285 lines
11 KiB
Haskell
285 lines
11 KiB
Haskell
{-# LANGUAGE FlexibleInstances #-}
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module TreeTrie where
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-- import Debug.Trace
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import Prelude hiding (null, seq)
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import qualified Data.Map.Strict as Map
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import qualified Data.Set as Set
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import Test.HUnit
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import Test.QuickCheck
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import Control.Monad
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data Trie a = Mt
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| Ok a
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| Br (Map.Map Integer (Trie a), Trie a, Map.Map Char (Trie a)) -- Opens, Wild, rest
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deriving (Eq, Show)
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empty = Mt
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null Mt = True
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null _ = False
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makeTail _ r | null r = r
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makeTail 0 r = r
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makeTail n r = Br (Map.empty, makeTail (n - 1) r, Map.empty)
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stripTail _ r | null r = Just r
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stripTail 0 r = Just r
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stripTail n (Br (os, r, h)) | Map.null os && Map.null h = stripTail (n - 1) r
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stripTail _ _ = Nothing
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route _ Mt f = f
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route [] (Ok v) f = v
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route [] _ f = f
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route (_ : _) (Ok v) f = f
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route ('<' : nc : s) (Br (os, w, _)) f =
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let n = (read (nc : []) :: Integer) in
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case Map.lookup n os of
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Just r -> route s r f
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Nothing -> route s (makeTail n w) f
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route (x : s) (Br (_, w, h)) f = route s (Map.findWithDefault w x h) f
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get w h x = Map.findWithDefault w x h
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combine f leftEmpty rightEmpty r1 r2 = g r1 r2
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where g (Ok v) r2 = f (Ok v) r2
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g r1 (Ok v) = f r1 (Ok v)
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g r1 r2 | null r1 = collapse $ leftEmpty r2
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g r1 r2 | null r2 = collapse $ rightEmpty r1
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g r1 r2 = collapse $ foldKeys g r1 r2
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foldKeys g (Br (os1, w1, h1)) (Br (os2, w2, h2)) =
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Br (Set.foldr fo Map.empty sizes, w, Set.foldr f Map.empty keys)
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where sizes = Set.union (Map.keysSet os1) (Map.keysSet os2)
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w = g w1 w2
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fo size acc = let o1 = Map.findWithDefault (makeTail size w1) size os1 in
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let o2 = Map.findWithDefault (makeTail size w2) size os2 in
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let o = g o1 o2 in
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if stripTail size o == Just w then acc else Map.insert size o acc
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f x acc = update x (g (get w1 h1 x) (get w2 h2 x)) w acc
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keys = Set.union (Map.keysSet h1) (Map.keysSet h2)
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collapse (Br (os, Mt, h)) | Map.null os && Map.null h = empty
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collapse r = r
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update x k w h = if k == w then Map.delete x h else Map.insert x k h
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---------------------------------------------------------------------------
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union :: Ord t => Trie (Set.Set t) -> Trie (Set.Set t) -> Trie (Set.Set t)
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union = combine unionCombine id id
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unionCombine (Ok vs) (Ok ws) = Ok (Set.union vs ws)
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unionCombine r1 r2 | null r1 = r2
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unionCombine r1 r2 | null r2 = r1
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unions rs = foldr union empty rs
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intersection = combine intersectionCombine (const empty) (const empty)
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intersectionCombine (Ok vs) (Ok ws) = Ok (Set.union vs ws)
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intersectionCombine r1 r2 | null r1 = empty
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intersectionCombine r1 r2 | null r2 = empty
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difference = combine differenceCombine (const empty) id
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differenceCombine (Ok vs) (Ok ws) = let xs = Set.difference vs ws in
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if Set.null xs then empty else (Ok xs)
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differenceCombine r1 r2 | null r1 = empty
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differenceCombine r1 r2 | null r2 = r1
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---------------------------------------------------------------------------
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ok vs = Ok (Set.fromList vs)
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seqs _ r | null r = r
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seqs [] r = r
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seqs ('<' : n : s) r = Br (Map.singleton (read (n : []) :: Integer) (seqs s r), Mt, Map.empty)
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seqs ('*' : s) r = Br (Map.empty, seqs s r, Map.empty)
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seqs (x : s) r = Br (Map.empty, Mt, Map.singleton x (seqs s r))
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simpleTestCases = test [
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"seqs simple" ~:
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Br (Map.singleton 0 (ok [1]), Mt, Map.empty) ~=? seqs "<0" (ok [1]),
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"union simple1" ~:
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Br (Map.empty, Mt,
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Map.fromList [('a', ok [1]),
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('b', ok [2])]) ~=?
