Data.Monoid.Factorial

This module defines the FactorialMonoid class and some of its instances.

Classes

class MonoidNull m => FactorialMonoid m where

Class of monoids 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:

mconcat . factors == id
null == List.null . factors
List.all (\prime-> factors prime == [prime]) . factors
factors == unfoldr splitPrimePrefix == List.reverse . unfoldr (fmap swap . splitPrimeSuffix)
reverse == mconcat . List.reverse . factors
primePrefix == maybe mempty fst . splitPrimePrefix
primeSuffix == maybe mempty snd . splitPrimeSuffix
inits == List.map mconcat . List.inits . factors
tails == List.map mconcat . List.tails . factors
foldl f a == List.foldl f a . factors
foldl' f a == List.foldl' f a . factors
foldr f a == List.foldr f a . factors
span p m == (mconcat l, mconcat r) where (l, r) = List.span p (factors m)
List.all (List.all (not . pred) . factors) . split pred
mconcat . intersperse prime . split (== prime) == id
splitAt i m == (mconcat l, mconcat r) where (l, r) = List.splitAt i (factors m)
spanMaybe () (const $ bool Nothing (Maybe ()) . p) m == (takeWhile p m, dropWhile p m, ())
spanMaybe s0 (\s m-> Just $ f s m) m0 == (m0, mempty, foldl f s0 m0)
let (prefix, suffix, s') = spanMaybe s f m
    foldMaybe = foldl g (Just s)
    g s m = s >>= flip f m
in all ((Nothing ==) . foldMaybe) (inits prefix)
   && prefix == last (filter (isJust . foldMaybe) $ inits m)
   && Just s' == foldMaybe prefix
   && m == prefix <> suffix

A minimal instance definition must implement factors or splitPrimePrefix. Other methods are provided and should be implemented only for performance reasons.

Minimal complete definition

factors | splitPrimePrefix

Methods

factors :: m -> [m]

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

primePrefix :: m -> m

The prime prefix, mempty if none.

primeSuffix :: m -> m

The prime suffix, mempty if none.

splitPrimePrefix :: m -> Maybe (m, m)

Splits the argument into its prime prefix and the remaining suffix. Returns Nothing for mempty.

splitPrimeSuffix :: m -> Maybe (m, m)

Splits the argument into its prime suffix and the remaining prefix. Returns Nothing for mempty.

inits :: m -> [m]

Returns the list of all prefixes of the argument, mempty first.

tails :: m -> [m]

Returns the list of all suffixes of the argument, mempty last.

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

Like foldl from Data.List on the list of primes.

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

Like foldl' from Data.List on the list of primes.

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

Like foldr from Data.List on the list of primes.

length :: m -> Int

The length of the list of primes.

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

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

span :: (m -> Bool) -> m -> (m, m)

Like span from Data.List on the list of primes.

break :: (m -> Bool) -> m -> (m, m)

Equivalent to break from Data.List.

split :: (m -> Bool) -> m -> [m]

Splits the monoid into components delimited by prime separators satisfying the given predicate. The primes satisfying the predicate are not a part of the result.

takeWhile :: (m -> Bool) -> m -> m

Equivalent to takeWhile from Data.List.

dropWhile :: (m -> Bool) -> m -> m

Equivalent to dropWhile from Data.List.

spanMaybe :: s -> (s -> m -> Maybe s) -> m -> (m, m, s)

A stateful variant of span, threading the result of the test function as long as it returns Just.

spanMaybe' :: s -> (s -> m -> Maybe s) -> m -> (m, m, s)

Strict version of spanMaybe.

splitAt :: Int -> m -> (m, m)

Like splitAt from Data.List on the list of primes.

drop :: Int -> m -> m

Equivalent to drop from Data.List.

take :: Int -> m -> m

Equivalent to take from Data.List.

reverse :: m -> m

Equivalent to reverse from Data.List.

