libghc-type-level-numbers-doc 0.1.1.1-3 / usr / share / doc / libghc-type-level-numbers-doc / html / type-level-numbers.txt

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-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Type level numbers implemented using type families.
--   
--   This is type level numbers implemented using type families. Natural
--   numbers use binary encoding. With default context stack numbers up to
--   2^18-1 coudl be represented. Signed integer numbers use balanced
--   ternary encoding.
--   
--   Package is structured as folows:
--   
--   <ul>
--   <li>[<tt>TypeLevel.Number.Classes</tt>] contain generic type families
--   such as Add</li>
--   <li>[<tt>TypeLevel.Number.Nat</tt>] natural numbers implemented using
--   binary encoding</li>
--   <li>[<tt>TypeLevel.Number.Int</tt>] signed integers implemented using
--   balanced ternary encoding</li>
--   <li>[<tt>TypeLevel.Boolean</tt>] type level booleans</li>
--   </ul>
--   
--   So far comparison of numbers, subtraction and multiplication of
--   numbers are supported.
@package type-level-numbers
@version 0.1.1.1


module TypeLevel.Reify

-- | Value with type tag
data Witness t a
Witness :: a -> Witness t a
[getValue] :: Witness t a -> a

-- | Convert type level into value level using
class Reify t a
witness :: Reify t a => Witness t a
instance (Data.Data.Data t, Data.Data.Data a) => Data.Data.Data (TypeLevel.Reify.Witness t a)
instance GHC.Classes.Eq a => GHC.Classes.Eq (TypeLevel.Reify.Witness t a)
instance GHC.Show.Show a => GHC.Show.Show (TypeLevel.Reify.Witness t a)

module TypeLevel.Boolean

-- | Data type for truth
data True

-- | Data type for false.
data False

-- | Negation
notT :: a -> Not a

-- | And for boolean types
andT :: a -> b -> And a b

-- | Or for boolean types
orT :: a -> b -> Or a b

-- | Exlusive or for boolean types
xorT :: a -> b -> Xor a b
instance GHC.Show.Show TypeLevel.Boolean.False
instance GHC.Show.Show TypeLevel.Boolean.True
instance TypeLevel.Reify.Reify TypeLevel.Boolean.True GHC.Types.Bool
instance TypeLevel.Reify.Reify TypeLevel.Boolean.False GHC.Types.Bool


-- | This module contain interface type classes for operations with type
--   level numbers.
module TypeLevel.Number.Classes

-- | Type family for comparing two numbers. It's expected that for any two
--   valid <tt>n</tt> and <tt>m</tt> 'Compare n m' is equal to IsLess when
--   'n&lt;m', IsEqual when 'n=m' and IsGreater when 'n&gt;m'.
compareN :: n -> m -> Compare n m
data IsLesser
data IsEqual
data IsGreater

-- | Numbers n and m are instances of this class if and only is n &lt; m.
class Lesser n m

-- | Numbers n and m are instances of this class if and only is n &lt;= m.
class LesserEq n m

-- | Numbers n and m are instances of this class if and only is n &gt; m.
class Greater n m

-- | Numbers n and m are instances of this class if and only is n &gt;= m.
class GreaterEq n m

-- | Positive number.
class Positive n

-- | Non-zero number. For naturals it's same as positive
class NonZero n

-- | Next number.
nextN :: n -> Next n

-- | Previous number
prevN :: n -> Prev n

-- | Negate number.
negateN :: n -> Negate n

-- | Sum of two numbers.
addN :: n -> m -> Add n m

-- | Difference of two numbers.
subN :: n -> m -> Sub n m

-- | Product of two numbers.
mulN :: n -> m -> Mul n m

-- | Division of two numbers. <tt>n</tt> and <tt>m</tt> should be instances
--   of this class only if remainder of 'n/m' is zero.
divN :: n -> m -> Div n m

