Add support for column separators in arrays (jgm#127).

- Add [ColumnSeparator] to EArray.
- Readers.MathML can generate any of {CSNone, CSDashed, CSSolid}, which should round-trip through Writers.MathML
- {Readers,Writers}.TeX only support {CSNone, CSSolid}
- Readers.OMML currently generates CSNone, and Writers.OMML doesn't emit ColumnSeparator information

src/Text/TeXMath/Readers/MathML.hs

@@ -478,7 +478,8 @@ table e = do
   let (onlyAligns, exprs) = (map .map) fst &&& (map . map) snd $ rs
   let rs' = map (pad (maximum (map length rs))) exprs
   let aligns = map findAlign (transpose onlyAligns)
-  return $ EArray aligns rs'
+  colseps <- maybe (replicate (length aligns-1) CSNone) (map toColSep . T.splitOn " ") <$> findAttrQ "columnlines" e
+  return $ EArray aligns rs' colseps
   where
     findAlign xs = if null xs then AlignCenter
                     else foldl1 combine xs
@@ -602,6 +603,12 @@ toAlignment "center" = AlignCenter
 toAlignment "right" = AlignRight
 toAlignment _ = AlignCenter
 
+toColSep :: T.Text -> ColumnSeparator
+toColSep "none" = CSNone
+toColSep "dashed" = CSDashed
+toColSep "solid" = CSSolid
+toColSep _ = CSNone
+
 getPosition :: FormType -> TeXSymbolType
 getPosition (FPrefix) = Open
 getPosition (FPostfix) = Close

src/Text/TeXMath/Readers/OMML.hs

@@ -296,7 +296,7 @@ elemToExps' element | isElem "m" "eqArr" element =
   let expLst = mapMaybe elemToBases (elChildren element)
       expLst' = map (\es -> [map filterAmpersand es]) expLst
   in
-   return [EArray [] expLst']
+   return [EArray [] expLst' []]
 elemToExps' element | isElem "m" "f" element = do
   num <- filterChildName (hasElemName "m" "num") element
   den <- filterChildName (hasElemName "m" "den") element
@@ -365,7 +365,7 @@ elemToExps' element | isElem "m" "m" element =
                         (elChildren mr))
                 rows
   in
-   return [EArray [AlignCenter] rowExps]
+   return [EArray [AlignCenter] rowExps []]
 elemToExps' element | isElem "m" "nary" element = do
   let naryPr = filterChildName (hasElemName "m" "naryPr") element
       naryChr = naryPr >>=

src/Text/TeXMath/Readers/TeX.hs

@@ -25,7 +25,7 @@ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 module Text.TeXMath.Readers.TeX (readTeX)
 where
 
-import Data.List (intercalate, intersperse, find)
+import Data.List (intercalate, intersperse, find, elemIndices)
 import Data.Ratio ((%))
 import Control.Monad
 import Data.Char (isDigit, isAscii, isLetter)
@@ -250,7 +250,7 @@ genfrac _ = mzero
 substack :: Text -> TP Exp
 substack "\\substack" = do
   formulas <- braces $ ignorable >> (manyExp expr) `sepEndBy` endLine
-  return $ EArray [AlignCenter] $ map (\x -> [[x]]) formulas
+  return $ EArray [AlignCenter] (map (\x -> [[x]]) formulas) []
 substack _ = mzero
 
 asGroup :: [Exp] -> Exp
@@ -372,14 +372,16 @@ arrayLine = notFollowedBy (ctrlseq "end" >> return '\n') >>
                      optional (try (ctrlseq "hline" >> ignorable'))
   -- we don't represent the line, but it shouldn't crash parsing
 
-arrayAlignments :: TP [Alignment]
+arrayAlignments :: TP ([Alignment], [ColumnSeparator])
 arrayAlignments = try $ do
   as <- braces (many (letter <|> char '|'))
   let letterToAlignment 'l' = AlignLeft
       letterToAlignment 'c' = AlignCenter
       letterToAlignment 'r' = AlignRight
       letterToAlignment _   = AlignCenter
-  return $ map letterToAlignment $ filter (/= '|') as
+  let generate n f = map f [0..n-1]
+  let findColSeps = let seperatorPositions = elemIndices '|' as in generate (length as) (\i -> if i `elem` seperatorPositions then CSSolid else CSNone)
+  return $ (map letterToAlignment $ filter (/= '|') as, findColSeps)
 
 environment :: Text -> TP Exp
 environment "\\begin" = do
@@ -421,29 +423,31 @@ environments = M.fromList
   , ("equation", equation)
   ]
 
