split-0.2.5: Combinator library for splitting lists.

Copyright | (c) Brent Yorgey Louis Wasserman 2008-2012
License | BSD-style (see LICENSE)
Maintainer | Brent Yorgey <byorgey@gmail.com>
Stability | stable
Portability | Haskell 2010
Safe Haskell | Safe-Inferred
Language | Haskell2010

Data.List.Split.Internals

Contents

- Types and utilities
- Implementation
- Combinators
  - Basic strategies
  - Strategy transformers
  - Derived combinators
  - Convenience functions
- Other splitting methods

Description

Implementation module for Data.List.Split, a combinator library for splitting lists. See the Data.List.Split documentation for more description and examples.

Synopsis

- data Splitter a = Splitter {
  - delimiter :: Delimiter a
  - delimPolicy :: DelimPolicy
  - condensePolicy :: CondensePolicy
  - initBlankPolicy :: EndPolicy
  - finalBlankPolicy :: EndPolicy
  }
- defaultSplitter :: Splitter a
- newtype Delimiter a = Delimiter [a -> Bool]
- matchDelim :: Delimiter a -> [a] -> Maybe ([a], [a])
- data DelimPolicy
  - = Drop
  - | Keep
  - | KeepLeft
  - | KeepRight
- data CondensePolicy
  - = Condense
  - | DropBlankFields
  - | KeepBlankFields
- data EndPolicy
  - = DropBlank
  - | KeepBlank
- data Chunk a
  - = Delim [a]
  - | Text [a]
- type SplitList a = [Chunk a]
- fromElem :: Chunk a -> [a]
- isDelim :: Chunk a -> Bool
- isText :: Chunk a -> Bool
- splitInternal :: Delimiter a -> [a] -> SplitList a
- postProcess :: Splitter a -> SplitList a -> SplitList a
- doDrop :: DelimPolicy -> SplitList a -> SplitList a
- doCondense :: CondensePolicy -> SplitList a -> SplitList a
- insertBlanks :: CondensePolicy -> SplitList a -> SplitList a
- insertBlanks' :: CondensePolicy -> SplitList a -> SplitList a
- doMerge :: DelimPolicy -> SplitList a -> SplitList a
- mergeLeft :: SplitList a -> SplitList a
- mergeRight :: SplitList a -> SplitList a
- dropInitial :: EndPolicy -> SplitList a -> SplitList a
- dropFinal :: EndPolicy -> SplitList a -> SplitList a
- split :: Splitter a -> [a] -> [[a]]
- oneOf :: Eq a => [a] -> Splitter a
- onSublist :: Eq a => [a] -> Splitter a
- whenElt :: (a -> Bool) -> Splitter a
- dropDelims :: Splitter a -> Splitter a
- keepDelimsL :: Splitter a -> Splitter a
- keepDelimsR :: Splitter a -> Splitter a
- condense :: Splitter a -> Splitter a
- dropInitBlank :: Splitter a -> Splitter a
- dropFinalBlank :: Splitter a -> Splitter a
- dropInnerBlanks :: Splitter a -> Splitter a
- mapSplitter :: (b -> a) -> Splitter a -> Splitter b
- dropBlanks :: Splitter a -> Splitter a
- startsWith :: Eq a => [a] -> Splitter a
- startsWithOneOf :: Eq a => [a] -> Splitter a
- endsWith :: Eq a => [a] -> Splitter a
- endsWithOneOf :: Eq a => [a] -> Splitter a
- splitOneOf :: Eq a => [a] -> [a] -> [[a]]
- splitOn :: Eq a => [a] -> [a] -> [[a]]
- splitWhen :: (a -> Bool) -> [a] -> [[a]]
- endBy :: Eq a => [a] -> [a] -> [[a]]
- endByOneOf :: Eq a => [a] -> [a] -> [[a]]
- wordsBy :: (a -> Bool) -> [a] -> [[a]]
- linesBy :: (a -> Bool) -> [a] -> [[a]]
- build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a]
- chunksOf :: Int -> [e] -> [[e]]
- splitPlaces :: Integral a => [a] -> [e] -> [[e]]
- splitPlacesBlanks :: Integral a => [a] -> [e] -> [[e]]
- chop :: ([a] -> (b, [a])) -> [a] -> [b]
- divvy :: Int -> Int -> [a] -> [[a]]

# Types and utilities

data Splitter a Source #

A splitting strategy.

