24 days of Hackage, 2015: day 8: multiset; I wish this were in the standard containers package

Table of contents for the whole series

A table of contents is at the top of the article for day 1.

Day 8

(Reddit discussion)

I don’t remember when it was, but one day I got sick and tired of reimplementing in Haskell the same boilerplate logic when keeping track of many objects classified under the same key. This is a data structure known as a multiset, also known as a bag, in contrast with a regular set, which only keeps track of one unique object per key.

I was surprised that by the lack of a multiset module in the standard containers package, although not completely surprised because you can implement a multiset on top of a set, so in some sense a multiset is “superfluous”. Still, I was used to having a multiset available without any work (however trivial), because of long using a multiset in C++, which I’d used back in the 1990s from the original implementation of the Standard Template Library, and also Python’s collections library has a Counter class which serves a similar purpose.

Today I’ll briefly show some code using multiset and talk about why something like this maybe should be in the standard library.

The classic example of multiset use

Multisets are often used for counting things. Word count is a time-honored use case for multisets, so let’s implement a very simple word count program that break up text into “words” separated by spaces, while treating non-letters as spaces, count the words, and finally output a report which consists of a line for each word and its count, in descending order of count but ascending order of word.

For a bit more realism and efficiency even for a toy program, let’s have the input not be String, but the Text type from Data.Text.Lazy module of the text package. Let’s also build up the final Text report efficiently.

A sample HSpec test

Here’s a sample test (for fun you may wish to write a reasonable QuickCheck generators and tests for this problem). I apologize for the illegible Haskell multiline string literal; I wish Haskell had multiline string literals, interpolation, and all that good stuff other languages have!

(A tangent from day 9)

A number of people commented that I made a misleading remark above about string support in Haskell. It is true that the core Haskell syntax for strings is limited, but it is easy to work around that with Template Haskell, so see Day 9 for how to do this. I totally recommend using one of the libraries mentioned.

In brief, the ugly string literal I wrote can be written

      let expected = [hereLit|words 3
I 2
have 2
so 2
for 1
like 1
many 1
to 1

The code

{-# LANGUAGE OverloadedStrings #-}

module MultisetExampleSpec where

import MultisetExample (wordCount)

import Test.Hspec (Spec, hspec, describe, it, shouldBe)
import Test.Hspec.QuickCheck (prop)

-- | Required for auto-discovery.
spec :: Spec
spec =
  describe "multiset" $ do
    it "wordCount" $ do
      let input = "I have so   many words; words I so like to have words for!?"
      let expected = "words 3\n\
                     \I 2\n\
                     \have 2\n\
                     \so 2\n\
                     \for 1\n\
                     \like 1\n\
                     \many 1\n\
                     \to 1\n"
      wordCount input `shouldBe` expected

The solution

The code almost writes itself from a natural language description of the problem.

{-# LANGUAGE OverloadedStrings #-}

module MultisetExample where

import qualified Data.MultiSet as MultiSet
import qualified Data.Text.Lazy as LazyText
import qualified Data.Text.Lazy.Builder as LazyBuilder
import Data.Text.Lazy.Builder.Int (decimal)
import Data.Ord (Down(..))
import qualified Data.Char as Char
import qualified Data.List as List
import Control.Arrow ((>>>))
import Data.Monoid ((<>))

wordCount :: LazyText.Text -> LazyText.Text
wordCount =
  LazyText.map replaceNonLetterWithSpace
  >>> LazyText.words
  >>> MultiSet.fromList
  >>> MultiSet.toOccurList
  >>> List.sortOn (snd >>> Down)
  >>> map summarizeWordCount
  >>> mconcat
  >>> LazyBuilder.toLazyText

replaceNonLetterWithSpace :: Char -> Char
replaceNonLetterWithSpace c
  | Char.isLetter c = c
  | otherwise = ' '

summarizeWordCount :: (LazyText.Text, MultiSet.Occur) -> LazyBuilder.Builder
summarizeWordCount (word, count) =
  LazyBuilder.fromLazyText word <> " " <> decimal count <> "\n"

Let’s go through this step by step. Note that we’re using my favorite left-to-right composition operator >>> as opposed to the right-to-left composition operator . because it looks much more natural to me for pipelines, and because my description below top to bottom matches this syntax.

