{-# LANGUAGE Trustworthy #-}
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE ExistentialQuantification #-}
{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE NoImplicitPrelude #-}
{-# LANGUAGE MagicHash #-}
{-# LANGUAGE PolyKinds #-}

{-|
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 4.6.0.0
-}

module GHC.TypeLits
  ( -- * Kinds
    N.Natural, N.Nat, Symbol  -- Symbol is declared in GHC.Types in package ghc-prim

    -- * Linking type and value level
  , N.KnownNat, natVal, natVal'
  , KnownSymbol, symbolVal, symbolVal'
  , KnownChar, charVal, charVal'
  , N.SomeNat(..), SomeSymbol(..), SomeChar(..)
  , someNatVal, someSymbolVal, someCharVal
  , N.sameNat, sameSymbol, sameChar
  , OrderingI(..)
  , N.cmpNat, cmpSymbol, cmpChar


    -- * Functions on type literals
  , type (N.<=), type (N.<=?), type (N.+), type (N.*), type (N.^), type (N.-)
  , type N.Div, type N.Mod, type N.Log2
  , AppendSymbol
  , N.CmpNat, CmpSymbol, CmpChar
  , ConsSymbol, UnconsSymbol
  , CharToNat, NatToChar

  -- * User-defined type errors
  , TypeError
  , ErrorMessage(..)

  ) where

import GHC.Base(Eq(..), Ord(..), Ordering(..), String, otherwise)
import GHC.Types(Symbol, Char)
import GHC.Num(Integer, fromInteger)
import GHC.Show(Show(..))
import GHC.Read(Read(..))
import GHC.Real(toInteger)
import GHC.Prim(magicDict, Proxy#)
import Data.Maybe(Maybe(..))
import Data.Proxy (Proxy(..))
import Data.Type.Equality((:~:)(Refl))
import Data.Type.Ord(OrderingI(..))
import Unsafe.Coerce(unsafeCoerce)

import GHC.TypeLits.Internal(CmpSymbol, CmpChar)
import qualified GHC.TypeNats as 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
class KnownSymbol (n :: Symbol) where
  symbolSing :: SSymbol n

-- | @since 4.7.0.0
natVal :: forall n proxy. N.KnownNat n => proxy n -> Integer
natVal :: forall (n :: Natural) (proxy :: Natural -> *).
KnownNat n =>
proxy n -> Integer
natVal proxy n
p = Natural -> Integer
forall a. Integral a => a -> Integer
toInteger (proxy n -> Natural
forall (n :: Natural) (proxy :: Natural -> *).
KnownNat n =>
proxy n -> Natural
N.natVal proxy n
p)

-- | @since 4.7.0.0
symbolVal :: forall n proxy. KnownSymbol n => proxy n -> String
symbolVal :: forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal proxy n
_ = case SSymbol n
forall (n :: Symbol). KnownSymbol n => SSymbol n
symbolSing :: SSymbol n of
                SSymbol String
x -> String
x

-- | @since 4.8.0.0
natVal' :: forall n. N.KnownNat n => Proxy# n -> Integer
natVal' :: forall (n :: Natural). KnownNat n => Proxy# n -> Integer
natVal' Proxy# n
p = Natural -> Integer
forall a. Integral a => a -> Integer
toInteger (Proxy# n -> Natural
forall (n :: Natural). KnownNat n => Proxy# n -> Natural
N.natVal' Proxy# n
p)

-- | @since 4.8.0.0
symbolVal' :: forall n. KnownSymbol n => Proxy# n -> String
symbolVal' :: forall (n :: Symbol). KnownSymbol n => Proxy# n -> String
symbolVal' Proxy# n
_ = case SSymbol n
forall (n :: Symbol). KnownSymbol n => SSymbol n
symbolSing :: SSymbol n of
                SSymbol String
x -> String
x


