Safe Haskell	Trustworthy
Language	Haskell2010

Data.Semigroup.Factorial

Contents

Classes
Monad function equivalents

Description

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

Synopsis

class Semigroup m => Factorial m where
- factors :: m -> [m]
- primePrefix :: m -> m
- primeSuffix :: m -> m
- foldl :: (a -> m -> a) -> a -> m -> a
- foldl' :: (a -> m -> a) -> a -> m -> a
- foldr :: (m -> a -> a) -> a -> m -> a
- length :: m -> Int
- foldMap :: Monoid n => (m -> n) -> m -> n
- reverse :: m -> m
class Factorial m => StableFactorial m
mapM :: (Factorial a, Monoid b, Monad m) => (a -> m b) -> a -> m b
mapM_ :: (Factorial a, Applicative m) => (a -> m b) -> a -> m ()

Classes

class Semigroup m => Factorial m where Source #

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:

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

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

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
factors . reverse == List.reverse . factors
primePrefix s == foldr const s s
primeSuffix s == primePrefix (reverse 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.

Minimal complete definition

factors | foldr

Methods

factors :: m -> [m] Source #

Returns a list of all prime factors; inverse of mconcat.

primePrefix :: m -> m Source #

The prime prefix; primePrefix mempty == mempty for monoids.

primeSuffix :: m -> m Source #

The prime suffix; primeSuffix mempty == mempty for monoids.

foldl :: (a -> m -> a) -> a -> m -> a Source #

Like foldl from Data.List on the list of prime factors.

foldl' :: (a -> m -> a) -> a -> m -> a Source #

Like foldl' from Data.List on the list of prime factors.

foldr :: (m -> a -> a) -> a -> m -> a Source #

Like foldr from Data.List on the list of prime factors.

length :: m -> Int Source #

The length of the list of prime factors.

foldMap :: Monoid n => (m -> n) -> m -> n Source #

Generalizes foldMap from Data.Foldable, except the function arguments are prime factors rather than the structure elements.

reverse :: m -> m Source #

Equivalent to reverse from Data.List.

