Safe Haskell	Trustworthy
Language	Haskell2010

Data.Monoid.Factorial

Description

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

Synopsis

module Data.Semigroup.Factorial
class (Factorial m, MonoidNull m) => FactorialMonoid m where
- splitPrimePrefix :: m -> Maybe (m, m)
- splitPrimeSuffix :: m -> Maybe (m, m)
- inits :: m -> [m]
- tails :: m -> [m]
- span :: (m -> Bool) -> m -> (m, m)
- break :: (m -> Bool) -> m -> (m, m)
- split :: (m -> Bool) -> m -> [m]
- takeWhile :: (m -> Bool) -> m -> m
- dropWhile :: (m -> Bool) -> m -> m
- spanMaybe :: s -> (s -> m -> Maybe s) -> m -> (m, m, s)
- spanMaybe' :: s -> (s -> m -> Maybe s) -> m -> (m, m, s)
- splitAt :: Int -> m -> (m, m)
- drop :: Int -> m -> m
- take :: Int -> m -> m
type StableFactorialMonoid m = (StableFactorial m, FactorialMonoid m, PositiveMonoid m)

Documentation

module Data.Semigroup.Factorial

class (Factorial m, MonoidNull m) => FactorialMonoid m where Source #

Class of monoids that can be split into irreducible (i.e., atomic or prime) factors in a unique way. Note that mempty is not considered a factor. 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 in addition to those of Factorial:

null == List.null . 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
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 should implement splitPrimePrefix for performance reasons, and other methods where beneficial.

Minimal complete definition

Nothing

Methods

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

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

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

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

inits :: m -> [m] Source #

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

tails :: m -> [m] Source #

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

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

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

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

Equivalent to break from Data.List.

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

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 Source #

Equivalent to takeWhile from Data.List.

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

Equivalent to dropWhile from Data.List.

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

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) Source #

Strict version of spanMaybe.

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

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

drop :: Int -> m -> m Source #

Equivalent to drop from Data.List.

take :: Int -> m -> m Source #

Equivalent to take from Data.List.