-- | This type represents unknown type-level symbols.
data SomeSymbol = forall n. KnownSymbol n => SomeSymbol (Proxy n)
                  -- ^ @since 4.7.0.0

-- | @since 4.16.0.0
class KnownChar (n :: Char) where
  charSing :: SChar n

charVal :: forall n proxy. KnownChar n => proxy n -> Char
charVal :: forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal proxy n
_ = case SChar n
forall (n :: Char). KnownChar n => SChar n
charSing :: SChar n of
                 SChar Char
x -> Char
x

charVal' :: forall n. KnownChar n => Proxy# n -> Char
charVal' :: forall (n :: Char). KnownChar n => Proxy# n -> Char
charVal' Proxy# n
_ = case SChar n
forall (n :: Char). KnownChar n => SChar n
charSing :: SChar n of
                SChar Char
x -> Char
x

data SomeChar = forall n. KnownChar n => SomeChar (Proxy n)

-- | Convert an integer into an unknown type-level natural.
--
-- @since 4.7.0.0
someNatVal :: Integer -> Maybe N.SomeNat
someNatVal :: Integer -> Maybe SomeNat
someNatVal Integer
n
  | Integer
n Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
>= Integer
0        = SomeNat -> Maybe SomeNat
forall a. a -> Maybe a
Just (Natural -> SomeNat
N.someNatVal (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger Integer
n))
  | Bool
otherwise     = Maybe SomeNat
forall a. Maybe a
Nothing

-- | Convert a string into an unknown type-level symbol.
--
-- @since 4.7.0.0
someSymbolVal :: String -> SomeSymbol
someSymbolVal :: String -> SomeSymbol
someSymbolVal String
n   = (KnownSymbol Any => Proxy Any -> SomeSymbol)
-> SSymbol Any -> Proxy Any -> SomeSymbol
forall (a :: Symbol) b.
(KnownSymbol a => Proxy a -> b) -> SSymbol a -> Proxy a -> b
withSSymbol KnownSymbol Any => Proxy Any -> SomeSymbol
forall (n :: Symbol). KnownSymbol n => Proxy n -> SomeSymbol
SomeSymbol (String -> SSymbol Any
forall (s :: Symbol). String -> SSymbol s
SSymbol String
n) Proxy Any
forall {k} (t :: k). Proxy t
Proxy
{-# NOINLINE someSymbolVal #-}
-- For details see Note [NOINLINE someNatVal] in "GHC.TypeNats"
-- The issue described there applies to `someSymbolVal` as well.

-- | @since 4.7.0.0
instance Eq SomeSymbol where
  SomeSymbol Proxy n
x == :: SomeSymbol -> SomeSymbol -> Bool
== SomeSymbol Proxy n
y = Proxy n -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal Proxy n
x String -> String -> Bool
forall a. Eq a => a -> a -> Bool
== Proxy n -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal Proxy n
y

-- | @since 4.7.0.0
instance Ord SomeSymbol where
  compare :: SomeSymbol -> SomeSymbol -> Ordering
compare (SomeSymbol Proxy n
x) (SomeSymbol Proxy n
y) = String -> String -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (Proxy n -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal Proxy n
x) (Proxy n -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal Proxy n
y)

-- | @since 4.7.0.0
instance Show SomeSymbol where
  showsPrec :: Int -> SomeSymbol -> ShowS
showsPrec Int
p (SomeSymbol Proxy n
x) = Int -> String -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec Int
p (Proxy n -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal Proxy n
x)

-- | @since 4.7.0.0
instance Read SomeSymbol where
  readsPrec :: Int -> ReadS SomeSymbol
readsPrec Int
p String
xs = [ (String -> SomeSymbol
someSymbolVal String
a, String
ys) | (String
a,String
ys) <- Int -> ReadS String
forall a. Read a => Int -> ReadS a
readsPrec Int
p String
xs ]