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union (seqs "a" (ok [1])) (seqs "b" (ok [2])),
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"union simple2" ~:
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Br (Map.empty, Mt,
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Map.fromList [('a', ok [1,2]),
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('b', ok [2])]) ~=?
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unions [seqs "a" (ok [1]),
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seqs "b" (ok [2]),
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seqs "a" (ok [2])],
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"union idem" ~:
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(seqs "abc" (ok [1])) ~=?
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union (seqs "abc" (ok [1])) (seqs "abc" (ok [1])),
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"union wild" ~:
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Br (Map.singleton 1 (Br (Map.empty,
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ok [1],
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Map.singleton 'a' (ok [1,2]))),
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ok [1],
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Map.empty) ~=?
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union (seqs "*" (ok [1])) (seqs "<1a" (ok [2])),
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"route union wild1" ~: Set.fromList [1,2] ~=?
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route "<1a" (union
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(seqs "*" (ok [1]))
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(seqs "<1a" (ok [2]))) Set.empty,
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"route union wild2" ~: Set.fromList [1] ~=?
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route "<1b" (union
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(seqs "*" (ok [1]))
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(seqs "<1a" (ok [2]))) Set.empty,
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"route union wild3" ~: Set.fromList [1] ~=?
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route "<0" (union
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(seqs "*" (ok [1]))
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(seqs "<1a" (ok [2]))) Set.empty,
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"route union wild4" ~: Set.fromList [1] ~=?
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route "<2aa" (union
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(seqs "*" (ok [1]))
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(seqs "<1a" (ok [2]))) Set.empty,
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"intersection simple1" ~:
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seqs "a" (ok [1,2]) ~=? intersection (seqs "a" (ok [1])) (seqs "a" (ok [2])),
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"intersection simple2" ~:
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empty ~=? intersection (seqs "a" (ok [1])) (seqs "b" (ok [2])),
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"intersection idem" ~:
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(seqs "abc" (ok [1])) ~=?
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intersection (seqs "abc" (ok [1])) (seqs "abc" (ok [1])),
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"difference simple1" ~:
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seqs "a" (ok [1]) ~=? difference (seqs "a" (ok [1,2])) (seqs "a" (ok [2])),
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"difference simple1a" ~:
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seqs "ab" (ok [1]) ~=? difference (seqs "ab" (ok [1,2])) (seqs "ab" (ok [2])),
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"difference simple2" ~:
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empty ~=? difference (seqs "a" (ok [1])) (seqs "a" (ok [1])),
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"difference wild" ~:
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Br (Map.empty,
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ok [1],
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Map.fromList [('a', Mt)]) ~=?
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difference (seqs "*" (ok [1])) (seqs "a" (ok [1])),
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"difference wild 2" ~:
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Br (Map.singleton 1 (Br (Map.empty,
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ok [1],
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Map.singleton 'a' Mt)),
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ok [1],
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Map.empty) ~=?
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difference (seqs "*" (ok [1])) (seqs "<1a" (ok [1])),
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"difference wild 3" ~:
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Br (Map.singleton 0 Mt,
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ok [1],
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Map.empty) ~=?
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difference (seqs "*" (ok [1])) (seqs "<0" (ok [1])),
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"union after difference" ~:
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seqs "*" (ok [1]) ~=?
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union (difference (seqs "*" (ok [1])) (seqs "a" (ok [1]))) (seqs "a" (ok [1])),
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"union after difference 2" ~:
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Br (Map.empty,
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ok [1],
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Map.fromList [('a', ok [2])]) ~=?
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union (difference (seqs "*" (ok [1])) (seqs "a" (ok [1]))) (seqs "a" (ok [2])),
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"intersection no overlap opens" ~:
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empty ~=?