Instances

Instances details

FactorialMonoid ByteString Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: ByteString -> Maybe (ByteString, ByteString) Source # splitPrimeSuffix :: ByteString -> Maybe (ByteString, ByteString) Source # inits :: ByteString -> [ByteString] Source # tails :: ByteString -> [ByteString] Source # span :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString) Source # break :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString) Source # split :: (ByteString -> Bool) -> ByteString -> [ByteString] Source # takeWhile :: (ByteString -> Bool) -> ByteString -> ByteString Source # dropWhile :: (ByteString -> Bool) -> ByteString -> ByteString Source # spanMaybe :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s) Source # spanMaybe' :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s) Source # splitAt :: Int -> ByteString -> (ByteString, ByteString) Source # drop :: Int -> ByteString -> ByteString Source # take :: Int -> ByteString -> ByteString Source #
FactorialMonoid ByteString Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: ByteString -> Maybe (ByteString, ByteString) Source # splitPrimeSuffix :: ByteString -> Maybe (ByteString, ByteString) Source # inits :: ByteString -> [ByteString] Source # tails :: ByteString -> [ByteString] Source # span :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString) Source # break :: (ByteString -> Bool) -> ByteString -> (ByteString, ByteString) Source # split :: (ByteString -> Bool) -> ByteString -> [ByteString] Source # takeWhile :: (ByteString -> Bool) -> ByteString -> ByteString Source # dropWhile :: (ByteString -> Bool) -> ByteString -> ByteString Source # spanMaybe :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s) Source # spanMaybe' :: s -> (s -> ByteString -> Maybe s) -> ByteString -> (ByteString, ByteString, s) Source # splitAt :: Int -> ByteString -> (ByteString, ByteString) Source # drop :: Int -> ByteString -> ByteString Source # take :: Int -> ByteString -> ByteString Source #
FactorialMonoid IntSet Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: IntSet -> Maybe (IntSet, IntSet) Source # splitPrimeSuffix :: IntSet -> Maybe (IntSet, IntSet) Source # inits :: IntSet -> [IntSet] Source # tails :: IntSet -> [IntSet] Source # span :: (IntSet -> Bool) -> IntSet -> (IntSet, IntSet) Source # break :: (IntSet -> Bool) -> IntSet -> (IntSet, IntSet) Source # split :: (IntSet -> Bool) -> IntSet -> [IntSet] Source # takeWhile :: (IntSet -> Bool) -> IntSet -> IntSet Source # dropWhile :: (IntSet -> Bool) -> IntSet -> IntSet Source # spanMaybe :: s -> (s -> IntSet -> Maybe s) -> IntSet -> (IntSet, IntSet, s) Source # spanMaybe' :: s -> (s -> IntSet -> Maybe s) -> IntSet -> (IntSet, IntSet, s) Source # splitAt :: Int -> IntSet -> (IntSet, IntSet) Source # drop :: Int -> IntSet -> IntSet Source # take :: Int -> IntSet -> IntSet Source #
FactorialMonoid ByteStringUTF8 Source #
Instance details Defined in Data.Monoid.Instances.ByteString.UTF8 Methods splitPrimePrefix :: ByteStringUTF8 -> Maybe (ByteStringUTF8, ByteStringUTF8) Source # splitPrimeSuffix :: ByteStringUTF8 -> Maybe (ByteStringUTF8, ByteStringUTF8) Source # inits :: ByteStringUTF8 -> [ByteStringUTF8] Source # tails :: ByteStringUTF8 -> [ByteStringUTF8] Source # span :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8) Source # break :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8) Source # split :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> [ByteStringUTF8] Source # takeWhile :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> ByteStringUTF8 Source # dropWhile :: (ByteStringUTF8 -> Bool) -> ByteStringUTF8 -> ByteStringUTF8 Source # spanMaybe :: s -> (s -> ByteStringUTF8 -> Maybe s) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8, s) Source # spanMaybe' :: s -> (s -> ByteStringUTF8 -> Maybe s) -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8, s) Source # splitAt :: Int -> ByteStringUTF8 -> (ByteStringUTF8, ByteStringUTF8) Source # drop :: Int -> ByteStringUTF8 -> ByteStringUTF8 Source # take :: Int -> ByteStringUTF8 -> ByteStringUTF8 Source #
