Modulemonoid-subclasses-1.2.5.1Haskell2010

Data.Semigroup.Factorial

This module defines the Semigroup => Factorial => StableFactorial classes and some of their instances.

2 classes
2 values

Packagemonoid-subclasses-1.2.5.1
Exports4
LanguageHaskell2010
LicenceBSD-3-Clause
SourceFactorial.hs

Classes

2 declarations

classclass Semigroup m => Factorial m where

Class of semigroups that can be split into irreducible (i.e., atomic or prime) factors in a unique way. Factors of a Product are literally its prime factors:

Property

prop> factors (Product 12) == [Product 2, Product 2, Product 3]

Factors of a list are not its elements but all its single-item sublists:

Property

prop> factors "abc" == ["a", "b", "c"]

The methods of this class satisfy the following laws:

maybe id sconcat  . nonEmpty . factors == id
List.all (\prime-> factors prime == [prime]) . factors
primePrefix s == foldr const s s
foldl f a == List.foldl f a . factors
foldl' f a == List.foldl' f a . factors
foldr f a == List.foldr f a . factors

A minimal instance definition must implement factors or foldr. Other methods can and should be implemented only for performance reasons.

Methods

factors :: m -> [m]
Returns a list of all prime factors; inverse of mconcat.
primePrefix :: m -> m
The prime prefix; primePrefix mempty == mempty for monoids.
primeSuffix :: m -> m
The prime suffix; primeSuffix mempty == mempty for monoids.
foldl :: (a -> m -> a) -> a -> m -> a
Like foldl from Data.List on the list of prime factors.
foldl' :: (a -> m -> a) -> a -> m -> a
Like foldl' from Data.List on the list of prime factors.
foldr :: (m -> a -> a) -> a -> m -> a
Like foldr from Data.List on the list of prime factors.
length :: m -> Int
The length of the list of prime factors.
foldMap :: Monoid n => (m -> n) -> m -> n
Generalizes foldMap from Data.Foldable, except the function arguments are prime factors rather than the structure elements.
reverse :: m -> m
Equivalent to reverse from Data.List.

Instances26Factorial, …

Factorial ByteStringDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial ByteStringDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial IntSetDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial ByteStringUTF8Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.ByteString.UTF8
Factorial TextDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial TextDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial ()Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Integral a => Factorial (Product a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Ord a => Factorial (Set a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial (IntMap a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial (Seq a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial (Vector a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial [x]Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial a => Factorial (Dual a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
Factorial a => Factorial (Maybe a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial m => Factorial (OffsetPositioned m)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Positioned
(Integral a, Eq a) => Factorial (Sum a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
(FactorialMonoid m, StableFactorial m) => Factorial (Shadowed m)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.PrefixMemory
(Factorial a, PositiveMonoid a) => Factorial (Concat a)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Concat
(StableFactorial a, MonoidNull a) => Factorial (Measured a)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Measured
(StableFactorial m, TextualMonoid m) => Factorial (LinePositioned m)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Positioned
Ord k => Factorial (Map k v)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
(FactorialMonoid a, FactorialMonoid b) => Factorial (Stateful a b)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Stateful
(Factorial a, Factorial b, MonoidNull a, MonoidNull b) => Factorial (a, b)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
(Factorial a, Factorial b, Factorial c, MonoidNull a, MonoidNull b, MonoidNull c) => Factorial (a, b, c)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
(Factorial a, Factorial b, Factorial c, Factorial d, MonoidNull a, MonoidNull b, MonoidNull c, MonoidNull d) => Factorial (a, b, c, d)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial

classclass Factorial m => StableFactorial m

A subclass of Factorial whose instances satisfy the following additional laws:

factors (a <> b) == factors a <> factors b
factors . reverse == List.reverse . factors
primeSuffix s == primePrefix (reverse s)

Instances16StableFactorial, …

StableFactorial ByteStringDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial ByteStringDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial TextDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial TextDefined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial ()Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial (Seq a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial (Sum Natural)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial (Vector a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial [x]Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial a => StableFactorial (Dual a)Defined in monoid-subclasses-1.2.5.1 · Data.Semigroup.Factorial
StableFactorial m => StableFactorial (OffsetPositioned m)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Positioned
(Factorial a, PositiveMonoid a) => StableFactorial (Concat a)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Concat
(StableFactorial a, MonoidNull a) => StableFactorial (Measured a)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Measured
(StableFactorial m, FactorialMonoid m) => StableFactorial (Shadowed m)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.PrefixMemory
(StableFactorial m, TextualMonoid m) => StableFactorial (LinePositioned m)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Positioned
(FactorialMonoid a, FactorialMonoid b, StableFactorial a, StableFactorial b) => StableFactorial (Stateful a b)Defined in monoid-subclasses-1.2.5.1 · Data.Monoid.Instances.Stateful

Monad function equivalents

2 declarations

valuemapM

:: (Factorial a, Semigroup b, Monoid b, Monad m)
=> a -> m b
-> a
-> m b

A mapM equivalent.

valuemapM_ :: (Factorial a, Applicative m) => (a -> m b) -> a -> m ()

A mapM_ equivalent.