Instances

FactorialMonoid ()

Methods

factors :: () -> [()]

primePrefix :: () -> ()

primeSuffix :: () -> ()

splitPrimePrefix :: () -> Maybe ((), ())

splitPrimeSuffix :: () -> Maybe ((), ())

inits :: () -> [()]

tails :: () -> [()]

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

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

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

length :: () -> Int

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

span :: (() -> Bool) -> () -> ((), ())

break :: (() -> Bool) -> () -> ((), ())

split :: (() -> Bool) -> () -> [()]

takeWhile :: (() -> Bool) -> () -> ()

dropWhile :: (() -> Bool) -> () -> ()

spanMaybe :: s -> (s -> () -> Maybe s) -> () -> ((), (), s)

spanMaybe' :: s -> (s -> () -> Maybe s) -> () -> ((), (), s)

splitAt :: Int -> () -> ((), ())

drop :: Int -> () -> ()

take :: Int -> () -> ()

reverse :: () -> ()

FactorialMonoid ByteString

Methods

factors :: ByteString -> [ByteString]

primePrefix :: ByteString -> ByteString

primeSuffix :: ByteString -> ByteString

splitPrimePrefix :: ByteString -> Maybe (ByteString, ByteString)

splitPrimeSuffix :: ByteString -> Maybe (ByteString, ByteString)

inits :: ByteString -> [ByteString]

tails :: 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

span :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString)

break :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString)

split :: (ByteString -> Bool) -> ByteString -> [ByteString]

takeWhile :: (ByteString -> Bool) -> ByteString -> ByteString

dropWhile :: (ByteString -> Bool) -> ByteString -> ByteString

spanMaybe :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s)

spanMaybe' :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s)

splitAt :: Int -> ByteString -> (ByteString, ByteString)

drop :: Int -> ByteString -> ByteString

take :: Int -> ByteString -> ByteString

reverse :: ByteString -> ByteString

FactorialMonoid ByteString

Methods

factors :: ByteString -> [ByteString]

primePrefix :: ByteString -> ByteString

primeSuffix :: ByteString -> ByteString

splitPrimePrefix :: ByteString -> Maybe (ByteString, ByteString)

splitPrimeSuffix :: ByteString -> Maybe (ByteString, ByteString)

inits :: ByteString -> [ByteString]

tails :: 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

span :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString)

break :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString)

split :: (ByteString -> Bool) -> ByteString -> [ByteString]

takeWhile :: (ByteString -> Bool) -> ByteString -> ByteString

dropWhile :: (ByteString -> Bool) -> ByteString -> ByteString

spanMaybe :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s)

spanMaybe' :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s)

splitAt :: Int -> ByteString -> (ByteString, ByteString)

drop :: Int -> ByteString -> ByteString

take :: Int -> ByteString -> ByteString

reverse :: ByteString -> ByteString

FactorialMonoid IntSet

Methods

factors :: IntSet -> [IntSet]

primePrefix :: IntSet -> IntSet

primeSuffix :: IntSet -> IntSet

splitPrimePrefix :: IntSet -> Maybe (IntSet, IntSet)

splitPrimeSuffix :: IntSet -> Maybe (IntSet, IntSet)

inits :: IntSet -> [IntSet]

tails :: 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

span :: (IntSet -> Bool) -> IntSet -> (IntSet, IntSet)

break :: (IntSet -> Bool) -> IntSet -> (IntSet, IntSet)

split :: (IntSet -> Bool) -> IntSet -> [IntSet]

takeWhile :: (IntSet -> Bool) -> IntSet -> IntSet

dropWhile :: (IntSet -> Bool) -> IntSet -> IntSet

spanMaybe :: s -> (s -> IntSet -> Maybe s) -> IntSet -> (IntSet, IntSet, s)

spanMaybe' :: s -> (s -> IntSet -> Maybe s) -> IntSet -> (IntSet, IntSet, s)

splitAt :: Int -> IntSet -> (IntSet, IntSet)

drop :: Int -> IntSet -> IntSet

take :: Int -> IntSet -> IntSet

reverse :: IntSet -> IntSet

FactorialMonoid Text

Methods

factors :: Text -> [Text]

primePrefix :: Text -> Text

primeSuffix :: Text -> Text

splitPrimePrefix :: Text -> Maybe (Text, Text)

splitPrimeSuffix :: Text -> Maybe (Text, Text)

inits :: Text -> [Text]

tails :: 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

span :: (Text -> Bool) -> Text -> (Text, Text)

break :: (Text -> Bool) -> Text -> (Text, Text)

split :: (Text -> Bool) -> Text -> [Text]

takeWhile :: (Text -> Bool) -> Text -> Text

dropWhile :: (Text -> Bool) -> Text -> Text

spanMaybe :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s)

spanMaybe' :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s)

splitAt :: Int -> Text -> (Text, Text)

