Further work

1 files changed, 73 insertions, 0 deletions

diff --git a/edit-lens/src/Control/Edit/String/Affected.lhs b/edit-lens/src/Control/Edit/String/Affected.lhs
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+++ b/edit-lens/src/Control/Edit/String/Affected.lhs
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+\begin{comment}
+\begin{code}
+module Control.Edit.String.Affected
+  ( affected
+  ) where
+
+import Control.Lens
+import Control.Lens.TH
+
+import Control.Edit
+import Control.Edit.String
+
+import Numeric.Natural
+import Numeric.Interval (Interval, (...))
+import qualified Numeric.Interval as Int
+
+import Data.Sequence (Seq((:<|), (:|>)))
+import qualified Data.Sequence as Seq
+
+import Data.Map.Lazy (Map)
+import qualified Data.Map.Lazy as Map
+
+import Data.Monoid
+
+import Control.Monad
+
+import Data.Maybe (fromMaybe, maybeToList, listToMaybe, catMaybes, isNothing, isJust, mapMaybe)
+\end{code}
+\end{comment}
+
+Um eine obere Schranke an das von einer Serie von edits betroffene Intervall zu bestimmen ordnen wir zunächst jeder von mindestens einem atomaren edit betroffenen Position $n$ im Eingabe-Wort einen $\text{offset}_n = \text{\# deletions} - \text{\# inserts}$ zu.
+Das gesuchte Intervall ist nun $(\text{minK}, \text{maxK})$, mit $\text{minK}$ der Position im Eingabe-Wort mit niedrigstem $\text{offset}$ und $\text{maxK}$ die Position im Eingabe-Wort mit höchstem $\text{offset}$, $\text{maxK}^\prime$, modifiziert um das Maximum aus $\{ 0 \} \cup \{ \text{maxK}_n \colon n \in \{ 0 \ldots \text{maxK}^\prime \} \}$ wobei $\text{maxK}_n = -1 \cdot (n + \text{offset}_n)$ an Position $n$ ist.
+
+\begin{code}
+affected :: forall char. StringEdits Natural char -> Maybe (Interval Natural)
+-- ^ For a given set of edits @es@ return the interval @i = a ... b@ such that for any given string @str@ of sufficient length the following holds:
+--
+--   - For all @n :: Natural@: @n < a ==> str ! n == (str `apply` es) ! n@
+--   - There exists a @k :: Integer@ such that for all @n :: Integer@: @n > b ==> str ! (n + k) == (str `apply` es) ! n@
+--
+-- Intuitively: for any character @c@ of the new string @str `apply` es@ there exists a corresponding character in @str@ (offset by either 0 or a constant shift @k@) if the index of @c@ is /not/ contained in @affected es@.
+\end{code}
+\begin{comment}
+\begin{code}
+affected SEFail = Nothing
+affected (StringEdits es) = Just . toInterval $ go es Map.empty
+  where
+    toInterval :: Map Natural Integer -> Interval Natural
+    toInterval map
+      | Just (((minK, _), _), ((maxK, _), _)) <- (,) <$> Map.minViewWithKey map <*> Map.maxViewWithKey map
+      = let
+          maxV' = maximum . (0 :) $ do
+            offset <- [0..maxK]
+            v <- maybeToList $ Map.lookup (maxK - offset) map
+            v' <- maybeToList . fmap fromInteger $ negate v <$ guard (v <= 0)
+            guard $ v' >= succ offset
+            return $ v' - offset
+        in (minK Int.... maxK + maxV')
+      | otherwise
+      = Int.empty
+    go :: Seq (StringEdit Natural char) -> Map Natural Integer -> Map Natural Integer
+    go Seq.Empty offsets = offsets
+    go (es :> e) offsets = go es offsets'
+      where
+        p = e ^. sePos
+        -- p' = fromIntegral $ Map.foldrWithKey (\k o p -> bool (fromIntegral p) (o + p) $ k < fromIntegral p) (fromIntegral p) offsets
+        offsets' = Map.alter (Just . myOffset . fromMaybe 0) p offsets
+        myOffset :: Integer -> Integer
+        myOffset
+          | Insert _ _ <- e = pred
+          | Delete _   <- e = succ
+\end{code}
+\end{comment}