├── Examples ├── align.gr ├── chess.gr ├── cross.gr ├── diam.gr ├── digits.gr ├── nether.gr ├── noq.gr ├── prelude.gr ├── square.gr ├── whole-chess.gr └── word.gr ├── Expression.hs ├── LICENSE ├── Matcher.hs ├── Parser.hs ├── PrattParser.hs ├── README.md ├── grime.hs ├── rungrime └── tutorial.md /Examples/align.gr: -------------------------------------------------------------------------------- 1 | | Align two #-characters horizontally or vertically. 2 | \#.*\#|\#/./*/\# -------------------------------------------------------------------------------- /Examples/chess.gr: -------------------------------------------------------------------------------- 1 | | Match a chessboard of _# of size at least 3x3 2 | (\#\#|\#/\#|\_\_|\_/\_)#!&[#_]{3-} -------------------------------------------------------------------------------- /Examples/cross.gr: -------------------------------------------------------------------------------- 1 | | Match a "cross" of #-chars. 2 | E=\.+/+ 3 | F=\#+/+ 4 | EFE/F/EFE&E/F/E F E/F/E -------------------------------------------------------------------------------- /Examples/diam.gr: -------------------------------------------------------------------------------- 1 | | Match a diamond shape, like this: 2 | | X 3 | | / \ 4 | |X X 5 | | \ / 6 | | X 7 | C=./+ 8 | T=\X|CTC/\/.+\\ 9 | B=\X|\\.+\//CBC 10 | CTC/\X.+\X/CBC -------------------------------------------------------------------------------- /Examples/digits.gr: -------------------------------------------------------------------------------- 1 | | Match a 2x2 or larger rectangle of digits. 2 | d{2-} -------------------------------------------------------------------------------- /Examples/nether.gr: -------------------------------------------------------------------------------- 1 | | Match a rectangular "nether portal". 2 | .\X+./\X/+\.{2-22,3-22}\X/+/.\X+. -------------------------------------------------------------------------------- /Examples/noq.gr: -------------------------------------------------------------------------------- 1 | | Match a 4x4 rectangle without q or Q. 2 | [,qQ]{4} -------------------------------------------------------------------------------- /Examples/prelude.gr: -------------------------------------------------------------------------------- 1 | | Verify Prelude syntax: every column has at most one ( or ), 2 | | and they are balanced if their y-coords are ignored. 3 | A=[,()]/* 4 | P=A*|P(A/\(/A)P(A/\)/A)P 5 | e`P 6 | -------------------------------------------------------------------------------- /Examples/square.gr: -------------------------------------------------------------------------------- 1 | | Verify that input is a square. 2 | S=.|S./+/.+ 3 | e`S 4 | -------------------------------------------------------------------------------- /Examples/whole-chess.gr: -------------------------------------------------------------------------------- 1 | | Verify that input is a chessboard of #_. 2 | e`(\#\#|\#/\#|\_\_|\_/\_)#!&[#_]+/+ 3 | -------------------------------------------------------------------------------- /Examples/word.gr: -------------------------------------------------------------------------------- 1 | | Find the word GOLF in any orientation. 2 | G=\G 3 | O=\O 4 | L=\L 5 | F=\F 6 | GOLF|FLOG|G/O/L/F|F/L/O/G|G.../.O../..L./...F|...G/..O./.L../F...