base-4.20.2.0: Core data structures and operations

Safe Haskell | Safe
Language | Haskell2010

GHC.TypeLits

Contents

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

Description

GHC's `DataKinds` language extension lifts data constructors, natural numbers, and strings to the type level. This module provides the primitives needed for working with type-level numbers (the `Nat` kind), strings (the `Symbol` kind), and characters (the `Char` kind). It also defines the `TypeError` type family, a feature that makes use of type-level strings to support user defined type errors.

For now, this module is the API for working with type-level literals. However, please note that it is a work in progress and is subject to change. Once the design of the `DataKinds` feature is more stable, this will be considered only an internal GHC module, and the programmer interface for working with type-level data will be defined in a separate library.

Since: base-4.6.0.0

Synopsis

- data Natural
- type Nat = Natural
- data Symbol
- class KnownNat (n :: Nat) where
  - natSing :: SNat n
- natVal :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Integer
- natVal' :: forall (n :: Nat). KnownNat n => Proxy# n -> Integer
- class KnownSymbol (n :: Symbol) where
  - symbolSing :: SSymbol n
- symbolVal :: forall (n :: Symbol) proxy. KnownSymbol n => proxy n -> String
- symbolVal' :: forall (n :: Symbol). KnownSymbol n => Proxy# n -> String
- class KnownChar (n :: Char) where
  - charSing :: SChar n
- charVal :: forall (n :: Char) proxy. KnownChar n => proxy n -> Char
- charVal' :: forall (n :: Char). KnownChar n => Proxy# n -> Char
- data SomeNat = KnownNat n => SomeNat (Proxy n)
- data SomeSymbol = KnownSymbol n => SomeSymbol (Proxy n)
- data SomeChar = KnownChar n => SomeChar (Proxy n)
- someNatVal :: Integer -> Maybe SomeNat
- someSymbolVal :: String -> SomeSymbol
- someCharVal :: Char -> SomeChar
- sameNat :: forall (a :: Nat) (b :: Nat) proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> Maybe (a :~: b)
- sameSymbol :: forall (a :: Symbol) (b :: Symbol) proxy1 proxy2. (KnownSymbol a, KnownSymbol b) => proxy1 a -> proxy2 b -> Maybe (a :~: b)
- sameChar :: forall (a :: Char) (b :: Char) proxy1 proxy2. (KnownChar a, KnownChar b) => proxy1 a -> proxy2 b -> Maybe (a :~: b)
- decideNat :: forall (a :: Nat) (b :: Nat) proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> Either ((a :~: b) -> Void) (a :~: b)
- decideSymbol :: forall (a :: Symbol) (b :: Symbol) proxy1 proxy2. (KnownSymbol a, KnownSymbol b) => proxy1 a -> proxy2 b -> Either ((a :~: b) -> Void) (a :~: b)
- decideChar :: forall (a :: Char) (b :: Char) proxy1 proxy2. (KnownChar a, KnownChar b) => proxy1 a -> proxy2 b -> Either ((a :~: b) -> Void) (a :~: b)
- data OrderingI (a :: k) (b :: k) where
  - LTI :: forall {k} (a :: k) (b :: k). Compare a b ~ 'LT => OrderingI a b
  - EQI :: forall {k} (a :: k). Compare a a ~ 'EQ => OrderingI a a
  - GTI :: forall {k} (a :: k) (b :: k). Compare a b ~ 'GT => OrderingI a b
- cmpNat :: forall (a :: Nat) (b :: Nat) proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> OrderingI a b
- cmpSymbol :: forall (a :: Symbol) (b :: Symbol) proxy1 proxy2. (KnownSymbol a, KnownSymbol b) => proxy1 a -> proxy2 b -> OrderingI a b
- cmpChar :: forall (a :: Char) (b :: Char) proxy1 proxy2. (KnownChar a, KnownChar b) => proxy1 a -> proxy2 b -> OrderingI a b
- data SNat (n :: Nat)
- data SSymbol (s :: Symbol)
- data SChar (s :: Char)
- pattern SNat :: () => KnownNat n => SNat n
- pattern SSymbol :: () => KnownSymbol s => SSymbol s
- pattern SChar :: () => KnownChar c => SChar c
- fromSNat :: forall (n :: Nat). SNat n -> Integer
- fromSSymbol :: forall (s :: Symbol). SSymbol s -> String
- fromSChar :: forall (c :: Char). SChar c -> Char
- withSomeSNat :: Integer -> (forall (n :: Nat). Maybe (SNat n) -> r) -> r
- withSomeSSymbol :: String -> (forall (s :: Symbol). SSymbol s -> r) -> r
- withSomeSChar :: Char -> (forall (c :: Char). SChar c -> r) -> r
- withKnownNat :: forall (n :: Nat) r. SNat n -> (KnownNat n => r) -> r
- withKnownSymbol :: forall (s :: Symbol) r. SSymbol s -> (KnownSymbol s => r) -> r
- withKnownChar :: forall (c :: Char) r. SChar c -> (KnownChar c => r) -> r
- type (<=) (x :: t) (y :: t) = Assert (x <=? y) (LeErrMsg x y :: Constraint)
- type (<=?) (m :: k) (n :: k) = OrdCond (Compare m n) 'True 'True 'False
- type family (a :: Natural) + (b :: Natural) :: Natural where ...
- type family (a :: Natural) * (b :: Natural) :: Natural where ...
- type family (a :: Natural) ^ (b :: Natural) :: Natural where ...
- type family (a :: Natural) - (b :: Natural) :: Natural where ...
- type family Div (a :: Natural) (b :: Natural) :: Natural where ...
- type family Mod (a :: Natural) (b :: Natural) :: Natural where ...
- type family Log2 (a :: Natural) :: Natural where ...
- type family AppendSymbol (a :: Symbol) (b :: Symbol) :: Symbol where ...
- type family CmpNat (a :: Natural) (b :: Natural) :: Ordering where ...
- type family CmpSymbol (a :: Symbol) (b :: Symbol) :: Ordering where ...
- type family CmpChar (a :: Char) (b :: Char) :: Ordering where ...
- type family ConsSymbol (a :: Char) (b :: Symbol) :: Symbol where ...
- type family UnconsSymbol (a :: Symbol) :: Maybe (Char, Symbol) where ...
- type family CharToNat (a :: Char) :: Natural where ...
- type family NatToChar (a :: Natural) :: Char where ...
- type family TypeError (a :: ErrorMessage) :: b where ...
- data ErrorMessage
  - = Text Symbol
  - | ShowType t
  - | ErrorMessage :<>: ErrorMessage
  - | ErrorMessage :$$: ErrorMessage