Instances

Factorial () Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: () -> [()] Source # primePrefix :: () -> () Source # primeSuffix :: () -> () Source # foldl :: (a -> () -> a) -> a -> () -> a Source # foldl' :: (a -> () -> a) -> a -> () -> a Source # foldr :: (() -> a -> a) -> a -> () -> a Source # length :: () -> Int Source # foldMap :: Monoid n => (() -> n) -> () -> n Source # reverse :: () -> () Source #
Factorial ByteString Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: ByteString -> [ByteString] Source # primePrefix :: ByteString -> ByteString Source # primeSuffix :: ByteString -> ByteString Source # foldl :: (a -> ByteString -> a) -> a -> ByteString -> a Source # foldl' :: (a -> ByteString -> a) -> a -> ByteString -> a Source # foldr :: (ByteString -> a -> a) -> a -> ByteString -> a Source # length :: ByteString -> Int Source # foldMap :: Monoid n => (ByteString -> n) -> ByteString -> n Source # reverse :: ByteString -> ByteString Source #
Factorial ByteString Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: ByteString -> [ByteString] Source # primePrefix :: ByteString -> ByteString Source # primeSuffix :: ByteString -> ByteString Source # foldl :: (a -> ByteString -> a) -> a -> ByteString -> a Source # foldl' :: (a -> ByteString -> a) -> a -> ByteString -> a Source # foldr :: (ByteString -> a -> a) -> a -> ByteString -> a Source # length :: ByteString -> Int Source # foldMap :: Monoid n => (ByteString -> n) -> ByteString -> n Source # reverse :: ByteString -> ByteString Source #
Factorial IntSet Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: IntSet -> [IntSet] Source # primePrefix :: IntSet -> IntSet Source # primeSuffix :: IntSet -> IntSet Source # foldl :: (a -> IntSet -> a) -> a -> IntSet -> a Source # foldl' :: (a -> IntSet -> a) -> a -> IntSet -> a Source # foldr :: (IntSet -> a -> a) -> a -> IntSet -> a Source # length :: IntSet -> Int Source # foldMap :: Monoid n => (IntSet -> n) -> IntSet -> n Source # reverse :: IntSet -> IntSet Source #
Factorial Text Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Text -> [Text] Source # primePrefix :: Text -> Text Source # primeSuffix :: Text -> Text Source # foldl :: (a -> Text -> a) -> a -> Text -> a Source # foldl' :: (a -> Text -> a) -> a -> Text -> a Source # foldr :: (Text -> a -> a) -> a -> Text -> a Source # length :: Text -> Int Source # foldMap :: Monoid n => (Text -> n) -> Text -> n Source # reverse :: Text -> Text Source #
Factorial Text Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Text -> [Text] Source # primePrefix :: Text -> Text Source # primeSuffix :: Text -> Text Source # foldl :: (a -> Text -> a) -> a -> Text -> a Source # foldl' :: (a -> Text -> a) -> a -> Text -> a Source # foldr :: (Text -> a -> a) -> a -> Text -> a Source # length :: Text -> Int Source # foldMap :: Monoid n => (Text -> n) -> Text -> n Source # reverse :: Text -> Text Source #
Factorial ByteStringUTF8 Source #
Instance details Defined in Data.Monoid.Instances.ByteString.UTF8 Methods factors :: ByteStringUTF8 -> [ByteStringUTF8] Source # primePrefix :: ByteStringUTF8 -> ByteStringUTF8 Source # primeSuffix :: ByteStringUTF8 -> ByteStringUTF8 Source # foldl :: (a -> ByteStringUTF8 -> a) -> a -> ByteStringUTF8 -> a Source # foldl' :: (a -> ByteStringUTF8 -> a) -> a -> ByteStringUTF8 -> a Source # foldr :: (ByteStringUTF8 -> a -> a) -> a -> ByteStringUTF8 -> a Source # length :: ByteStringUTF8 -> Int Source # foldMap :: Monoid n => (ByteStringUTF8 -> n) -> ByteStringUTF8 -> n Source # reverse :: ByteStringUTF8 -> ByteStringUTF8 Source #
Factorial [x] Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: [x] -> [[x]] Source # primePrefix :: [x] -> [x] Source # primeSuffix :: [x] -> [x] Source # foldl :: (a -> [x] -> a) -> a -> [x] -> a Source # foldl' :: (a -> [x] -> a) -> a -> [x] -> a Source # foldr :: ([x] -> a -> a) -> a -> [x] -> a Source # length :: [x] -> Int Source # foldMap :: Monoid n => ([x] -> n) -> [x] -> n Source # reverse :: [x] -> [x] Source #
Factorial a => Factorial (Maybe a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Maybe a -> [Maybe a] Source # primePrefix :: Maybe a -> Maybe a Source # primeSuffix :: Maybe a -> Maybe a Source # foldl :: (a0 -> Maybe a -> a0) -> a0 -> Maybe a -> a0 Source # foldl' :: (a0 -> Maybe a -> a0) -> a0 -> Maybe a -> a0 Source # foldr :: (Maybe a -> a0 -> a0) -> a0 -> Maybe a -> a0 Source # length :: Maybe a -> Int Source # foldMap :: Monoid n => (Maybe a -> n) -> Maybe a -> n Source # reverse :: Maybe a -> Maybe a Source #