|F.../.L../..O./...G|...F/..L./.O../G... -------------------------------------------------------------------------------- /Expression.hs: -------------------------------------------------------------------------------- 1 | module Expression where 2 | 3 | import Data.Set (Set, toAscList) 4 | import Data.Map (Map) 5 | import Data.Monoid (Monoid(..), (<>)) 6 | 7 | -- The label of a variable 8 | type Label = Maybe Char 9 | 10 | -- Context anchor label; begins from 0 11 | type AnchorLabel = Int 12 | 13 | type Coord = (Int, Int) -- x, y 14 | type Size = (Int, Int) -- w, h 15 | type Rect = (Int, Int, Int, Int) -- x, y, w, h 16 | type Range = (Int, Maybe Int) 17 | 18 | -- Dihedral group D4 of orientations 19 | -- Rot n is rotation by n*90 degrees 20 | -- RefRot n is Rot n, then reflection by vertical line 21 | data D4 = Rot Int | RefRot Int 22 | deriving (Eq, Ord) 23 | 24 | instance Show D4 where 25 | show (Rot 0) = "" 26 | show (Rot n) = "o" ++ show n 27 | show (RefRot n) = "o" ++ show (n + 4) 28 | 29 | axisPreserving :: D4 -> Bool 30 | axisPreserving (Rot 0) = True 31 | axisPreserving (Rot 2) = True 32 | axisPreserving (RefRot 0) = True 33 | axisPreserving (RefRot 2) = True 34 | axisPreserving _ = False 35 | 36 | instance Monoid D4 where 37 | mempty = Rot 0 38 | mappend (Rot m) (Rot n) = Rot $ (m + n) `mod` 4 39 | mappend (RefRot m) (Rot n) = RefRot $ (m + n) `mod` 4 40 | mappend (Rot m) (RefRot n) = RefRot $ (n - m) `mod` 4 41 | mappend (RefRot m) (RefRot n) = Rot $ (n - m) `mod` 4 42 | 43 | -- An expression that may or may not match a rectangle of characters 44 | data Expr = Border -- Matches the rectangle border symbol 45 | | Edge -- Matches an edge segment 46 | | AnyRect -- Mathces any rectangle 47 | | AnyChar -- Matches any single character (not border) 48 | | SomeChar Bool 49 | (Set (Maybe Char)) -- Matches if flag XOR char in set; Nothing matches border 50 | | Var D4 Label -- Matches the given oriented variable 51 | | Expr :> Expr -- Horizontal concatenation 52 | | Expr :^ Expr -- Vertical concatenation 53 | | Expr :| Expr -- Disjunction 54 | | Expr :& Expr -- Conjunction 55 | | Expr :~ Expr -- Exclusive OR 56 | | Not Expr -- Negation 57 | | Sized Range Range Expr -- Size range 58 | | Grid Range Range Expr -- Grid of repetitions 59 | | Count Range Expr -- Count number of matches 60 | | InContext Expr -- Context brackets 61 | | Anchor AnchorLabel -- Context anchor 62 | | Fixed Expr -- Fixed orientation 63 | deriving (Eq) 64 | 65 | instance Show Expr where 66 | show Border = "b" 67 | show Edge = "e" 68 | show AnyRect = "$" 69 | show AnyChar = "." 70 | show (SomeChar isPos charSet) = 71 | if isPos 72 | then "[p:" ++ concatMap (maybe "\\b" $ \c -> if c == '\\' then "\\\\" else [c]) (toAscList charSet) ++ "]" 73 | else "[n:" ++ concatMap (maybe "\\b" $ \c -> if c == '\\' then "\\\\" else [c]) (toAscList charSet) ++ "]" 74 | show (Var rot Nothing) = "_" ++ show rot 75 | show (Var rot (Just a)) = [a] ++ show rot 76 | show (e1 :> e2) = show e1 ++ show e2 77 | show (e1 :^ e2) = "(" ++ show e1 ++ "/" ++ show e2 ++ ")" 78 | show (e1 :| e2) = "(" ++ show e1 ++ "|" ++ show e2 ++ ")" 79 | show (e1 :& e2) = "(" ++ show e1 ++ "&" ++ show e2 ++ ")" 80 | show (e1 :~ e2) = "(" ++ show e1 ++ "~" ++ show e2 ++ ")" 81 | show (Not e) = "(" ++ show e ++ ")!" 82 | show (Sized (x1,x2) (y1,y2) e) = 83 | "(" ++ show e ++ "){" ++ show x1 ++ "-" ++ sx2 ++ "," ++ show y1 ++ "-" ++ sy2 ++ "}" 84 | where sx2 = case x2 of Nothing -> ""; Just x -> show x 85 | sy2 = case y2 of Nothing -> ""; Just y -> show y 86 | show (Grid (x1,x2) (y1,y2) e) = 87 | "(" ++ show e ++ "):" ++ show x1 ++ "-" ++ sx2 ++ "," ++ show y1 ++ "-" ++ sy2 ++ "}" 88 | where sx2 = case x2 of Nothing -> ""; Just x -> show x 89 | sy2 = case y2 of Nothing -> ""; Just y -> show y 90 | show (Count (low, high) e) = 91 | "(" ++ show e ++ ")#" ++ show low ++ "-" ++ showHigh ++ "}" 92 | where showHigh = case high of Nothing -> ""; Just n -> show n 93 | show (InContext