drop :: Int -> Text -> Text

take :: Int -> Text -> Text

reverse :: Text -> Text

FactorialMonoid Text

Methods

factors :: Text -> [Text]

primePrefix :: Text -> Text

primeSuffix :: Text -> Text

splitPrimePrefix :: Text -> Maybe (Text, Text)

splitPrimeSuffix :: Text -> Maybe (Text, Text)

inits :: Text -> [Text]

tails :: 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

span :: (Text -> Bool) -> Text -> (Text, Text)

break :: (Text -> Bool) -> Text -> (Text, Text)

split :: (Text -> Bool) -> Text -> [Text]

takeWhile :: (Text -> Bool) -> Text -> Text

dropWhile :: (Text -> Bool) -> Text -> Text

spanMaybe :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s)

spanMaybe' :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s)

splitAt :: Int -> Text -> (Text, Text)

drop :: Int -> Text -> Text

take :: Int -> Text -> Text

reverse :: Text -> Text

FactorialMonoid ByteStringUTF8

Methods

factors :: ByteStringUTF8 -> [ByteStringUTF8]

primePrefix :: ByteStringUTF8 -> ByteStringUTF8

primeSuffix :: ByteStringUTF8 -> ByteStringUTF8

splitPrimePrefix :: ByteStringUTF8 -> Maybe (ByteStringUTF8, ByteStringUTF8)

splitPrimeSuffix :: ByteStringUTF8 -> Maybe (ByteStringUTF8, ByteStringUTF8)

inits :: ByteStringUTF8 -> [ByteStringUTF8]

tails :: 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

span :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8)

break :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8)

split :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> [ByteStringUTF8]

takeWhile :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> ByteStringUTF8

dropWhile :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> ByteStringUTF8

spanMaybe :: s -> (s -> ByteStringUTF8 -> Maybe s) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8, s)

spanMaybe' :: s -> (s -> ByteStringUTF8 -> Maybe s) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8, s)

splitAt :: Int -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8)

drop :: Int -> ByteStringUTF8 -> ByteStringUTF8

take :: Int -> ByteStringUTF8 -> ByteStringUTF8

reverse :: ByteStringUTF8 -> ByteStringUTF8

FactorialMonoid [x]

Methods

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

primePrefix :: [x] -> [x]

primeSuffix :: [x] -> [x]

splitPrimePrefix :: [x] -> Maybe ([x], [x])

splitPrimeSuffix :: [x] -> Maybe ([x], [x])

inits :: [x] -> [[x]]

tails :: [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

span :: ([x] -> Bool) -> [x] -> ([x], [x])

break :: ([x] -> Bool) -> [x] -> ([x], [x])

split :: ([x] -> Bool) -> [x] -> [[x]]

takeWhile :: ([x] -> Bool) -> [x] -> [x]

dropWhile :: ([x] -> Bool) -> [x] -> [x]

spanMaybe :: s -> (s -> [x] -> Maybe s) -> [x] -> ([x], [x], s)

spanMaybe' :: s -> (s -> [x] -> Maybe s) -> [x] -> ([x], [x], s)

splitAt :: Int -> [x] -> ([x], [x])

drop :: Int -> [x] -> [x]

take :: Int -> [x] -> [x]

reverse :: [x] -> [x]

FactorialMonoid a => FactorialMonoid (Maybe a)

Methods

factors :: Maybe a -> [Maybe a]

primePrefix :: Maybe a -> Maybe a

primeSuffix :: Maybe a -> Maybe a

splitPrimePrefix :: Maybe a -> Maybe (Maybe a, Maybe a)

splitPrimeSuffix :: Maybe a -> Maybe (Maybe a, Maybe a)

inits :: Maybe a -> [Maybe a]

tails :: Maybe a -> [Maybe a]

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

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

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

length :: Maybe a -> Int

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

span :: (Maybe a -> Bool) -> Maybe a -> (Maybe a, Maybe a)

break :: (Maybe a -> Bool) -> Maybe a -> (Maybe a, Maybe a)

split :: (Maybe a -> Bool) -> Maybe a -> [Maybe a]

takeWhile :: (Maybe a -> Bool) -> Maybe a -> Maybe a

dropWhile :: (Maybe a -> Bool) -> Maybe a -> Maybe a

spanMaybe :: s -> (s -> Maybe a -> Maybe s) -> Maybe a -> (Maybe a, Maybe a, s)

spanMaybe' :: s -> (s -> Maybe a -> Maybe s) -> Maybe a -> (Maybe a, Maybe a, s)

splitAt :: Int -> Maybe a -> (Maybe a, Maybe a)

drop :: Int -> Maybe a -> Maybe a

take :: Int -> Maybe a -> Maybe a

reverse :: Maybe a -> Maybe a

FactorialMonoid a => FactorialMonoid (Dual a)