FactorialMonoid Text Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Text -> Maybe (Text, Text) Source # splitPrimeSuffix :: Text -> Maybe (Text, Text) Source # inits :: Text -> [Text] Source # tails :: Text -> [Text] Source # span :: (Text -> Bool) -> Text -> (Text, Text) Source # break :: (Text -> Bool) -> Text -> (Text, Text) Source # split :: (Text -> Bool) -> Text -> [Text] Source # takeWhile :: (Text -> Bool) -> Text -> Text Source # dropWhile :: (Text -> Bool) -> Text -> Text Source # spanMaybe :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s) Source # spanMaybe' :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s) Source # splitAt :: Int -> Text -> (Text, Text) Source # drop :: Int -> Text -> Text Source # take :: Int -> Text -> Text Source #
FactorialMonoid Text Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Text -> Maybe (Text, Text) Source # splitPrimeSuffix :: Text -> Maybe (Text, Text) Source # inits :: Text -> [Text] Source # tails :: Text -> [Text] Source # span :: (Text -> Bool) -> Text -> (Text, Text) Source # break :: (Text -> Bool) -> Text -> (Text, Text) Source # split :: (Text -> Bool) -> Text -> [Text] Source # takeWhile :: (Text -> Bool) -> Text -> Text Source # dropWhile :: (Text -> Bool) -> Text -> Text Source # spanMaybe :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s) Source # spanMaybe' :: s -> (s -> Text -> Maybe s) -> Text -> (Text, Text, s) Source # splitAt :: Int -> Text -> (Text, Text) Source # drop :: Int -> Text -> Text Source # take :: Int -> Text -> Text Source #
FactorialMonoid () Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: () -> Maybe ((), ()) Source # splitPrimeSuffix :: () -> Maybe ((), ()) Source # inits :: () -> [()] Source # tails :: () -> [()] Source # span :: (() -> Bool) -> () -> ((), ()) Source # break :: (() -> Bool) -> () -> ((), ()) Source # split :: (() -> Bool) -> () -> [()] Source # takeWhile :: (() -> Bool) -> () -> () Source # dropWhile :: (() -> Bool) -> () -> () Source # spanMaybe :: s -> (s -> () -> Maybe s) -> () -> ((), (), s) Source # spanMaybe' :: s -> (s -> () -> Maybe s) -> () -> ((), (), s) Source # splitAt :: Int -> () -> ((), ()) Source # drop :: Int -> () -> () Source # take :: Int -> () -> () Source #
FactorialMonoid (IntMap a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: IntMap a -> Maybe (IntMap a, IntMap a) Source # splitPrimeSuffix :: IntMap a -> Maybe (IntMap a, IntMap a) Source # inits :: IntMap a -> [IntMap a] Source # tails :: IntMap a -> [IntMap a] Source # span :: (IntMap a -> Bool) -> IntMap a -> (IntMap a, IntMap a) Source # break :: (IntMap a -> Bool) -> IntMap a -> (IntMap a, IntMap a) Source # split :: (IntMap a -> Bool) -> IntMap a -> [IntMap a] Source # takeWhile :: (IntMap a -> Bool) -> IntMap a -> IntMap a Source # dropWhile :: (IntMap a -> Bool) -> IntMap a -> IntMap a Source # spanMaybe :: s -> (s -> IntMap a -> Maybe s) -> IntMap a -> (IntMap a, IntMap a, s) Source # spanMaybe' :: s -> (s -> IntMap a -> Maybe s) -> IntMap a -> (IntMap a, IntMap a, s) Source # splitAt :: Int -> IntMap a -> (IntMap a, IntMap a) Source # drop :: Int -> IntMap a -> IntMap a Source # take :: Int -> IntMap a -> IntMap a Source #
FactorialMonoid (Seq a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Seq a -> Maybe (Seq a, Seq a) Source # splitPrimeSuffix :: Seq a -> Maybe (Seq a, Seq a) Source # inits :: Seq a -> [Seq a] Source # tails :: Seq a -> [Seq a] Source # span :: (Seq a -> Bool) -> Seq a -> (Seq a, Seq a) Source # break :: (Seq a -> Bool) -> Seq a -> (Seq a, Seq a) Source # split :: (Seq a -> Bool) -> Seq a -> [Seq a] Source # takeWhile :: (Seq a -> Bool) -> Seq a -> Seq a Source # dropWhile :: (Seq a -> Bool) -> Seq a -> Seq a Source # spanMaybe :: s -> (s -> Seq a -> Maybe s) -> Seq a -> (Seq a, Seq a, s) Source # spanMaybe' :: s -> (s -> Seq a -> Maybe s) -> Seq a -> (Seq a, Seq a, s) Source # splitAt :: Int -> Seq a -> (Seq a, Seq a) Source # drop :: Int -> Seq a -> Seq a Source # take :: Int -> Seq a -> Seq a Source #