# Kinds

data Natural #

#### Instances

Instances details

PrintfArg Natural Source # | Since: base-4.8.0.0
Instance details Defined in Text.Printf Methods formatArg :: Natural -> FieldFormatter Source # parseFormat :: Natural -> ModifierParser Source #
Bits Natural | Since: base-4.8.0

Instance details

Defined in GHC.Internal.Bits

Methods

(.&.) :: Natural -> Natural -> Natural Source #

(.|.) :: Natural -> Natural -> Natural Source #

xor :: Natural -> Natural -> Natural Source #

complement :: Natural -> Natural Source #

shift :: Natural -> Int -> Natural Source #

rotate :: Natural -> Int -> Natural Source #

zeroBits :: Natural Source #

bit :: Int -> Natural Source #

setBit :: Natural -> Int -> Natural Source #

clearBit :: Natural -> Int -> Natural Source #

complementBit :: Natural -> Int -> Natural Source #

testBit :: Natural -> Int -> Bool Source #

bitSizeMaybe :: Natural -> Maybe Int Source #

bitSize :: Natural -> Int Source #

isSigned :: Natural -> Bool Source #

shiftL :: Natural -> Int -> Natural Source #

unsafeShiftL :: Natural -> Int -> Natural Source #

shiftR :: Natural -> Int -> Natural Source #

unsafeShiftR :: Natural -> Int -> Natural Source #

rotateL :: Natural -> Int -> Natural Source #

rotateR :: Natural -> Int -> Natural Source #

popCount :: Natural -> Int Source #

Data Natural | Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Natural -> c Natural Source #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Natural Source #

toConstr :: Natural -> Constr Source #

dataTypeOf :: Natural -> DataType Source #

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Natural) Source #

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Natural) Source #

gmapT :: (forall b. Data b => b -> b) -> Natural -> Natural Source #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source #

