{-# LANGUAGE MagicHash #-}
{-# LANGUAGE UndecidableInstances #-}

-- | This module provides a type-level representation for term-level
-- 'P.Integer's. This type-level representation is also named 'P.Integer',
-- So import this module qualified to avoid name conflicts.
--
-- @
-- import "KindInteger" qualified as K
-- @
--
-- The implementation details are the same as the ones for type-level 'Natural's
-- in "GHC.TypeNats" as of @base-4.18@, and it will continue to evolve together
-- with @base@, trying to follow its API as much as possible until the day
-- @base@ provides its own type-level integer, making this module redundant.
module KindInteger
  ( -- * Integer Kind
    Integer
  , type P
  , type N
  , Normalize

    -- * Linking type and value level
  , KnownInteger(integerSing), integerVal, integerVal'
  , SomeInteger(..)
  , someIntegerVal
  , sameInteger

    -- ** Singleton values
  , SInteger
  , pattern SInteger
  , fromSInteger
  , withSomeSInteger
  , withKnownInteger

    -- * Arithmethic
  , type (+), type (*), type (^), type (-)
  , Negate, Div, Mod, Quot, Rem, Log2

    -- * Comparisons
  , CmpInteger
  , cmpInteger
  , type (==?), type (==), type (/=?), type (/=)
  ) where

import GHC.Base (WithDict(..))
import GHC.Types (TYPE, Constraint)
import GHC.Show (appPrec, appPrec1)
import GHC.Prim (Proxy#)
import GHC.TypeLits qualified as L
import Data.Proxy
import Data.Type.Coercion
import Data.Type.Equality (TestEquality(..), (:~:)(..))
import Data.Type.Bool (If)
import Data.Type.Ord
import Numeric.Natural (Natural)
import Prelude hiding (Integer, (==), (/=))
import Prelude qualified as P
import Unsafe.Coerce(unsafeCoerce)

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

-- | Type-level version of 'P.Integer', only ever used as a /kind/
-- for 'P' and 'N'
--
-- * A positive number /+x/ is represented as @'P' x@.
--
-- * A negative number /-x/ is represented as @'N' x@.
--
-- * /Zero/ can be represented as @'P' 0@ or @'N' 0@. For consistency, all
-- /zero/ outputs from type families in this "KindInteger" module use the
-- @'P' 0@, but don't assume that this will be the case elsewhere. So, if you
-- need to treat /zero/ specially in some situation, be sure to handle both the
-- @'P' 0@ and @'N' 0@ cases.
data Integer
  = Positive Natural
  | Negative Natural

-- | * A positive number /+x/ is represented as @'P' x@.
--
-- * /Zero/ can be represented as @'P' 0@ (see notes at 'Integer').
type P (x :: Natural) = 'Positive x :: Integer

-- | * A negative number /-x/ is represented as @'N' x@.
--
-- * /Zero/ can be represented as @'N' 0@ (but often isn't, see notes at 'Integer').
type N (x :: Natural) = 'Negative x :: Integer

-- Not used:
--
-- typeIntegerToTermInteger :: Integer -> P.Integer
-- typeIntegerToTermInteger (P n) = toInteger n
-- typeIntegerToTermInteger (N n) = negate (toInteger n)

termIntegerToTypeInteger :: P.Integer -> Integer
termIntegerToTypeInteger :: Integer -> Integer
termIntegerToTypeInteger Integer
i = let n :: Natural
n = Integer -> Natural
forall a. Num a => Integer -> a
fromInteger Integer
i
                             in  if Integer
i Integer -> Integer -> Bool
forall a. Ord a => a -> a -> Bool
>= Integer
0 then Natural -> Integer
Positive Natural
n else Natural -> Integer
Negative Natural
n

-- | We are not interested in giving any instance to type-level 'Integer's,
-- so we implement 'showsPrec' here.
showsPrecInteger :: Int -> Integer -> ShowS
showsPrecInteger :: Int -> Integer -> ShowS
showsPrecInteger Int
p Integer
i = Bool -> ShowS -> ShowS
showParen (Int
p Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
appPrec) (ShowS -> ShowS) -> ShowS -> ShowS
forall a b. (a -> b) -> a -> b
$ case Integer
i of
  Positive Natural
x -> String -> ShowS
showString String
"P " ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Natural -> ShowS
forall a. Show a => a -> ShowS
shows Natural
x
  Negative Natural
x -> String -> ShowS
showString String
"N " ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Natural -> ShowS
forall a. Show a => a -> ShowS
shows Natural
x