Ord a => FactorialMonoid (Set a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Set a -> Maybe (Set a, Set a) Source # splitPrimeSuffix :: Set a -> Maybe (Set a, Set a) Source # inits :: Set a -> [Set a] Source # tails :: Set a -> [Set a] Source # span :: (Set a -> Bool) -> Set a -> (Set a, Set a) Source # break :: (Set a -> Bool) -> Set a -> (Set a, Set a) Source # split :: (Set a -> Bool) -> Set a -> [Set a] Source # takeWhile :: (Set a -> Bool) -> Set a -> Set a Source # dropWhile :: (Set a -> Bool) -> Set a -> Set a Source # spanMaybe :: s -> (s -> Set a -> Maybe s) -> Set a -> (Set a, Set a, s) Source # spanMaybe' :: s -> (s -> Set a -> Maybe s) -> Set a -> (Set a, Set a, s) Source # splitAt :: Int -> Set a -> (Set a, Set a) Source # drop :: Int -> Set a -> Set a Source # take :: Int -> Set a -> Set a Source #
FactorialMonoid a => FactorialMonoid (Identity a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Identity a -> Maybe (Identity a, Identity a) Source # splitPrimeSuffix :: Identity a -> Maybe (Identity a, Identity a) Source # inits :: Identity a -> [Identity a] Source # tails :: Identity a -> [Identity a] Source # span :: (Identity a -> Bool) -> Identity a -> (Identity a, Identity a) Source # break :: (Identity a -> Bool) -> Identity a -> (Identity a, Identity a) Source # split :: (Identity a -> Bool) -> Identity a -> [Identity a] Source # takeWhile :: (Identity a -> Bool) -> Identity a -> Identity a Source # dropWhile :: (Identity a -> Bool) -> Identity a -> Identity a Source # spanMaybe :: s -> (s -> Identity a -> Maybe s) -> Identity a -> (Identity a, Identity a, s) Source # spanMaybe' :: s -> (s -> Identity a -> Maybe s) -> Identity a -> (Identity a, Identity a, s) Source # splitAt :: Int -> Identity a -> (Identity a, Identity a) Source # drop :: Int -> Identity a -> Identity a Source # take :: Int -> Identity a -> Identity a Source #
FactorialMonoid a => FactorialMonoid (Dual a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Dual a -> Maybe (Dual a, Dual a) Source # splitPrimeSuffix :: Dual a -> Maybe (Dual a, Dual a) Source # inits :: Dual a -> [Dual a] Source # tails :: Dual a -> [Dual a] Source # span :: (Dual a -> Bool) -> Dual a -> (Dual a, Dual a) Source # break :: (Dual a -> Bool) -> Dual a -> (Dual a, Dual a) Source # split :: (Dual a -> Bool) -> Dual a -> [Dual a] Source # takeWhile :: (Dual a -> Bool) -> Dual a -> Dual a Source # dropWhile :: (Dual a -> Bool) -> Dual a -> Dual a Source # spanMaybe :: s -> (s -> Dual a -> Maybe s) -> Dual a -> (Dual a, Dual a, s) Source # spanMaybe' :: s -> (s -> Dual a -> Maybe s) -> Dual a -> (Dual a, Dual a, s) Source # splitAt :: Int -> Dual a -> (Dual a, Dual a) Source # drop :: Int -> Dual a -> Dual a Source # take :: Int -> Dual a -> Dual a Source #
Integral a => FactorialMonoid (Product a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Product a -> Maybe (Product a, Product a) Source # splitPrimeSuffix :: Product a -> Maybe (Product a, Product a) Source # inits :: Product a -> [Product a] Source # tails :: Product a -> [Product a] Source # span :: (Product a -> Bool) -> Product a -> (Product a, Product a) Source # break :: (Product a -> Bool) -> Product a -> (Product a, Product a) Source # split :: (Product a -> Bool) -> Product a -> [Product a] Source # takeWhile :: (Product a -> Bool) -> Product a -> Product a Source # dropWhile :: (Product a -> Bool) -> Product a -> Product a Source # spanMaybe :: s -> (s -> Product a -> Maybe s) -> Product a -> (Product a, Product a, s) Source # spanMaybe' :: s -> (s -> Product a -> Maybe s) -> Product a -> (Product a, Product a, s) Source # splitAt :: Int -> Product a -> (Product a, Product a) Source # drop :: Int -> Product a -> Product a Source # take :: Int -> Product a -> Product a Source #