e) = "<" ++ show e ++ ">" 94 | show (Anchor n) = show n 95 | show (Fixed e) = "(" ++ show e ++ ")oF" 96 | 97 | -- Rotate and/or reflect an expression 98 | orient :: Expr -> D4 -> Expr 99 | orient Border _ = Border 100 | orient Edge _ = Edge 101 | orient AnyRect _ = AnyRect 102 | orient AnyChar _ = AnyChar 103 | orient e@(SomeChar _ _) _ = e 104 | orient (Var rot1 label) rot2 = Var (rot2 <> rot1) label 105 | orient e@(e1 :> e2) rot = case rot of 106 | Rot 0 -> e 107 | Rot 1 -> orient e2 rot :^ orient e1 rot 108 | Rot 2 -> orient e2 rot :> orient e1 rot 109 | Rot 3 -> orient e1 rot :^ orient e2 rot 110 | RefRot 0 -> orient e2 rot :> orient e1 rot 111 | RefRot 1 -> orient e2 rot :^ orient e1 rot 112 | RefRot 2 -> orient e1 rot :> orient e2 rot 113 | RefRot 3 -> orient e1 rot :^ orient e2 rot 114 | orient e@(e1 :^ e2) rot = case rot of 115 | Rot 0 -> e 116 | Rot 1 -> orient e1 rot :> orient e2 rot 117 | Rot 2 -> orient e2 rot :^ orient e1 rot 118 | Rot 3 -> orient e2 rot :> orient e1 rot 119 | RefRot 0 -> orient e1 rot :^ orient e2 rot 120 | RefRot 1 -> orient e2 rot :> orient e1 rot 121 | RefRot 2 -> orient e2 rot :^ orient e1 rot 122 | RefRot 3 -> orient e1 rot :> orient e2 rot 123 | orient (e1 :| e2) rot = orient e1 rot :| orient e2 rot 124 | orient (e1 :& e2) rot = orient e1 rot :& orient e2 rot 125 | orient (e1 :~ e2) rot = orient e1 rot :~ orient e2 rot 126 | orient (Not e) rot = Not $ orient e rot 127 | orient (Sized (x1,x2) (y1,y2) e) rot = 128 | if axisPreserving rot 129 | then Sized (x1,x2) (y1,y2) $ orient e rot 130 | else Sized (y1,y2) (x1,x2) $ orient e rot 131 | orient (Grid (x1,x2) (y1,y2) e) rot = 132 | if axisPreserving rot 133 | then Grid (x1,x2) (y1,y2) $ orient e rot 134 | else Grid (y1,y2) (x1,x2) $ orient e rot 135 | orient (Count range e) rot = Count range $ orient e rot 136 | orient (InContext e) rot = InContext $ orient e rot 137 | orient e@(Anchor _) _ = e 138 | orient e@(Fixed _) _ = e 139 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2015 Ilkka Törmä 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | 23 | -------------------------------------------------------------------------------- /Matcher.hs: -------------------------------------------------------------------------------- 1 | module Matcher where 2 | 3 | import Expression 4 | import Prelude hiding (lookup) 5 | import Data.Map.Strict (Map, empty, lookup, insert) 6 | import qualified Data.Map.Strict as Map (filter, size) 7 | import Data.Set (member) 8 | import Data.Monoid (Any(Any), getAny, mempty) 9 | import Data.Maybe (isNothing) 10 | import qualified Data.List.Ordered as Asc (member, isect, union, unionAll, nub) 11 | import Control.Applicative ((<$>), liftA2) 12 | import Control.Monad.Trans.Class (lift) 13 | import Control.Monad.Writer.Lazy (WriterT, tell, listens, runWriterT) 14 | import Control.Monad.Reader (ReaderT, asks, reader, local, runReaderT) 15 | import Control.Monad.State.Lazy (State, gets, modify, evalState) 16 | 17 | -- A fuzzy match 18 | data Match = NoMatch 19 | | Unknown 20 | | Match 21 | deriving (Eq,Ord,Show) 22 | 23 | invert :: Match -> Match 24 | invert Match = NoMatch 25 | invert NoMatch = Match 26 | invert Unknown = Unknown 27 | 28 | -- Short-circuiting monadic utility functions for fuzzy matches 29 | (&?) :: (Monad m) => m Match -> m Match -> m Match 30 | f &? g = do 31 | a <- f 32 | case a of 33 | NoMatch -> return NoMatch 34 | _ -> do 35 | b <- g 36 | return $ case (a,b) of 37 | (_, NoMatch) -> NoMatch 38 | (Match, Match) -> Match 39 | _ -> Unknown 40 | 41 | (|?) :: (Monad m) => m Match -> m Match -> m Match 42 | f |? g = do 43 | a <- f 44 | case a of 45 | Match -> return Match 46 | _ -> do 47 | b <- g 48 | return $ case (a,b) of 49 | (_, Match) -> Match 50 | (NoMatch, NoMatch) -> NoMatch 51 | _ -> Unknown 52 | 53 | anyMatch :: (Monad m) => [a] -> (a -> m Match) -> m Match 54 | anyMatch xs f = foldr (|?) (return NoMatch) $ f <$> xs 55 | 56 | allMatch :: (Monad m) => [a] -> (a -> m Match) -> m Match 57 | allMatch xs f = foldr (&?) (return Match) $ f <$> xs 58 | 59 | -- Keep those that match, signal if any was unknown 60 | filterMatch :: (Monad m) => [a] -> (a -> m Match) -> m ([a], Bool) 61 | filterMatch [] _ = return ([], False) 62 | filterMatch (x : xs) p = do 63 | res <- p x 64 | (found, unk) <- filterMatch xs p 65 | return $ case res of 66 | Match -> (x:found, unk) 67 | Unknown -> (found, True) 68 | NoMatch -> (found, unk) 69 | 70 | -- Sum of two strictly ordered lists 71 | ascSum :: [Int] -> [Int] -> [Int] 72 | ascSum xs = go 73 | where go (y:ys) = Asc.nub . Asc.union [y + x | x <- xs] $ go ys 74 | go [] = [] 75 | 76 | -- A memoization of matches 77 | type Classification = Map (Rect, D4, Label) Match 78 | 79 | -- A changing context for matching in a matrix 80 | data Context = Context {size :: Size, 81 | matrix :: Map Coord Char, 82 | clauses :: Map Label Expr, 83 | hasBorders :: Bool, 84 | anchors :: [Rect], 85 | depth :: Int} 86 | deriving (Show) 87 | 88 | -- A monad for performing matching in a matrix 89 | -- The String is for logging, and the Any for keeping track of new definite matches or non-matches 90 | type Matcher a = WriterT (String, Any) (ReaderT Context (State Classification)) a 91 | 92 | -- Modify context anchors, increase logging depth 93 | withAnchors :: ([Rect] -> [Rect]) -> Matcher a -> Matcher a 94 | withAnchors f = local $ \con -> con{anchors = f $ anchors con, depth = depth con + 1} 95 | 96 | -- Helper function for logging 97 | logMsg :: String -> Matcher () 98 | logMsg message = do 99 | level <- asks depth 100 | tell (replicate level ' ' ++ message, mempty) 101 | 102 | -- Possible widths and heights of matching rectangles 103 | -- May give false positives, but never false negatives 104 | sizes :: Expr -> Matcher ([Int], [Int]) 105 | sizes expr = do 106 | numVars <- asks $ Map.size . clauses 107 | go numVars expr 108 | where 109 | go :: Int -> Expr -> Matcher ([Int], [Int]) 110 | go _ Border = return ([1], [1]) 111 | go _ Edge = do 112 | (maxX, maxY) <- asks size 113 | return ([0..maxX+2], [0..maxY+2]) 114 | go _ AnyRect = do 115 | (maxX, maxY) <- asks size 116 | return ([0..maxX+2], [0..maxY+2]) 117 | go _ AnyChar = return ([1], [1]) 118 | go _ (SomeChar _ _) = return ([1], [1]) 119 | go 0 (Var _ _) = do 120 | (maxX, maxY) <- asks size 121 | return ([0..maxX+2], [0..maxY+2]) 122 | go n (Var rot label) = do 123 | Just expr <- asks $ lookup label . clauses 124 | go (n-1) $ orient expr rot 125 | go n (e1 :> e2) = do 126 | (ws1, hs1) <- go n e1 127 | (ws2, hs2) <- go n e2 128 | return (ascSum ws1 ws2, Asc.isect hs1 hs2) 129 | go n (e1 :^ e2) = do 130 | (ws1, hs1) <- go n e1 131 | (ws2, hs2) <- go n e2 132 | return (Asc.isect ws1 ws2, ascSum hs1 hs2) 133 | go n (e1 :| e2) = do 134 | (ws1, hs1) <- go n e1 135 | (ws2, hs2) <- go n e2 136 | return (Asc.nub $ Asc.union ws1 ws2, Asc.nub $ Asc.union hs1 hs2) 137 | go n (e1 :& e2) = do 138 | (ws1, hs1) <- go n e1 139 | (ws2, hs2) <- go n e2 140 | return (Asc.isect ws1 ws2, Asc.isect hs1 hs2) 141 | go n (e1 :~ e2) = do 142 | (ws1, hs1) <- go n e1 143 | (ws2, hs2) <- go n e2 144 | return (Asc.nub $ Asc.union ws1 ws2, Asc.nub $ Asc.union hs1 hs2) 145 | go _ (Not _) = do 146 | (maxX, maxY) <- asks size 147 | return ([0..maxX+2], [0..maxY+2]) 148 | go n (Sized (x1,x2) (y1,y2) e) = do 149 | (maxX, maxY) <- asks size 150 | (ws, hs) <- case e of 151 | Border -> return ([0..maxX+2], [0..maxY+2]) 152 | AnyChar -> return ([0..maxX+2], [0..maxY+2]) 153 | SomeChar _ _ -> return ([0..maxX+2], [0..maxY+2]) 154 | _ -> go n e 155 | let wRange = case x2 of Just high -> [x1..high] 156 | Nothing -> [x1..] 