Constructors

Splitter |

Fields

- delimiter :: Delimiter a

  What delimiter to split on

- delimPolicy :: DelimPolicy

  What to do with delimiters (drop from output, keep as separate elements in output, or merge with previous or following chunks)

- condensePolicy :: CondensePolicy

  What to do with multiple consecutive delimiters

- initBlankPolicy :: EndPolicy

  Drop an initial blank?

- finalBlankPolicy :: EndPolicy

  Drop a final blank?

defaultSplitter :: Splitter a Source #

The default splitting strategy: keep delimiters in the output as separate chunks, don't condense multiple consecutive delimiters into one, keep initial and final blank chunks. Default delimiter is the constantly false predicate.

Note that `defaultSplitter` should normally not be used; use `oneOf`, `onSublist`, or `whenElt` instead, which are the same as the `defaultSplitter` with just the delimiter overridden.

The `defaultSplitter` strategy with any delimiter gives a maximally information-preserving splitting strategy, in the sense that (a) taking the `concat` of the output yields the original list, and (b) given only the output list, we can reconstruct a `Splitter` which would produce the same output list again given the original input list. This default strategy can be overridden to allow discarding various sorts of information.

newtype Delimiter a Source #

A delimiter is a list of predicates on elements, matched by some contiguous subsequence of a list.

Constructors

Delimiter [a -> Bool] |

matchDelim :: Delimiter a -> [a] -> Maybe ([a], [a]) Source #

Try to match a delimiter at the start of a list, either failing or decomposing the list into the portion which matched the delimiter and the remainder.

data DelimPolicy Source #

What to do with delimiters?

Constructors

Drop | Drop delimiters from the output.
Keep | Keep delimiters as separate chunks of the output.
KeepLeft | Keep delimiters in the output, prepending them to the following chunk.
KeepRight | Keep delimiters in the output, appending them to the previous chunk.

#### Instances

Instances details

Show DelimPolicy Source # |
Instance details Defined in Data.List.Split.Internals Methods showsPrec :: Int -> DelimPolicy -> ShowS Source # show :: DelimPolicy -> String Source # showList :: [DelimPolicy] -> ShowS Source #
Eq DelimPolicy Source # |
Instance details Defined in Data.List.Split.Internals Methods (==) :: DelimPolicy -> DelimPolicy -> Bool Source # (/=) :: DelimPolicy -> DelimPolicy -> Bool Source #

data CondensePolicy Source #

What to do with multiple consecutive delimiters?

Constructors

Condense | Condense into a single delimiter.
DropBlankFields | Keep consecutive delimiters separate, but don't insert blank chunks in between them.
KeepBlankFields | Insert blank chunks between consecutive delimiters.

#### Instances

Instances details

Show CondensePolicy Source # |
Instance details Defined in Data.List.Split.Internals Methods showsPrec :: Int -> CondensePolicy -> ShowS Source # show :: CondensePolicy -> String Source # showList :: [CondensePolicy] -> ShowS Source #
Eq CondensePolicy Source # |
Instance details Defined in Data.List.Split.Internals Methods (==) :: CondensePolicy -> CondensePolicy -> Bool Source # (/=) :: CondensePolicy -> CondensePolicy -> Bool Source #

data EndPolicy Source #

What to do with a blank chunk at either end of the list (i.e. when the list begins or ends with a delimiter).

Constructors

DropBlank |
KeepBlank |

#### Instances

Instances details

Show EndPolicy Source # |
Instance details Defined in Data.List.Split.Internals Methods showsPrec :: Int -> EndPolicy -> ShowS Source # show :: EndPolicy -> String Source # showList :: [EndPolicy] -> ShowS Source #
Eq EndPolicy Source # |
Instance details Defined in Data.List.Split.Internals Methods (==) :: EndPolicy -> EndPolicy -> Bool Source # (/=) :: EndPolicy -> EndPolicy -> Bool Source #

data Chunk a Source #

Tag chunks as delimiters or text.