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

-- | This class gives the integer associated with a type-level integer.
-- There are instances of the class for every integer.
class KnownInteger (i :: Integer) where
  integerSing :: SInteger i

-- | Positive numbers and zero.
instance L.KnownNat x => KnownInteger (P x) where
  integerSing :: SInteger (P x)
integerSing = Integer -> SInteger (P x)
forall (i :: Integer). Integer -> SInteger i
UnsafeSInteger (Proxy x -> Integer
forall (n :: Natural) (proxy :: Natural -> Type).
KnownNat n =>
proxy n -> Integer
L.natVal (forall (t :: Natural). Proxy t
forall {k} (t :: k). Proxy t
Proxy @x))

-- | Negative numbers and zero.
instance L.KnownNat x => KnownInteger (N x) where
  integerSing :: SInteger (N x)
integerSing = Integer -> SInteger (N x)
forall (i :: Integer). Integer -> SInteger i
UnsafeSInteger (Integer -> Integer
forall a. Num a => a -> a
negate (Proxy x -> Integer
forall (n :: Natural) (proxy :: Natural -> Type).
KnownNat n =>
proxy n -> Integer
L.natVal (forall (t :: Natural). Proxy t
forall {k} (t :: k). Proxy t
Proxy @x)))

-- | Term-level 'P.Integer' representation of the type-level 'Integer' @i@.
integerVal :: forall i proxy. KnownInteger i => proxy i -> P.Integer
integerVal :: forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal proxy i
_ = case SInteger i
forall (i :: Integer). KnownInteger i => SInteger i
integerSing :: SInteger i of UnsafeSInteger Integer
x -> Integer
x

-- | Term-level 'P.Integer' representation of the type-level 'Integer' @i@.
integerVal' :: forall i. KnownInteger i => Proxy# i -> P.Integer
integerVal' :: forall (i :: Integer). KnownInteger i => Proxy# i -> Integer
integerVal' Proxy# i
_ = case SInteger i
forall (i :: Integer). KnownInteger i => SInteger i
integerSing :: SInteger i of UnsafeSInteger Integer
x -> Integer
x

-- | This type represents unknown type-level 'Integer'.
data SomeInteger = forall n. KnownInteger n => SomeInteger (Proxy n)

-- | Convert a term-level 'P.Integer' into an unknown type-level 'Integer'.
someIntegerVal :: P.Integer -> SomeInteger
someIntegerVal :: Integer -> SomeInteger
someIntegerVal Integer
i = Integer
-> (forall (n :: Integer). SInteger n -> SomeInteger)
-> SomeInteger
forall r. Integer -> (forall (n :: Integer). SInteger n -> r) -> r
withSomeSInteger Integer
i (\(SInteger n
si :: SInteger i) ->
                   SInteger n -> (KnownInteger n => SomeInteger) -> SomeInteger
forall (i :: Integer) r. SInteger i -> (KnownInteger i => r) -> r
withKnownInteger SInteger n
si (forall (n :: Integer). KnownInteger n => Proxy n -> SomeInteger
SomeInteger @i Proxy n
forall {k} (t :: k). Proxy t
Proxy))

instance Eq SomeInteger where
  SomeInteger Proxy n
x == :: SomeInteger -> SomeInteger -> Bool
== SomeInteger Proxy n
y = Proxy n -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal Proxy n
x Integer -> Integer -> Bool
forall a. Eq a => a -> a -> Bool
P.== Proxy n -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal Proxy n
y

instance Ord SomeInteger where
  compare :: SomeInteger -> SomeInteger -> Ordering
compare (SomeInteger Proxy n
x) (SomeInteger Proxy n
y) =
    Integer -> Integer -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (Proxy n -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal Proxy n
x) (Proxy n -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal Proxy n
y)

instance Show SomeInteger where
  showsPrec :: Int -> SomeInteger -> ShowS
showsPrec Int
p (SomeInteger Proxy n
x) = Int -> Integer -> ShowS
forall a. Show a => Int -> a -> ShowS
showsPrec Int
p (Proxy n -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal Proxy n
x)

instance Read SomeInteger where
  readsPrec :: Int -> ReadS SomeInteger
readsPrec Int
p String
xs = do (Integer
a, String
ys) <- Int -> ReadS Integer
forall a. Read a => Int -> ReadS a
readsPrec Int
p String
xs
                      [(Integer -> SomeInteger
someIntegerVal Integer
a, String
ys)]

--------------------------------------------------------------------------------
-- Within this module, we use these “normalization” tools to make sure that
-- /zero/ is always represented as @'P' 0@. We don't export any of these
-- normalization tools to end-users because it seems like we can't make them
-- reliable enough so as to offer a decent user experience. So, we just tell
-- users to deal with the fact that both @'P' 0@ and @'N' 0@ mean /zero/.

