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| Data.Ring.Module | | Portability | non-portable (MPTCs) | | Stability | experimental | | Maintainer | ekmett@gmail.com |
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| Description |
| Left- and right- modules over rings, semirings, and Seminearrings.
To avoid a proliferation of classes. These only require that there
be an addition and multiplication operation for the Ring
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| Synopsis |
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| Documentation |
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| module Data.Ring |
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(x * y) *. m = x * (y *. m) | | | Methods | | |  Instances | | LeftModule Natural Ordering | | LeftModule Natural Ordering | | LeftModule Natural () | | LeftModule Natural () | | LeftModule Natural All | | LeftModule Natural All | | LeftModule Natural Any | | LeftModule Natural Any | | LeftModule Natural ([] a) | | LeftModule Natural ([] a) | | Monoid m => LeftModule Natural (Dual m) | | Monoid m => LeftModule Natural (Dual m) | | LeftModule Natural (Endo a) | | LeftModule Natural (Endo a) | | Num a => LeftModule Natural (Sum a) | | Num a => LeftModule Natural (Sum a) | | Num a => LeftModule Natural (Product a) | | Num a => LeftModule Natural (Product a) | | LeftModule Natural (First a) | | LeftModule Natural (First a) | | LeftModule Natural (Last a) | | LeftModule Natural (Last a) | | CharReducer m => LeftModule Natural (UTF8 m) | | CharReducer m => LeftModule Natural (UTF8 m) | | LeftModule Natural (SourcePosition f) | | LeftModule Natural (SourcePosition f) | | Monoid m => LeftModule Natural (Self m) | | Monoid m => LeftModule Natural (Self m) | | Monoid m => LeftModule Natural (FromString m) | | Monoid m => LeftModule Natural (FromString m) | | Multiplicative m => LeftModule Natural (Log m) | | Multiplicative m => LeftModule Natural (Log m) | | Applicative f => LeftModule Natural (Traversal f) | | Applicative f => LeftModule Natural (Traversal f) | | Monad f => LeftModule Natural (Action f) | | Monad f => LeftModule Natural (Action f) | | LeftModule Natural (Free a) | | LeftModule Natural (Free a) | | Enum a => LeftModule Natural (BitSet a) | | Enum a => LeftModule Natural (BitSet a) | | (HasUnionWith f, Ord r, Eq r, RightSemiNearRing r) => LeftModule r (UnionWith f r) | | (LeftModule r m, LeftModule r n) => LeftModule r ((,) m n) | | (LeftModule r m, Applicative f) => LeftModule r (App f m) | | (LeftModule r m, Monad f) => LeftModule r (Mon f m) | | Monoid m => LeftModule Natural (a -> m) | | Monoid m => LeftModule Natural (a -> m) | | Eq a => LeftModule Natural (RLE Seq a) | | Eq a => LeftModule Natural (RLE Seq a) | | Category k => LeftModule Natural (GEndo k a) | | Category k => LeftModule Natural (GEndo k a) | | Alternative f => LeftModule Natural (Alt f a) | | Alternative f => LeftModule Natural (Alt f a) | | MonadPlus f => LeftModule Natural (MonadSum f a) | | MonadPlus f => LeftModule Natural (MonadSum f a) | | (LeftModule r m, LeftModule r n, LeftModule r o) => LeftModule r ((,,) m n o) | | Monoid m => LeftModule Natural (CMonoid m m m) | | Monoid m => LeftModule Natural (CMonoid m m m) | | (LeftModule r m, LeftModule r n, LeftModule r o, LeftModule r p) => LeftModule r ((,,,) m n o p) | | (LeftModule r m, LeftModule r n, LeftModule r o, LeftModule r p, LeftModule r q) => LeftModule r ((,,,,) m n o p q) | | (Bounded a, Enum a) => LeftModule (BitSet a) (BitSet a) |
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(m .* x) * y = m .* (x * y) | | | Methods | | | | Instances | | RightModule Natural Ordering | | RightModule Natural Ordering | | RightModule Natural () | | RightModule Natural () | | RightModule Natural All | | RightModule Natural All | | RightModule Natural Any | | RightModule Natural Any | | RightModule Natural ([] a) | | RightModule Natural ([] a) | | Monoid m => RightModule Natural (Dual m) | | Monoid m => RightModule Natural (Dual m) | | RightModule Natural (Endo a) | | RightModule Natural (Endo a) | | Num a => RightModule Natural (Sum a) | | Num a => RightModule Natural (Sum a) | | Num a => RightModule Natural (Product a) | | Num a => RightModule Natural (Product a) | | RightModule Natural (First a) | | RightModule Natural (First a) | | RightModule Natural (Last a) | | RightModule Natural (Last a) | | CharReducer m => RightModule Natural (UTF8 m) | | CharReducer m => RightModule Natural (UTF8 m) | | RightModule Natural (SourcePosition f) | | RightModule