A spelling corrector in Haskell

October 31, 2009 at 03:07 PM | categories: Uncategorized | View Comments

Update: Thanks to the commenters on this blog and on Reddit, I've got a much improved and more readable Haskell port of the spelling corrector.

On Wednesday I attended the StackOverflow DevDay in London, which was a day of excellent talks by engaging speakers. Michael Sparks gave a talk on Python, where he built up Peter Norvig's spelling corrector line by line as we watched. I was impressed by how easy it was to understand the source code, and the style struck me as being particularly functional. So, I was compelled to translate the Python source into Haskell.

This post is also a Literate Haskell program, meaning that you should be able to copy the text from the page, paste it into a .lhs file, and compile it. Snippets starting with > are Haskell; in between is Peter's original program, and my commentary on the differences.

 # Python region looks like this:
import re, collections

> -- Haskell region looks like this:
> module Main where
> import Char
> import qualified Data.List as List
> import qualified Data.Map as Map
> import qualified Data.Set as Set
> import Data.Ord
> import IO
> import List

Every language needs some imports. The Python program only has two; we're using a scattering of functions outside of the prelude (Haskell's standard library), so we need to import a bit more:

  • Char gives us toLower and isAlpha
  • Data.List gives us foldl'
  • Data.Map gives us the Map type
  • Data.Set gives us the Set type
  • Data.Ord gives us the comparing function
  • IO gives us isEOF
  • List gives us maximumBy
def words(text): return re.findall('[a-z]+', text.lower())

> lowerWords = filter (not . null) . map (map toLower . filter isAlpha) . words

The Haskell prelude already has a function called words, which splits a string by spaces. filter isAlpha and filter (not . null) approximate the Python regular expression:

  • filter isAlpha drops all characters outside of a-z
  • filter (not . null) excludes any empty strings (such as sequences of numbers or punctuation in the original text)
def train(features):
    model = collections.defaultdict(lambda: 1)
    for f in features:
        model[f] += 1
    return model

> train = List.foldl' (\dict word -> Map.insertWith' (+) word (1::Int) dict) Map.empty 

Haskell doesn't need an explicit loop here: we use foldl' to iterate over the list of words and add each one to a map. The Map.insertWith' function either inserts a value (if missing), or extracts the existing value, applies it to a function, and inserts the result back in the map.

NWORDS = train(words(file('big.txt').read()))

> readNWORDS = readFile "big.txt" >>= return . train . lowerWords

A big difference in the Haskell version is that file I/O is encapsulated in an IO monad. So whereas Python's NWORDS variable is an actual dictionary, readNWORDS is a I/O value that, when executed, reads and parses a file and yields a dictionary.

alphabet = 'abcdefghijklmnopqrstuvwxyz'

> alphabet = [ 'a' .. 'z' ]

I put a cheeky shortcut in the Haskell version. (It makes no difference to the line count.)

def edits1(word):
   s = [(word[:i], word[i:]) for i in range(len(word) + 1)]
   deletes    = [a + b[1:] for a, b in s if b]
   transposes = [a + b[1] + b[0] + b[2:] for a, b in s if len(b)>1]
   replaces   = [a + c + b[1:] for a, b in s for c in alphabet if b]
   inserts    = [a + c + b     for a, b in s for c in alphabet]
   return set(deletes + transposes + replaces + inserts)

> edits1 word =
>     let s = [ (take i word, drop i word) | i <- [ 0 .. length word ] ]
>         deletes    = [ a ++ tail b | (a, b) <- s, not $ null b ]
>         transposes = [ a ++ b!!1 : b!!0 : drop 2 b | (a, b) <- s, not $ null b, not $ null $ tail b ]
>         replaces   = [ a ++ c : tail b | (a, b) <- s, c <- alphabet, not $ null b ]
>         inserts    = [ a ++ c : b | (a, b) <- s, c <- alphabet ]
>     in Set.fromList (deletes ++ transposes ++ replaces ++ inserts)

The Haskell and Python versions of this function are fairly close. The main differences:

  • Haskell uses the let ... in keywords to declare values
  • List comprehension syntax is very similar, if you replace Python's for and in with Haskell's | and <-. (Recurring theme: Haskell prefers symbols to keywords.)
  • [ start .. end ] is Haskell's built-in range syntax. It's lazy, and generates elements only on demand, which means it's fine to construct an infinite list like this: [ 1 .. ]
  • Python has neat string slicing syntax:
  • [:i] is replaced with take i, to take the first i characters
  • [i:] is replaced with drop i, to take all but the first i characters
  • Subscripts can be replaced with the !! operators, which does the same thing, but with O(N) complexity. Remember Haskell's strings are lists of characters, not arrays (although see Data.ByteString).
  • Python's if keyword maps to different things depending on the context. Here it's used to ask 'is the string empty?', and we replace it with the not and null functions.
  • ++ and : stand in for Python's + operator, depending on whether we're concatenating two lists (a ++ b) or pushing a single element onto the start of a list (head : tail)

I'm not totally convinced about the performance of the Haskell version, since take and drop are O(N) and not O(1). However, N is small here, being the length of a word. If it's a problem we could use ByteString instead for O(1) complexity at the price of having to copy strings.

def known_edits2(word):
    return set(e2 for e1 in edits1(word) for e2 in edits1(e1) if e2 in NWORDS)

> known_edits2 knownWords = Set.unions . Set.elems . Set.map (Set.intersection knownWords . edits1) . edits1

Here I replaced the Python list comprehensions with Haskell's built-in set functions. We can't iterate directly over a set in Haskell, so if we used a list comprehension here, we'd to use elems to produce a list from the set and fromList to turn the result into a set again. Here I feel that the Python version demonstrates the intent more clearly, which is to produce a set of edits from edit1, then run those through edit1 again, and keep only the edits that turn out to be real words.

Read from right to left, what the Haskell version does is:

  • Produces a set of edits to a word using edit1
  • For each edit in the set, produce another set of edits using edit1, and keep only those edits-of-edits that can be found in knownWords. We now have a set of sets.
  • Turn a set of sets into a list of sets, using elems
  • Collapse that list of sets into a single set of words using unions
def known(words): return set(w for w in words if w in NWORDS)

> -- no Haskell equivalent

The known function actually disappears in the Haskell version. Because it takes a set of known words instead of a map of word frequencies, it turns into a direct call to intersection lower down.

def correct(word):
    candidates = known([word]) or known(edits1(word)) or known_edits2(word) or [word]
    return max(candidates, key=NWORDS.get)

> correct nwords word = 
>     let knownWords = Map.keysSet nwords
>         candidates = Set.elems
>                    $ head
>                    $ filter (not . Set.null)
>                    $ [ Set.intersection knownWords $ Set.singleton word,
>                        Set.intersection knownWords $ edits1 word,
>                        known_edits2 knownWords word,
>                        Set.singleton word ]
>       in maximumBy (comparing (\w -> w `Map.lookup` nwords)) candidates

Python has a magic short-circuiting or operator, which we have to fake by putting together a list of sets and finding the first non-empty one. Because Haskell is lazy this does in fact short-circuit: for instance, we never make a call to known_edits2 if we can already find word in knownWords.

I'm not a fan of maximumBy in Haskell, which makes you compare two items yourself; I prefer the Python version, which is similar to .NET's OrderBy function. Here, though, the comparing function in Data.Ord makes the code a little less verbose.

Finally, here's a little command-line demo that corrects words the user types in. It's only at this point that the Haskell version touches the text file that the Python program encapsulates in the NWORDS variable; the Haskell version passes the dictionary through each function that needs it. I could have done a direct translation of the Python, but this would have meant writing most of the program as imperative IO monad code, which wasn't really the point of the Haskell translation.

> prompt nwords = do
>     eof <- isEOF
>     if eof
>       then return ()
>       else do
>           getLine >>= putStrLn . correct nwords
>           prompt nwords
> main = readNWORDS >>= prompt
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