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Natural -> r Source #

gmapQ :: (forall d. Data d => d -> u) -> Natural -> [u] Source #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Natural -> u Source #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Natural -> m Natural Source #

Enum Natural | Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Enum

Methods

succ :: Natural -> Natural Source #

pred :: Natural -> Natural Source #

toEnum :: Int -> Natural Source #

fromEnum :: Natural -> Int Source #

enumFrom :: Natural -> [Natural] Source #

enumFromThen :: Natural -> Natural -> [Natural] Source #

enumFromTo :: Natural -> Natural -> [Natural] Source #

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source #

Ix Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Ix Methods range :: (Natural, Natural) -> [Natural] Source # index :: (Natural, Natural) -> Natural -> Int Source # unsafeIndex :: (Natural, Natural) -> Natural -> Int Source # inRange :: (Natural, Natural) -> Natural -> Bool Source # rangeSize :: (Natural, Natural) -> Int Source # unsafeRangeSize :: (Natural, Natural) -> Int Source #
Num Natural | Note that `Natural`'s `Num` instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though. Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Num Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Read Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS Natural Source # readList :: ReadS [Natural] Source # readPrec :: ReadPrec Natural Source # readListPrec :: ReadPrec [Natural] Source #
Integral Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Real Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # divMod :: Natural -> Natural -> (Natural, Natural) Source # toInteger :: Natural -> Integer Source #
Real Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Real Methods toRational :: Natural -> Rational Source #
Show Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Internal.Show Methods showsPrec :: Int -> Natural -> ShowS Source # show :: Natural -> String Source # showList :: [Natural] -> ShowS Source #
Eq Natural |
Instance details Defined in GHC.Num.Natural Methods (==) :: Natural -> Natural -> Bool Source # (/=) :: Natural -> Natural -> Bool Source #
Ord Natural |
Instance details Defined in GHC.Num.Natural Methods compare :: Natural -> Natural -> Ordering Source # (<) :: Natural -> Natural -> Bool Source # (<=) :: Natural -> Natural -> Bool Source # (>) :: Natural -> Natural -> Bool Source # (>=) :: Natural -> Natural -> Bool Source # max :: Natural -> Natural -> Natural Source # min :: Natural -> Natural -> Natural Source #
KnownNat n => HasResolution (n :: Nat) Source # | For example, `Fixed 1000` will give you a `Fixed` with a resolution of 1000.
Instance details Defined in Data.Fixed Methods resolution :: p n -> Integer Source #
TestCoercion SNat | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestEquality SNat | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b) Source #
type Compare (a :: Natural) (b :: Natural) |
Instance details Defined in GHC.Internal.Data.Type.Ord type Compare (a :: Natural) (b :: Natural) = CmpNat a b

type Nat = Natural Source #

A type synonym for `Natural`.

Previously, this was an opaque data type, but it was changed to a type synonym.

Since: base-4.16.0.0

data Symbol Source #

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

#### Instances

Instances details

SingKind Symbol | Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Associated Types

type DemoteRep Symbol |
Instance details Defined in GHC.Internal.Generics type DemoteRep Symbol = String

Methods

fromSing :: forall (a :: Symbol). Sing a -> DemoteRep Symbol

TestCoercion SSymbol | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods testCoercion :: forall (a :: Symbol) (b :: Symbol). SSymbol a -> SSymbol b -> Maybe (Coercion a b) Source #
TestEquality SSymbol | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods testEquality :: forall (a :: Symbol) (b :: Symbol). SSymbol a -> SSymbol b -> Maybe (a :~: b) Source #
KnownSymbol a => SingI (a :: Symbol) | Since: base-4.9.0.0
Instance details Defined in GHC.Internal.Generics Methods sing :: Sing a
type DemoteRep Symbol |
Instance details Defined in GHC.Internal.Generics type DemoteRep Symbol = String
data Sing (s :: Symbol) |