Natural (SourcePosition f) | | Monoid m => RightModule Natural (Self m) | | Monoid m => RightModule Natural (Self m) | | Monoid m => RightModule Natural (FromString m) | | Monoid m => RightModule Natural (FromString m) | | Multiplicative m => RightModule Natural (Log m) | | Multiplicative m => RightModule Natural (Log m) | | Applicative f => RightModule Natural (Traversal f) | | Applicative f => RightModule Natural (Traversal f) | | Monad f => RightModule Natural (Action f) | | Monad f => RightModule Natural (Action f) | | RightModule Natural (Free a) | | RightModule Natural (Free a) | | Enum a => RightModule Natural (BitSet a) | | Enum a => RightModule Natural (BitSet a) | | (HasUnionWith f, Ord r, Eq r, RightSemiNearRing r) => RightModule r (UnionWith f r) | | (RightModule r m, RightModule r n) => RightModule r ((,) m n) | | (RightModule r m, Applicative f) => RightModule r (App f m) | | (RightModule r m, Monad f) => RightModule r (Mon f m) | | Monoid m => RightModule Natural (a -> m) | | Monoid m => RightModule Natural (a -> m) | | Eq a => RightModule Natural (RLE Seq a) | | Eq a => RightModule Natural (RLE Seq a) | | Category k => RightModule Natural (GEndo k a) | | Category k => RightModule Natural (GEndo k a) | | Alternative f => RightModule Natural (Alt f a) | | Alternative f => RightModule Natural (Alt f a) | | MonadPlus f => RightModule Natural (MonadSum f a) | | MonadPlus f => RightModule Natural (MonadSum f a) | | (RightModule r m, RightModule r n, RightModule r o) => RightModule r ((,,) m n o) | | Monoid m => RightModule Natural (CMonoid m m m) | | Monoid m => RightModule Natural (CMonoid m m m) | | (RightModule r m, RightModule r n, RightModule r o, RightModule r p) => RightModule r ((,,,) m n o p) | | (RightModule r m, RightModule r n, RightModule r o, RightModule r p, RightModule r q) => RightModule r ((,,,,) m n o p q) | | (Bounded a, Enum a) => RightModule (BitSet a) (BitSet a) |
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(x *. m) .* y = x *. (m .* y) | | | Instances | | Module Natural Ordering | | Module Natural Ordering | | Module Natural () | | Module Natural () | | Module Natural All | | Module Natural All | | Module Natural Any | | Module Natural Any | | Module Natural ([] a) | | Module Natural ([] a) | | Monoid m => Module Natural (Dual m) | | Monoid m => Module Natural (Dual m) | | Module Natural (Endo a) | | Module Natural (Endo a) | | Num a => Module Natural (Sum a) | | Num a => Module Natural (Sum a) | | Num a => Module Natural (Product a) | | Num a => Module Natural (Product a) | | Module Natural (First a) | | Module Natural (First a) | | Module Natural (Last a) | | Module Natural (Last a) | | CharReducer m => Module Natural (UTF8 m) | | CharReducer m => Module Natural (UTF8 m) | | Module Natural (SourcePosition f) | | Module Natural (SourcePosition f) | | Monoid m => Module Natural (Self m) | | Monoid m => Module Natural (Self m) | | Monoid m => Module Natural (FromString m) | | Monoid m => Module Natural (FromString m) | | Multiplicative m => Module Natural (Log m) | | Multiplicative m => Module Natural (Log m) | | Applicative f => Module Natural (Traversal f) | | Applicative f => Module Natural (Traversal f) | | Monad f => Module Natural (Action f) | | Monad f => Module Natural (Action f) | | Module Natural (Free a) | | Module Natural (Free a) | | Enum a => Module Natural (BitSet a) | | Enum a => Module Natural (BitSet a) | | (HasUnionWith f, Ord r, Eq r, RightSemiNearRing r) => Module r (UnionWith f r) | | (Module r m, Module r n) => Module r ((,) m n) | | (Module r m, Applicative f) => Module r (App f m) | | (Module r m, Monad f) => Module r (Mon f m) | | Monoid m => Module Natural (a -> m) | | Monoid m => Module Natural (a -> m) | | Eq a => Module Natural (RLE Seq a) | | Eq a => Module Natural (RLE Seq a) | | Category k => Module Natural (GEndo k a) | | Category k => Module Natural (GEndo k a) | | Alternative f => Module Natural (Alt f a) | | Alternative f => Module Natural (Alt f a) | | MonadPlus f => Module Natural (MonadSum f a) | | MonadPlus f => Module Natural (MonadSum f a) | | (Module r m, Module r n, Module r o) => Module r ((,,) m n o) | | Monoid m => Module Natural (CMonoid m m m) | | Monoid m => Module Natural (CMonoid m m m) | | (Module r m, Module r n, Module r o, Module r p) => Module r ((,,,) m n o p) | | (Module r m, Module r n, Module r o, Module r p, Module r q) => Module r ((,,,,) m n o p q) | | (Bounded a, Enum a) => Module (BitSet a) (BitSet a) |
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