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June 2, 2018 12:15
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Something like Cocke-Younger-Kasami in Haskell (no Chomsky Normal Form required). Not well optimized, but appears to work.
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module Main where | |
import Data.Either | |
import Data.List | |
import Data.Array.IArray as A | |
import Control.Arrow (second) | |
import Control.Monad.Except | |
-- Partition a number n into exactly l parts of sizes \in \{1..f\} | |
-- 1st arg: the number to be partitioned | |
-- 2nd arg: = no. of elts in a partitioning | |
-- 3rd arg: max size of a single element of a partitioning | |
posPartitionsL :: (Integral a) => a -> a -> a -> [[a]] | |
posPartitionsL 0 _ _ = [] | |
posPartitionsL _ 0 _ = [[]] | |
posPartitionsL n 1 f | f < n = [] | |
posPartitionsL n 1 _ = [[n]] | |
posPartitionsL n l f = | |
concat [ map (k:) (posPartitionsL (n-k) (l-1) f) | k <- [1..min n f] ] | |
listcorrespondences :: Eq a => [[a]] -> [[a]] -> [[a]] | |
listcorrespondences as bs = zipWith (Data.List.intersect) as bs | |
-- Epsilon excluded. | |
data CFG a = | |
CFG { numnt :: Integer, | |
rules :: [(Integer, Either [Integer] [a])] } | |
deriving (Show) | |
cykparse :: (Eq a) => CFG a -> [a] -> Except [Char] [Integer] | |
cykparse cfg w = do | |
c <- cyk cfg w | |
return $ fst $ (A.!) c (length w, 1) | |
-- A list of unique nonterminals and a detailed resolution of the ambiguity | |
type CykStruct = Array (Int, Int) ([Integer], [(Integer, [(Int, Int)])]) | |
cyk :: Eq a => CFG a -> [a] -> Except [Char] CykStruct | |
cyk _ [] = throwError "CYK called on empty string" | |
cyk cfg (h:t) = | |
let | |
crules = [(x',i) | (i,x) <- rules cfg, isRight x, let x' = fromRight [] x] | |
n = length (h:t) | |
arr = A.array ((1,1), (n,n)) entries | |
entries = [ ((1,i), (suitablents, map (\x -> (x,[])) suitablents)) | |
| i <- [1..n] | c <- (h:t) | |
, let suitablents = [j | (x',j) <- crules, c`elem`x' ] ] | |
in | |
return $ cykparse' cfg arr n 2 | |
fromRight :: b -> Either a b -> b | |
fromRight _ (Right x) = x | |
fromRight d (Left _) = d | |
fromLeft :: a -> Either a b -> a | |
fromLeft _ (Left x) = x | |
fromLeft d (Right _) = d | |
cykparse' :: CFG a -> CykStruct | |
-> Int -> Int -> CykStruct | |
cykparse' _ a n j | n < j = a | |
cykparse' cfg a n j = | |
let | |
syntacticRules = [(x',i) | (i,x) <- rules cfg, isLeft x, let x' = fromLeft [] x] | |
a' = a // [ ((j,i), | |
(nub $ map fst contents, contents)) | |
| i <- [1..n-j+1] | |
, let contents = [ (nt, origins) | |
| (x',nt) <- syntacticRules | |
, length x' <= j | |
, partit <- posPartitionsL j (length x') (j-1) | |
, let origins = map (second (+i)) (zip partit (scanl (+) 0 partit)) | |
, let ntsequence :: [[Integer]] = map (\(k,s') -> fst ((A.!) a (k,s'))) origins | |
, let intersects :: [[Integer]] = (listcorrespondences (map return x') ntsequence) | |
, any (const True) intersects && not (any null intersects) ] | |
] | |
// [ ((j,i), ([],[])) | i <- [n-j+2..n] ] | |
in | |
cykparse' cfg a' n (j+1) | |
-- Example: Dyck_2 grammar | |
dyckab :: CFG Char | |
dyckab = CFG 3 [(0, Left [0,0]), (0, Left [1,2]), (0, Left [1,0,2]), (1, Right "a"), (2, Right "b")] | |
main :: IO () | |
main = do | |
putStrLn "~ Ready ~" | |
s <- getLine | |
let g = dyckab | |
let result = runExcept (cykparse g s) | |
case result of | |
Right x -> putStrLn (show x) | |
Left y -> putStrLn ("Error: " ++ y) | |
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