-- | Usually numbers have non-unique representation. This type family is
--   canonical representation of number.
instance GHC.Show.Show TypeLevel.Number.Classes.IsLesser
instance GHC.Show.Show TypeLevel.Number.Classes.IsEqual
instance GHC.Show.Show TypeLevel.Number.Classes.IsGreater
instance TypeLevel.Number.Classes.OneOfTwo a a b
instance TypeLevel.Number.Classes.OneOfTwo a b a
instance TypeLevel.Number.Classes.OneOfTwo a a a
instance TypeLevel.Number.Classes.Compare n m ~ TypeLevel.Number.Classes.IsLesser => TypeLevel.Number.Classes.Lesser n m
instance TypeLevel.Number.Classes.Compare n m ~ TypeLevel.Number.Classes.IsGreater => TypeLevel.Number.Classes.Greater n m
instance TypeLevel.Number.Classes.OneOfTwo (TypeLevel.Number.Classes.Compare n m) TypeLevel.Number.Classes.IsLesser TypeLevel.Number.Classes.IsEqual => TypeLevel.Number.Classes.LesserEq n m
instance TypeLevel.Number.Classes.OneOfTwo (TypeLevel.Number.Classes.Compare n m) TypeLevel.Number.Classes.IsGreater TypeLevel.Number.Classes.IsEqual => TypeLevel.Number.Classes.GreaterEq n m


-- | This is type level natural numbers. They are represented using binary
--   encoding which means that reasonable large numbers could be
--   represented. With default context stack depth (20) maximal number is
--   2^18-1 (262143).
--   
--   <pre>
--   Z           = 0
--   I Z         = 1
--   O (I Z)     = 2
--   I (I Z)     = 3
--   O (O (I Z)) = 4
--   ...
--   </pre>
--   
--   It's easy to see that representation for each number is not unique.
--   One could add any numbers of leading zeroes:
--   
--   <pre>
--   I Z = I (O Z) = I (O (O Z)) = 1
--   </pre>
--   
--   In order to enforce uniqueness of representation only numbers without
--   leading zeroes are members of Nat type class. This means than types
--   are equal if and only if numbers are equal.
--   
--   Natural numbers support comparison and following operations: Next,
--   Prev, Add, Sub, Mul. All operations on numbers return normalized
--   numbers.
--   
--   Interface type classes are reexported from TypeLevel.Number.Classes
module TypeLevel.Number.Nat

-- | One bit.
data I n

-- | Zero bit.
data O n

-- | Bit stream terminator.
data Z

-- | Type class for natural numbers. Only numbers without leading zeroes
--   are members of this type class.
class Nat n

-- | Convert natural number to integral value. It's not checked whether
--   value could be represented.
toInt :: (Nat n, Integral i) => n -> i

-- | Some natural number
data SomeNat
[SomeNat] :: Nat n => n -> SomeNat

-- | Apply function which could work with any <a>Nat</a> value only know at
--   runtime.
withNat :: forall i a. (Integral i) => (forall n. Nat n => n -> a) -> i -> a

-- | Create type for natural number.
natT :: Integer -> TypeQ

-- | Create value for type level natural. Value itself is undefined.
nat :: Integer -> ExpQ
instance TypeLevel.Number.Nat.Nat TypeLevel.Number.Nat.Types.Z
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z)
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O n))
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I (TypeLevel.Number.Nat.Types.O n))
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I n))
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I (TypeLevel.Number.Nat.Types.I n))
instance TypeLevel.Number.Nat.Number_Is_Denormalized TypeLevel.Number.Nat.Types.Z => TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O TypeLevel.Number.Nat.Types.Z)
instance (TypeLevel.Number.Nat.Nat n, TypeLevel.Number.Classes.Positive n) => TypeLevel.Number.Nat.Pos n
instance GHC.Show.Show TypeLevel.Number.Nat.SomeNat
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Integer.Type.Integer
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Integer.Type.Integer
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Integer.Type.Integer
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Types.Int
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Types.Int
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Types.Int
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Word.Word8
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.O n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z)))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Word.Word8
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.I n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z)))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Word.Word8
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Word.Word16
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.O n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z)))))))))))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Word.Word16
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.I n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z)))))))))))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Word.Word16
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Word.Word32
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Word.Word32
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Word.Word32
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Word.Word64
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Word.Word64
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Word.Word64
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Int.Int8
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.O n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Int.Int8
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.I n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Int.Int8
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Int.Int16
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.O n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z))))))))))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Int.Int16
instance (TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n), TypeLevel.Number.Classes.Lesser (TypeLevel.Number.Nat.Types.I n) (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.O (TypeLevel.Number.Nat.Types.I TypeLevel.Number.Nat.Types.Z))))))))))))))))) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Int.Int16
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Int.Int32
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Int.Int32
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Int.Int32
instance TypeLevel.Reify.Reify TypeLevel.Number.Nat.Types.Z GHC.Int.Int64
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.O n) GHC.Int.Int64
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Reify.Reify (TypeLevel.Number.Nat.Types.I n) GHC.Int.Int64
instance GHC.Show.Show TypeLevel.Number.Nat.Types.Z
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => GHC.Show.Show (TypeLevel.Number.Nat.Types.O n)
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => GHC.Show.Show (TypeLevel.Number.Nat.Types.I n)
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Number.Classes.Positive (TypeLevel.Number.Nat.Types.I n)
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Number.Classes.Positive (TypeLevel.Number.Nat.Types.O n)
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.I n) => TypeLevel.Number.Classes.NonZero (TypeLevel.Number.Nat.Types.I n)
instance TypeLevel.Number.Nat.Nat (TypeLevel.Number.Nat.Types.O n) => TypeLevel.Number.Classes.NonZero (TypeLevel.Number.Nat.Types.O n)