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intersection (seqs "<2aa" (ok [1])) (seqs "<1b" (ok [2])),
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"intersection no overlap opens 2" ~:
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Br (Map.empty, Mt, Map.singleton 'x' (ok [1,2])) ~=?
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(intersection
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(union (seqs "x" (ok [1])) (seqs "<2aa" (ok [1])))
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(union (seqs "x" (ok [2])) (seqs "<1b" (ok [2])))),
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"intersection no overlap opens 3" ~:
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Br (Map.fromList [(1,Br (Map.empty,
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ok [3,4],
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Map.fromList [('b', ok [2,3,4])])),
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(2,Br (Map.empty,
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Br (Map.empty, ok [3,4], Map.empty),
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Map.fromList [('a',Br (Map.empty,
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ok [3,4],
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Map.fromList [('a',
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ok [1,3,4])]))]))],
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ok [3,4],
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Map.empty) ~=?
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(intersection
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(union (seqs "*" (ok [3])) (seqs "<2aa" (ok [1])))
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(union (seqs "*" (ok [4])) (seqs "<1b" (ok [2]))))
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]
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---------------------------------------------------------------------------
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newtype Pattern = Pattern { getPattern :: String } deriving (Eq, Ord, Show)
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newtype Message = Message { getMessage :: String } deriving (Eq, Ord, Show)
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instance Arbitrary Pattern where
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arbitrary = liftM Pattern $ sized $ trieNoLargerThan
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where leaf = oneof $ [return "x",
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return "y",
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return "z",
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return "*"]
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trieNoLargerThan leafLimit =
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if leafLimit >= 1
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then frequency [(2, leaf), (3, node leafLimit)]
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else leaf
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node leafLimit =
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do degree <- choose (0, min 4 leafLimit)
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kids <- genChildren leafLimit degree
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return $ "<" ++ show degree ++ concat kids
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genChildren leafLimit 0 = return []
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genChildren leafLimit degree =
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do childLimit <- choose (1, leafLimit - (degree - 1))
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child <- trieNoLargerThan childLimit
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rest <- genChildren (leafLimit - childLimit) (degree - 1)
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return (child : rest)
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instance Arbitrary Message where
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arbitrary = do Pattern p <- arbitrary
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m <- sequence $ [if c == '*'
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then do Message m <- scale (`div` 2) arbitrary
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return m
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else return (c : [])
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| c <- p]
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return $ Message $ concat m
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instance Arbitrary (Set.Set Integer) where
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arbitrary = resize 5 $ sized set
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where set 0 = return Set.empty
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set n = do v <- arbitrary `suchThat` (\v -> v >= 0)
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s <- set (n - 1)
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return $ Set.insert v s
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genTrie k 0 = return Mt
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genTrie k n = do Pattern p <- arbitrary
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rest <- genTrie k (n - 1)
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return $ union (seqs p k) rest
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type TrieOfPids = Trie (Set.Set Integer)
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instance Arbitrary TrieOfPids where
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-- arbitrary = do vs <- arbitrary
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-- resize 6 $ sized $ genTrie (Ok vs)
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arbitrary = resize 6 $ sized $ genTrie (ok [1])
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isWild (Br (os, w, h)) = Map.null os && Map.null h
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isWild _ = False
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trieContains t (Message m) = not $ Set.null $ route m t Set.empty
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combineBasics :: (TrieOfPids -> TrieOfPids -> TrieOfPids) ->
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(Bool -> Bool -> Bool) ->
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(TrieOfPids, TrieOfPids, Message) ->
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Property
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combineBasics tf bf (trie1, trie2, element) =
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not (isWild trie1) && not (isWild trie2) && (p || q1 || q2) ==> p == q
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where p = combined `trieContains` element
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q1 = trie1 `trieContains` element
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q2 = trie2 `trieContains` element
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q = bf q1 q2
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combined = tf trie1 trie2
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unionBasics = combineBasics union (||)
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intersectionBasics = combineBasics intersection (&&)
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differenceBasics = combineBasics difference (\ x y -> x && not y)
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qCheck name t = do putStrLn name
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quickCheckWith stdArgs { maxSuccess = 500 } t
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main = do runTestTT simpleTestCases
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qCheck "differenceBasics" differenceBasics
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qCheck "intersectionBasics" intersectionBasics
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qCheck "unionBasics" unionBasics
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