Constructors

Delim [a] |
Text [a] |

#### Instances

Instances details

Show a => Show (Chunk a) Source # |
Instance details Defined in Data.List.Split.Internals Methods showsPrec :: Int -> Chunk a -> ShowS Source # show :: Chunk a -> String Source # showList :: [Chunk a] -> ShowS Source #
Eq a => Eq (Chunk a) Source # |
Instance details Defined in Data.List.Split.Internals Methods (==) :: Chunk a -> Chunk a -> Bool Source # (/=) :: Chunk a -> Chunk a -> Bool Source #

type SplitList a = [Chunk a] Source #

Internal representation of a split list that tracks which pieces are delimiters and which aren't.

fromElem :: Chunk a -> [a] Source #

Untag a `Chunk`.

isDelim :: Chunk a -> Bool Source #

Test whether a `Chunk` is a delimiter.

isText :: Chunk a -> Bool Source #

Test whether a `Chunk` is text.

# Implementation

splitInternal :: Delimiter a -> [a] -> SplitList a Source #

Given a delimiter to use, split a list into an internal representation with chunks tagged as delimiters or text. This transformation is lossless; in particular,

      concatMap fromElem (splitInternal d l) == l.

postProcess :: Splitter a -> SplitList a -> SplitList a Source #

Given a split list in the internal tagged representation, produce a new internal tagged representation corresponding to the final output, according to the strategy defined by the given `Splitter`.

doDrop :: DelimPolicy -> SplitList a -> SplitList a Source #

Drop delimiters if the `DelimPolicy` is `Drop`.

doCondense :: CondensePolicy -> SplitList a -> SplitList a Source #

Condense multiple consecutive delimiters into one if the `CondensePolicy` is `Condense`.

insertBlanks :: CondensePolicy -> SplitList a -> SplitList a Source #

Insert blank chunks between any remaining consecutive delimiters (unless the condense policy is `DropBlankFields`), and at the beginning or end if the first or last element is a delimiter.

insertBlanks' :: CondensePolicy -> SplitList a -> SplitList a Source #

Insert blank chunks between consecutive delimiters.

doMerge :: DelimPolicy -> SplitList a -> SplitList a Source #

Merge delimiters into adjacent chunks according to the `DelimPolicy`.

mergeLeft :: SplitList a -> SplitList a Source #

Merge delimiters with adjacent chunks to the right (yes, that's not a typo: the delimiters should end up on the left of the chunks, so they are merged with chunks to their right).

mergeRight :: SplitList a -> SplitList a Source #

Merge delimiters with adjacent chunks to the left.

dropInitial :: EndPolicy -> SplitList a -> SplitList a Source #

Drop an initial blank chunk according to the given `EndPolicy`.

dropFinal :: EndPolicy -> SplitList a -> SplitList a Source #

Drop a final blank chunk according to the given `EndPolicy`.

# Combinators

split :: Splitter a -> [a] -> [[a]] Source #

Split a list according to the given splitting strategy. This is how to "run" a `Splitter` that has been built using the other combinators.

## Basic strategies

All these basic strategies have the same parameters as the `defaultSplitter` except for the delimiters.

oneOf :: Eq a => [a] -> Splitter a Source #

A splitting strategy that splits on any one of the given elements.

    >>> split (oneOf ",;") "hi;there,world"
    ["hi",";","there",",","world"]

    >>> split (oneOf "xyz") "aazbxyzcxd"
    ["aa","z","b","x","","y","","z","c","x","d"]

onSublist :: Eq a => [a] -> Splitter a Source #

A splitting strategy that splits on the given list, when it is encountered as an exact subsequence.

    >>> split (onSublist "xyz") "aazbxyzcxd"
    ["aazb","xyz","cxd"]

Note that splitting on the empty list is a special case, which splits just before every element of the list being split.

    >>> split (onSublist "") "abc"
    ["","","a","","b","","c"]

    >>> split (dropDelims . dropBlanks $ onSublist "") "abc"
    ["a","b","c"]

However, if you want to break a list into singleton elements like this, you are better off using ``chunksOf` 1`, or better yet, ``map` (:[])`.

whenElt :: (a -> Bool) -> Splitter a Source #

A splitting strategy that splits on any elements that satisfy the given predicate.

    >>> split (whenElt (<0)) [2,4,-3,6,-9,1 :: Int]
    [[2,4],[-3],[6],[-9],[1]]

## Strategy transformers

dropDelims :: Splitter a -> Splitter a Source #

Drop delimiters from the output (the default is to keep them).

