Data.Semigroup.Factorial

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

Classes

class 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:

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
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.

Minimal complete definition

factors | foldr

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.

Instances

Factorial ByteString

Defined in Data.Semigroup.Factorial

Methods

factors :: ByteString -> [ByteString]

primePrefix :: ByteString -> ByteString

primeSuffix :: ByteString -> ByteString

foldl :: (a -> ByteString -> a) -> a -> ByteString -> a

foldl' :: (a -> ByteString -> a) -> a -> ByteString -> a

foldr :: (ByteString -> a -> a) -> a -> ByteString -> a

length :: ByteString -> Int

foldMap :: Monoid n => (ByteString -> n) -> ByteString -> n

reverse :: ByteString -> ByteString

Factorial ByteString

Defined in Data.Semigroup.Factorial

Methods

factors :: ByteString -> [ByteString]

primePrefix :: ByteString -> ByteString

primeSuffix :: ByteString -> ByteString

foldl :: (a -> ByteString -> a) -> a -> ByteString -> a

foldl' :: (a -> ByteString -> a) -> a -> ByteString -> a

foldr :: (ByteString -> a -> a) -> a -> ByteString -> a

length :: ByteString -> Int

foldMap :: Monoid n => (ByteString -> n) -> ByteString -> n

reverse :: ByteString -> ByteString

Factorial IntSet

Defined in Data.Semigroup.Factorial

Methods

factors :: IntSet -> [IntSet]

primePrefix :: IntSet -> IntSet

primeSuffix :: IntSet -> IntSet

foldl :: (a -> IntSet -> a) -> a -> IntSet -> a

foldl' :: (a -> IntSet -> a) -> a -> IntSet -> a

foldr :: (IntSet -> a -> a) -> a -> IntSet -> a

length :: IntSet -> Int

foldMap :: Monoid n => (IntSet -> n) -> IntSet -> n

reverse :: IntSet -> IntSet

Factorial ByteStringUTF8

Defined in Data.Monoid.Instances.ByteString.UTF8

Methods

factors :: ByteStringUTF8 -> [ByteStringUTF8]

primePrefix :: ByteStringUTF8 -> ByteStringUTF8

primeSuffix :: ByteStringUTF8 -> ByteStringUTF8

foldl :: (a -> ByteStringUTF8 -> a) -> a -> ByteStringUTF8 -> a

foldl' :: (a -> ByteStringUTF8 -> a) -> a -> ByteStringUTF8 -> a

foldr :: (ByteStringUTF8 -> a -> a) -> a -> ByteStringUTF8 -> a

length :: ByteStringUTF8 -> Int

foldMap :: Monoid n => (ByteStringUTF8 -> n) -> ByteStringUTF8 -> n

reverse :: ByteStringUTF8 -> ByteStringUTF8

Factorial Text

Defined in Data.Semigroup.Factorial

Methods

factors :: Text -> [Text]

primePrefix :: Text -> Text

primeSuffix :: Text -> Text

foldl :: (a -> Text -> a) -> a -> Text -> a

foldl' :: (a -> Text -> a) -> a -> Text -> a

foldr :: (Text -> a -> a) -> a -> Text -> a

length :: Text -> Int

foldMap :: Monoid n => (Text -> n) -> Text -> n

reverse :: Text -> Text

Factorial Text

Defined in Data.Semigroup.Factorial

Methods

factors :: Text -> [Text]

primePrefix :: Text -> Text

primeSuffix :: Text -> Text

foldl :: (a -> Text -> a) -> a -> Text -> a

foldl' :: (a -> Text -> a) -> a -> Text -> a

foldr :: (Text -> a -> a) -> a -> Text -> a

length :: Text -> Int

foldMap :: Monoid n => (Text -> n) -> Text -> n

reverse :: Text -> Text

Factorial ()

Defined in Data.Semigroup.Factorial

Methods

factors :: () -> [()]

primePrefix :: () -> ()

primeSuffix :: () -> ()

foldl :: (a -> () -> a) -> a -> () -> a

foldl' :: (a -> () -> a) -> a -> () -> a

foldr :: (() -> a -> a) -> a -> () -> a

length :: () -> Int

foldMap :: Monoid n => (() -> n) -> () -> n

reverse :: () -> ()