(Integral a, Eq a) => FactorialMonoid (Sum a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Sum a -> Maybe (Sum a, Sum a) Source # splitPrimeSuffix :: Sum a -> Maybe (Sum a, Sum a) Source # inits :: Sum a -> [Sum a] Source # tails :: Sum a -> [Sum a] Source # span :: (Sum a -> Bool) -> Sum a -> (Sum a, Sum a) Source # break :: (Sum a -> Bool) -> Sum a -> (Sum a, Sum a) Source # split :: (Sum a -> Bool) -> Sum a -> [Sum a] Source # takeWhile :: (Sum a -> Bool) -> Sum a -> Sum a Source # dropWhile :: (Sum a -> Bool) -> Sum a -> Sum a Source # spanMaybe :: s -> (s -> Sum a -> Maybe s) -> Sum a -> (Sum a, Sum a, s) Source # spanMaybe' :: s -> (s -> Sum a -> Maybe s) -> Sum a -> (Sum a, Sum a, s) Source # splitAt :: Int -> Sum a -> (Sum a, Sum a) Source # drop :: Int -> Sum a -> Sum a Source # take :: Int -> Sum a -> Sum a Source #
(FactorialMonoid a, PositiveMonoid a) => FactorialMonoid (Concat a) Source #
Instance details Defined in Data.Monoid.Instances.Concat Methods splitPrimePrefix :: Concat a -> Maybe (Concat a, Concat a) Source # splitPrimeSuffix :: Concat a -> Maybe (Concat a, Concat a) Source # inits :: Concat a -> [Concat a] Source # tails :: Concat a -> [Concat a] Source # span :: (Concat a -> Bool) -> Concat a -> (Concat a, Concat a) Source # break :: (Concat a -> Bool) -> Concat a -> (Concat a, Concat a) Source # split :: (Concat a -> Bool) -> Concat a -> [Concat a] Source # takeWhile :: (Concat a -> Bool) -> Concat a -> Concat a Source # dropWhile :: (Concat a -> Bool) -> Concat a -> Concat a Source # spanMaybe :: s -> (s -> Concat a -> Maybe s) -> Concat a -> (Concat a, Concat a, s) Source # spanMaybe' :: s -> (s -> Concat a -> Maybe s) -> Concat a -> (Concat a, Concat a, s) Source # splitAt :: Int -> Concat a -> (Concat a, Concat a) Source # drop :: Int -> Concat a -> Concat a Source # take :: Int -> Concat a -> Concat a Source #
(StableFactorial a, FactorialMonoid a) => FactorialMonoid (Measured a) Source #
Instance details Defined in Data.Monoid.Instances.Measured Methods splitPrimePrefix :: Measured a -> Maybe (Measured a, Measured a) Source # splitPrimeSuffix :: Measured a -> Maybe (Measured a, Measured a) Source # inits :: Measured a -> [Measured a] Source # tails :: Measured a -> [Measured a] Source # span :: (Measured a -> Bool) -> Measured a -> (Measured a, Measured a) Source # break :: (Measured a -> Bool) -> Measured a -> (Measured a, Measured a) Source # split :: (Measured a -> Bool) -> Measured a -> [Measured a] Source # takeWhile :: (Measured a -> Bool) -> Measured a -> Measured a Source # dropWhile :: (Measured a -> Bool) -> Measured a -> Measured a Source # spanMaybe :: s -> (s -> Measured a -> Maybe s) -> Measured a -> (Measured a, Measured a, s) Source # spanMaybe' :: s -> (s -> Measured a -> Maybe s) -> Measured a -> (Measured a, Measured a, s) Source # splitAt :: Int -> Measured a -> (Measured a, Measured a) Source # drop :: Int -> Measured a -> Measured a Source # take :: Int -> Measured a -> Measured a Source #
(StableFactorial m, TextualMonoid m) => FactorialMonoid (LinePositioned m) Source #
Instance details Defined in Data.Monoid.Instances.Positioned Methods splitPrimePrefix :: LinePositioned m -> Maybe (LinePositioned m, LinePositioned m) Source # splitPrimeSuffix :: LinePositioned m -> Maybe (LinePositioned m, LinePositioned m) Source # inits :: LinePositioned m -> [LinePositioned m] Source # tails :: LinePositioned m -> [LinePositioned m] Source # span :: (LinePositioned m -> Bool) -> LinePositioned m -> (LinePositioned m, LinePositioned m) Source # break :: (LinePositioned m -> Bool) -> LinePositioned m -> (LinePositioned m, LinePositioned m) Source # split :: (LinePositioned m -> Bool) -> LinePositioned m -> [LinePositioned m] Source # takeWhile :: (LinePositioned m -> Bool) -> LinePositioned m -> LinePositioned m Source # dropWhile :: (LinePositioned m -> Bool) -> LinePositioned m -> LinePositioned m Source # spanMaybe :: s -> (s -> LinePositioned m -> Maybe s) -> LinePositioned m -> (LinePositioned m, LinePositioned m, s) Source # spanMaybe' :: s -> (s -> LinePositioned m -> Maybe s) -> LinePositioned m -> (LinePositioned m, LinePositioned m, s) Source # splitAt :: Int -> LinePositioned m -> (LinePositioned m, LinePositioned m) Source # drop :: Int -> LinePositioned m -> LinePositioned m Source # take :: Int -> LinePositioned m -> LinePositioned m Source #