(Update on syntax)

Here is the pipeline part of the code in more traditional right-to-left syntax. I think it’s important to be able to read and write in both styles:

-- | Same thing, using traditional right-to-left composition.
wordCountTraditional :: LazyText.Text -> LazyText.Text
wordCountTraditional =
  . mconcat
  . map summarizeWordCount
  . List.sortOn (Down . snd)
  . MultiSet.toOccurList
  . MultiSet.fromList
  . LazyText.words
  . LazyText.map replaceNonLetterWithSpace

Get the words from text

First, replace all non-letters with spaces for the purpose of this problem, then use the words from Data.Text.Lazy (which we imported as LazyText) to break up into words (real tokenization would have more sophisticated rules). By the way, this is done very efficiently because GHC performs fusion in order to do the replacement and the breaking up into words in a single pass, rather than two as written in the code. Fusion is a really, really cool optimization that we rely on for our Haskell code to be super-efficient:

wordCount =
  LazyText.map replaceNonLetterWithSpace
  >>> LazyText.words

Put the words into a multiset

Next, we get the list words into a multiset. MultiSet conveniently has a constructor for that, fromList :: Ord a => [a] -> MultiSet a, and it does this in O(n log n) time because of the use of comparison through Ord to construct a tree (exercise for you if you wish: use one of the hash table libraries in Hackage to create a MultiHashSet instead).

  >>> MultiSet.fromList

Count the words

We grab a list of word/count pairs (in ascending order of words) using toOccurList :: MultiSet a -> [(a, Occur)] where type Occur = Int:

  >>> MultiSet.toOccurList

Sort the word/count list

We sort using the “Schwartzian transform” for efficiency using Data.List.sortOn of type sortOn :: Ord b => (a -> b) -> [a] -> [a]; recall we want the count (the second element of the tuple we get back from the multiset) to be descending.

Documentation of Data.Ord.Down explains how this “newtype hack” is used to change the default ordering comparison during a sort.

  >>> List.sortOn (snd >>> Down)

Make a report for each word/count

  >>> map summarizeWordCount
  >>> mconcat

where our summarizing function, for efficiency in avoiding unnecessary allocations, does not construct a Text but rather a builder, since we don’t need this information for each as Text but plan to combine the reports for all the lines into one Text at the end.

summarizeWordCount :: (LazyText.Text, MultiSet.Occur) -> LazyBuilder.Builder
summarizeWordCount (word, count) =
  LazyBuilder.fromLazyText word <> " " <> decimal count <> "\n"

(If you’re curious how the builder works, check out the source code. It uses higher-rank types, unsafe operations, and strictness annotations.)

Make the final report

Just materialize the Text from the builder:

  >>> LazyBuilder.toLazyText

What should go into a standard library?

I mentioned that I think this should go into the standard library, for convenience. The argument for not putting something into the standard library is always, everyone think their useful thing should be in there, but there’s no way that can happen, and so choices have to be made. Given that, I cannot really argue based on my own experience or perception of my experience that an entire community would benefit from my favorite things being made “standard”. I’d like to think that we have the technology now to collect real data to determine people’s real needs and change the way we make libraries discoverable and usable. Even something like mining Stack Overflow questions could bring up many interesting statistics about what people need. Such data gathering would not substitute for expert curation, of course, but surely would be useful.

There is another argument for not having something like multiset be incorporated: it’s easy to implement once you have the regular set. If you look at the source code, the following basically says it all. A multiset is just a map from a key to a count.

newtype MultiSet a = MS { unMS :: Map a Occur }

type Occur = Int

Everything else is a straightforward wrapper.

But that’s like saying a language should not have any syntactic sugar. I think “library sugar” is as valuable as syntactic sugar.


Multisets are useful. You could implement one yourself. Or you could use the multiset package someone already wrote for us.

All the code

All my code for my article series are at this GitHub repo.

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