Methods

factors :: Dual a -> [Dual a]

primePrefix :: Dual a -> Dual a

primeSuffix :: Dual a -> Dual a

splitPrimePrefix :: Dual a -> Maybe (Dual a, Dual a)

splitPrimeSuffix :: Dual a -> Maybe (Dual a, Dual a)

inits :: Dual a -> [Dual a]

tails :: Dual a -> [Dual a]

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

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

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

length :: Dual a -> Int

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

span :: (Dual a -> Bool) -> Dual a -> (Dual a, Dual a)

break :: (Dual a -> Bool) -> Dual a -> (Dual a, Dual a)

split :: (Dual a -> Bool) -> Dual a -> [Dual a]

takeWhile :: (Dual a -> Bool) -> Dual a -> Dual a

dropWhile :: (Dual a -> Bool) -> Dual a -> Dual a

spanMaybe :: s -> (s -> Dual a -> Maybe s) -> Dual a -> (Dual a, Dual a, s)

spanMaybe' :: s -> (s -> Dual a -> Maybe s) -> Dual a -> (Dual a, Dual a, s)

splitAt :: Int -> Dual a -> (Dual a, Dual a)

drop :: Int -> Dual a -> Dual a

take :: Int -> Dual a -> Dual a

reverse :: Dual a -> Dual a

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

Methods

factors :: Sum a -> [Sum a]

primePrefix :: Sum a -> Sum a

primeSuffix :: Sum a -> Sum a

splitPrimePrefix :: Sum a -> Maybe (Sum a, Sum a)

splitPrimeSuffix :: Sum a -> Maybe (Sum a, Sum a)

inits :: Sum a -> [Sum a]

tails :: Sum a -> [Sum a]

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

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

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

length :: Sum a -> Int

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

span :: (Sum a -> Bool) -> Sum a -> (Sum a, Sum a)

break :: (Sum a -> Bool) -> Sum a -> (Sum a, Sum a)

split :: (Sum a -> Bool) -> Sum a -> [Sum a]

takeWhile :: (Sum a -> Bool) -> Sum a -> Sum a

dropWhile :: (Sum a -> Bool) -> Sum a -> Sum a

spanMaybe :: s -> (s -> Sum a -> Maybe s) -> Sum a -> (Sum a, Sum a, s)

spanMaybe' :: s -> (s -> Sum a -> Maybe s) -> Sum a -> (Sum a, Sum a, s)

splitAt :: Int -> Sum a -> (Sum a, Sum a)

drop :: Int -> Sum a -> Sum a

take :: Int -> Sum a -> Sum a

reverse :: Sum a -> Sum a

Integral a => FactorialMonoid (Product a)

Methods

factors :: Product a -> [Product a]

primePrefix :: Product a -> Product a

primeSuffix :: Product a -> Product a

splitPrimePrefix :: Product a -> Maybe (Product a, Product a)

splitPrimeSuffix :: Product a -> Maybe (Product a, Product a)

inits :: Product a -> [Product a]

tails :: Product a -> [Product a]

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

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

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

length :: Product a -> Int

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

span :: (Product a -> Bool) -> Product a -> (Product a, Product a)

break :: (Product a -> Bool) -> Product a -> (Product a, Product a)

split :: (Product a -> Bool) -> Product a -> [Product a]

takeWhile :: (Product a -> Bool) -> Product a -> Product a

dropWhile :: (Product a -> Bool) -> Product a -> Product a

spanMaybe :: s -> (s -> Product a -> Maybe s) -> Product a -> (Product a, Product a, s)

spanMaybe' :: s -> (s -> Product a -> Maybe s) -> Product a -> (Product a, Product a, s)

splitAt :: Int -> Product a -> (Product a, Product a)

drop :: Int -> Product a -> Product a

take :: Int -> Product a -> Product a

reverse :: Product a -> Product a

FactorialMonoid (IntMap a)

