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


-- | Unary natural numbers relying on the singletons infrastructure.
--   
--   Unary natural number relying on the <a>singletons</a> infrastructure.
--   More information about the general usage of singletons can be found on
--   the <a>singletons github</a> page.
@package singleton-nats
@version 0.4.2

module Data.Nat
data Nat
Z :: Nat
S :: Nat -> Nat
natPlus :: Nat -> Nat -> Nat
natMul :: Nat -> Nat -> Nat
natMinus :: Nat -> Nat -> Nat
natAbs :: Nat -> Nat
natSignum :: Nat -> Nat

-- | Converts a runtime <a>Integer</a> to an existentially wrapped
--   <a>Nat</a>. Returns <a>Nothing</a> if the argument is negative
someNatVal :: Integer -> Maybe (SomeSing Nat)
type SNat = (Sing :: Nat -> Type)

-- | The singleton kind-indexed data family.
class PNum a
class SNum a
data SSym0 (l_abr3 :: TyFun Nat Nat)
SSym0KindInference :: SSym0
type SSym1 (t_abr2 :: Nat) = S t_abr2
type ZSym0 = Z

-- | Provides a shorthand for <a>Nat</a>-s using <a>GHC.TypeLits</a>, for
--   example:
--   
--   <pre>
--   &gt;&gt;&gt; :kind! Lit 3
--   Lit 3 :: Nat
--   = 'S ('S ('S 'Z))
--   </pre>
data LitSym0 (l_alr9 :: TyFun Nat Nat)
LitSym0KindInference :: LitSym0
type LitSym1 (t_alr8 :: Nat) = Lit t_alr8
type SLit n = Sing (Lit n)

-- | Shorthand for <a>SNat</a> literals using <tt>TypeApplications</tt>.
--   
--   <pre>
--   &gt;&gt;&gt; :set -XTypeApplications
--   
--   &gt;&gt;&gt; sLit @5
--   SS (SS (SS (SS (SS SZ))))
--   </pre>
sLit :: forall (n :: Nat). SingI (Lit n) => Sing (Lit n)
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.LitSym0
instance GHC.Classes.Ord Data.Nat.Nat
instance GHC.Show.Show Data.Nat.Nat
instance GHC.Classes.Eq Data.Nat.Nat
instance GHC.Classes.Eq (Data.Nat.SNat n)
instance GHC.Classes.Ord (Data.Nat.SNat n)
instance Data.Singletons.Prelude.Eq.PEq Data.Nat.Nat
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.FromInteger_6989586621679057055Sym0
instance Data.Singletons.Prelude.Num.PNum Data.Nat.Nat
instance Data.Singletons.Prelude.Num.SNum Data.Nat.Nat
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.Let6989586621679057047Scrutinee_6989586621679048427Sym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.Signum_6989586621679057037Sym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.Abs_6989586621679057024Sym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.TFHelper_6989586621679057007Sym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.TFHelper_6989586621679057007Sym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.TFHelper_6989586621679056981Sym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.TFHelper_6989586621679056981Sym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.TFHelper_6989586621679056955Sym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.TFHelper_6989586621679056955Sym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.Compare_6989586621679056870Sym0
instance Data.Singletons.Prelude.Ord.POrd Data.Nat.Nat
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.Compare_6989586621679056870Sym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.ShowsPrec_6989586621679055869Sym0
instance Data.Singletons.Prelude.Show.PShow Data.Nat.Nat
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.ShowsPrec_6989586621679055869Sym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.ShowsPrec_6989586621679055869Sym2
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatMulSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatMulSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatPlusSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatPlusSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatMinusSym1
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatMinusSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatAbsSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.NatSignumSym0
instance Data.Singletons.SuppressUnusedWarnings.SuppressUnusedWarnings Data.Nat.SSym0
instance GHC.Num.Num Data.Nat.Nat
instance Data.Singletons.Internal.SingKind Data.Nat.Nat
instance Data.Singletons.Prelude.Show.SShow Data.Nat.Nat => Data.Singletons.Prelude.Show.SShow Data.Nat.Nat
instance Data.Singletons.Prelude.Ord.SOrd Data.Nat.Nat => Data.Singletons.Prelude.Ord.SOrd Data.Nat.Nat
instance Data.Singletons.Prelude.Eq.SEq Data.Nat.Nat => Data.Singletons.Prelude.Eq.SEq Data.Nat.Nat
instance Data.Singletons.Decide.SDecide Data.Nat.Nat => Data.Singletons.Decide.SDecide Data.Nat.Nat
instance Data.Singletons.ShowSing.ShowSing Data.Nat.Nat => Data.Singletons.ShowSing.ShowSing Data.Nat.Nat
instance Data.Singletons.ShowSing.ShowSing Data.Nat.Nat => GHC.Show.Show (Data.Singletons.Internal.Sing z)
instance Data.Singletons.Internal.SingI 'Data.Nat.Z
instance Data.Singletons.Internal.SingI n => Data.Singletons.Internal.SingI ('Data.Nat.S n)