157 | hRange = case y2 of Just high -> [y1..high] 158 | Nothing -> [y1..] 159 | return (Asc.isect ws wRange, Asc.isect hs hRange) 160 | go _ (Grid (x1,x2) (y1,y2) e) = do 161 | (maxX, maxY) <- asks size 162 | return ([0..maxX+2], [0..maxY+2]) -- TODO: implement 163 | go _ (Count (low, high) e) = do 164 | (maxX, maxY) <- asks size 165 | return ([0..maxX+2], [0..maxY+2]) 166 | go _ (InContext e) = do 167 | (maxX, maxY) <- asks size 168 | return ([0..maxX+2], [0..maxY+2]) 169 | go _ (Anchor n) = do 170 | anchors <- asks anchors 171 | (maxX, maxY) <- asks size 172 | return $ if length anchors > n 173 | then let (_, _, w, h) = anchors !! n in ([w], [h]) 174 | else ([0..maxX+2], [0..maxY+2]) 175 | go n (Fixed e) = go n e 176 | 177 | -- Does the pattern match? Update all sub-rectangles as needed 178 | matches :: Expr -> Rect -> Matcher Match 179 | 180 | matches Border (x, y, 1, 1) = do 181 | ch <- lift $ asks $ lookup (x, y) . matrix 182 | return $ case ch of 183 | Nothing -> Match 184 | Just _ -> NoMatch 185 | matches Border _ = return NoMatch 186 | 187 | matches Edge (x, y, w, h) = do 188 | (maxX, maxY) <- asks size 189 | return $ if (x == 0 || x == maxX) && w == 0 && y >= 0 && y+h <= maxY || 190 | (y == 0 || y == maxY) && h == 0 && x >= 0 && x+w <= maxX 191 | then Match 192 | else NoMatch 193 | 194 | matches AnyRect _ = return Match 195 | 196 | matches AnyChar (x, y, 1, 1) = do 197 | ch <- lift $ asks $ lookup (x, y) . matrix 198 | return $ case ch of 199 | Nothing -> NoMatch 200 | Just _ -> Match 201 | matches AnyChar _ = return NoMatch 202 | 203 | matches (SomeChar isPos cs) (x, y, 1, 1) = do 204 | ch <- lift $ asks $ lookup (x, y) . matrix 205 | return $ if (ch `member` cs) == isPos then Match else NoMatch 206 | matches (SomeChar _ _) _ = return NoMatch 207 | 208 | matches (Var rot label) rect = do 209 | memoed <- gets $ lookup (rect, rot, label) 210 | case memoed of 211 | Just b -> do 212 | logMsg $ "Lookup " ++ show rot ++ show label ++ " at " ++ show rect ++ ": " ++ show b ++ "\n" 213 | return b 214 | Nothing -> do 215 | modify $ insert (rect, rot, label) Unknown 216 | logMsg $ "Checking " ++ show rot ++ show label ++ " at " ++ show rect ++ "\n" 217 | Just expr <- lift $ asks $ lookup label . clauses 218 | match <- withAnchors (const []) $ matches (orient expr rot) rect 219 | logMsg $ "Checked " ++ show rot ++ show label ++ " at " ++ show rect ++ ": " ++ show match ++ "\n" 220 | tell (mempty, Any $ match /= Unknown) 221 | modify $ insert (rect, rot, label) match 222 | return match 223 | 224 | matches (lExp :> rExp) (x, y, w, h) = do 225 | (wsl, hsl) <- sizes lExp 226 | (wsr, hsr) <- sizes rExp 227 | let cuts = Asc.isect wsl . reverse . map (w -) $ takeWhile (<= w) wsr 228 | if h `Asc.member` Asc.isect hsl hsr 229 | then anyMatch cuts $ \i -> matches lExp (x, y, i, h) &? matches rExp (x+i, y, w-i, h) 230 | else return NoMatch 231 | 232 | matches (tExp :^ bExp) (x, y, w, h) = do 233 | (wsl, hsl) <- sizes tExp 234 | (wsr, hsr) <- sizes bExp 235 | let cuts = Asc.isect hsl . reverse . map (h -) $ takeWhile (<= h) hsr 236 | if w `Asc.member` Asc.isect wsl wsr 237 | then anyMatch cuts $ \j -> matches tExp (x, y, w, j) &? matches bExp (x, y+j, w, h-j) 238 | else return NoMatch 239 | 240 | matches (exp1 :| exp2) rect = matches exp1 rect |? matches exp2 rect 241 | 242 | matches (exp1 :& exp2) rect = matches exp1 rect &? matches exp2 rect 243 | 244 | matches (exp1 :~ exp2) rect = do 245 | first <- matches exp1 rect 246 | second <- matches exp2 rect 247 | return $ case (first, second) of 248 | (Unknown, _) -> Unknown 249 | (_, Unknown) -> Unknown 250 | _ -> if first /= second then Match else NoMatch 251 | 252 | matches (Not expr) rect = invert <$> matches expr rect 253 | 254 | matches (Sized (x1, x2) (y1, y2) expr) r@(x, y, w, h) = do 255 | let xOk = x1 <= w && case x2 of Nothing -> True; Just x3 -> w <= x3 256 | yOk = y1 <= h && case y2 of Nothing -> True; Just y3 -> h <= y3 257 | return (if xOk && yOk then Match else NoMatch) &? case expr of 258 | Border -> allCells 259 | AnyChar -> allCells 260 | SomeChar _ _ -> allCells 261 | _ -> matches expr r 262 | where allCells = allMatch [(x+i, y+j, 1, 1) | i <- [0..w-1], j <- [0..h-1]] $ 263 | matches expr 264 | 265 | matches (Grid (0, _) _ _) (_, _, 0, _) = return Match 266 | matches (Grid _ (0, _) _) (_, _, _, 0) = return Match 267 | matches (Grid xr@(x1, x2) yr@(y1, y2) expr) r@(x, y, w, h) = do 268 | (ws, hs) <- sizes expr 269 | goWith ws hs 270 | where goWith widths heights = go False False 0 0 [x] [y] 271 | where 272 | -- Arguments: 273 | -- a) Have we placed double vertical lines 274 | -- b) Have we placed double horizontal lines 275 | -- c) How many vertical lines have we placed 276 | -- d) How many horizontal lines have we placed 277 | -- e) List of vertical cell borders (reversed) 278 | -- f) List of horizontal cell borders (reversed) 279 | go :: Bool -> Bool -> Int -> Int -> [Int] -> [Int] -> Matcher Match 280 | go vOverlap hOverlap numV numH vs@(ver:vers) hs@(hor:hors) 281 | -- More than allowed vertical lines 282 | | Just n <- x2, numV > n = return NoMatch 283 | -- More than allowed horizontal lines 284 | | Just n <- y2, numH > n = return NoMatch 285 | -- Reached lower right corner 286 | | ver == x + w, hor == y + h, vOverlap || x1 <= numV, hOverlap || y1 <= numH = return Match 287 | -- Incomplete grid => extend 288 | | otherwise = do 289 | let vMin = case () of 290 | -- About to reach upper bound on vertical lines => go to end 291 | _ | x2 == Just (numV + 1) -> x+w 292 | -- No upper bound or already seen overlap => advance at least one cell 293 | | isNothing x2 || vOverlap -> ver + 1 294 | -- Otherwise may stay in place 295 | | otherwise -> ver 296 | -- Options for new vertical line 297 | vCuts = map (ver +) widths `Asc.isect` [vMin .. x+w] 298 | hMin = case () of 299 | _ | y2 == Just (numH + 1) -> y+h 300 | | isNothing y2 || hOverlap -> hor + 1 301 | | otherwise -> hor 302 | hCuts = map (hor +) heights `Asc.isect` [hMin .. y+h] 303 | -- Only consider vertical lines that produce matches on the right margin 304 | (vMargin, unkV) <- filterMatch vCuts $ \newVer -> 305 | allMatch [(ver, h1, newVer-ver, h2-h1) | (h1, h2) <- zip (tail hs) hs] $ matches expr 306 | -- Same for bottom margin 307 | (hMargin, unkH) <- filterMatch hCuts $ \newHor -> 308 | allMatch [(v1, hor, v2-v1, newHor-hor) | (v1, v2) <- zip (tail vs) vs] $ matches expr 309 | -- Same for corner rectangle 310 | (pairs, unkP) <- filterMatch [(newV, newH) | numV == numH, newV <- vMargin, newH <- hMargin] $ \(newV, newH) -> 311 | matches expr (ver, hor, newV-ver, newH-hor) 312 | -- Recurse for all possible choices of new lines 313 | found <- anyMatch ([(numV, numH+1, vs, newHor:hs) | numV <= numH, ver == x+w, newHor <- hMargin] ++ 314 | [(numV+1, numH, newVer:vs, hs) | numV >= numH, hor == y+h, newVer <- vMargin] ++ 315 | [(numV+1, numH+1, newVer:vs, newHor:hs) | (newVer, newHor) <- pairs]) $ \(newNumV, newNumH, newVers, newHors) -> 316 | go (vOverlap || overlap newVers) (hOverlap || overlap newHors) newNumV newNumH newVers newHors 317 | return $ if unkV || unkH || unkP then max Unknown found else found 318 | overlap (a:b:c) = a == b 319 | overlap _ = False 320 | 321 | matches (Count (low, high) expr) (x, y, w, h) = do 322 | (ws, hs) <- sizes expr 323 | let allRects = [(x', y', w', h') | 324 | w' <- Asc.isect ws [0..w], h' <- Asc.isect hs [0..h], 325 | x' <- [x..x+w-w'], y' <- [y..y+h-h']] 326 | total = length allRects 327 | go 0 0 total allRects 328 | where go :: Int -> Int -> Int -> [Rect] -> Matcher Match 329 | go found unk left _ | found >= low, Nothing <- high = return Match 330 | | found >= low, Just n <- high, n >= found + left + unk = return Match 331 | | found + unk + left < low = return NoMatch 332 | | found + left < low = return Unknown 333 | | Just n <- high, found > n = return NoMatch 334 | go found unk left [] = error "Unreachable state." 335 | go found unk left (r:rs) = do 336 | matchR <- matches expr r 337 | case matchR of 338 | Match -> go (found+1) unk (left-1) rs 339 | NoMatch -> go found unk (left-1) rs 340 | Unknown -> go found (unk+1) (left-1) rs 341 | 342 | matches (InContext expr) r@(x, y, w, h) = do 343 | (ws, hs) <- sizes expr 344 | (maxX', maxY') <- asks size 345 | addBorders <- asks hasBorders 346 | let (minX, maxX, minY, maxY) = if addBorders 347 | then (-1, maxX'+1, -1, maxY'+1) 348 | else ( 0, maxX', 0, maxY') 349 | surrounding = [(x', y', w', h') | 350 | w' <- Asc.isect ws [w .. maxX - minX], 351 | h' <- Asc.isect hs [h .. maxY - minY], 352 | x' <- [max minX $ x + w - w' .. min x $ maxX - w'], 353 | y' <- [max minY $ y + h - h' .. min y $ maxY - h']] 354 | withAnchors (r:) $ anyMatch surrounding $ matches expr 355 | 356 | matches (Anchor n) r = do 357 | anchs <- asks anchors 358 | return $ if anchs !! n == r then Match else NoMatch 359 | 360 | matches (Fixed e) r = matches e r 361 | 362 | -- Collect definite matches of Nothing for the given rectangles, possibly looping until no uncertainty remains. 363 | -- Also collect logs for debugging. 364 | matchAllEmpty :: Size -> Bool -> Map Coord Char -> Map Label Expr -> [Rect] -> ([Rect], String) 365 | matchAllEmpty size hasBorders matrix clauses rects = 366 | flip evalState empty . 367 | flip runReaderT context . 368 | fmap (\(a,(b,_)) -> (a,b)) . 369 | runWriterT $ 370 | go rects 371 | where context = Context {size = size, matrix = matrix, hasBorders = hasBorders, clauses = clauses, anchors = [], depth = 0} 372 | selfAndMatch rect = (,) rect <$> matches (Var (Rot 0) Nothing) rect 373 | go :: [Rect] -> Matcher [Rect] 374 | go currRects = do 375 | logMsg "Matching...\n" 376 | modify $ Map.filter (/= Unknown) 377 | (currMatches, changed) <- listens (getAny . snd) $ mapM selfAndMatch currRects 378 | logMsg $ "Matching complete, change = " ++ show changed ++ "\n" 379 | if and [match /= Unknown | (_, match) <- currMatches] || not changed 380 | then return $ [rect | (rect, Match) <- currMatches] 381 | else do 382 | remainingMatches <- go [rect | (rect, Unknown) <- currMatches] 383 | return $ [rect | (rect, Match) <- currMatches] ++ remainingMatches 384 | -------------------------------------------------------------------------------- /Parser.hs: -------------------------------------------------------------------------------- 1 | module Parser (Option(..), parseGrFile, parseMatFile, parseOptions) where 2 | 3 | import Expression 4 | import PrattParser 5 | import Data.Maybe (catMaybes) 6 | import Data.List ((\\), sort, nub) 7 | import Data.Set (fromAscList) 8 | import Data.Map.Strict (Map, empty, insert, fromList) 9 | import