base-4.9.1.0: 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 :: *
- 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 = 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 :: Nat) <=? (n :: Nat) :: Bool
- 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 :: Nat) (n :: Nat) :: Ordering
- type family CmpSymbol (m :: Symbol) (n :: Symbol) :: Ordering
- type family TypeError (a :: ErrorMessage) :: b where ...
- data ErrorMessage
  - = Text Symbol
  - | ShowType t
  - | ErrorMessage :<>: ErrorMessage
  - | ErrorMessage :$$: ErrorMessage

# Kinds

data Nat :: * Source #

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

Instances

type (==) Nat a b # |
type (==) Nat a b

data Symbol :: * Source #

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

Instances

type (==) Symbol a b # |
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 :: 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.

type family (m :: Nat) * (n :: Nat) :: Nat infixl 7 Source #

Multiplication of type-level naturals.

type family (m :: Nat) ^ (n :: Nat) :: Nat infixr 8 Source #

Exponentiation of type-level naturals.

type family (m :: Nat) - (n :: Nat) :: Nat infixl 6 Source #

Subtraction of type-level naturals.

Since: 4.7.0.0

type family CmpNat (m :: Nat) (n :: Nat) :: Ordering Source #

Comparison of type-level naturals, as a function.

Since: 4.7.0.0

type family CmpSymbol (m :: Symbol) (n :: Symbol) :: Ordering Source #

Comparison of type-level symbols, as a function.

Since: 4.7.0.0

# 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-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.