Methods

factors :: IntMap a -> [IntMap a]

primePrefix :: IntMap a -> IntMap a

primeSuffix :: IntMap a -> IntMap a

splitPrimePrefix :: IntMap a -> Maybe (IntMap a, IntMap a)

splitPrimeSuffix :: IntMap a -> Maybe (IntMap a, IntMap a)

inits :: IntMap a -> [IntMap a]

tails :: IntMap a -> [IntMap a]

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

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

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

length :: IntMap a -> Int

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

span :: (IntMap a -> Bool) -> IntMap a -> (IntMap a, IntMap a)

break :: (IntMap a -> Bool) -> IntMap a -> (IntMap a, IntMap a)

split :: (IntMap a -> Bool) -> IntMap a -> [IntMap a]

takeWhile :: (IntMap a -> Bool) -> IntMap a -> IntMap a

dropWhile :: (IntMap a -> Bool) -> IntMap a -> IntMap a

spanMaybe :: s -> (s -> IntMap a -> Maybe s) -> IntMap a -> (IntMap a, IntMap a, s)

spanMaybe' :: s -> (s -> IntMap a -> Maybe s) -> IntMap a -> (IntMap a, IntMap a, s)

splitAt :: Int -> IntMap a -> (IntMap a, IntMap a)

drop :: Int -> IntMap a -> IntMap a

take :: Int -> IntMap a -> IntMap a

reverse :: IntMap a -> IntMap a

FactorialMonoid (Seq a)

Methods

factors :: Seq a -> [Seq a]

primePrefix :: Seq a -> Seq a

primeSuffix :: Seq a -> Seq a

splitPrimePrefix :: Seq a -> Maybe (Seq a, Seq a)

splitPrimeSuffix :: Seq a -> Maybe (Seq a, Seq a)

inits :: Seq a -> [Seq a]

tails :: Seq a -> [Seq a]

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

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

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

length :: Seq a -> Int

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

span :: (Seq a -> Bool) -> Seq a -> (Seq a, Seq a)

break :: (Seq a -> Bool) -> Seq a -> (Seq a, Seq a)

split :: (Seq a -> Bool) -> Seq a -> [Seq a]

takeWhile :: (Seq a -> Bool) -> Seq a -> Seq a

dropWhile :: (Seq a -> Bool) -> Seq a -> Seq a

spanMaybe :: s -> (s -> Seq a -> Maybe s) -> Seq a -> (Seq a, Seq a, s)

spanMaybe' :: s -> (s -> Seq a -> Maybe s) -> Seq a -> (Seq a, Seq a, s)

splitAt :: Int -> Seq a -> (Seq a, Seq a)

drop :: Int -> Seq a -> Seq a

take :: Int -> Seq a -> Seq a

reverse :: Seq a -> Seq a

Ord a => FactorialMonoid (Set a)

Methods

factors :: Set a -> [Set a]

primePrefix :: Set a -> Set a

primeSuffix :: Set a -> Set a

splitPrimePrefix :: Set a -> Maybe (Set a, Set a)

splitPrimeSuffix :: Set a -> Maybe (Set a, Set a)

inits :: Set a -> [Set a]

tails :: Set a -> [Set a]

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

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

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

length :: Set a -> Int

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

span :: (Set a -> Bool) -> Set a -> (Set a, Set a)

break :: (Set a -> Bool) -> Set a -> (Set a, Set a)

split :: (Set a -> Bool) -> Set a -> [Set a]

takeWhile :: (Set a -> Bool) -> Set a -> Set a

dropWhile :: (Set a -> Bool) -> Set a -> Set a

spanMaybe :: s -> (s -> Set a -> Maybe s) -> Set a -> (Set a, Set a, s)

spanMaybe' :: s -> (s -> Set a -> Maybe s) -> Set a -> (Set a, Set a, s)

splitAt :: Int -> Set a -> (Set a, Set a)

drop :: Int -> Set a -> Set a

take :: Int -> Set a -> Set a

reverse :: Set a -> Set a

FactorialMonoid (Vector a)

Methods

factors :: Vector a -> [Vector a]

primePrefix :: Vector a -> Vector a

primeSuffix :: Vector a -> Vector a

splitPrimePrefix :: Vector a -> Maybe (Vector a, Vector a)

splitPrimeSuffix :: Vector a -> Maybe (Vector a, Vector a)

inits :: Vector a -> [Vector a]

tails :: Vector a -> [Vector a]