Instance details

Defined in GHC.Internal.Generics

data Sing (s :: Symbol) where

- SSym :: forall (s :: Symbol). KnownSymbol s => Sing s

type Compare (a :: Symbol) (b :: Symbol) |
Instance details Defined in GHC.Internal.Data.Type.Ord type Compare (a :: Symbol) (b :: Symbol) = CmpSymbol a b

# 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

Methods

natSing :: SNat n Source #

natVal :: forall (n :: Nat) proxy. KnownNat n => proxy n -> Integer Source #

Since: base-4.7.0.0

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

Since: base-4.8.0.0

class KnownSymbol (n :: Symbol) where 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: base-4.7.0.0

Methods

symbolSing :: SSymbol n Source #

symbolVal :: forall (n :: Symbol) proxy. KnownSymbol n => proxy n -> String Source #

Since: base-4.7.0.0

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

Since: base-4.8.0.0

class KnownChar (n :: Char) where Source #

Since: base-4.16.0.0

Methods

charSing :: SChar n Source #

charVal :: forall (n :: Char) proxy. KnownChar n => proxy n -> Char Source #

charVal' :: forall (n :: Char). KnownChar n => Proxy# n -> Char Source #

data SomeNat Source #

This type represents unknown type-level natural numbers.

Since: base-4.10.0.0

Constructors

KnownNat n => SomeNat (Proxy n) |

#### Instances

Instances details

Read SomeNat | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeNats Methods readsPrec :: Int -> ReadS SomeNat Source # readList :: ReadS [SomeNat] Source # readPrec :: ReadPrec SomeNat Source # readListPrec :: ReadPrec [SomeNat] Source #
Show SomeNat | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeNats Methods showsPrec :: Int -> SomeNat -> ShowS Source # show :: SomeNat -> String Source # showList :: [SomeNat] -> ShowS Source #
Eq SomeNat | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeNats Methods (==) :: SomeNat -> SomeNat -> Bool Source # (/=) :: SomeNat -> SomeNat -> Bool Source #
Ord SomeNat | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeNats 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 #

data SomeSymbol Source #

This type represents unknown type-level symbols.

Constructors

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

#### Instances

Instances details

Read SomeSymbol | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeLits Methods readsPrec :: Int -> ReadS SomeSymbol Source # readList :: ReadS [SomeSymbol] Source # readPrec :: ReadPrec SomeSymbol Source # readListPrec :: ReadPrec [SomeSymbol] Source #
Show SomeSymbol | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeLits Methods showsPrec :: Int -> SomeSymbol -> ShowS Source # show :: SomeSymbol -> String Source # showList :: [SomeSymbol] -> ShowS Source #
Eq SomeSymbol | Since: base-4.7.0.0
Instance details Defined in GHC.Internal.TypeLits Methods (==) :: SomeSymbol -> SomeSymbol -> Bool Source # (/=) :: SomeSymbol -> SomeSymbol -> Bool Source #
Ord SomeSymbol | Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.TypeLits

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 #

data SomeChar Source #

Constructors

KnownChar n => SomeChar (Proxy n) |

#### Instances

Instances details

Read SomeChar |
Instance details Defined in GHC.Internal.TypeLits Methods readsPrec :: Int -> ReadS SomeChar Source # readList :: ReadS [SomeChar] Source # readPrec :: ReadPrec SomeChar Source # readListPrec :: ReadPrec [SomeChar] Source #
Show SomeChar |
Instance details Defined in GHC.Internal.TypeLits Methods showsPrec :: Int -> SomeChar -> ShowS Source # show :: SomeChar -> String Source # showList :: [SomeChar] -> ShowS Source #
Eq SomeChar |
Instance details Defined in GHC.Internal.TypeLits Methods (==) :: SomeChar -> SomeChar -> Bool Source # (/=) :: SomeChar -> SomeChar -> Bool Source #
Ord SomeChar |
Instance details Defined in GHC.Internal.TypeLits Methods compare :: SomeChar -> SomeChar -> Ordering Source # (<) :: SomeChar -> SomeChar -> Bool Source # (<=) :: SomeChar -> SomeChar -> Bool Source # (>) :: SomeChar -> SomeChar -> Bool Source # (>=) :: SomeChar -> SomeChar -> Bool Source # max :: SomeChar -> SomeChar -> SomeChar Source # min :: SomeChar -> SomeChar -> SomeChar Source #

someNatVal :: Integer -> Maybe SomeNat Source #

Convert an integer into an unknown type-level natural.

