Ideas.Common.Algebra.Field

Contents

• Semi-ring
• Ring
• Field
• Additive monoid
• Multiplicative monoid
• Datatype for safe numeric operators
• CoSemiRing, CoRing, and CoField (for matching)

Description

Synopsis

• class SemiRing a where
  • (|+|) :: a -> a -> a
  • zero :: a
  • sum :: [a] -> a
  • (|*|) :: a -> a -> a
  • one :: a
  • product :: [a] -> a
• class SemiRing a => Ring a where
  • plusInverse :: a -> a
  • (|-|) :: a -> a -> a
• class Ring a => Field a where
  • timesInverse :: a -> a
  • (|/|) :: a -> a -> a
• newtype Additive a = Additive {
  • fromAdditive :: a
  }
• newtype Multiplicative a = Multiplicative {
  • fromMultiplicative :: a
  }
• data SafeNum a
• safeNum :: SafeNum a -> Either String a
• class CoSemiRing a where
  • isPlus :: a -> Maybe (a, a)
  • isZero :: a -> Bool
  • isTimes :: a -> Maybe (a, a)
  • isOne :: a -> Bool
• class CoSemiRing a => CoRing a where
  • isNegate :: a -> Maybe a
  • isMinus :: a -> Maybe (a, a)
• class CoRing a => CoField a where
  • isRecip :: a -> Maybe a
  • isDivision :: a -> Maybe (a, a)

Semi-ring

Ring

Field

Additive monoid

Multiplicative monoid

Datatype for safe numeric operators

CoSemiRing, CoRing, and CoField (for matching)