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

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

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

length :: Vector a -> Int

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

span :: (Vector a -> Bool) -> Vector a -> (Vector a, Vector a)

break :: (Vector a -> Bool) -> Vector a -> (Vector a, Vector a)

split :: (Vector a -> Bool) -> Vector a -> [Vector a]

takeWhile :: (Vector a -> Bool) -> Vector a -> Vector a

dropWhile :: (Vector a -> Bool) -> Vector a -> Vector a

spanMaybe :: s -> (s -> Vector a -> Maybe s) -> Vector a -> (Vector a, Vector a, s)

spanMaybe' :: s -> (s -> Vector a -> Maybe s) -> Vector a -> (Vector a, Vector a, s)

splitAt :: Int -> Vector a -> (Vector a, Vector a)

drop :: Int -> Vector a -> Vector a

take :: Int -> Vector a -> Vector a

reverse :: Vector a -> Vector a

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

Methods

factors :: Concat a -> [Concat a]

primePrefix :: Concat a -> Concat a

primeSuffix :: Concat a -> Concat a

splitPrimePrefix :: Concat a -> Maybe (Concat a, Concat a)

splitPrimeSuffix :: Concat a -> Maybe (Concat a, Concat a)

inits :: Concat a -> [Concat a]

tails :: Concat a -> [Concat a]

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

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

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

length :: Concat a -> Int

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

span :: (Concat a -> Bool) -> Concat a -> (Concat a, Concat a)

break :: (Concat a -> Bool) -> Concat a -> (Concat a, Concat a)

split :: (Concat a -> Bool) -> Concat a -> [Concat a]

takeWhile :: (Concat a -> Bool) -> Concat a -> Concat a

dropWhile :: (Concat a -> Bool) -> Concat a -> Concat a

spanMaybe :: s -> (s -> Concat a -> Maybe s) -> Concat a -> (Concat a, Concat a, s)

spanMaybe' :: s -> (s -> Concat a -> Maybe s) -> Concat a -> (Concat a, Concat a, s)

splitAt :: Int -> Concat a -> (Concat a, Concat a)

drop :: Int -> Concat a -> Concat a

take :: Int -> Concat a -> Concat a

reverse :: Concat a -> Concat a

StableFactorialMonoid a => FactorialMonoid (Measured a)

Methods

factors :: Measured a -> [Measured a]

primePrefix :: Measured a -> Measured a

primeSuffix :: Measured a -> Measured a

splitPrimePrefix :: Measured a -> Maybe (Measured a, Measured a)

splitPrimeSuffix :: Measured a -> Maybe (Measured a, Measured a)

inits :: Measured a -> [Measured a]

tails :: Measured a -> [Measured a]

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

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

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

length :: Measured a -> Int

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

span :: (Measured a -> Bool) -> Measured a -> (Measured a, Measured a)

break :: (Measured a -> Bool) -> Measured a -> (Measured a, Measured a)

split :: (Measured a -> Bool) -> Measured a -> [Measured a]

takeWhile :: (Measured a -> Bool) -> Measured a -> Measured a

dropWhile :: (Measured a -> Bool) -> Measured a -> Measured a

spanMaybe :: s -> (s -> Measured a -> Maybe s) -> Measured a -> (Measured a, Measured a, s)

spanMaybe' :: s -> (s -> Measured a -> Maybe s) -> Measured a -> (Measured a, Measured a, s)

splitAt :: Int -> Measured a -> (Measured a, Measured a)

drop :: Int -> Measured a -> Measured a

take :: Int -> Measured a -> Measured a

reverse :: Measured a -> Measured a

(StableFactorialMonoid m, TextualMonoid m) => FactorialMonoid (LinePositioned m)

Methods

factors :: LinePositioned m -> [LinePositioned m]

primePrefix :: LinePositioned m -> LinePositioned m

primeSuffix :: LinePositioned m -> LinePositioned m

splitPrimePrefix :: LinePositioned m -> Maybe (LinePositioned m, LinePositioned m)

splitPrimeSuffix :: LinePositioned m -> Maybe (LinePositioned m, LinePositioned m)

inits :: LinePositioned m -> [LinePositioned m]

tails :: 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

span :: (LinePositioned m -> Bool) -> LinePositioned m -> (LinePositioned m, LinePositioned m)

break :: (LinePositioned m -> Bool) -> LinePositioned m -> (LinePositioned m, LinePositioned m)

split :: (LinePositioned m -> Bool) -> LinePositioned m -> [LinePositioned m]