(StableFactorial m, FactorialMonoid m) => FactorialMonoid (OffsetPositioned m) Source #
Instance details Defined in Data.Monoid.Instances.Positioned Methods splitPrimePrefix :: OffsetPositioned m -> Maybe (OffsetPositioned m, OffsetPositioned m) Source # splitPrimeSuffix :: OffsetPositioned m -> Maybe (OffsetPositioned m, OffsetPositioned m) Source # inits :: OffsetPositioned m -> [OffsetPositioned m] Source # tails :: OffsetPositioned m -> [OffsetPositioned m] Source # span :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m) Source # break :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m) Source # split :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> [OffsetPositioned m] Source # takeWhile :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> OffsetPositioned m Source # dropWhile :: (OffsetPositioned m -> Bool) -> OffsetPositioned m -> OffsetPositioned m Source # spanMaybe :: s -> (s -> OffsetPositioned m -> Maybe s) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, s) Source # spanMaybe' :: s -> (s -> OffsetPositioned m -> Maybe s) -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m, s) Source # splitAt :: Int -> OffsetPositioned m -> (OffsetPositioned m, OffsetPositioned m) Source # drop :: Int -> OffsetPositioned m -> OffsetPositioned m Source # take :: Int -> OffsetPositioned m -> OffsetPositioned m Source #
(StableFactorial m, FactorialMonoid m) => FactorialMonoid (Shadowed m) Source #
Instance details Defined in Data.Monoid.Instances.PrefixMemory Methods splitPrimePrefix :: Shadowed m -> Maybe (Shadowed m, Shadowed m) Source # splitPrimeSuffix :: Shadowed m -> Maybe (Shadowed m, Shadowed m) Source # inits :: Shadowed m -> [Shadowed m] Source # tails :: Shadowed m -> [Shadowed m] Source # span :: (Shadowed m -> Bool) -> Shadowed m -> (Shadowed m, Shadowed m) Source # break :: (Shadowed m -> Bool) -> Shadowed m -> (Shadowed m, Shadowed m) Source # split :: (Shadowed m -> Bool) -> Shadowed m -> [Shadowed m] Source # takeWhile :: (Shadowed m -> Bool) -> Shadowed m -> Shadowed m Source # dropWhile :: (Shadowed m -> Bool) -> Shadowed m -> Shadowed m Source # spanMaybe :: s -> (s -> Shadowed m -> Maybe s) -> Shadowed m -> (Shadowed m, Shadowed m, s) Source # spanMaybe' :: s -> (s -> Shadowed m -> Maybe s) -> Shadowed m -> (Shadowed m, Shadowed m, s) Source # splitAt :: Int -> Shadowed m -> (Shadowed m, Shadowed m) Source # drop :: Int -> Shadowed m -> Shadowed m Source # take :: Int -> Shadowed m -> Shadowed m Source #
FactorialMonoid (Vector a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Vector a -> Maybe (Vector a, Vector a) Source # splitPrimeSuffix :: Vector a -> Maybe (Vector a, Vector a) Source # inits :: Vector a -> [Vector a] Source # tails :: Vector a -> [Vector a] Source # span :: (Vector a -> Bool) -> Vector a -> (Vector a, Vector a) Source # break :: (Vector a -> Bool) -> Vector a -> (Vector a, Vector a) Source # split :: (Vector a -> Bool) -> Vector a -> [Vector a] Source # takeWhile :: (Vector a -> Bool) -> Vector a -> Vector a Source # dropWhile :: (Vector a -> Bool) -> Vector a -> Vector a Source # spanMaybe :: s -> (s -> Vector a -> Maybe s) -> Vector a -> (Vector a, Vector a, s) Source # spanMaybe' :: s -> (s -> Vector a -> Maybe s) -> Vector a -> (Vector a, Vector a, s) Source # splitAt :: Int -> Vector a -> (Vector a, Vector a) Source # drop :: Int -> Vector a -> Vector a Source # take :: Int -> Vector a -> Vector a Source #