    >>> split (oneOf ":") "a:b:c"
    ["a",":","b",":","c"]

    >>> split (dropDelims $ oneOf ":") "a:b:c"
    ["a","b","c"]

keepDelimsL :: Splitter a -> Splitter a Source #

Keep delimiters in the output by prepending them to adjacent chunks.

    >>> split (keepDelimsL $ oneOf "xyz") "aazbxyzcxd"
    ["aa","zb","x","y","zc","xd"]

keepDelimsR :: Splitter a -> Splitter a Source #

Keep delimiters in the output by appending them to adjacent chunks.

    >>> split (keepDelimsR $ oneOf "xyz") "aazbxyzcxd"
    ["aaz","bx","y","z","cx","d"]

condense :: Splitter a -> Splitter a Source #

Condense multiple consecutive delimiters into one.

    >>> split (condense $ oneOf "xyz") "aazbxyzcxd"
    ["aa","z","b","xyz","c","x","d"]

    >>> split (dropDelims $ oneOf "xyz") "aazbxyzcxd"
    ["aa","b","","","c","d"]

    >>> split (condense . dropDelims $ oneOf "xyz") "aazbxyzcxd"
    ["aa","b","c","d"]

dropInitBlank :: Splitter a -> Splitter a Source #

Don't generate a blank chunk if there is a delimiter at the beginning.

    >>> split (oneOf ":") ":a:b"
    ["",":","a",":","b"]

    >>> split (dropInitBlank $ oneOf ":") ":a:b"
    [":","a",":","b"]

dropFinalBlank :: Splitter a -> Splitter a Source #

Don't generate a blank chunk if there is a delimiter at the end.

    >>> split (oneOf ":") "a:b:"
    ["a",":","b",":",""]

    >>> split (dropFinalBlank $ oneOf ":") "a:b:"
    ["a",":","b",":"]

dropInnerBlanks :: Splitter a -> Splitter a Source #

Don't generate blank chunks between consecutive delimiters.

    >>> split (oneOf ":") "::b:::a"
    ["",":","",":","b",":","",":","",":","a"]

    >>> split (dropInnerBlanks $ oneOf ":") "::b:::a"
    ["",":",":","b",":",":",":","a"]

mapSplitter :: (b -> a) -> Splitter a -> Splitter b Source #

Split over a different type of element by performing a preprocessing step.

    >>> split (mapSplitter snd $ oneOf "-_") $ zip [0..] "a-bc_d"
    [[(0,'a')],[(1,'-')],[(2,'b'),(3,'c')],[(4,'_')],[(5,'d')]]

    >>> import Data.Char (toLower)
    >>> split (mapSplitter toLower $ dropDelims $ whenElt (== 'x')) "abXcxd"
    ["ab","c","d"]

## Derived combinators

dropBlanks :: Splitter a -> Splitter a Source #

Drop all blank chunks from the output, and condense consecutive delimiters into one. Equivalent to ``dropInitBlank` . `dropFinalBlank` . `condense``.

    >>> split (oneOf ":") "::b:::a"
    ["",":","",":","b",":","",":","",":","a"]

    >>> split (dropBlanks $ oneOf ":") "::b:::a"
    ["::","b",":::","a"]

startsWith :: Eq a => [a] -> Splitter a Source #

Make a strategy that splits a list into chunks that all start with the given subsequence (except possibly the first). Equivalent to ``dropInitBlank` . `keepDelimsL` . `onSublist``.

    >>> split (startsWith "app") "applyapplicativeapplaudapproachapple"
    ["apply","applicative","applaud","approach","apple"]

startsWithOneOf :: Eq a => [a] -> Splitter a Source #

Make a strategy that splits a list into chunks that all start with one of the given elements (except possibly the first). Equivalent to ``dropInitBlank` . `keepDelimsL` . `oneOf``. example:

    >>> split (startsWithOneOf ['A'..'Z']) "ACamelCaseIdentifier"
    ["A","Camel","Case","Identifier"]

endsWith :: Eq a => [a] -> Splitter a Source #

Make a strategy that splits a list into chunks that all end with the given subsequence, except possibly the last. Equivalent to ``dropFinalBlank` . `keepDelimsR` . `onSublist``.