Factorial a => Factorial (Dual a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Dual a -> [Dual a]

primePrefix :: Dual a -> Dual a

primeSuffix :: Dual a -> Dual a

foldl :: (a0 -> Dual a -> a0) -> a0 -> Dual a -> a0

foldl' :: (a0 -> Dual a -> a0) -> a0 -> Dual a -> a0

foldr :: (Dual a -> a0 -> a0) -> a0 -> Dual a -> a0

length :: Dual a -> Int

foldMap :: Monoid n => (Dual a -> n) -> Dual a -> n

reverse :: Dual a -> Dual a

Integral a => Factorial (Product a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Product a -> [Product a]

primePrefix :: Product a -> Product a

primeSuffix :: Product a -> Product a

foldl :: (a0 -> Product a -> a0) -> a0 -> Product a -> a0

foldl' :: (a0 -> Product a -> a0) -> a0 -> Product a -> a0

foldr :: (Product a -> a0 -> a0) -> a0 -> Product a -> a0

length :: Product a -> Int

foldMap :: Monoid n => (Product a -> n) -> Product a -> n

reverse :: Product a -> Product a

(Integral a, Eq a) => Factorial (Sum a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Sum a -> [Sum a]

primePrefix :: Sum a -> Sum a

primeSuffix :: Sum a -> Sum a

foldl :: (a0 -> Sum a -> a0) -> a0 -> Sum a -> a0

foldl' :: (a0 -> Sum a -> a0) -> a0 -> Sum a -> a0

foldr :: (Sum a -> a0 -> a0) -> a0 -> Sum a -> a0

length :: Sum a -> Int

foldMap :: Monoid n => (Sum a -> n) -> Sum a -> n

reverse :: Sum a -> Sum a

Factorial (IntMap a)

Defined in Data.Semigroup.Factorial

Methods

factors :: IntMap a -> [IntMap a]

primePrefix :: IntMap a -> IntMap a

primeSuffix :: IntMap a -> IntMap a

foldl :: (a0 -> IntMap a -> a0) -> a0 -> IntMap a -> a0

foldl' :: (a0 -> IntMap a -> a0) -> a0 -> IntMap a -> a0

foldr :: (IntMap a -> a0 -> a0) -> a0 -> IntMap a -> a0

length :: IntMap a -> Int

foldMap :: Monoid n => (IntMap a -> n) -> IntMap a -> n

reverse :: IntMap a -> IntMap a

Factorial (Seq a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Seq a -> [Seq a]

primePrefix :: Seq a -> Seq a

primeSuffix :: Seq a -> Seq a

foldl :: (a0 -> Seq a -> a0) -> a0 -> Seq a -> a0

foldl' :: (a0 -> Seq a -> a0) -> a0 -> Seq a -> a0

foldr :: (Seq a -> a0 -> a0) -> a0 -> Seq a -> a0

length :: Seq a -> Int

foldMap :: Monoid n => (Seq a -> n) -> Seq a -> n

reverse :: Seq a -> Seq a

Ord a => Factorial (Set a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Set a -> [Set a]

primePrefix :: Set a -> Set a

primeSuffix :: Set a -> Set a

foldl :: (a0 -> Set a -> a0) -> a0 -> Set a -> a0

foldl' :: (a0 -> Set a -> a0) -> a0 -> Set a -> a0

foldr :: (Set a -> a0 -> a0) -> a0 -> Set a -> a0

length :: Set a -> Int

foldMap :: Monoid n => (Set a -> n) -> Set a -> n

reverse :: Set a -> Set a

(Factorial a, PositiveMonoid a) => Factorial (Concat a)

Defined in Data.Monoid.Instances.Concat

Methods

factors :: Concat a -> [Concat a]

primePrefix :: Concat a -> Concat a

primeSuffix :: Concat a -> Concat a

foldl :: (a0 -> Concat a -> a0) -> a0 -> Concat a -> a0

foldl' :: (a0 -> Concat a -> a0) -> a0 -> Concat a -> a0

foldr :: (Concat a -> a0 -> a0) -> a0 -> Concat a -> a0

length :: Concat a -> Int

foldMap :: Monoid n => (Concat a -> n) -> Concat a -> n

reverse :: Concat a -> Concat a

(StableFactorial a, MonoidNull a) => Factorial (Measured a)

Defined in Data.Monoid.Instances.Measured

Methods

factors :: Measured a -> [Measured a]

primePrefix :: Measured a -> Measured a

primeSuffix :: Measured a -> Measured a

foldl :: (a0 -> Measured a -> a0) -> a0 -> Measured a -> a0

foldl' :: (a0 -> Measured a -> a0) -> a0 -> Measured a -> a0

foldr :: (Measured a -> a0 -> a0) -> a0 -> Measured a -> a0

length :: Measured a -> Int

foldMap :: Monoid n => (Measured a -> n) -> Measured a -> n

reverse :: Measured a -> Measured a

(StableFactorial m, TextualMonoid m) => Factorial (LinePositioned m)