-- | Make sure /zero/ is represented as @'P' 0@, not as @'N' 0@
--
-- Notice that all the tools in the "KindInteger" can readily handle
-- non-'Normalize'd inputs. This 'Normalize' type-family is offered offered
-- only as a convenience in case you want to simplify /your/ dealing with
-- /zeros/.
type family Normalize (i :: Integer) :: Integer where
  Normalize (N 0) = P 0
  Normalize i     = i

-- | Construct a 'Normalize'd 'N'egative type-level 'Integer'.
--
-- To be used for producing all negative outputs in this module.
type NN (a :: Natural) = Normalize (N a) :: Integer

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

infixl 6 +, -
infixl 7 *, `Div`, `Mod`, `Quot`, `Rem`
infixr 8 ^

-- | Negation of type-level 'Integer's.
type family Negate (x :: Integer) :: Integer where
  Negate (P 0) = P 0
  Negate (P x) = N x
  Negate (N x) = P x

-- | Addition of type-level 'Integer's.
type (a :: Integer) + (b :: Integer) = Add_ (Normalize a) (Normalize b) :: Integer
type family Add_ (a :: Integer) (b :: Integer) :: Integer where
  Add_ (P a) (P b) = P (a L.+ b)
  Add_ (N a) (N b) = NN (a L.+ b)
  Add_ (P a) (N b) = If (b <=? a) (P (a L.- b)) (NN (b L.- a))
  Add_ (N a) (P b) = Add_ (P b) (N a)

-- | Multiplication of type-level 'Integer's.
type (a :: Integer) * (b :: Integer) = Mul_ (Normalize a) (Normalize b) :: Integer
type family Mul_ (a :: Integer) (b :: Integer) :: Integer where
  Mul_ (P a) (P b) = P (a L.* b)
  Mul_ (N a) (N b) = Mul_ (P a) (P b)
  Mul_ (P a) (N b) = NN (a L.* b)
  Mul_ (N a) (P b) = Mul_ (P a) (N b)

-- | Exponentiation of type-level 'Integer's.
--
-- * Exponentiation by negative 'Integer' doesn't type-check.
type (a :: Integer) ^ (b :: Integer) = Pow_ (Normalize a) (Normalize b) :: Integer
type family Pow_ (a :: Integer) (b :: Integer) :: Integer where
  Pow_ (P a) (P b) = P (a L.^ b)
  Pow_ (N a) (P b) = NN (a L.^ b)
  Pow_ _     (N _) = L.TypeError ('L.Text "KindInteger.(^): Negative exponent")

-- | Subtraction of type-level 'Integer's.
type (a :: Integer) - (b :: Integer) = a + Negate b :: Integer

-- | Division ('floor'ed) of type-level 'Integer's.
--
-- @
-- forall (a :: 'Integer') (b :: 'Integer').
--   /such that/ (b '/=' 0).
--     a  '=='  'Div' a b '*' 'Negate' b '+' 'Mod' a b
-- @
--
-- * Division by /zero/ doesn't type-check.
type Div (a :: Integer) (b :: Integer) = Div_ (Normalize a) (Normalize b) :: Integer
type family Div_ (a :: Integer) (b :: Integer) :: Integer where
  Div_ _ (P 0) = L.TypeError ('L.Text "KindInteger.Div: Division by zero")
  Div_ (P a) (P b) = P (L.Div a b)
  Div_ (N a) (N b) = Div_ (P a) (P b)
  Div_ (P a) (N b) = NN (If (b L.* (L.Div a b) ==? a) (L.Div a b) (L.Div a b L.+ 1))
  Div_ (N a) (P b) = Div_ (P a) (N b)

