Safe Haskell | Safe-Inferred |
---|---|
Language | Haskell2010 |
Data.Group
Documentation
class Monoid m => Group m where Source #
A
Group
is a
Monoid
plus a function,
invert
, such that:
a <> invert a == mempty
invert a <> a == mempty
Minimal complete definition
Instances
Group () Source # | |
Group a => Group ( Identity a) Source # |
|
Group a => Group ( Dual a) Source # | |
Num a => Group ( Sum a) Source # | |
Fractional a => Group ( Product a) Source # | |
Group a => Group ( Down a) Source # | |
Group b => Group (a -> b) Source # | |
( Group a, Group b) => Group (a, b) Source # | |
Group a => Group ( Op a b) Source # | |
Group ( Proxy x) Source # |
Trivial group, Functor style. |
( Group a, Group b, Group c) => Group (a, b, c) Source # | |
Group a => Group ( Const a x) Source # |
|
( Group (f a), Group (g a)) => Group ((f :*: g) a) Source # |
Product of groups, Functor style. |
( Group a, Group b, Group c, Group d) => Group (a, b, c, d) Source # | |
Group (f (g a)) => Group ((f :.: g) a) Source # | |
( Group a, Group b, Group c, Group d, Group e) => Group (a, b, c, d, e) Source # | |
class Group g => Abelian g Source #
Instances
class Group a => Cyclic a where Source #
A
Group
G is
Cyclic
if there exists an element x of G such that for all y in G, there exists an n, such that
y = pow x n
Instances
Cyclic () Source # | |
Defined in Data.Group |
|
Cyclic a => Cyclic ( Identity a) Source # | |
Defined in Data.Group |
|
Integral a => Cyclic ( Sum a) Source # | |
Defined in Data.Group |
|
Cyclic a => Cyclic ( Down a) Source # | |
Defined in Data.Group |
|
Cyclic ( Proxy x) Source # | |
Defined in Data.Group |
|
Cyclic a => Cyclic ( Const a x) Source # | |
Defined in Data.Group |