Defined in Data.Monoid.Instances.Positioned

Methods

factors :: LinePositioned m -> [LinePositioned m]

primePrefix :: LinePositioned m -> LinePositioned m

primeSuffix :: LinePositioned m -> LinePositioned m

foldl :: (a -> LinePositioned m -> a) -> a -> LinePositioned m -> a

foldl' :: (a -> LinePositioned m -> a) -> a -> LinePositioned m -> a

foldr :: (LinePositioned m -> a -> a) -> a -> LinePositioned m -> a

length :: LinePositioned m -> Int

foldMap :: Monoid n => (LinePositioned m -> n) -> LinePositioned m -> n

reverse :: LinePositioned m -> LinePositioned m

StableFactorial m => Factorial (OffsetPositioned m)

Defined in Data.Monoid.Instances.Positioned

Methods

factors :: OffsetPositioned m -> [OffsetPositioned m]

primePrefix :: OffsetPositioned m -> OffsetPositioned m

primeSuffix :: OffsetPositioned m -> OffsetPositioned m

foldl :: (a -> OffsetPositioned m -> a) -> a -> OffsetPositioned m -> a

foldl' :: (a -> OffsetPositioned m -> a) -> a -> OffsetPositioned m -> a

foldr :: (OffsetPositioned m -> a -> a) -> a -> OffsetPositioned m -> a

length :: OffsetPositioned m -> Int

foldMap :: Monoid n => (OffsetPositioned m -> n) -> OffsetPositioned m -> n

reverse :: OffsetPositioned m -> OffsetPositioned m

(FactorialMonoid m, StableFactorial m) => Factorial (Shadowed m)

Defined in Data.Monoid.Instances.PrefixMemory

Methods

factors :: Shadowed m -> [Shadowed m]

primePrefix :: Shadowed m -> Shadowed m

primeSuffix :: Shadowed m -> Shadowed m

foldl :: (a -> Shadowed m -> a) -> a -> Shadowed m -> a

foldl' :: (a -> Shadowed m -> a) -> a -> Shadowed m -> a

foldr :: (Shadowed m -> a -> a) -> a -> Shadowed m -> a

length :: Shadowed m -> Int

foldMap :: Monoid n => (Shadowed m -> n) -> Shadowed m -> n

reverse :: Shadowed m -> Shadowed m

Factorial (Vector a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Vector a -> [Vector a]

primePrefix :: Vector a -> Vector a

primeSuffix :: Vector a -> Vector a

foldl :: (a0 -> Vector a -> a0) -> a0 -> Vector a -> a0

foldl' :: (a0 -> Vector a -> a0) -> a0 -> Vector a -> a0

foldr :: (Vector a -> a0 -> a0) -> a0 -> Vector a -> a0

length :: Vector a -> Int

foldMap :: Monoid n => (Vector a -> n) -> Vector a -> n

reverse :: Vector a -> Vector a

Factorial a => Factorial (Maybe a)

Defined in Data.Semigroup.Factorial

Methods

factors :: Maybe a -> [Maybe a]

primePrefix :: Maybe a -> Maybe a

primeSuffix :: Maybe a -> Maybe a

foldl :: (a0 -> Maybe a -> a0) -> a0 -> Maybe a -> a0

foldl' :: (a0 -> Maybe a -> a0) -> a0 -> Maybe a -> a0

foldr :: (Maybe a -> a0 -> a0) -> a0 -> Maybe a -> a0

length :: Maybe a -> Int

foldMap :: Monoid n => (Maybe a -> n) -> Maybe a -> n

reverse :: Maybe a -> Maybe a

Factorial [x]

Defined in Data.Semigroup.Factorial

Methods

factors :: [x] -> [[x]]

primePrefix :: [x] -> [x]

primeSuffix :: [x] -> [x]

foldl :: (a -> [x] -> a) -> a -> [x] -> a

foldl' :: (a -> [x] -> a) -> a -> [x] -> a

foldr :: ([x] -> a -> a) -> a -> [x] -> a

length :: [x] -> Int

foldMap :: Monoid n => ([x] -> n) -> [x] -> n

reverse :: [x] -> [x]

Ord k => Factorial (Map k v)

Defined in Data.Semigroup.Factorial

Methods

factors :: Map k v -> [Map k v]

primePrefix :: Map k v -> Map k v

primeSuffix :: Map k v -> Map k v

foldl :: (a -> Map k v -> a) -> a -> Map k v -> a

foldl' :: (a -> Map k v -> a) -> a -> Map k v -> a

foldr :: (Map k v -> a -> a) -> a -> Map k v -> a

length :: Map k v -> Int

foldMap :: Monoid n => (Map k v -> n) -> Map k v -> n

reverse :: Map k v -> Map k v

(FactorialMonoid a, FactorialMonoid b) => Factorial (Stateful a b)