-- | Modulus ('floor'ed division) of type-level 'Integer's.
--
-- @
-- forall (a :: 'Integer') (b :: 'Integer').
--   /such that/ (b '/=' 0).
--     a  '=='  'Div' a b '*' 'Negate' b '+' 'Mod' a b
-- @
--
-- * Modulus by /zero/ doesn't type-check.
type Mod (a :: Integer) (b :: Integer) = Div a b * Negate b + a :: Integer

-- | Division ('truncate'd) of type-level 'Integer's.
--
-- @
-- forall (a :: 'Integer') (b :: 'Integer').
--   /such that/ (b '/=' 0).
--     a  '=='  'Quot' a b '*' 'Negate' b '+' 'Rem' a b
-- @
--
-- * Division by /zero/ doesn't type-check.
type Quot (a :: Integer) (b :: Integer) = Quot_ (Normalize a) (Normalize b) :: Integer
type family Quot_ (a :: Integer) (b :: Integer) :: Integer where
  Quot_ _ (P 0) = L.TypeError ('L.Text "KindInteger.Quot: Division by zero")
  Quot_ (P a) (P b) = P (L.Div a b)
  Quot_ (N a) (N b) = Quot_ (P a) (P b)
  Quot_ (P a) (N b) = Negate (Quot_ (P a) (P b))
  Quot_ (N a) (P b) = Quot_ (P a) (N b)

-- | Remainder ('truncate'd division) of type-level 'Integer's.
--
-- @
-- forall (a :: 'Integer') (b :: 'Integer').
--   /such that/ (b '/=' 0).
--     a  '=='  'Quot' a b '*' 'Negate' b '+' 'Rem' a b
-- @
--
-- * Remainder by /zero/ doesn't type-check.
type Rem (a :: Integer) (b :: Integer) = Quot a b * Negate b + a :: Integer

-- | Log base 2 ('floor'ed) of type-level 'Integer's.
--
-- * Logarithm of /zero/ doesn't type-check.
--
-- * Logarithm of negative number doesn't type-check.
type Log2 (a :: Integer) = Log2_ (Normalize a) :: Integer
type family Log2_ (a :: Integer) :: Integer where
  Log2_ (P 0) = L.TypeError ('L.Text "KindInteger.Log2: Logarithm of zero")
  Log2_ (P a) = P (L.Log2 a)
  Log2_ (N a) = L.TypeError ('L.Text "KindInteger.Log2: Logarithm of negative number")

-- | Comparison of type-level 'Integer's, as a function.
type CmpInteger (a :: Integer) (b :: Integer) = CmpInteger_ (Normalize a) (Normalize b) :: Ordering
type family CmpInteger_ (a :: Integer) (b :: Integer) :: Ordering where
  CmpInteger_ a a = 'EQ
  CmpInteger_ (P a) (P b) = Compare a b
  CmpInteger_ (N a) (N b) = Compare b a
  CmpInteger_ (N _) (P _) = 'LT
  CmpInteger_ (P _) (N _) = 'GT

-- | "Data.Type.Ord" support for type-level 'Integer's.
type instance Compare (a :: Integer) (b :: Integer) = CmpInteger a b :: Ordering

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

-- | We either get evidence that this function was instantiated with the
-- same type-level 'Integer's, or 'Nothing'.
sameInteger
  :: forall a b proxy1 proxy2
  .  (KnownInteger a, KnownInteger b)
  => proxy1 a
  -> proxy2 b
  -> Maybe (a :~: b)
sameInteger :: forall (a :: Integer) (b :: Integer) (proxy1 :: Integer -> Type)
       (proxy2 :: Integer -> Type).
(KnownInteger a, KnownInteger b) =>
proxy1 a -> proxy2 b -> Maybe (a :~: b)
sameInteger proxy1 a
_ proxy2 b
_ = SInteger a -> SInteger b -> Maybe (a :~: b)
forall {k} (f :: k -> Type) (a :: k) (b :: k).
TestEquality f =>
f a -> f b -> Maybe (a :~: b)
forall (a :: Integer) (b :: Integer).
SInteger a -> SInteger b -> Maybe (a :~: b)
testEquality (forall (i :: Integer). KnownInteger i => SInteger i
integerSing @a) (forall (i :: Integer). KnownInteger i => SInteger i
integerSing @b)