Factorial a => Factorial (Dual a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Dual a -> [Dual a] Source # primePrefix :: Dual a -> Dual a Source # primeSuffix :: Dual a -> Dual a Source # foldl :: (a0 -> Dual a -> a0) -> a0 -> Dual a -> a0 Source # foldl' :: (a0 -> Dual a -> a0) -> a0 -> Dual a -> a0 Source # foldr :: (Dual a -> a0 -> a0) -> a0 -> Dual a -> a0 Source # length :: Dual a -> Int Source # foldMap :: Monoid n => (Dual a -> n) -> Dual a -> n Source # reverse :: Dual a -> Dual a Source #
(Integral a, Eq a) => Factorial (Sum a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Sum a -> [Sum a] Source # primePrefix :: Sum a -> Sum a Source # primeSuffix :: Sum a -> Sum a Source # foldl :: (a0 -> Sum a -> a0) -> a0 -> Sum a -> a0 Source # foldl' :: (a0 -> Sum a -> a0) -> a0 -> Sum a -> a0 Source # foldr :: (Sum a -> a0 -> a0) -> a0 -> Sum a -> a0 Source # length :: Sum a -> Int Source # foldMap :: Monoid n => (Sum a -> n) -> Sum a -> n Source # reverse :: Sum a -> Sum a Source #
Integral a => Factorial (Product a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Product a -> [Product a] Source # primePrefix :: Product a -> Product a Source # primeSuffix :: Product a -> Product a Source # foldl :: (a0 -> Product a -> a0) -> a0 -> Product a -> a0 Source # foldl' :: (a0 -> Product a -> a0) -> a0 -> Product a -> a0 Source # foldr :: (Product a -> a0 -> a0) -> a0 -> Product a -> a0 Source # length :: Product a -> Int Source # foldMap :: Monoid n => (Product a -> n) -> Product a -> n Source # reverse :: Product a -> Product a Source #
Factorial (IntMap a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: IntMap a -> [IntMap a] Source # primePrefix :: IntMap a -> IntMap a Source # primeSuffix :: IntMap a -> IntMap a Source # foldl :: (a0 -> IntMap a -> a0) -> a0 -> IntMap a -> a0 Source # foldl' :: (a0 -> IntMap a -> a0) -> a0 -> IntMap a -> a0 Source # foldr :: (IntMap a -> a0 -> a0) -> a0 -> IntMap a -> a0 Source # length :: IntMap a -> Int Source # foldMap :: Monoid n => (IntMap a -> n) -> IntMap a -> n Source # reverse :: IntMap a -> IntMap a Source #
Factorial (Seq a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Seq a -> [Seq a] Source # primePrefix :: Seq a -> Seq a Source # primeSuffix :: Seq a -> Seq a Source # foldl :: (a0 -> Seq a -> a0) -> a0 -> Seq a -> a0 Source # foldl' :: (a0 -> Seq a -> a0) -> a0 -> Seq a -> a0 Source # foldr :: (Seq a -> a0 -> a0) -> a0 -> Seq a -> a0 Source # length :: Seq a -> Int Source # foldMap :: Monoid n => (Seq a -> n) -> Seq a -> n Source # reverse :: Seq a -> Seq a Source #
Ord a => Factorial (Set a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Set a -> [Set a] Source # primePrefix :: Set a -> Set a Source # primeSuffix :: Set a -> Set a Source # foldl :: (a0 -> Set a -> a0) -> a0 -> Set a -> a0 Source # foldl' :: (a0 -> Set a -> a0) -> a0 -> Set a -> a0 Source # foldr :: (Set a -> a0 -> a0) -> a0 -> Set a -> a0 Source # length :: Set a -> Int Source # foldMap :: Monoid n => (Set a -> n) -> Set a -> n Source # reverse :: Set a -> Set a Source #
Factorial (Vector a) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Vector a -> [Vector a] Source # primePrefix :: Vector a -> Vector a Source # primeSuffix :: Vector a -> Vector a Source # foldl :: (a0 -> Vector a -> a0) -> a0 -> Vector a -> a0 Source # foldl' :: (a0 -> Vector a -> a0) -> a0 -> Vector a -> a0 Source # foldr :: (Vector a -> a0 -> a0) -> a0 -> Vector a -> a0 Source # length :: Vector a -> Int Source # foldMap :: Monoid n => (Vector a -> n) -> Vector a -> n Source # reverse :: Vector a -> Vector a Source #
(StableFactorial m, TextualMonoid m) => Factorial (LinePositioned m) Source #
Instance details Defined in Data.Monoid.Instances.Positioned Methods factors :: LinePositioned m -> [LinePositioned m] Source # primePrefix :: LinePositioned m -> LinePositioned m Source # primeSuffix :: LinePositioned m -> LinePositioned m Source # foldl :: (a -> LinePositioned m -> a) -> a -> LinePositioned m -> a Source # foldl' :: (a -> LinePositioned m -> a) -> a -> LinePositioned m -> a Source # foldr :: (LinePositioned m -> a -> a) -> a -> LinePositioned m -> a Source # length :: LinePositioned m -> Int Source # foldMap :: Monoid n => (LinePositioned m -> n) -> LinePositioned m -> n Source # reverse :: LinePositioned m -> LinePositioned m Source #
StableFactorial m => Factorial (OffsetPositioned m) Source #
Instance details Defined in Data.Monoid.Instances.Positioned Methods factors :: OffsetPositioned m -> [OffsetPositioned m] Source # primePrefix :: OffsetPositioned m -> OffsetPositioned m Source # primeSuffix :: OffsetPositioned m -> OffsetPositioned m Source # foldl :: (a -> OffsetPositioned m -> a) -> a -> OffsetPositioned m -> a Source # foldl' :: (a -> OffsetPositioned m -> a) -> a -> OffsetPositioned m -> a Source # foldr :: (OffsetPositioned m -> a -> a) -> a -> OffsetPositioned m -> a Source # length :: OffsetPositioned m -> Int Source # foldMap :: Monoid n => (OffsetPositioned m -> n) -> OffsetPositioned m -> n Source # reverse :: OffsetPositioned m -> OffsetPositioned m Source #