takeWhile :: (LinePositioned m -> Bool) -> LinePositioned m -> LinePositioned m

dropWhile :: (LinePositioned m -> Bool) -> LinePositioned m -> LinePositioned m

spanMaybe :: s -> (s -> LinePositioned m -> Maybe s) -> LinePositioned m -> (LinePositioned m, LinePositioned m, s)

spanMaybe' :: s -> (s -> LinePositioned m -> Maybe s) -> LinePositioned m -> (LinePositioned m, LinePositioned m, s)

splitAt :: Int -> LinePositioned m -> (LinePositioned m, LinePositioned m)

drop :: Int -> LinePositioned m -> LinePositioned m

take :: Int -> LinePositioned m -> LinePositioned m

reverse :: LinePositioned m -> LinePositioned m

StableFactorialMonoid m => FactorialMonoid (OffsetPositioned m)

Methods

factors :: OffsetPositioned m -> [OffsetPositioned m]

primePrefix :: OffsetPositioned m -> OffsetPositioned m

primeSuffix :: OffsetPositioned m -> OffsetPositioned m

splitPrimePrefix :: OffsetPositioned m -> Maybe (OffsetPositioned m, OffsetPositioned m)

splitPrimeSuffix :: OffsetPositioned m -> Maybe (OffsetPositioned m, OffsetPositioned m)

inits :: OffsetPositioned m -> [OffsetPositioned m]

tails :: 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

span :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m)

break :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m)

split :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> [OffsetPositioned m]

takeWhile :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> OffsetPositioned m

dropWhile :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> OffsetPositioned m

spanMaybe :: s -> (s -> OffsetPositioned m -> Maybe s) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, s)

spanMaybe' :: s -> (s -> OffsetPositioned m -> Maybe s) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, s)

splitAt :: Int -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m)

drop :: Int -> OffsetPositioned m -> OffsetPositioned m

take :: Int -> OffsetPositioned m -> OffsetPositioned m

reverse :: OffsetPositioned m -> OffsetPositioned m

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

Methods

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

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

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

splitPrimePrefix :: (a, b) -> Maybe ((a, b), (a, b))

splitPrimeSuffix :: (a, b) -> Maybe ((a, b), (a, b))

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

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

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

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

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

length :: (a, b) -> Int

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

span :: ((a, b) -> Bool) -> (a, b) -> ((a, b), (a, b))

break :: ((a, b) -> Bool) -> (a, b) -> ((a, b), (a, b))

split :: ((a, b) -> Bool) -> (a, b) -> [(a, b)]

takeWhile :: ((a, b) -> Bool) -> (a, b) -> (a, b)

dropWhile :: ((a, b) -> Bool) -> (a, b) -> (a, b)

spanMaybe :: s -> (s -> (a, b) -> Maybe s) -> (a, b) -> ((a, b), (a, b), s)

spanMaybe' :: s -> (s -> (a, b) -> Maybe s) -> (a, b) -> ((a, b), (a, b), s)

splitAt :: Int -> (a, b) -> ((a, b), (a, b))

drop :: Int -> (a, b) -> (a, b)

take :: Int -> (a, b) -> (a, b)

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

Ord k => FactorialMonoid (Map k v)

Methods

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

primePrefix :: Map k v -> Map k v

primeSuffix :: Map k v -> Map k v

splitPrimePrefix :: Map k v -> Maybe (Map k v, Map k v)

splitPrimeSuffix :: Map k v -> Maybe (Map k v, Map k v)

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

tails :: 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

span :: (Map k v -> Bool) -> Map k v -> (Map k v, Map k v)

break :: (Map k v -> Bool) -> Map k v -> (Map k v, Map k v)

split :: (Map k v -> Bool) -> Map k v -> [Map k v]

takeWhile :: (Map k v -> Bool) -> Map k v -> Map k v

dropWhile :: (Map k v -> Bool) -> Map k v -> Map k v

spanMaybe :: s -> (s -> Map k v -> Maybe s) -> Map k v -> (Map k v, Map k v, s)

spanMaybe' :: s -> (s -> Map k v -> Maybe s) -> Map k v -> (Map k v, Map k v, s)

splitAt :: Int -> Map k v -> (Map k v, Map k v)

drop :: Int -> Map k v -> Map k v

take :: Int -> Map k v -> Map k v

reverse :: Map k v -> Map k v

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

Methods

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

primePrefix :: Stateful a b -> Stateful a b

primeSuffix :: Stateful a b -> Stateful a b

splitPrimePrefix :: Stateful a b -> Maybe (Stateful a b, Stateful a b)

splitPrimeSuffix :: Stateful a b -> Maybe (Stateful a b, Stateful a b)