    >>> split (endsWith "ly") "happilyslowlygnarlylily"
    ["happily","slowly","gnarly","lily"]

endsWithOneOf :: Eq a => [a] -> Splitter a Source #

Make a strategy that splits a list into chunks that all end with one of the given elements, except possibly the last. Equivalent to ``dropFinalBlank` . `keepDelimsR` . `oneOf``.

    >>> split (condense $ endsWithOneOf ".,?! ") "Hi, there!  How are you?"
    ["Hi, ","there!  ","How ","are ","you?"]

## Convenience functions

splitOneOf :: Eq a => [a] -> [a] -> [[a]] Source #

Split on any of the given elements. Equivalent to ``split` . `dropDelims` . `oneOf``.

    >>> splitOneOf ";.," "foo,bar;baz.glurk"
    ["foo","bar","baz","glurk"]

splitOn :: Eq a => [a] -> [a] -> [[a]] Source #

Split on the given sublist. Equivalent to ``split` . `dropDelims` . `onSublist``.

    >>> splitOn ":" "12:35:07"
    ["12","35","07"]

    >>> splitOn "x" "axbxc"
    ["a","b","c"]

    >>> splitOn "x" "axbxcx"
    ["a","b","c",""]

    >>> splitOn ".." "a..b...c....d.."
    ["a","b",".c","","d",""]

In some parsing combinator frameworks this is also known as `sepBy`.

Note that this is the right inverse of the `intercalate` function from Data.List, that is,

    intercalate x . splitOn x === id

``splitOn` x . `intercalate` x` is the identity on certain lists, but it is tricky to state the precise conditions under which this holds. (For example, it is not enough to say that `x` does not occur in any elements of the input list. Working out why is left as an exercise for the reader.)

splitWhen :: (a -> Bool) -> [a] -> [[a]] Source #

Split on elements satisfying the given predicate. Equivalent to ``split` . `dropDelims` . `whenElt``.

    >>> splitWhen (<0) [1,3,-4,5,7,-9,0,2]
    [[1,3],[5,7],[0,2]]

    >>> splitWhen (<0) [1,-2,3,4,-5,-6,7,8,-9]
    [[1],[3,4],[],[7,8],[]]

endBy :: Eq a => [a] -> [a] -> [[a]] Source #

Split into chunks terminated by the given subsequence. Equivalent to ``split` . `dropFinalBlank` . `dropDelims` . `onSublist``.

    >>> endBy ".;" "foo.;bar.;baz.;"
    ["foo","bar","baz"]

Note also that the `lines` function from Data.List is equivalent to ``endBy` "\n"`.

endByOneOf :: Eq a => [a] -> [a] -> [[a]] Source #

Split into chunks terminated by one of the given elements. Equivalent to ``split` . `dropFinalBlank` . `dropDelims` . `oneOf``.

    >>> endByOneOf ";," "foo;bar,baz;"
    ["foo","bar","baz"]

wordsBy :: (a -> Bool) -> [a] -> [[a]] Source #

Split into "words", with word boundaries indicated by the given predicate. Satisfies ``words` === wordsBy `isSpace``; equivalent to ``split` . `dropBlanks` . `dropDelims` . `whenElt``.

    >>> wordsBy (`elem` ",;.?! ") "Hello there, world! How?"
    ["Hello","there","world","How"]

    >>> wordsBy (=='x') "dogxxxcatxbirdxx"
    ["dog","cat","bird"]

linesBy :: (a -> Bool) -> [a] -> [[a]] Source #

Split into "lines", with line boundaries indicated by the given predicate. Satisfies ``lines` === linesBy (=='n')`; equivalent to ``split` . `dropFinalBlank` . `dropDelims` . `whenElt``.

    >>> linesBy (==';') "foo;bar;;baz;"
    ["foo","bar","","baz"]

    >>> linesBy (=='x') "dogxxxcatxbirdxx"
    ["dog","","","cat","bird",""]

# Other splitting methods

build :: ((a -> [a] -> [a]) -> [a] -> [a]) -> [a] Source #

Standard build function, specialized to building lists.

Usually build is given the rank-2 type

    build :: (forall b. (a -> b -> b) -> b -> b) -> [a]

but since we only use it when `(b ~ [a])`, we give it the more restricted type signature in order to avoid needing a non-Haskell2010 extension.