-alignsFromRows :: Alignment -> [ArrayLine] -> [Alignment]
-alignsFromRows _ [] = []
-alignsFromRows defaultAlignment (r:_) = replicate (length r) defaultAlignment
+alignsFromRows :: Alignment -> ColumnSeparator -> [ArrayLine] -> ([Alignment], [ColumnSeparator])
+alignsFromRows _ _ [] = ([], [])
+alignsFromRows defaultAlignment defaultColSep (r:_) = let n = length r in (replicate n defaultAlignment, replicate (n-1) defaultColSep)
 
 matrixWith :: Text -> Text -> TP Exp
 matrixWith opendelim closedelim = do
   lines' <- sepEndBy1 arrayLine endLineAMS
-  let aligns = alignsFromRows AlignCenter lines'
+  let (aligns, colseps) = alignsFromRows AlignCenter CSNone lines'
   return $ if T.null opendelim && T.null closedelim
-              then EArray aligns lines'
+              then EArray aligns lines' colseps
               else EDelimited opendelim closedelim
-                       [Right $ EArray aligns lines']
+                       [Right $ EArray aligns lines' colseps]
 
 stdarray :: TP Exp
 stdarray = do
-  aligns <- arrayAlignments
+  (aligns, colseps) <- arrayAlignments
+  --aligns <- arrayAlignments
   lines' <- sepEndBy1 arrayLine endLine
-  return $ EArray aligns lines'
+  return $ EArray aligns lines' colseps
 
 gather :: TP Exp
 gather = do
   rows <- sepEndBy arrayLine endLineAMS
-  return $ EArray (alignsFromRows AlignCenter rows) rows
+  let (aligns, colseps) = (alignsFromRows AlignCenter CSNone rows)
+  return $ EArray aligns rows colseps
 
 equation :: TP Exp
 equation = do
@@ -454,24 +458,25 @@ eqnarray :: TP Exp
 eqnarray = do
   rows <- sepEndBy1 arrayLine endLine
   let n = maximum $ map length rows
-  return $ EArray (take n $ cycle [AlignRight, AlignCenter, AlignLeft]) rows
+  return $ EArray (take n $ cycle [AlignRight, AlignCenter, AlignLeft]) rows (replicate (n-1) CSNone)
 
 align :: TP Exp
 align = do
   rows <- sepEndBy1 arrayLine endLineAMS
   let n = maximum $ map length rows
-  return $ EArray (take n $ cycle [AlignRight, AlignLeft]) rows
+  return $ EArray (take n $ cycle [AlignRight, AlignLeft]) rows (replicate (n-1) CSNone)
 
 flalign :: TP Exp
 flalign = do
   rows <- sepEndBy1 arrayLine endLineAMS
   let n = maximum $ map length rows
-  return $ EArray (take n $ cycle [AlignLeft, AlignRight]) rows
+  return $ EArray (take n $ cycle [AlignLeft, AlignRight]) rows (replicate (n-1) CSNone)
 
 cases :: TP Exp
 cases = do
   rs <- sepEndBy1 arrayLine endLineAMS
-  return $ EDelimited "{" "" [Right $ EArray (alignsFromRows AlignLeft rs) rs]
+  let (aligns, colseps) = (alignsFromRows AlignLeft CSNone rs)
+  return $ EDelimited "{" "" [Right $ EArray aligns rs colseps]
 
 variable :: TP Exp
 variable = do

src/Text/TeXMath/Types.hs

@@ -22,7 +22,7 @@ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 
 module Text.TeXMath.Types (Exp(..), TeXSymbolType(..), ArrayLine,
                            FractionType(..), TextType(..),
-                           Alignment(..), DisplayType(..),
+                           Alignment(..), ColumnSeparator(..), DisplayType(..),
                            Operator(..), FormType(..), Record(..),
                            Property, Position(..), Env, defaultEnv,
                            InEDelimited)
@@ -38,6 +38,9 @@ data TeXSymbolType = Ord | Op | Bin | Rel | Open | Close | Pun | Accent
 data Alignment = AlignLeft | AlignCenter | AlignRight
                  deriving (Show, Read, Eq, Ord, Data, Typeable)
 