Defined in Data.Monoid.Instances.Stateful

Methods

factors :: Stateful a b -> [Stateful a b]

primePrefix :: Stateful a b -> Stateful a b

primeSuffix :: Stateful a b -> Stateful a b

foldl :: (a0 -> Stateful a b -> a0) -> a0 -> Stateful a b -> a0

foldl' :: (a0 -> Stateful a b -> a0) -> a0 -> Stateful a b -> a0

foldr :: (Stateful a b -> a0 -> a0) -> a0 -> Stateful a b -> a0

length :: Stateful a b -> Int

foldMap :: Monoid n => (Stateful a b -> n) -> Stateful a b -> n

reverse :: Stateful a b -> Stateful a b

(Factorial a, Factorial b, MonoidNull a, MonoidNull b) => Factorial (a, b)

Defined in Data.Semigroup.Factorial

Methods

factors :: (a, b) -> [(a, b)]

primePrefix :: (a, b) -> (a, b)

primeSuffix :: (a, b) -> (a, b)

foldl :: (a0 -> (a, b) -> a0) -> a0 -> (a, b) -> a0

foldl' :: (a0 -> (a, b) -> a0) -> a0 -> (a, b) -> a0

foldr :: ((a, b) -> a0 -> a0) -> a0 -> (a, b) -> a0

length :: (a, b) -> Int

foldMap :: Monoid n => ((a, b) -> n) -> (a, b) -> n

reverse :: (a, b) -> (a, b)

(Factorial a, Factorial b, Factorial c, MonoidNull a, MonoidNull b, MonoidNull c) => Factorial (a, b, c)

Defined in Data.Semigroup.Factorial

Methods

factors :: (a, b, c) -> [(a, b, c)]

primePrefix :: (a, b, c) -> (a, b, c)

primeSuffix :: (a, b, c) -> (a, b, c)

foldl :: (a0 -> (a, b, c) -> a0) -> a0 -> (a, b, c) -> a0

foldl' :: (a0 -> (a, b, c) -> a0) -> a0 -> (a, b, c) -> a0

foldr :: ((a, b, c) -> a0 -> a0) -> a0 -> (a, b, c) -> a0

length :: (a, b, c) -> Int

foldMap :: Monoid n => ((a, b, c) -> n) -> (a, b, c) -> n

reverse :: (a, b, c) -> (a, b, c)

(Factorial a, Factorial b, Factorial c, Factorial d, MonoidNull a, MonoidNull b, MonoidNull c, MonoidNull d) => Factorial (a, b, c, d)

Defined in Data.Semigroup.Factorial

Methods

factors :: (a, b, c, d) -> [(a, b, c, d)]

primePrefix :: (a, b, c, d) -> (a, b, c, d)

primeSuffix :: (a, b, c, d) -> (a, b, c, d)

foldl :: (a0 -> (a, b, c, d) -> a0) -> a0 -> (a, b, c, d) -> a0

foldl' :: (a0 -> (a, b, c, d) -> a0) -> a0 -> (a, b, c, d) -> a0

foldr :: ((a, b, c, d) -> a0 -> a0) -> a0 -> (a, b, c, d) -> a0

length :: (a, b, c, d) -> Int

foldMap :: Monoid n => ((a, b, c, d) -> n) -> (a, b, c, d) -> n

reverse :: (a, b, c, d) -> (a, b, c, d)

class 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)

Instances

StableFactorial ByteString

Defined in Data.Semigroup.Factorial

StableFactorial ByteString

Defined in Data.Semigroup.Factorial

StableFactorial Text

Defined in Data.Semigroup.Factorial

StableFactorial Text

Defined in Data.Semigroup.Factorial

StableFactorial ()

Defined in Data.Semigroup.Factorial

StableFactorial a => StableFactorial (Dual a)

Defined in Data.Semigroup.Factorial

StableFactorial (Sum Natural)

Defined in Data.Semigroup.Factorial

StableFactorial (Seq a)

Defined in Data.Semigroup.Factorial

(Factorial a, PositiveMonoid a) => StableFactorial (Concat a)

Defined in Data.Monoid.Instances.Concat

(StableFactorial a, MonoidNull a) => StableFactorial (Measured a)

Defined in Data.Monoid.Instances.Measured

(StableFactorial m, TextualMonoid m) => StableFactorial (LinePositioned m)

Defined in Data.Monoid.Instances.Positioned

StableFactorial m => StableFactorial (OffsetPositioned m)

Defined in Data.Monoid.Instances.Positioned

(StableFactorial m, FactorialMonoid m) => StableFactorial (Shadowed m)

Defined in Data.Monoid.Instances.PrefixMemory

StableFactorial (Vector a)

Defined in Data.Semigroup.Factorial

StableFactorial [x]

Defined in Data.Semigroup.Factorial

(FactorialMonoid a, FactorialMonoid b, StableFactorial a, StableFactorial b) => StableFactorial (Stateful a b)

Defined in Data.Monoid.Instances.Stateful

Monad function equivalents

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

A mapM equivalent.

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

A mapM_ equivalent.