Note that the 0.1.4.3 release of this package did away with a custom `build` implementation in favor of importing one from GHC.Exts, which was (reportedly) faster for some applications. However, in the interest of simplicity and complete Haskell2010 compliance as `split` is being included in the Haskel Platform, version 0.2.1.0 has gone back to defining `build` manually. This is in line with `split`'s design philosophy of having efficiency as a non-goal.

chunksOf :: Int -> [e] -> [[e]] Source #

``chunksOf` n` splits a list into length-n pieces. The last piece will be shorter if `n` does not evenly divide the length of the list. If `n <= 0`, ``chunksOf` n l` returns an infinite list of empty lists.

    >>> chunksOf 3 [1..12]
    [[1,2,3],[4,5,6],[7,8,9],[10,11,12]]

    >>> chunksOf 3 "Hello there"
    ["Hel","lo ","the","re"]

    >>> chunksOf 3 ([] :: [Int])
    []

Note that ``chunksOf` n []` is `[]`, not `[[]]`. This is intentional, and satisfies the property that

    chunksOf n xs ++ chunksOf n ys == chunksOf n (xs ++ ys)

whenever `n` evenly divides the length of `xs`.

splitPlaces :: Integral a => [a] -> [e] -> [[e]] Source #

Split a list into chunks of the given lengths.

    >>> splitPlaces [2,3,4] [1..20]
    [[1,2],[3,4,5],[6,7,8,9]]

    >>> splitPlaces [4,9] [1..10]
    [[1,2,3,4],[5,6,7,8,9,10]]

    >>> splitPlaces [4,9,3] [1..10]
    [[1,2,3,4],[5,6,7,8,9,10]]

If the input list is longer than the total of the given lengths, then the remaining elements are dropped. If the list is shorter than the total of the given lengths, then the result may contain fewer chunks than requested, and the last chunk may be shorter than requested.

splitPlacesBlanks :: Integral a => [a] -> [e] -> [[e]] Source #

Split a list into chunks of the given lengths. Unlike `splitPlaces`, the output list will always be the same length as the first input argument. If the input list is longer than the total of the given lengths, then the remaining elements are dropped. If the list is shorter than the total of the given lengths, then the last several chunks will be shorter than requested or empty.

    >>> splitPlacesBlanks [2,3,4] [1..20]
    [[1,2],[3,4,5],[6,7,8,9]]

    >>> splitPlacesBlanks [4,9] [1..10]
    [[1,2,3,4],[5,6,7,8,9,10]]

    >>> splitPlacesBlanks [4,9,3] [1..10]
    [[1,2,3,4],[5,6,7,8,9,10],[]]

Notice the empty list in the output of the third example, which differs from the behavior of `splitPlaces`.

chop :: ([a] -> (b, [a])) -> [a] -> [b] Source #

A useful recursion pattern for processing a list to produce a new list, often used for "chopping" up the input list. Typically chop is called with some function that will consume an initial prefix of the list and produce a value and the rest of the list.

For example, many common Prelude functions can be implemented in terms of `chop`:

    group :: (Eq a) => [a] -> [[a]]
    group = chop (\ xs@(x:_) -> span (==x) xs)

    words :: String -> [String]
    words = filter (not . null) . chop (break isSpace . dropWhile isSpace)

divvy :: Int -> Int -> [a] -> [[a]] Source #

Divides up an input list into a set of sublists, according to `n` and `m` input specifications you provide. Each sublist will have `n` items, and the start of each sublist will be offset by `m` items from the previous one.

    >>> divvy 5 5 [1..15]
    [[1,2,3,4,5],[6,7,8,9,10],[11,12,13,14,15]]

    >>> divvy 5 2 [1..15]
    [[1,2,3,4,5],[3,4,5,6,7],[5,6,7,8,9],[7,8,9,10,11],[9,10,11,12,13],[11,12,13,14,15]]

In the case where a source list's trailing elements do no fill an entire sublist, those trailing elements will be dropped.

    >>> divvy 5 2 [1..10]
    [[1,2,3,4,5],[3,4,5,6,7],[5,6,7,8,9]]

As an example, you can generate a moving average over a list of prices:

    type Prices = [Float]
    type AveragePrices = [Float]

    average :: [Float] -> Float
    average xs = sum xs / (fromIntegral $ length xs)

    simpleMovingAverage :: Prices -> AveragePrices
    simpleMovingAverage = map average . divvy 20 1