-- | Convert a character into an unknown type-level char.
--
-- | @since 4.16.0.0
someCharVal :: Char -> SomeChar
someCharVal :: Char -> SomeChar
someCharVal Char
n   = (KnownChar Any => Proxy Any -> SomeChar)
-> SChar Any -> Proxy Any -> SomeChar
forall (a :: Char) b.
(KnownChar a => Proxy a -> b) -> SChar a -> Proxy a -> b
withSChar KnownChar Any => Proxy Any -> SomeChar
forall (n :: Char). KnownChar n => Proxy n -> SomeChar
SomeChar (Char -> SChar Any
forall (s :: Char). Char -> SChar s
SChar Char
n) Proxy Any
forall {k} (t :: k). Proxy t
Proxy
{-# NOINLINE someCharVal #-}

instance Eq SomeChar where
  SomeChar Proxy n
x == :: SomeChar -> SomeChar -> Bool
== SomeChar Proxy n
y = Proxy n -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal Proxy n
x Char -> Char -> Bool
forall a. Eq a => a -> a -> Bool
== Proxy n -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal Proxy n
y

instance Ord SomeChar where
  compare :: SomeChar -> SomeChar -> Ordering
compare (SomeChar Proxy n
x) (SomeChar Proxy n
y) = Char -> Char -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (Proxy n -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal Proxy n
x) (Proxy n -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal Proxy n
y)

instance Show SomeChar where
  showsPrec :: Int -> SomeChar -> ShowS
showsPrec Int
p (SomeChar Proxy n
x) = Int -> Char -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec Int
p (Proxy n -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal Proxy n
x)

instance Read SomeChar where
  readsPrec :: Int -> ReadS SomeChar
readsPrec Int
p String
xs = [ (Char -> SomeChar
someCharVal Char
a, String
ys) | (Char
a,String
ys) <- Int -> ReadS Char
forall a. Read a => Int -> ReadS a
readsPrec Int
p String
xs ]

--------------------------------------------------------------------------------

-- | Concatenation of type-level symbols.
--
-- @since 4.10.0.0
type family AppendSymbol (m ::Symbol) (n :: Symbol) :: Symbol

-- | A description of a custom type error.
data {-kind-} ErrorMessage = Text Symbol
                             -- ^ Show the text as is.

                           | forall t. ShowType t
                             -- ^ Pretty print the type.
                             -- @ShowType :: k -> ErrorMessage@

                           | ErrorMessage :<>: ErrorMessage
                             -- ^ Put two pieces of error message next
                             -- to each other.

                           | ErrorMessage :$$: ErrorMessage
                             -- ^ Stack two pieces of error message on top
                             -- of each other.

infixl 5 :$$:
infixl 6 :<>:

-- | The type-level equivalent of 'Prelude.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 4.9.0.0
type family TypeError (a :: ErrorMessage) :: b where


-- Char-related type families

-- | Extending a type-level symbol with a type-level character
--
-- @since 4.16.0.0
type family ConsSymbol (a :: Char) (b :: Symbol) :: Symbol

-- | 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 4.16.0.0
type family UnconsSymbol (a :: Symbol) :: Maybe (Char, Symbol)

-- | Convert a character to its Unicode code point (cf. `Data.Char.ord`)
--
-- @since 4.16.0.0
type family CharToNat (c :: Char) :: N.Nat

-- | Convert a Unicode code point to a character (cf. `Data.Char.chr`)
--
-- @since 4.16.0.0
type family NatToChar (n :: N.Nat) :: Char