FactorialMonoid a => FactorialMonoid (Maybe a) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Maybe a -> Maybe (Maybe a, Maybe a) Source # splitPrimeSuffix :: Maybe a -> Maybe (Maybe a, Maybe a) Source # inits :: Maybe a -> [Maybe a] Source # tails :: Maybe a -> [Maybe a] Source # span :: (Maybe a -> Bool) -> Maybe a -> (Maybe a, Maybe a) Source # break :: (Maybe a -> Bool) -> Maybe a -> (Maybe a, Maybe a) Source # split :: (Maybe a -> Bool) -> Maybe a -> [Maybe a] Source # takeWhile :: (Maybe a -> Bool) -> Maybe a -> Maybe a Source # dropWhile :: (Maybe a -> Bool) -> Maybe a -> Maybe a Source # spanMaybe :: s -> (s -> Maybe a -> Maybe s) -> Maybe a -> (Maybe a, Maybe a, s) Source # spanMaybe' :: s -> (s -> Maybe a -> Maybe s) -> Maybe a -> (Maybe a, Maybe a, s) Source # splitAt :: Int -> Maybe a -> (Maybe a, Maybe a) Source # drop :: Int -> Maybe a -> Maybe a Source # take :: Int -> Maybe a -> Maybe a Source #
FactorialMonoid [x] Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: [x] -> Maybe ([x], [x]) Source # splitPrimeSuffix :: [x] -> Maybe ([x], [x]) Source # inits :: [x] -> [[x]] Source # tails :: [x] -> [[x]] Source # span :: ([x] -> Bool) -> [x] -> ([x], [x]) Source # break :: ([x] -> Bool) -> [x] -> ([x], [x]) Source # split :: ([x] -> Bool) -> [x] -> [[x]] Source # takeWhile :: ([x] -> Bool) -> [x] -> [x] Source # dropWhile :: ([x] -> Bool) -> [x] -> [x] Source # spanMaybe :: s -> (s -> [x] -> Maybe s) -> [x] -> ([x], [x], s) Source # spanMaybe' :: s -> (s -> [x] -> Maybe s) -> [x] -> ([x], [x], s) Source # splitAt :: Int -> [x] -> ([x], [x]) Source # drop :: Int -> [x] -> [x] Source # take :: Int -> [x] -> [x] Source #
Ord k => FactorialMonoid (Map k v) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Map k v -> Maybe (Map k v, Map k v) Source # splitPrimeSuffix :: Map k v -> Maybe (Map k v, Map k v) Source # inits :: Map k v -> [Map k v] Source # tails :: Map k v -> [Map k v] Source # span :: (Map k v -> Bool) -> Map k v -> (Map k v, Map k v) Source # break :: (Map k v -> Bool) -> Map k v -> (Map k v, Map k v) Source # split :: (Map k v -> Bool) -> Map k v -> [Map k v] Source # takeWhile :: (Map k v -> Bool) -> Map k v -> Map k v Source # dropWhile :: (Map k v -> Bool) -> Map k v -> Map k v Source # spanMaybe :: s -> (s -> Map k v -> Maybe s) -> Map k v -> (Map k v, Map k v, s) Source # spanMaybe' :: s -> (s -> Map k v -> Maybe s) -> Map k v -> (Map k v, Map k v, s) Source # splitAt :: Int -> Map k v -> (Map k v, Map k v) Source # drop :: Int -> Map k v -> Map k v Source # take :: Int -> Map k v -> Map k v Source #
(FactorialMonoid a, FactorialMonoid b) => FactorialMonoid (Stateful a b) Source #
Instance details Defined in Data.Monoid.Instances.Stateful Methods splitPrimePrefix :: Stateful a b -> Maybe (Stateful a b, Stateful a b) Source # splitPrimeSuffix :: Stateful a b -> Maybe (Stateful a b, Stateful a b) Source # inits :: Stateful a b -> [Stateful a b] Source # tails :: Stateful a b -> [Stateful a b] Source # span :: (Stateful a b -> Bool) -> Stateful a b -> (Stateful a b, Stateful a b) Source # break :: (Stateful a b -> Bool) -> Stateful a b -> (Stateful a b, Stateful a b) Source # split :: (Stateful a b -> Bool) -> Stateful a b -> [Stateful a b] Source # takeWhile :: (Stateful a b -> Bool) -> Stateful a b -> Stateful a b Source # dropWhile :: (Stateful a b -> Bool) -> Stateful a b -> Stateful a b Source # spanMaybe :: s -> (s -> Stateful a b -> Maybe s) -> Stateful a b -> (Stateful a b, Stateful a b, s) Source # spanMaybe' :: s -> (s -> Stateful a b -> Maybe s) -> Stateful a b -> (Stateful a b, Stateful a b, s) Source # splitAt :: Int -> Stateful a b -> (Stateful a b, Stateful a b) Source # drop :: Int -> Stateful a b -> Stateful a b Source # take :: Int -> Stateful a b -> Stateful a b Source #
