Data.Monoid.Factorial

monoid-subclasses-0.4.3.1: Subclasses of Monoid

Safe Haskell | Trustworthy
Language | Haskell2010

Data.Monoid.Factorial

Contents

- Classes
- Monad function equivalents

Description

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

Synopsis

- class MonoidNull m => FactorialMonoid m where
- class (FactorialMonoid m, PositiveMonoid m) => StableFactorialMonoid m
- mapM :: (FactorialMonoid a, Monoid b, Monad m) => (a -> m b) -> a -> m b
- mapM_ :: (FactorialMonoid a, Monad m) => (a -> m b) -> a -> m ()

# 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 (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 #
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 #
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.