--------------------------------------------------------------------------------

-- | We either get evidence that this function was instantiated with the
-- same type-level symbols, or 'Nothing'.
--
-- @since 4.7.0.0
sameSymbol :: (KnownSymbol a, KnownSymbol b) =>
              proxy1 a -> proxy2 b -> Maybe (a :~: b)
sameSymbol :: forall (a :: Symbol) (b :: Symbol) (proxy1 :: Symbol -> *)
       (proxy2 :: Symbol -> *).
(KnownSymbol a, KnownSymbol b) =>
proxy1 a -> proxy2 b -> Maybe (a :~: b)
sameSymbol proxy1 a
x proxy2 b
y
  | proxy1 a -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal proxy1 a
x String -> String -> Bool
forall a. Eq a => a -> a -> Bool
== proxy2 b -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal proxy2 b
y  = (a :~: b) -> Maybe (a :~: b)
forall a. a -> Maybe a
Just ((Any :~: Any) -> a :~: b
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl)
  | Bool
otherwise                   = Maybe (a :~: b)
forall a. Maybe a
Nothing


-- | We either get evidence that this function was instantiated with the
-- same type-level characters, or 'Nothing'.
--
-- @since 4.16.0.0
sameChar :: (KnownChar a, KnownChar b) =>
              proxy1 a -> proxy2 b -> Maybe (a :~: b)
sameChar :: forall (a :: Char) (b :: Char) (proxy1 :: Char -> *)
       (proxy2 :: Char -> *).
(KnownChar a, KnownChar b) =>
proxy1 a -> proxy2 b -> Maybe (a :~: b)
sameChar proxy1 a
x proxy2 b
y
  | proxy1 a -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal proxy1 a
x Char -> Char -> Bool
forall a. Eq a => a -> a -> Bool
== proxy2 b -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal proxy2 b
y  = (a :~: b) -> Maybe (a :~: b)
forall a. a -> Maybe a
Just ((Any :~: Any) -> a :~: b
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl)
  | Bool
otherwise                = Maybe (a :~: b)
forall a. Maybe a
Nothing

-- | Like 'sameSymbol', but if the symbols aren't equal, this additionally
-- provides proof of LT or GT.
-- @since 4.16.0.0
cmpSymbol :: forall a b proxy1 proxy2. (KnownSymbol a, KnownSymbol b)
          => proxy1 a -> proxy2 b -> OrderingI a b
cmpSymbol :: forall (a :: Symbol) (b :: Symbol) (proxy1 :: Symbol -> *)
       (proxy2 :: Symbol -> *).
(KnownSymbol a, KnownSymbol b) =>
proxy1 a -> proxy2 b -> OrderingI a b
cmpSymbol proxy1 a
x proxy2 b
y = case String -> String -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (proxy1 a -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal proxy1 a
x) (proxy2 b -> String
forall (n :: Symbol) (proxy :: Symbol -> *).
KnownSymbol n =>
proxy n -> String
symbolVal proxy2 b
y) of
  Ordering
EQ -> case (Any :~: Any, Any :~: Any) -> (CmpSymbol a b :~: 'EQ, a :~: b)
forall a b. a -> b
unsafeCoerce (Any :~: Any
forall {k} (a :: k). a :~: a
Refl, Any :~: Any
forall {k} (a :: k). a :~: a
Refl) :: (CmpSymbol a b :~: 'EQ, a :~: b) of
    (CmpSymbol a b :~: 'EQ
Refl, a :~: b
Refl) -> OrderingI a b
forall {k} (a :: k). (Compare a a ~ 'EQ) => OrderingI a a
EQI
  Ordering
LT -> case (Any :~: Any) -> CmpSymbol a b :~: 'LT
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl :: (CmpSymbol a b :~: 'LT) of
    CmpSymbol a b :~: 'LT
Refl -> OrderingI a b
forall {k} (a :: k) (b :: k). (Compare a b ~ 'LT) => OrderingI a b
LTI
  Ordering
GT -> case (Any :~: Any) -> CmpSymbol a b :~: 'GT
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl :: (CmpSymbol a b :~: 'GT) of
    CmpSymbol a b :~: 'GT
Refl -> OrderingI a b
forall {k} (a :: k) (b :: k). (Compare a b ~ 'GT) => OrderingI a b
GTI

