomeNat -> String Source showList :: [SomeNat] -> ShowS Source

data SomeSymbol Source

This type represents unknown type-level symbols.

Constructors

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

Instances

Eq SomeSymbol |
Methods (==) :: SomeSymbol -> SomeSymbol -> Bool Source (/=) :: SomeSymbol -> SomeSymbol -> Bool Source
Ord SomeSymbol |
Methods compare :: SomeSymbol -> SomeSymbol -> Ordering Source (<) :: SomeSymbol -> SomeSymbol -> Bool Source (<=) :: SomeSymbol -> SomeSymbol -> Bool Source (>) :: SomeSymbol -> SomeSymbol -> Bool Source (>=) :: SomeSymbol -> SomeSymbol -> Bool Source max :: SomeSymbol -> SomeSymbol -> SomeSymbol Source min :: SomeSymbol -> SomeSymbol -> SomeSymbol Source
Read SomeSymbol |
Methods readsPrec :: Int -> ReadS SomeSymbol Source readList :: ReadS [SomeSymbol] Source readPrec :: ReadPrec SomeSymbol Source readListPrec :: ReadPrec [SomeSymbol] Source
Show SomeSymbol |
Methods showsPrec :: Int -> SomeSymbol -> ShowS Source show :: SomeSymbol -> String Source showList :: [SomeSymbol] -> ShowS Source

someNatVal :: Integer -> Maybe SomeNat Source

Convert an integer into an unknown type-level natural.

Since: 4.7.0.0

someSymbolVal :: String -> SomeSymbol Source

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) Source

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) Source

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 Source

Comparison of type-level naturals, as a constraint.

type family m <=? n :: 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 + n :: Nat infixl 6 Source

Addition of type-level naturals.

type family m * n :: Nat infixl 7 Source

Multiplication of type-level naturals.

type family m ^ n :: Nat infixr 8 Source

Exponentiation of type-level naturals.

type family m - n :: Nat infixl 6 Source

Subtraction of type-level naturals.

Since: 4.7.0.0

type family CmpNat m n :: Ordering Source

Comparison of type-level naturals, as a function.

Since: 4.7.0.0

type family CmpSymbol m n :: Ordering Source

Comparison of type-level symbols, as a function.

Since: 4.7.0.0

# User-defined type errors

type family TypeError a :: b Source

The type-level equivalent of `error`.

The polymorphic kind of this type allows it to be used in several settings. For instance, it can be used as a constraint, e.g. to provide a better error message for a non-existant instance,

@`-- in a context instance TypeError (Text "Cannot `Show` functions." :$$: Text "Perhaps there is a missing argument?") => Show (a -> b) where showsPrec = error "unreachable"` @

It can also be placed on the right-hand side of a type-level function to provide an error for an invalid case,

@`type family ByteSize x where ByteSize Word16 = 2 ByteSize Word8 = 1 ByteSize a = TypeError (Text "The type " :<>: ShowType a :<>: Text " is not exportable.")` @

Since: 4.9.0.0

data ErrorMessage Source

A description of a custom type error.

Constructors

Text Symbol | Show the text as is.
ShowType t | Pretty print the type. `ShowType :: k -> ErrorMessage`
ErrorMessage :<>: ErrorMessage infixl 6 | Put two pieces of error message next to each other.
ErrorMessage :$$: ErrorMessage infixl 5 | Stack two pieces of error message on top of each other.