(StableFactorial a, MonoidNull a) => Factorial (Measured a) Source #
Instance details Defined in Data.Monoid.Instances.Measured Methods factors :: Measured a -> [Measured a] Source # primePrefix :: Measured a -> Measured a Source # primeSuffix :: Measured a -> Measured a Source # foldl :: (a0 -> Measured a -> a0) -> a0 -> Measured a -> a0 Source # foldl' :: (a0 -> Measured a -> a0) -> a0 -> Measured a -> a0 Source # foldr :: (Measured a -> a0 -> a0) -> a0 -> Measured a -> a0 Source # length :: Measured a -> Int Source # foldMap :: Monoid n => (Measured a -> n) -> Measured a -> n Source # reverse :: Measured a -> Measured a Source #
(Factorial a, PositiveMonoid a) => Factorial (Concat a) Source #
Instance details Defined in Data.Monoid.Instances.Concat Methods factors :: Concat a -> [Concat a] Source # primePrefix :: Concat a -> Concat a Source # primeSuffix :: Concat a -> Concat a Source # foldl :: (a0 -> Concat a -> a0) -> a0 -> Concat a -> a0 Source # foldl' :: (a0 -> Concat a -> a0) -> a0 -> Concat a -> a0 Source # foldr :: (Concat a -> a0 -> a0) -> a0 -> Concat a -> a0 Source # length :: Concat a -> Int Source # foldMap :: Monoid n => (Concat a -> n) -> Concat a -> n Source # reverse :: Concat a -> Concat a Source #
(Factorial a, Factorial b, MonoidNull a, MonoidNull b) => Factorial (a, b) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: (a, b) -> [(a, b)] Source # primePrefix :: (a, b) -> (a, b) Source # primeSuffix :: (a, b) -> (a, b) Source # foldl :: (a0 -> (a, b) -> a0) -> a0 -> (a, b) -> a0 Source # foldl' :: (a0 -> (a, b) -> a0) -> a0 -> (a, b) -> a0 Source # foldr :: ((a, b) -> a0 -> a0) -> a0 -> (a, b) -> a0 Source # length :: (a, b) -> Int Source # foldMap :: Monoid n => ((a, b) -> n) -> (a, b) -> n Source # reverse :: (a, b) -> (a, b) Source #
Ord k => Factorial (Map k v) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: Map k v -> [Map k v] Source # primePrefix :: Map k v -> Map k v Source # primeSuffix :: Map k v -> Map k v Source # foldl :: (a -> Map k v -> a) -> a -> Map k v -> a Source # foldl' :: (a -> Map k v -> a) -> a -> Map k v -> a Source # foldr :: (Map k v -> a -> a) -> a -> Map k v -> a Source # length :: Map k v -> Int Source # foldMap :: Monoid n => (Map k v -> n) -> Map k v -> n Source # reverse :: Map k v -> Map k v Source #
(FactorialMonoid a, FactorialMonoid b) => Factorial (Stateful a b) Source #
Instance details Defined in Data.Monoid.Instances.Stateful Methods factors :: Stateful a b -> [Stateful a b] Source # primePrefix :: Stateful a b -> Stateful a b Source # primeSuffix :: Stateful a b -> Stateful a b Source # foldl :: (a0 -> Stateful a b -> a0) -> a0 -> Stateful a b -> a0 Source # foldl' :: (a0 -> Stateful a b -> a0) -> a0 -> Stateful a b -> a0 Source # foldr :: (Stateful a b -> a0 -> a0) -> a0 -> Stateful a b -> a0 Source # length :: Stateful a b -> Int Source # foldMap :: Monoid n => (Stateful a b -> n) -> Stateful a b -> n Source # reverse :: Stateful a b -> Stateful a b Source #
(Factorial a, Factorial b, Factorial c, MonoidNull a, MonoidNull b, MonoidNull c) => Factorial (a, b, c) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: (a, b, c) -> [(a, b, c)] Source # primePrefix :: (a, b, c) -> (a, b, c) Source # primeSuffix :: (a, b, c) -> (a, b, c) Source # foldl :: (a0 -> (a, b, c) -> a0) -> a0 -> (a, b, c) -> a0 Source # foldl' :: (a0 -> (a, b, c) -> a0) -> a0 -> (a, b, c) -> a0 Source # foldr :: ((a, b, c) -> a0 -> a0) -> a0 -> (a, b, c) -> a0 Source # length :: (a, b, c) -> Int Source # foldMap :: Monoid n => ((a, b, c) -> n) -> (a, b, c) -> n Source # reverse :: (a, b, c) -> (a, b, c) Source #
(Factorial a, Factorial b, Factorial c, Factorial d, MonoidNull a, MonoidNull b, MonoidNull c, MonoidNull d) => Factorial (a, b, c, d) Source #
Instance details Defined in Data.Semigroup.Factorial Methods factors :: (a, b, c, d) -> [(a, b, c, d)] Source # primePrefix :: (a, b, c, d) -> (a, b, c, d) Source # primeSuffix :: (a, b, c, d) -> (a, b, c, d) Source # foldl :: (a0 -> (a, b, c, d) -> a0) -> a0 -> (a, b, c, d) -> a0 Source # foldl' :: (a0 -> (a, b, c, d) -> a0) -> a0 -> (a, b, c, d) -> a0 Source # foldr :: ((a, b, c, d) -> a0 -> a0) -> a0 -> (a, b, c, d) -> a0 Source # length :: (a, b, c, d) -> Int Source # foldMap :: Monoid n => ((a, b, c, d) -> n) -> (a, b, c, d) -> n Source # reverse :: (a, b, c, d) -> (a, b, c, d) Source #