-- | Like 'sameChar', but if the Chars aren't equal, this additionally
-- provides proof of LT or GT.
-- @since 4.16.0.0
cmpChar :: forall a b proxy1 proxy2. (KnownChar a, KnownChar b)
        => proxy1 a -> proxy2 b -> OrderingI a b
cmpChar :: forall (a :: Char) (b :: Char) (proxy1 :: Char -> *)
       (proxy2 :: Char -> *).
(KnownChar a, KnownChar b) =>
proxy1 a -> proxy2 b -> OrderingI a b
cmpChar proxy1 a
x proxy2 b
y = case Char -> Char -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (proxy1 a -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal proxy1 a
x) (proxy2 b -> Char
forall (n :: Char) (proxy :: Char -> *).
KnownChar n =>
proxy n -> Char
charVal proxy2 b
y) of
  Ordering
EQ -> case (Any :~: Any, Any :~: Any) -> (CmpChar a b :~: 'EQ, a :~: b)
forall a b. a -> b
unsafeCoerce (Any :~: Any
forall {k} (a :: k). a :~: a
Refl, Any :~: Any
forall {k} (a :: k). a :~: a
Refl) :: (CmpChar a b :~: 'EQ, a :~: b) of
    (CmpChar a b :~: 'EQ
Refl, a :~: b
Refl) -> OrderingI a b
forall {k} (a :: k). (Compare a a ~ 'EQ) => OrderingI a a
EQI
  Ordering
LT -> case (Any :~: Any) -> CmpChar a b :~: 'LT
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl :: (CmpChar a b :~: 'LT) of
    CmpChar a b :~: 'LT
Refl -> OrderingI a b
forall {k} (a :: k) (b :: k). (Compare a b ~ 'LT) => OrderingI a b
LTI
  Ordering
GT -> case (Any :~: Any) -> CmpChar a b :~: 'GT
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl :: (CmpChar a b :~: 'GT) of
    CmpChar a b :~: 'GT
Refl -> OrderingI a b
forall {k} (a :: k) (b :: k). (Compare a b ~ 'GT) => OrderingI a b
GTI


--------------------------------------------------------------------------------
-- PRIVATE:

newtype SSymbol (s :: Symbol) = SSymbol String

data WrapS a b = WrapS (KnownSymbol a => Proxy a -> b)

-- See Note [magicDictId magic] in "basicType/MkId.hs"
withSSymbol :: (KnownSymbol a => Proxy a -> b)
            -> SSymbol a      -> Proxy a -> b
withSSymbol :: forall (a :: Symbol) b.
(KnownSymbol a => Proxy a -> b) -> SSymbol a -> Proxy a -> b
withSSymbol KnownSymbol a => Proxy a -> b
f SSymbol a
x Proxy a
y = WrapS a b -> SSymbol a -> Proxy a -> b
forall a. a
magicDict ((KnownSymbol a => Proxy a -> b) -> WrapS a b
forall (a :: Symbol) b.
(KnownSymbol a => Proxy a -> b) -> WrapS a b
WrapS KnownSymbol a => Proxy a -> b
f) SSymbol a
x Proxy a
y

newtype SChar (s :: Char) = SChar Char

data WrapC a b = WrapC (KnownChar a => Proxy a -> b)

-- See Note [q] in "basicType/MkId.hs"
withSChar :: (KnownChar a => Proxy a -> b)
            -> SChar a      -> Proxy a -> b
withSChar :: forall (a :: Char) b.
(KnownChar a => Proxy a -> b) -> SChar a -> Proxy a -> b
withSChar KnownChar a => Proxy a -> b
f SChar a
x Proxy a
y = WrapC a b -> SChar a -> Proxy a -> b
forall a. a
magicDict ((KnownChar a => Proxy a -> b) -> WrapC a b
forall (a :: Char) b. (KnownChar a => Proxy a -> b) -> WrapC a b
WrapC KnownChar a => Proxy a -> b
f) SChar a
x Proxy a
y