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

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

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

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

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

length :: Stateful a b -> Int

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

span :: (Stateful a b -> Bool) -> Stateful a b -> (Stateful a b, Stateful a b)

break :: (Stateful a b -> Bool) -> Stateful a b -> (Stateful a b, Stateful a b)

split :: (Stateful a b -> Bool) -> Stateful a b -> [Stateful a b]

takeWhile :: (Stateful a b -> Bool) -> Stateful a b -> Stateful a b

dropWhile :: (Stateful a b -> Bool) -> Stateful a b -> Stateful a b

spanMaybe :: s -> (s -> Stateful a b -> Maybe s) -> Stateful a b -> (Stateful a b, Stateful a b, s)

spanMaybe' :: s -> (s -> Stateful a b -> Maybe s) -> Stateful a b -> (Stateful a b, Stateful a b, s)

splitAt :: Int -> Stateful a b -> (Stateful a b, Stateful a b)

drop :: Int -> Stateful a b -> Stateful a b

take :: Int -> Stateful a b -> Stateful a b

reverse :: Stateful a b -> Stateful a b

(FactorialMonoid a, FactorialMonoid b, FactorialMonoid c) => FactorialMonoid (a, b, c)

Methods

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

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

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

splitPrimePrefix :: (a, b, c) -> Maybe ((a, b, c), (a, b, c))

splitPrimeSuffix :: (a, b, c) -> Maybe ((a, b, c), (a, b, c))

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

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

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

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

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

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

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

span :: ((a, b, c) -> Bool) -> (a, b, c) -> ((a, b, c), (a, b, c))

break :: ((a, b, c) -> Bool) -> (a, b, c) -> ((a, b, c), (a, b, c))

split :: ((a, b, c) -> Bool) -> (a, b, c) -> [(a, b, c)]

takeWhile :: ((a, b, c) -> Bool) -> (a, b, c) -> (a, b, c)

dropWhile :: ((a, b, c) -> Bool) -> (a, b, c) -> (a, b, c)

spanMaybe :: s -> (s -> (a, b, c) -> Maybe s) -> (a, b, c) -> ((a, b, c), (a, b, c), s)

spanMaybe' :: s -> (s -> (a, b, c) -> Maybe s) -> (a, b, c) -> ((a, b, c), (a, b, c), s)

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

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

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

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

(FactorialMonoid a, FactorialMonoid b, FactorialMonoid c, FactorialMonoid d) => FactorialMonoid (a, b, c, d)

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)

splitPrimePrefix :: (a, b, c, d) -> Maybe ((a, b, c, d), (a, b, c, d))

splitPrimeSuffix :: (a, b, c, d) -> Maybe ((a, b, c, d), (a, b, c, d))

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

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

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

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

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

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

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

span :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d))

break :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d))

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

takeWhile :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> (a, b, c, d)

dropWhile :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> (a, b, c, d)

spanMaybe :: s -> (s -> (a, b, c, d) -> Maybe s) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), s)

spanMaybe' :: s -> (s -> (a, b, c, d) -> Maybe s) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), s)

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

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

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

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

class (FactorialMonoid m, PositiveMonoid m) => StableFactorialMonoid m

A subclass of FactorialMonoid whose instances satisfy this additional law:

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

Instances

StableFactorialMonoid ()

StableFactorialMonoid ByteString

StableFactorialMonoid ByteString

StableFactorialMonoid Text

StableFactorialMonoid Text

StableFactorialMonoid [x]

StableFactorialMonoid a => StableFactorialMonoid (Dual a)

StableFactorialMonoid (Seq a)

StableFactorialMonoid (Vector a)

(FactorialMonoid a, PositiveMonoid a) => StableFactorialMonoid (Concat a)

StableFactorialMonoid a => StableFactorialMonoid (Measured a)

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

StableFactorialMonoid m => StableFactorialMonoid (OffsetPositioned m)

(StableFactorialMonoid a, StableFactorialMonoid b) => StableFactorialMonoid (Stateful a b)

Monad function equivalents

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

A mapM equivalent.

mapM_ :: (FactorialMonoid a, Monad m) => (a -> m b) -> a -> m ()

A mapM_ equivalent.