-- | Like 'sameInteger', but if the type-level 'Integer's aren't equal, this
-- additionally provides proof of 'LT' or 'GT'.
cmpInteger
  :: forall a b proxy1 proxy2
  .  (KnownInteger a, KnownInteger b)
  => proxy1 a
  -> proxy2 b
  -> OrderingI a b
cmpInteger :: forall (a :: Integer) (b :: Integer) (proxy1 :: Integer -> Type)
       (proxy2 :: Integer -> Type).
(KnownInteger a, KnownInteger b) =>
proxy1 a -> proxy2 b -> OrderingI a b
cmpInteger proxy1 a
x proxy2 b
y = case Integer -> Integer -> Ordering
forall a. Ord a => a -> a -> Ordering
compare (proxy1 a -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal proxy1 a
x) (proxy2 b -> Integer
forall (i :: Integer) (proxy :: Integer -> Type).
KnownInteger i =>
proxy i -> Integer
integerVal proxy2 b
y) of
  Ordering
EQ -> case (Any :~: Any, Any :~: Any)
-> (CmpInteger_ (Normalize a) (Normalize 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) :: (CmpInteger a b :~: 'EQ, a :~: b) of
    (CmpInteger_ (Normalize a) (Normalize b) :~: 'EQ
Refl, a :~: b
Refl) -> OrderingI a a
OrderingI a b
forall {k} (a :: k). (Compare a a ~ 'EQ) => OrderingI a a
EQI
  Ordering
LT -> case (Any :~: Any) -> CmpInteger_ (Normalize a) (Normalize b) :~: 'LT
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl :: (CmpInteger a b :~: 'LT) of
    CmpInteger_ (Normalize a) (Normalize 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) -> CmpInteger_ (Normalize a) (Normalize b) :~: 'GT
forall a b. a -> b
unsafeCoerce Any :~: Any
forall {k} (a :: k). a :~: a
Refl :: (CmpInteger a b :~: 'GT) of
    CmpInteger_ (Normalize a) (Normalize b) :~: 'GT
Refl -> OrderingI a b
forall {k} (a :: k) (b :: k). (Compare a b ~ 'GT) => OrderingI a b
GTI

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

-- | Singleton type for a type-level 'Integer' @i@.
newtype SInteger (i :: Integer) = UnsafeSInteger P.Integer

-- | A explicitly bidirectional pattern synonym relating an 'SInteger' to a
-- 'KnownInteger' constraint.
--
-- As an __expression__: Constructs an explicit @'SInteger' i@ value from an
-- implicit @'KnownInteger' i@ constraint:
--
-- @
-- 'SInteger' @i :: 'KnownInteger' i => 'SInteger' i
-- @
--
-- As a __pattern__: Matches on an explicit @'SInteger' i@ value bringing
-- an implicit @'KnownInteger' i@ constraint into scope:
--
-- @
-- f :: 'SInteger' i -> ..
-- f SInteger = {- SInteger i in scope -}
-- @
pattern SInteger :: forall i. () => KnownInteger i => SInteger i
pattern $mSInteger :: forall {r} {i :: Integer}.
SInteger i -> (KnownInteger i => r) -> ((# #) -> r) -> r
$bSInteger :: forall (i :: Integer). KnownInteger i => SInteger i
SInteger <- (knownIntegerInstance -> KnownIntegeregerInstance)
  where SInteger = SInteger i
forall (i :: Integer). KnownInteger i => SInteger i
integerSing

-- | An internal data type that is only used for defining the 'SInteger' pattern
-- synonym.
data KnownIntegeregerInstance (i :: Integer) where
  KnownIntegeregerInstance :: KnownInteger i => KnownIntegeregerInstance i

-- | An internal function that is only used for defining the 'SInteger' pattern
-- synonym.
knownIntegerInstance :: SInteger i -> KnownIntegeregerInstance i
knownIntegerInstance :: forall (i :: Integer). SInteger i -> KnownIntegeregerInstance i
knownIntegerInstance SInteger i
si = SInteger i
-> (KnownInteger i => KnownIntegeregerInstance i)
-> KnownIntegeregerInstance i
forall (i :: Integer) r. SInteger i -> (KnownInteger i => r) -> r
withKnownInteger SInteger i
si KnownIntegeregerInstance i
KnownInteger i => KnownIntegeregerInstance i
forall (i :: Integer). KnownInteger i => KnownIntegeregerInstance i
KnownIntegeregerInstance