Since: base-4.7.0.0

someSymbolVal :: String -> SomeSymbol Source #

Convert a string into an unknown type-level symbol.

Since: base-4.7.0.0

someCharVal :: Char -> SomeChar Source #

Convert a character into an unknown type-level char.

Since: base-4.16.0.0

sameNat :: forall (a :: Nat) (b :: Nat) 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

sameSymbol :: forall (a :: Symbol) (b :: Symbol) proxy1 proxy2. (KnownSymbol a, KnownSymbol b) => proxy1 a -> proxy2 b -> Maybe (a :~: b) Source #

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

Since: base-4.7.0.0

sameChar :: forall (a :: Char) (b :: Char) proxy1 proxy2. (KnownChar a, KnownChar b) => proxy1 a -> proxy2 b -> Maybe (a :~: b) Source #

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

Since: base-4.16.0.0

decideNat :: forall (a :: Nat) (b :: Nat) proxy1 proxy2. (KnownNat a, KnownNat b) => proxy1 a -> proxy2 b -> Either ((a :~: b) -> Void) (a :~: b) Source #

We either get evidence that this function was instantiated with the same type-level numbers, or that the type-level numbers are distinct.

Since: base-4.19.0.0

decideSymbol :: forall (a :: Symbol) (b :: Symbol) proxy1 proxy2. (KnownSymbol a, KnownSymbol b) => proxy1 a -> proxy2 b -> Either ((a :~: b) -> Void) (a :~: b) Source #

We either get evidence that this function was instantiated with the same type-level symbols, or that the type-level symbols are distinct.

Since: base-4.19.0.0

decideChar :: forall (a :: Char) (b :: Char) proxy1 proxy2. (KnownChar a, KnownChar b) => proxy1 a -> proxy2 b -> Either ((a :~: b) -> Void) (a :~: b) Source #

We either get evidence that this function was instantiated with the same type-level characters, or that the type-level characters are distinct.

Since: base-4.19.0.0

data OrderingI (a :: k) (b :: k) where Source #

Ordering data type for type literals that provides proof of their ordering.

Since: base-4.16.0.0

Constructors

LTI :: forall {k} (a :: k) (b :: k). Compare a b ~ 'LT => OrderingI a b |
EQI :: forall {k} (a :: k). Compare a a ~ 'EQ => OrderingI a a |
GTI :: forall {k} (a :: k) (b :: k). Compare a b ~ 'GT => OrderingI a b |

#### Instances

Instances details

Show (OrderingI a b) |
Instance details Defined in GHC.Internal.Data.Type.Ord Methods showsPrec :: Int -> OrderingI a b -> ShowS Source # show :: OrderingI a b -> String Source # showList :: [OrderingI a b] -> ShowS Source #
Eq (OrderingI a b) |
Instance details Defined in GHC.Internal.Data.Type.Ord Methods (==) :: OrderingI a b -> OrderingI a b -> Bool Source # (/=) :: OrderingI a b -> OrderingI a b -> Bool Source #

cmpNat :: forall (a :: Nat) (b :: Nat) 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

cmpSymbol :: forall (a :: Symbol) (b :: Symbol) proxy1 proxy2. (KnownSymbol a, KnownSymbol b) => proxy1 a -> proxy2 b -> OrderingI a b Source #

Like `sameSymbol`, but if the symbols aren't equal, this additionally provides proof of LT or GT.

Since: base-4.16.0.0

cmpChar :: forall (a :: Char) (b :: Char) proxy1 proxy2. (KnownChar a, KnownChar b) => proxy1 a -> proxy2 b -> OrderingI a b Source #

Like `sameChar`, but if the Chars aren't equal, this additionally provides proof of LT or GT.