(FactorialMonoid a, FactorialMonoid b) => FactorialMonoid (a, b) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: (a, b) -> Maybe ((a, b), (a, b)) Source # splitPrimeSuffix :: (a, b) -> Maybe ((a, b), (a, b)) Source # inits :: (a, b) -> [(a, b)] Source # tails :: (a, b) -> [(a, b)] Source # span :: ((a, b) -> Bool) -> (a, b) -> ((a, b), (a, b)) Source # break :: ((a, b) -> Bool) -> (a, b) -> ((a, b), (a, b)) Source # split :: ((a, b) -> Bool) -> (a, b) -> [(a, b)] Source # takeWhile :: ((a, b) -> Bool) -> (a, b) -> (a, b) Source # dropWhile :: ((a, b) -> Bool) -> (a, b) -> (a, b) Source # spanMaybe :: s -> (s -> (a, b) -> Maybe s) -> (a, b) -> ((a, b), (a, b), s) Source # spanMaybe' :: s -> (s -> (a, b) -> Maybe s) -> (a, b) -> ((a, b), (a, b), s) Source # splitAt :: Int -> (a, b) -> ((a, b), (a, b)) Source # drop :: Int -> (a, b) -> (a, b) Source # take :: Int -> (a, b) -> (a, b) Source #
FactorialMonoid a => FactorialMonoid (Const a b) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: Const a b -> Maybe (Const a b, Const a b) Source # splitPrimeSuffix :: Const a b -> Maybe (Const a b, Const a b) Source # inits :: Const a b -> [Const a b] Source # tails :: Const a b -> [Const a b] Source # span :: (Const a b -> Bool) -> Const a b -> (Const a b, Const a b) Source # break :: (Const a b -> Bool) -> Const a b -> (Const a b, Const a b) Source # split :: (Const a b -> Bool) -> Const a b -> [Const a b] Source # takeWhile :: (Const a b -> Bool) -> Const a b -> Const a b Source # dropWhile :: (Const a b -> Bool) -> Const a b -> Const a b Source # spanMaybe :: s -> (s -> Const a b -> Maybe s) -> Const a b -> (Const a b, Const a b, s) Source # spanMaybe' :: s -> (s -> Const a b -> Maybe s) -> Const a b -> (Const a b, Const a b, s) Source # splitAt :: Int -> Const a b -> (Const a b, Const a b) Source # drop :: Int -> Const a b -> Const a b Source # take :: Int -> Const a b -> Const a b Source #
(FactorialMonoid a, FactorialMonoid b, FactorialMonoid c) => FactorialMonoid (a, b, c) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: (a, b, c) -> Maybe ((a, b, c), (a, b, c)) Source # splitPrimeSuffix :: (a, b, c) -> Maybe ((a, b, c), (a, b, c)) Source # inits :: (a, b, c) -> [(a, b, c)] Source # tails :: (a, b, c) -> [(a, b, c)] Source # span :: ((a, b, c) -> Bool) -> (a, b, c) -> ((a, b, c), (a, b, c)) Source # break :: ((a, b, c) -> Bool) -> (a, b, c) -> ((a, b, c), (a, b, c)) Source # split :: ((a, b, c) -> Bool) -> (a, b, c) -> [(a, b, c)] Source # takeWhile :: ((a, b, c) -> Bool) -> (a, b, c) -> (a, b, c) Source # dropWhile :: ((a, b, c) -> Bool) -> (a, b, c) -> (a, b, c) Source # spanMaybe :: s -> (s -> (a, b, c) -> Maybe s) -> (a, b, c) -> ((a, b, c), (a, b, c), s) Source # spanMaybe' :: s -> (s -> (a, b, c) -> Maybe s) -> (a, b, c) -> ((a, b, c), (a, b, c), s) Source # splitAt :: Int -> (a, b, c) -> ((a, b, c), (a, b, c)) Source # drop :: Int -> (a, b, c) -> (a, b, c) Source # take :: Int -> (a, b, c) -> (a, b, c) Source #
(FactorialMonoid a, FactorialMonoid b, FactorialMonoid c, FactorialMonoid d) => FactorialMonoid (a, b, c, d) Source #
Instance details Defined in Data.Monoid.Factorial Methods splitPrimePrefix :: (a, b, c, d) -> Maybe ((a, b, c, d), (a, b, c, d)) Source # splitPrimeSuffix :: (a, b, c, d) -> Maybe ((a, b, c, d), (a, b, c, d)) Source # inits :: (a, b, c, d) -> [(a, b, c, d)] Source # tails :: (a, b, c, d) -> [(a, b, c, d)] Source # span :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d)) Source # break :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d)) Source # split :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> [(a, b, c, d)] Source # takeWhile :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> (a, b, c, d) Source # dropWhile :: ((a, b, c, d) -> Bool) -> (a, b, c, d) -> (a, b, c, d) Source # spanMaybe :: s -> (s -> (a, b, c, d) -> Maybe s) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), s) Source # spanMaybe' :: s -> (s -> (a, b, c, d) -> Maybe s) -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d), s) Source # splitAt :: Int -> (a, b, c, d) -> ((a, b, c, d), (a, b, c, d)) Source # drop :: Int -> (a, b, c, d) -> (a, b, c, d) Source # take :: Int -> (a, b, c, d) -> (a, b, c, d) Source #

type StableFactorialMonoid m = (StableFactorial m, FactorialMonoid m, PositiveMonoid m) Source #

Deprecated: Use Data.Semigroup.Factorial.StableFactorial instead.