{-# LANGUAGE NoImplicitPrelude #-} module Number.ResidueClass.Maybe where import qualified Number.ResidueClass as Res import qualified Algebra.IntegralDomain as Integral import qualified Algebra.Ring as Ring import qualified Algebra.Additive as Additive import qualified Algebra.ZeroTestable as ZeroTestable import Algebra.ZeroTestable(isZero) import PreludeBase import NumericPrelude infix 7 /:, `Cons` {- | Here we try to provide implementations for 'zero' and 'one' by making the modulus optional. We have to provide non-modulus operations for the cases where both operands have Nothing modulus. This is problematic since operations like '(\/)' depend essentially on the modulus. A working version with disabled 'zero' and 'one' can be found ResidueClass. -} data T a = Cons {modulus :: !(Maybe a) -- ^ the modulus can be Nothing to denote a generic constant like 'zero' and 'one' which could not be bound to a specific modulus so far ,representative :: !a } deriving (Show, Read) -- | @r \/: m@ is the residue class containing @r@ with respect to the modulus @m@ (/:) :: (Integral.C a) => a -> a -> T a (/:) r m = Cons (Just m) (mod r m) matchMaybe :: Maybe a -> Maybe a -> Maybe a matchMaybe Nothing y = y matchMaybe x _ = x isCompatibleMaybe :: (Eq a) => Maybe a -> Maybe a -> Bool isCompatibleMaybe Nothing _ = True isCompatibleMaybe _ Nothing = True isCompatibleMaybe (Just x) (Just y) = x == y -- | Check if two residue classes share the same modulus isCompatible :: (Eq a) => T a -> T a -> Bool isCompatible x y = isCompatibleMaybe (modulus x) (modulus y) lift2 :: (Eq a) => (a -> a -> a -> a) -> (a -> a -> a) -> (T a -> T a -> T a) lift2 f g x y = if isCompatible x y then let m = matchMaybe (modulus x) (modulus y) in Cons m (maybe g f m (representative x) (representative y)) else error "ResidueClass: Incompatible operands" instance (Eq a, ZeroTestable.C a, Integral.C a) => Eq (T a) where (==) x y = if isCompatible x y then maybe (==) (\m x' y' -> isZero (mod (x'-y') m)) (matchMaybe (modulus x) (modulus y)) (representative x) (representative y) else error "ResidueClass.(==): Incompatible operands" instance (Eq a, Integral.C a) => Additive.C (T a) where zero = Cons Nothing zero (+) = lift2 Res.add (+) (-) = lift2 Res.sub (-) negate (Cons m r) = Cons m (negate r) instance (Eq a, Integral.C a) => Ring.C (T a) where one = Cons Nothing one (*) = lift2 Res.mul (*) fromInteger = Cons Nothing . fromInteger