Since: base-4.16.0.0

## Singleton values

data SNat (n :: Nat) Source #

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 ``SNat` n` (aside from bottom).

The definition of `SNat` is intentionally left abstract. To obtain an `SNat` value, use one of the following:

1. The `natSing` method of `KnownNat`.
2. The `SNat` pattern synonym.
3. The `withSomeSNat` function, which creates an `SNat` from a `Natural` number.

Since: base-4.18.0.0

#### Instances

Instances details

TestCoercion SNat | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods testCoercion :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (Coercion a b) Source #
TestEquality SNat | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods testEquality :: forall (a :: Nat) (b :: Nat). SNat a -> SNat b -> Maybe (a :~: b) Source #
Show (SNat n) | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeNats Methods showsPrec :: Int -> SNat n -> ShowS Source # show :: SNat n -> String Source # showList :: [SNat n] -> ShowS Source #
Eq (SNat n) | Since: base-4.19.0.0
Instance details Defined in GHC.Internal.TypeNats Methods (==) :: SNat n -> SNat n -> Bool Source # (/=) :: SNat n -> SNat n -> Bool Source #
Ord (SNat n) | Since: base-4.19.0.0
Instance details Defined in GHC.Internal.TypeNats Methods compare :: SNat n -> SNat n -> Ordering Source # (<) :: SNat n -> SNat n -> Bool Source # (<=) :: SNat n -> SNat n -> Bool Source # (>) :: SNat n -> SNat n -> Bool Source # (>=) :: SNat n -> SNat n -> Bool Source # max :: SNat n -> SNat n -> SNat n Source # min :: SNat n -> SNat n -> SNat n Source #

data SSymbol (s :: Symbol) Source #

A value-level witness for a type-level symbol. This is commonly referred to as a singleton type, as for each `s`, there is a single value that inhabits the type ``SSymbol` s` (aside from bottom).

The definition of `SSymbol` is intentionally left abstract. To obtain an `SSymbol` value, use one of the following:

1. The `symbolSing` method of `KnownSymbol`.
2. The `SSymbol` pattern synonym.
3. The `withSomeSSymbol` function, which creates an `SSymbol` from a `String`.

Since: base-4.18.0.0

#### Instances

Instances details

TestCoercion SSymbol | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods testCoercion :: forall (a :: Symbol) (b :: Symbol). SSymbol a -> SSymbol b -> Maybe (Coercion a b) Source #
TestEquality SSymbol | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods testEquality :: forall (a :: Symbol) (b :: Symbol). SSymbol a -> SSymbol b -> Maybe (a :~: b) Source #
Show (SSymbol s) | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods showsPrec :: Int -> SSymbol s -> ShowS Source # show :: SSymbol s -> String Source # showList :: [SSymbol s] -> ShowS Source #
Eq (SSymbol s) | Since: base-4.19.0.0
Instance details Defined in GHC.Internal.TypeLits Methods (==) :: SSymbol s -> SSymbol s -> Bool Source # (/=) :: SSymbol s -> SSymbol s -> Bool Source #
Ord (SSymbol s) | Since: base-4.19.0.0

Instance details

Defined in GHC.Internal.TypeLits

Methods

compare :: SSymbol s -> SSymbol s -> Ordering Source #

(<) :: SSymbol s -> SSymbol s -> Bool Source #

(<=) :: SSymbol s -> SSymbol s -> Bool Source #

(>) :: SSymbol s -> SSymbol s -> Bool Source #

(>=) :: SSymbol s -> SSymbol s -> Bool Source #

max :: SSymbol s -> SSymbol s -> SSymbol s Source #

min :: SSymbol s -> SSymbol s -> SSymbol s Source #

data SChar (s :: Char) Source #

A value-level witness for a type-level character. This is commonly referred to as a singleton type, as for each `c`, there is a single value that inhabits the type ``SChar` c` (aside from bottom).

The definition of `SChar` is intentionally left abstract. To obtain an `SChar` value, use one of the following:

1. The `charSing` method of `KnownChar`.
2. The `SChar` pattern synonym.
3. The `withSomeSChar` function, which creates an `SChar` from a `Char`.

