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


-- | A type for integers modulo some constant.
--   
--   This module provides a convenient type for working with integers
--   modulo some constant. It saves you from manually wrapping numeric
--   operations all over the place and prevents a range of simple mistakes.
--   It also provides some really cute syntax for these types like
--   <tt>ℤ/7</tt> for integers modulo 7.
@package modular-arithmetic
@version 1.0.0.0


-- | This module provides types for working with integers modulo some
--   constant.
--   
--   This module uses some new Haskell features introduced in 7.6. In
--   particular, it needs DataKinds and type literals (GHC.TypeLits). The
--   TypeOperators extension is needed for the nice infix syntax.
--   
--   These types are created with the type constructor <tt>Mod</tt> (or its
--   synonym <tt>/</tt>). To work with integers mod 7, you could write:
--   <tt> Int <a>Mod</a> 7 Integer <a>Mod</a> 7 Integer/7 ℤ/7 </tt>
--   
--   (The last is a synonym for <tt>Integer</tt> provided by this library.
--   In Emacs, you can use the Tex input mode to type it with Bbb{Z}.)
--   
--   All the usual typeclasses are defined for these types. You can also
--   get the constant using <tt>bound</tt> or extract the underlying value
--   using <tt>unMod</tt>.
--   
--   Here is a quick example: <tt> *Data.Modular&gt; (10 :: ℤ<i>7) * (11 ::
--   ℤ</i>7) 5 </tt>
--   
--   It also works correctly with negative numeric literals: <tt>
--   *Data.Modular&gt; (-10 :: ℤ<i>7) * (11 :: ℤ</i>7) 2 </tt>
module Data.Modular

-- | Extract the underlying integral value from a modular type.
unMod :: i Mod n -> i

-- | Wraps the underlying type into the modular type, wrapping as
--   appropriate.
toMod :: (Integral i, SingI n) => i -> i Mod n

-- | The actual type, wrapping an underlying <tt>Integeral</tt> type
--   <tt>i</tt> in a newtype annotated with the bound.
data Mod i (n :: Nat)

-- | A synonym for <tt>Mod</tt>, inspired by the ℤ/n syntax from
--   mathematics.
type (/) = Mod

-- | A synonym for Integer, also inspired by the ℤ/n syntax.
type ℤ = Integer
instance Eq i => Eq (Mod i n)
instance Ord i => Ord (Mod i n)
instance (Integral i, SingI Nat n) => Integral (Mod i n)
instance (Integral i, SingI Nat n) => Real (Mod i n)
instance (Integral i, SingI Nat n) => Bounded (Mod i n)
instance (Integral i, SingI Nat n) => Enum (Mod i n)
instance (Integral i, SingI Nat n) => Num (Mod i n)
instance (Read i, Integral i, SingI Nat n) => Read (Mod i n)
instance Show i => Show (Mod i n)