instance Show (SInteger i) where
  showsPrec :: Int -> SInteger i -> ShowS
showsPrec Int
p (UnsafeSInteger Integer
i) = Bool -> ShowS -> ShowS
showParen (Int
p Int -> Int -> Bool
forall a. Ord a => a -> a -> Bool
> Int
appPrec) (ShowS -> ShowS) -> ShowS -> ShowS
forall a b. (a -> b) -> a -> b
$
    String -> ShowS
showString String
"SInteger @" ShowS -> ShowS -> ShowS
forall b c a. (b -> c) -> (a -> b) -> a -> c
.
    Int -> Integer -> ShowS
showsPrecInteger Int
appPrec1 (Integer -> Integer
termIntegerToTypeInteger Integer
i)

instance TestEquality SInteger where
  testEquality :: forall (a :: Integer) (b :: Integer).
SInteger a -> SInteger b -> Maybe (a :~: b)
testEquality (UnsafeSInteger Integer
x) (UnsafeSInteger Integer
y)
    | Integer
x Integer -> Integer -> Bool
forall a. Eq a => a -> a -> Bool
P.== Integer
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

instance TestCoercion SInteger where
  testCoercion :: forall (a :: Integer) (b :: Integer).
SInteger a -> SInteger b -> Maybe (Coercion a b)
testCoercion SInteger a
x SInteger b
y = ((a :~: b) -> Coercion a b)
-> Maybe (a :~: b) -> Maybe (Coercion a b)
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: Type -> Type) a b. Functor f => (a -> b) -> f a -> f b
fmap (\a :~: b
Refl -> Coercion a b
forall {k} (a :: k) (b :: k). Coercible a b => Coercion a b
Coercion) (SInteger a -> SInteger b -> Maybe (a :~: b)
forall {k} (f :: k -> Type) (a :: k) (b :: k).
TestEquality f =>
f a -> f b -> Maybe (a :~: b)
forall (a :: Integer) (b :: Integer).
SInteger a -> SInteger b -> Maybe (a :~: b)
testEquality SInteger a
x SInteger b
y)

-- | Return the type-level 'P.Integer' number corresponding to @i@ in
-- a @'SInteger' i@ value.
fromSInteger :: SInteger i -> P.Integer
fromSInteger :: forall (i :: Integer). SInteger i -> Integer
fromSInteger (UnsafeSInteger Integer
i) = Integer
i

-- | Convert an explicit @'SInteger' i@ value into an implicit
-- @'KnownInteger' i@ constraint.
withKnownInteger
  :: forall i rep (r :: TYPE rep). SInteger i -> (KnownInteger i => r) -> r
withKnownInteger :: forall (i :: Integer) r. SInteger i -> (KnownInteger i => r) -> r
withKnownInteger = forall (cls :: Constraint) meth r.
WithDict cls meth =>
meth -> (cls => r) -> r
withDict @(KnownInteger i)

-- | Convert a 'P.Integer' number into an @'SInteger' n@ value, where @n@ is a
-- fresh type-level 'Integer'.
withSomeSInteger
  :: forall rep (r :: TYPE rep). P.Integer -> (forall n. SInteger n -> r) -> r
withSomeSInteger :: forall r. Integer -> (forall (n :: Integer). SInteger n -> r) -> r
withSomeSInteger Integer
n forall (n :: Integer). SInteger n -> r
k = SInteger Any -> r
forall (n :: Integer). SInteger n -> r
k (Integer -> SInteger Any
forall (i :: Integer). Integer -> SInteger i
UnsafeSInteger Integer
n)
-- It's very important to keep this NOINLINE! See the docs at "GHC.TypeNats"
{-# NOINLINE withSomeSInteger #-}

--------------------------------------------------------------------------------
-- Extras

infixr 4 /=, /=?, ==, ==?

-- | This should be exported by "Data.Type.Ord".
type (a :: k) ==? (b :: k) = OrdCond (Compare a b) 'False 'True 'False :: Bool

-- | This should be exported by "Data.Type.Ord".
type (a :: k) == (b :: k) = (a ==? b) ~ 'True :: Constraint

-- | This should be exported by "Data.Type.Ord".
type (a :: k) /=? (b :: k) = OrdCond (Compare a b) 'True 'False 'True :: Bool

-- | This should be exported by "Data.Type.Ord".
type (a :: k) /= (b :: k) = (a /=? b) ~ 'True :: Constraint