Since: base-4.18.0.0

#### Instances

Instances details

TestCoercion SChar | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods testCoercion :: forall (a :: Char) (b :: Char). SChar a -> SChar b -> Maybe (Coercion a b) Source #
TestEquality SChar | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods testEquality :: forall (a :: Char) (b :: Char). SChar a -> SChar b -> Maybe (a :~: b) Source #
Show (SChar c) | Since: base-4.18.0.0
Instance details Defined in GHC.Internal.TypeLits Methods showsPrec :: Int -> SChar c -> ShowS Source # show :: SChar c -> String Source # showList :: [SChar c] -> ShowS Source #
Eq (SChar c) | Since: base-4.19.0.0
Instance details Defined in GHC.Internal.TypeLits Methods (==) :: SChar c -> SChar c -> Bool Source # (/=) :: SChar c -> SChar c -> Bool Source #
Ord (SChar c) | Since: base-4.19.0.0
Instance details Defined in GHC.Internal.TypeLits Methods compare :: SChar c -> SChar c -> Ordering Source # (<) :: SChar c -> SChar c -> Bool Source # (<=) :: SChar c -> SChar c -> Bool Source # (>) :: SChar c -> SChar c -> Bool Source # (>=) :: SChar c -> SChar c -> Bool Source # max :: SChar c -> SChar c -> SChar c Source # min :: SChar c -> SChar c -> SChar c Source #

pattern SNat :: () => KnownNat n => SNat n Source #

A explicitly bidirectional pattern synonym relating an `SNat` to a `KnownNat` constraint.

As an expression: Constructs an explicit ``SNat` n` value from an implicit ``KnownNat` n` constraint:

    SNat @n :: KnownNat n => SNat n

As a pattern: Matches on an explicit ``SNat` n` value bringing an implicit ``KnownNat` n` constraint into scope:

    f :: SNat n -> ..
    f SNat = {- KnownNat n in scope -}

Since: base-4.18.0.0

pattern SSymbol :: () => KnownSymbol s => SSymbol s Source #

A explicitly bidirectional pattern synonym relating an `SSymbol` to a `KnownSymbol` constraint.

As an expression: Constructs an explicit ``SSymbol` s` value from an implicit ``KnownSymbol` s` constraint:

    SSymbol @s :: KnownSymbol s => SSymbol s

As a pattern: Matches on an explicit ``SSymbol` s` value bringing an implicit ``KnownSymbol` s` constraint into scope:

    f :: SSymbol s -> ..
    f SSymbol = {- KnownSymbol s in scope -}

Since: base-4.18.0.0

pattern SChar :: () => KnownChar c => SChar c Source #

A explicitly bidirectional pattern synonym relating an `SChar` to a `KnownChar` constraint.

As an expression: Constructs an explicit ``SChar` c` value from an implicit ``KnownChar` c` constraint:

    SChar @c :: KnownChar c => SChar c

As a pattern: Matches on an explicit ``SChar` c` value bringing an implicit ``KnownChar` c` constraint into scope:

    f :: SChar c -> ..
    f SChar = {- KnownChar c in scope -}

Since: base-4.18.0.0

fromSNat :: forall (n :: Nat). SNat n -> Integer Source #

Return the `Integer` corresponding to `n` in an ``SNat` n` value. The returned `Integer` is always non-negative.

For a version of this function that returns a `Natural` instead of an `Integer`, see `fromSNat` in GHC.TypeNats.

Since: base-4.18.0.0

fromSSymbol :: forall (s :: Symbol). SSymbol s -> String Source #

Return the String corresponding to `s` in an ``SSymbol` s` value.

Since: base-4.18.0.0

fromSChar :: forall (c :: Char). SChar c -> Char Source #

Return the `Char` corresponding to `c` in an ``SChar` c` value.

Since: base-4.18.0.0

withSomeSNat :: Integer -> (forall (n :: Nat). Maybe (SNat n) -> r) -> r Source #

Attempt to convert an `Integer` into an ``SNat` n` value, where `n` is a fresh type-level natural number. If the `Integer` argument is non-negative, invoke the continuation with `Just sn`, where `sn` is the ``SNat` n` value. If the `Integer` argument is negative, invoke the continuation with `Nothing`.

