Data.Monoid.Textual

This module defines the TextualMonoid class and its most important instances for String and Text.

Documentation

class (IsString t, LeftReductiveMonoid t, LeftGCDMonoid t, FactorialMonoid t) => TextualMonoid t where

The TextualMonoid class is an extension of FactorialMonoid specialized for monoids that can contain characters. Its methods are generally equivalent to their namesake functions from Data.List and Data.Text, and they satisfy the following laws:

unfoldr splitCharacterPrefix . fromString == id
splitCharacterPrefix . primePrefix == fmap (\(c, t)-> (c, mempty)) . splitCharacterPrefix

map f . fromString == fromString . List.map f
concatMap (fromString . f) . fromString == fromString . List.concatMap f

foldl  ft fc a . fromString == List.foldl  fc a
foldr  ft fc a . fromString == List.foldr  fc a
foldl' ft fc a . fromString == List.foldl' fc a

scanl f c . fromString == fromString . List.scanl f c
scanr f c . fromString == fromString . List.scanr f c
mapAccumL f a . fromString == fmap fromString . List.mapAccumL f a
mapAccumL f a . fromString == fmap fromString . List.mapAccumL f a

takeWhile pt pc . fromString == fromString . takeWhile pc
dropWhile pt pc . fromString == fromString . dropWhile pc

mconcat . intersperse (singleton c) . split (== c) == id
find p . fromString == List.find p

A TextualMonoid may contain non-character data insterspersed between its characters. Every class method that returns a modified TextualMonoid instance generally preserves this non-character data. All of the following expressions are identities:

map id
concatMap singleton
foldl  (<>) (\a c-> a <> singleton c) mempty
foldr  (<>) ((<>) . singleton) mempty
foldl' (<>) (\a c-> a <> singleton c) mempty
scanl1 (const id)
scanr1 const
uncurry (mapAccumL (,))
uncurry (mapAccumR (,))
takeWhile (const True) (const True)
dropWhile (const False) (const False)

A minimal instance definition must implement splitCharacterPrefix.

Minimal complete definition

splitCharacterPrefix

Methods

fromText :: Text -> t

Contructs a new data type instance Like fromString, but from a Text input instead of String.

fromText == fromString . Text.unpack

singleton :: Char -> t

Creates a prime monoid containing a single character.

singleton c == fromString [c]

splitCharacterPrefix :: t -> Maybe (Char, t)

Specialized version of splitPrimePrefix. Every prime factor of a Textual monoid must consist of a single character or no character at all.

characterPrefix :: t -> Maybe Char

Extracts a single character that prefixes the monoid, if the monoid begins with a character. Otherwise returns Nothing.

characterPrefix == fmap fst . splitCharacterPrefix

map :: (Char -> Char) -> t -> t

Equivalent to map from Data.List with a Char -> Char function. Preserves all non-character data.

map f == concatMap (singleton . f)

concatMap :: (Char -> t) -> t -> t

Equivalent to concatMap from Data.List with a Char -> String function. Preserves all non-character data.

any :: (Char -> Bool) -> t -> Bool

Equivalent to any from Data.List. Ignores all non-character data.

all :: (Char -> Bool) -> t -> Bool

Equivalent to all from Data.List. Ignores all non-character data.

foldl :: (a -> t -> a) -> (a -> Char -> a) -> a -> t -> a

The first argument folds over the non-character prime factors, the second over characters. Otherwise equivalent to foldl from Data.List.

foldl' :: (a -> t -> a) -> (a -> Char -> a) -> a -> t -> a

Strict version of foldl.

foldr :: (t -> a -> a) -> (Char -> a -> a) -> a -> t -> a

The first argument folds over the non-character prime factors, the second over characters. Otherwise equivalent to foldr from Data.List.

scanl :: (Char -> Char -> Char) -> Char -> t -> t

Equivalent to scanl from Data.List when applied to a String, but preserves all non-character data.

scanl1 :: (Char -> Char -> Char) -> t -> t

Equivalent to scanl1 from Data.List when applied to a String, but preserves all non-character data.

scanl f c == scanl1 f . (singleton c <>)

scanr :: (Char -> Char -> Char) -> Char -> t -> t

Equivalent to scanr from Data.List when applied to a String, but preserves all non-character data.

scanr1 :: (Char -> Char -> Char) -> t -> t

Equivalent to scanr1 from Data.List when applied to a String, but preserves all non-character data.

scanr f c == scanr1 f . (<> singleton c)

mapAccumL :: (a -> Char -> (a, Char)) -> a -> t -> (a, t)

Equivalent to mapAccumL from Data.List when applied to a String, but preserves all non-character data.

mapAccumR :: (a -> Char -> (a, Char)) -> a -> t -> (a, t)

Equivalent to mapAccumR from Data.List when applied to a String, but preserves all non-character data.

takeWhile :: (t -> Bool) -> (Char -> Bool) -> t -> t

The first predicate tests the non-character data, the second one the characters. Otherwise equivalent to takeWhile from Data.List when applied to a String.

dropWhile :: (t -> Bool) -> (Char -> Bool) -> t -> t

The first predicate tests the non-character data, the second one the characters. Otherwise equivalent to dropWhile from Data.List when applied to a String.

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

'break pt pc' is equivalent to |span (not . pt) (not . pc)|.

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

'span pt pc t' is equivalent to |(takeWhile pt pc t, dropWhile pt pc t)|.

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

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

split p == Factorial.split (maybe False p . characterPrefix)

find :: (Char -> Bool) -> t -> Maybe Char

Like find from Data.List when applied to a String. Ignores non-character data.

Instances

TextualMonoid String

TextualMonoid Text

TextualMonoid Text

TextualMonoid ByteStringUTF8

TextualMonoid (Seq Char)

TextualMonoid (Vector Char)

(Eq a, TextualMonoid a, StableFactorialMonoid a) => TextualMonoid (Concat a)

(Eq a, TextualMonoid a, StableFactorialMonoid a) => TextualMonoid (Measured a)