Safe Haskell | None |
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- class Additive r where
- sum1 :: (Foldable1 f, Additive r) => f r -> r
- class Additive r => Abelian r
- class Additive r => Idempotent r
- sinnum1pIdempotent :: Natural -> r -> r
- class Additive m => Partitionable m where
- partitionWith :: (m -> m -> r) -> m -> NonEmpty r
Additive Semigroups
(a + b) + c = a + (b + c) sinnum 1 a = a sinnum (2 * n) a = sinnum n a + sinnum n a sinnum (2 * n + 1) a = sinnum n a + sinnum n a + a
Additive Abelian semigroups
class Additive r => Abelian r Source
an additive abelian semigroup
a + b = b + a
Additive Monoids
class Additive r => Idempotent r Source
An additive semigroup with idempotent addition.
a + a = a
Idempotent Bool | |
Idempotent () | |
Idempotent r => Idempotent (Complex r) | |
Idempotent r => Idempotent (Quaternion r) | |
Idempotent r => Idempotent (Dual r) | |
Idempotent r => Idempotent (Hyper' r) | |
Idempotent r => Idempotent (Hyper r) | |
Idempotent r => Idempotent (Dual' r) | |
Idempotent r => Idempotent (Quaternion' r) | |
Idempotent r => Idempotent (Trig r) | |
Band r => Idempotent (Log r) | |
Idempotent r => Idempotent (Opposite r) | |
Idempotent r => Idempotent (ZeroRng r) | |
Idempotent r => Idempotent (e -> r) | |
(Idempotent a, Idempotent b) => Idempotent (a, b) | |
(HasTrie e, Idempotent r) => Idempotent (:->: e r) | |
Idempotent r => Idempotent (Covector r a) | |
(Idempotent a, Idempotent b, Idempotent c) => Idempotent (a, b, c) | |
(Idempotent a, Idempotent b, Idempotent c, Idempotent d) => Idempotent (a, b, c, d) | |
(Idempotent a, Idempotent b, Idempotent c, Idempotent d, Idempotent e) => Idempotent (a, b, c, d, e) |
sinnum1pIdempotent :: Natural -> r -> rSource
Partitionable semigroups
class Additive m => Partitionable m whereSource
partitionWith :: (m -> m -> r) -> m -> NonEmpty rSource
partitionWith f c returns a list containing f a b for each a b such that a + b = c,
Partitionable Bool | |
Partitionable () | |
Partitionable Natural | |
Partitionable r => Partitionable (Complex r) | |
Partitionable r => Partitionable (Quaternion r) | |
Partitionable r => Partitionable (Dual r) | |
Partitionable r => Partitionable (Hyper' r) | |
Partitionable r => Partitionable (Hyper r) | |
Partitionable r => Partitionable (Dual' r) | |
Partitionable r => Partitionable (Quaternion' r) | |
Partitionable r => Partitionable (Trig r) | |
Factorable r => Partitionable (Log r) | |
(Partitionable a, Partitionable b) => Partitionable (a, b) | |
(Partitionable a, Partitionable b, Partitionable c) => Partitionable (a, b, c) | |
(Partitionable a, Partitionable b, Partitionable c, Partitionable d) => Partitionable (a, b, c, d) | |
(Partitionable a, Partitionable b, Partitionable c, Partitionable d, Partitionable e) => Partitionable (a, b, c, d, e) |