For a version of this function where the continuation uses `'SNat` n`instead of` `Maybe` (`SNat` n)@, see `withSomeSNat` in GHC.TypeNats.

Since: base-4.18.0.0

withSomeSSymbol :: String -> (forall (s :: Symbol). SSymbol s -> r) -> r Source #

Convert a `String` into an ``SSymbol` s` value, where `s` is a fresh type-level symbol.

Since: base-4.18.0.0

withSomeSChar :: Char -> (forall (c :: Char). SChar c -> r) -> r Source #

Convert a `Char` into an ``SChar` c` value, where `c` is a fresh type-level character.

Since: base-4.18.0.0

withKnownNat :: forall (n :: Nat) r. SNat n -> (KnownNat n => r) -> r Source #

Convert an explicit ``SNat` n` value into an implicit ``KnownNat` n` constraint.

Since: base-4.18.0.0

withKnownSymbol :: forall (s :: Symbol) r. SSymbol s -> (KnownSymbol s => r) -> r Source #

Convert an explicit ``SSymbol` s` value into an implicit ``KnownSymbol` s` constraint.

Since: base-4.18.0.0

withKnownChar :: forall (c :: Char) r. SChar c -> (KnownChar c => r) -> r Source #

Convert an explicit ``SChar` c` value into an implicit ``KnownChar` c` constraint.

Since: base-4.18.0.0

# Functions on type literals

type (<=) (x :: t) (y :: t) = Assert (x <=? y) (LeErrMsg x y :: Constraint) infix 4 Source #

Comparison (<=) of comparable types, as a constraint.

Since: base-4.16.0.0

type (<=?) (m :: k) (n :: k) = 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 (a :: Natural) + (b :: Natural) :: Natural where ... infixl 6 Source #

Addition of type-level naturals.

Since: base-4.7.0.0

type family (a :: Natural) * (b :: Natural) :: Natural where ... infixl 7 Source #

Multiplication of type-level naturals.

Since: base-4.7.0.0

type family (a :: Natural) ^ (b :: Natural) :: Natural where ... infixr 8 Source #

Exponentiation of type-level naturals.

Since: base-4.7.0.0

type family (a :: Natural) - (b :: Natural) :: Natural where ... infixl 6 Source #

Subtraction of type-level naturals.

Since: base-4.7.0.0

type family Div (a :: Natural) (b :: Natural) :: Natural where ... 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 (a :: Natural) (b :: Natural) :: Natural where ... 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 (a :: Natural) :: Natural where ... 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

type family AppendSymbol (a :: Symbol) (b :: Symbol) :: Symbol where ... Source #

Concatenation of type-level symbols.

Since: base-4.10.0.0

type family CmpNat (a :: Natural) (b :: Natural) :: Ordering where ... Source #

Comparison of type-level naturals, as a function.

Since: base-4.7.0.0

type family CmpSymbol (a :: Symbol) (b :: Symbol) :: Ordering where ... Source #

Comparison of type-level symbols, as a function.

Since: base-4.7.0.0

type family CmpChar (a :: Char) (b :: Char) :: Ordering where ... Source #

Comparison of type-level characters.

Since: base-4.16.0.0

type family ConsSymbol (a :: Char) (b :: Symbol) :: Symbol where ... Source #

Extending a type-level symbol with a type-level character

Since: base-4.16.0.0

type family UnconsSymbol (a :: Symbol) :: Maybe (Char, Symbol) where ... Source #

This type family yields type-level `Just` storing the first character of a symbol and its tail if it is defined and `Nothing` otherwise.

Since: base-4.16.0.0

type family CharToNat (a :: Char) :: Natural where ... Source #

Convert a character to its Unicode code point (cf. `ord`)

Since: base-4.16.0.0

type family NatToChar (a :: Natural) :: Char where ... Source #

Convert a Unicode code point to a character (cf. `chr`)

Since: base-4.16.0.0

# User-defined type errors

type family TypeError (a :: ErrorMessage) :: b where ... 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-existent 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: base-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.