+data ColumnSeparator = CSNone | CSDashed | CSSolid
+                 deriving (Show, Read, Eq, Ord, Data, Typeable)
+
 data FractionType = NormalFrac   -- ^ Displayed or textual, acc to 'DisplayType'
                   | DisplayFrac  -- ^ Force display mode
                   | InlineFrac   -- ^ Force inline mode (textual)
@@ -85,10 +88,11 @@ data Exp =
   | ESqrt Exp      -- ^ A square root.
   | EScaled Rational Exp -- ^ An expression that is scaled to some factor
                   -- of its normal size.
-  | EArray [Alignment] [ArrayLine] -- ^ An array or matrix.  The first argument
+  | EArray [Alignment] [ArrayLine] [ColumnSeparator] -- ^ An array or matrix.  The first argument
                   -- specifies the alignments of the columns; the second gives
-                  -- the contents of the lines.  All of these lists should be
-                  -- the same length.
+                  -- the contents of the lines; the third gives the type of separator between
+                  -- columns. The first two of these lists should be the same length, the last
+                  -- be one element shorter.
   | EText TextType T.Text  -- ^ Some normal text, possibly styled.
   | EStyled TextType [Exp] -- ^  A group of styled expressions.
   deriving (Show, Read, Eq, Ord, Data, Typeable)

src/Text/TeXMath/Writers/Eqn.hs

@@ -192,7 +192,7 @@ writeExp (EStyled ttype es) =
        TextBold   -> "bold " <> contents
        TextBoldItalic -> "bold italic " <> contents
        _   -> contents
-writeExp (EArray aligns rows) =
+writeExp (EArray aligns rows _) = -- TODO: does \matrix support column separators?
   "matrix{\n" <> T.concat cols <> "}"
   where cols = zipWith tocol aligns (transpose rows)
         tocol al cs =

src/Text/TeXMath/Writers/MathML.hs

@@ -113,14 +113,19 @@ makeText a s = case (leadingSp, trailingSp) of
           _           -> False
         attr = getMMLType a
 
-makeArray :: TextType -> [Alignment] -> [ArrayLine] -> Element
-makeArray tt as ls = unode "mtable" $
+makeArray :: TextType -> [Alignment] -> [ArrayLine] -> [ColumnSeparator] -> Element
+makeArray tt as ls cs = setColumnLines $ unode "mtable" $
   map (unode "mtr" .
     zipWith (\a -> setAlignment a .  unode "mtd". map (showExp tt)) as') ls
    where setAlignment AlignLeft    = withAttribute "columnalign" "left"
          setAlignment AlignRight   = withAttribute "columnalign" "right"
          setAlignment AlignCenter  = withAttribute "columnalign" "center"
+         setColumnLines            = withAttribute "columnlines" . T.intercalate " " $ map colSepToString cs'
+         colSepToString CSNone     = "none"
+         colSepToString CSDashed   = "dashed"
+         colSepToString CSSolid    = "solid"
          as'                       = as ++ cycle [AlignCenter]
+         cs'                       = cs ++ cycle [CSNone]
 
 -- Kept as String for Text.XML.Light
 withAttribute :: String -> T.Text -> Element -> Element
@@ -176,7 +181,7 @@ showExp tt e =
    ESqrt x          -> unode "msqrt" $ showExp tt x
    ERoot i x        -> unode "mroot" [showExp tt x, showExp tt i]
    EScaled s x      -> makeScaled s $ showExp tt x
-   EArray as ls     -> makeArray tt as ls
+   EArray as ls cs  -> makeArray tt as ls cs
    EText a s        -> makeText a s
    EStyled a es     -> makeStyled a $ map (showExp a) es
 

src/Text/TeXMath/Writers/OMML.hs

@@ -79,8 +79,8 @@ maximum' :: [Int] -> Int
 maximum' [] = 0
 maximum' xs = maximum xs
 
-makeArray :: [Element] -> [Alignment] -> [ArrayLine] -> Element
-makeArray props as rs = mnode "m" $ mProps : map toMr rs
+makeArray :: [Element] -> [Alignment] -> [ArrayLine] -> [ColumnSeparator] -> Element
+makeArray props as rs _ = mnode "m" $ mProps : map toMr rs
   where mProps = mnode "mPr"
                   [ mnodeA "baseJc" "center" ()
                   , mnodeA "plcHide" "1" ()
@@ -269,7 +269,7 @@ showExp props e =
                                           , mnode "e" $ showExp props x]]
    EBoxed   x       -> [mnode "borderBox" [ mnode "e" $ showExp props x]]
    EScaled _ x      -> showExp props x -- no support for scaler?
-   EArray as ls     -> [makeArray props as ls]
+   EArray as ls cs  -> [makeArray props as ls cs]
    EText a s        -> [makeText a s]
    EStyled a es     -> concatMap (showExp (setProps a)) es
 

src/Text/TeXMath/Writers/Pandoc.hs

@@ -155,4 +155,4 @@ expToInlines tt (EOver convertible b e)
 expToInlines _ (EUnderover _ _ _ _) = Nothing
 expToInlines _ (EPhantom _) = Nothing
 expToInlines _ (EBoxed _) = Nothing
-expToInlines _ (EArray _ _) = Nothing
+expToInlines _ (EArray _ _ _) = Nothing

