Safe Haskell | None |
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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 Mod
(or its synonym /
). To work with integers mod 7, you could write:
IntMod
7 IntegerMod
7 Integer/7 ℤ/7
(The last is a synonym for Integer
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 bound
or extract the underlying value
using unMod
.
Here is a quick example:
*Data.Modular> (10 :: ℤ7) * (11 :: ℤ7) 5
It also works correctly with negative numeric literals:
*Data.Modular> (-10 :: ℤ7) * (11 :: ℤ7) 2
Documentation
toMod :: forall n i. (Integral i, SingI n) => i -> i `Mod` nSource
Wraps the underlying type into the modular type, wrapping as appropriate.
The actual type, wrapping an underlying Integeral
type i
in a
newtype annotated with the bound.
(Integral i, SingI Nat n) => Bounded (Mod i n) | |
(Integral i, SingI Nat n) => Enum (Mod i n) | |
Eq i => Eq (Mod i n) | |
(Integral i, SingI Nat n) => Integral (Mod i n) | |
(Integral i, SingI Nat n) => Num (Mod i n) | |
Ord i => Ord (Mod i n) | |
(Read i, Integral i, SingI Nat n) => Read (Mod i n) | |
(Integral i, SingI Nat n) => Real (Mod i n) | |
Show i => Show (Mod i n) |