module TypeLevel.Number.Nat.Num
type N0 = Z
type N1 = I Z
type N2 = O (I Z)
type N3 = I (I Z)
type N4 = O (O (I Z))
type N5 = I (O (I Z))
type N6 = O (I (I Z))
type N7 = I (I (I Z))
type N8 = O (O (O (I Z)))
type N9 = I (O (O (I Z)))
n0 :: N0
n1 :: N1
n2 :: N2
n3 :: N3
n4 :: N4
n5 :: N5
n6 :: N6
n7 :: N7
n8 :: N8
n9 :: N9


-- | Type level signed integer numbers are implemented using balanced
--   ternary encoding much in the same way as natural numbers.
--   
--   Currently following operations are supported: Next, Prev, Add, Sub,
--   Mul.
module TypeLevel.Number.Int

-- | Digit stream terminator
data ZZ

-- | Digit -1
data Dn n

-- | Digit 0
data D0 n

-- | Digit 1
data D1 n

-- | Type class for type level integers. Only numbers without leading
--   zeroes are members of the class.
class IntT n

-- | Convert natural number to integral value. It's not checked whether
--   value could be represented.
toInt :: (IntT n, Integral i) => n -> i

-- | Some natural number
data SomeInt

-- | Apply function which could work with any <tt>Nat</tt> value only know
--   at runtime.
withInt :: forall i a. (Integral i) => (forall n. IntT n => n -> a) -> i -> a

-- | Generate type for integer number.
intT :: Integer -> TypeQ
instance TypeLevel.Number.Int.IntT TypeLevel.Number.Int.Types.ZZ
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 TypeLevel.Number.Int.Types.ZZ)
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn TypeLevel.Number.Int.Types.ZZ)
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn (TypeLevel.Number.Int.Types.Dn n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 (TypeLevel.Number.Int.Types.Dn n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 (TypeLevel.Number.Int.Types.Dn n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn (TypeLevel.Number.Int.Types.D0 n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 (TypeLevel.Number.Int.Types.D0 n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 (TypeLevel.Number.Int.Types.D0 n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn (TypeLevel.Number.Int.Types.D1 n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 (TypeLevel.Number.Int.Types.D1 n))
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 n) => TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 (TypeLevel.Number.Int.Types.D1 n))
instance GHC.Show.Show TypeLevel.Number.Int.Types.ZZ
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.Dn n) => GHC.Show.Show (TypeLevel.Number.Int.Types.Dn n)
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D0 n) => GHC.Show.Show (TypeLevel.Number.Int.Types.D0 n)
instance TypeLevel.Number.Int.IntT (TypeLevel.Number.Int.Types.D1 n) => GHC.Show.Show (TypeLevel.Number.Int.Types.D1 n)
instance GHC.Show.Show TypeLevel.Number.Int.SomeInt

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