src/Text/TeXMath/Writers/TeX.hs

@@ -115,25 +115,25 @@ writeExp (EDelimited "\x27E8" "\x27E9" [Right (EFraction NoLineFrac x y)]) = do
   writeBinom "\\bangle" x y
 writeExp (EDelimited open close [Right (EFraction NoLineFrac x y)]) = do
   writeExp (EDelimited open close [Right (EArray [AlignCenter]
-                   [[[x]],[[y]]])])
-writeExp (EDelimited open close [Right (EArray aligns rows)]) = do
+                   [[[x]],[[y]]] [])])
+writeExp (EDelimited open close [Right (EArray aligns rows colseps)]) = do
   env <- asks mathEnv
   case ("amsmath" `elem` env, open, close) of
        (True, "{", "") | aligns == [AlignLeft, AlignLeft] ->
-         table "cases" [] rows
+         table "cases" [] rows colseps
        (True, "(", ")") | all (== AlignCenter) aligns ->
-         table "pmatrix" [] rows
+         table "pmatrix" [] rows colseps
        (True, "[", "]") | all (== AlignCenter) aligns ->
-         table "bmatrix" [] rows
+         table "bmatrix" [] rows colseps
        (True, "{", "}") | all (== AlignCenter) aligns ->
-         table "Bmatrix" [] rows
+         table "Bmatrix" [] rows colseps
        (True, "\x2223", "\x2223") | all (== AlignCenter) aligns ->
-         table "vmatrix" [] rows
+         table "vmatrix" [] rows colseps
        (True, "\x2225", "\x2225") | all (== AlignCenter) aligns ->
-         table "Vmatrix" [] rows
+         table "Vmatrix" [] rows colseps
        _ -> do
          writeDelim DLeft open
-         writeExp (EArray aligns rows)
+         writeExp (EArray aligns rows colseps)
          writeDelim DRight close
 writeExp (EDelimited open close es) =  do
   writeDelim DLeft open
@@ -247,30 +247,33 @@ writeExp (EStyled ttype es) = do
   txtcmd <- (flip S.getLaTeXTextCommand ttype) <$> asks mathEnv
   tell [ControlSeq txtcmd]
   tellGroup (mapM_ writeExp $ everywhere (mkT (fromUnicode ttype)) es)
-writeExp (EArray [AlignRight, AlignLeft] rows) = do
+writeExp (EArray [AlignRight, AlignLeft] rows colseps) = do
   env <- asks mathEnv
   if "amsmath" `elem` env
-     then table "aligned" [] rows
-     else table "array" [AlignRight, AlignLeft] rows
-writeExp (EArray aligns rows) = do
+     then table "aligned" [] rows colseps
+     else table "array" [AlignRight, AlignLeft] rows colseps
+writeExp (EArray aligns rows colseps) = do
   env <- asks mathEnv
   if "amsmath" `elem` env && all (== AlignCenter) aligns
-     then table "matrix" [] rows
-     else table "array" aligns rows
+     then table "matrix" [] rows colseps
+     else table "array" aligns rows colseps
 
-table :: T.Text -> [Alignment] -> [ArrayLine] -> Math ()
-table name aligns rows = do
+table :: T.Text -> [Alignment] -> [ArrayLine] -> [ColumnSeparator] -> Math ()
+table name aligns rows colseps = do
   tell [ControlSeq "\\begin", Grouped [Literal name]]
   unless (null aligns) $
      tell [Grouped [Literal columnAligns]]
   tell [Token '\n']
   mapM_ row rows
   tell [ControlSeq "\\end", Grouped [Literal name]]
   where
-    columnAligns = T.pack $ map alignmentToLetter aligns
+    columnAligns = T.pack . concat $ zipWith (\a c -> alignmentToLetter a:colsepToString c) aligns (colseps ++ [CSNone])
     alignmentToLetter AlignLeft = 'l'
     alignmentToLetter AlignCenter = 'c'
     alignmentToLetter AlignRight = 'r'
+    colsepToString CSNone = ""
+    colsepToString CSDashed = "|" -- Lossy, CSDashed can only come from MathML input
+    colsepToString CSSolid = "|"
 
 row :: ArrayLine -> Math ()
 row []     = tell [Space, Literal "\\\\", Token '\n']
@@ -330,7 +333,7 @@ writeScript pos convertible b e1 = do
 
 -- Replace an array with a substack if appropriate.
 checkSubstack :: Exp -> Math ()
-checkSubstack e@(EArray [AlignCenter] rows) = do
+checkSubstack e@(EArray [AlignCenter] rows _) = do
   env <- asks mathEnv
   if "amsmath" `elem` env
      then do