class Factorial m => StableFactorial m Source #

A subclass of Factorial whose instances satisfy this additional law:

factors (a <> b) == factors a <> factors b

Instances

StableFactorial () Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial ByteString Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial ByteString Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial Text Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial Text Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial [x] Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial a => StableFactorial (Dual a) Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial (Sum Natural) Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial (Seq a) Source #
Instance details Defined in Data.Semigroup.Factorial
StableFactorial (Vector a) Source #
Instance details Defined in Data.Semigroup.Factorial
(StableFactorial m, TextualMonoid m) => StableFactorial (LinePositioned m) Source #
Instance details Defined in Data.Monoid.Instances.Positioned
StableFactorial m => StableFactorial (OffsetPositioned m) Source #
Instance details Defined in Data.Monoid.Instances.Positioned
(StableFactorial a, MonoidNull a) => StableFactorial (Measured a) Source #
Instance details Defined in Data.Monoid.Instances.Measured
(Factorial a, PositiveMonoid a) => StableFactorial (Concat a) Source #
Instance details Defined in Data.Monoid.Instances.Concat
(FactorialMonoid a, FactorialMonoid b, StableFactorial a, StableFactorial b) => StableFactorial (Stateful a b) Source #
Instance details Defined in Data.Monoid.Instances.Stateful

Monad function equivalents

mapM :: (Factorial a, Monoid b, Monad m) => (a -> m b) -> a -> m b Source #

A mapM equivalent.

mapM_ :: (Factorial a, Applicative m) => (a -> m b) -> a -> m () Source #

A mapM_ equivalent.