Control.Applicative((<$>), (<*), pure) 10 | import Text.Parsec (Parsec, ParseError, parse, runParser, try, (), (<|>), between, many, manyTill, many1, 11 | choice, optionMaybe, sepEndBy, notFollowedBy, lookAhead, eof, getState, putState) 12 | import Text.Parsec.Char (char, oneOf, noneOf, anyChar, string, upper, digit) 13 | 14 | -- Command-line and grammar options 15 | data Option = Entire 16 | | Number 17 | | AllMatches 18 | | Positions 19 | | Patterns 20 | | AddBorder 21 | | Debug0 22 | | Debug1 23 | deriving (Show, Eq) 24 | 25 | -- Parse a string of options 26 | options :: Parsec String () [Option] 27 | options = concat <$> many (choice option) "option string" 28 | where option = [char 'e' >> return [Entire], 29 | char 'n' >> return [Number], 30 | char 'a' >> return [AllMatches], 31 | char 'p' >> return [Positions], 32 | char 's' >> return [Patterns], 33 | char 'b' >> return [AddBorder], 34 | try $ string "d1" >> return [Debug0, Debug1], 35 | char 'd' >> optionMaybe (char '0') >> return [Debug0]] 36 | 37 | -- Parse an end of line 38 | endOfLine :: Parsec String s String 39 | endOfLine = try (string "\r\n") <|> (pure <$> oneOf "\n\r") "end of line" 40 | 41 | -- Parse a string with quotes, return a string without them 42 | quoted :: Parsec String Bool String 43 | quoted = concat <$> many (quote <|> escQuote <|> slash <|> escSlash <|> escBackslash <|> newLine <|> maybeEscaped) 44 | where quote = do 45 | char '"' 46 | inQuote <- getState 47 | putState $ not inQuote 48 | return "\"" 49 | escQuote = try $ string "\\\"" 50 | slash = char '/' >> return "/" 51 | escSlash = try $ string "\\/" 52 | escBackslash = try $ string "\\\\" 53 | newLine = do 54 | eol <- endOfLine 55 | inQuote <- getState 56 | putState False 57 | return $ if inQuote then "\"" ++ eol else eol 58 | maybeEscaped = do 59 | inQuote <- getState 60 | maybeEscape <- optionMaybe $ char '\\' 61 | symbol <- anyChar 62 | case (inQuote, maybeEscape) of 63 | (False, Just _) -> return $ '\\' : [symbol] 64 | (False, Nothing) -> return [symbol] 65 | (True, Just _) -> return [symbol] 66 | (True, Nothing) -> return $ '\\' : [symbol] 67 | 68 | -- Skip this token, or be at the end of a line 69 | skipOrEnd :: Parsec String () a -> Parsec String () () 70 | skipOrEnd p = (p >> return ()) <|> (lookAhead endOfLine >> return ()) <|> eof 71 | 72 | -- Special expressions 73 | flat :: Expr 74 | flat = Sized (0, Nothing) (0, Just 0) AnyRect 75 | thin :: Expr 76 | thin = Sized (0, Just 0) (0, Nothing) AnyRect 77 | 78 | -- Make a finite character class from string 79 | mkSomeChar :: Bool -> [Maybe Char] -> Expr 80 | mkSomeChar isPos = SomeChar isPos . fromAscList . sort 81 | 82 | -- Shorthand for nonterminal in standard orientation 83 | stdVar :: Label -> Expr 84 | stdVar = Var (Rot 0) 85 | 86 | -- Single-character expressions 87 | reservedChars :: [(Char, Expr)] 88 | reservedChars = [('$', AnyRect), 89 | ('.', AnyChar), 90 | ('f', flat), 91 | ('t', thin), 92 | ('_', stdVar Nothing), 93 | ('b', Border), 94 | ('e', Edge), 95 | ('d', mkSomeChar True $ map Just ['0'..'9']), 96 | ('u', mkSomeChar True $ map Just ['A'..'Z']), 97 | ('l', mkSomeChar True $ map Just ['a'..'z']), 98 | ('a', mkSomeChar True $ map Just $ ['A'..'Z'] ++ ['a'..'z']), 99 | ('n', mkSomeChar True $ map Just $ ['0'..'9'] ++ ['A'..'Z'] ++ ['a'..'z']), 100 | ('s', mkSomeChar True $ map Just $ ['!'..'/'] ++ [':'..'@'] ++ ['['..'`'] ++ ['{'..'~'])] 101 | 102 | -- Parse an escaped literal 103 | escapedLit :: Parsec String () Expr 104 | escapedLit = do 105 | char '\\' 106 | c <- anyChar 107 | return $ mkSomeChar True $ [Just c] 108 | 109 | -- Parse a nonterminal 110 | nonterm :: Parsec String () Expr 111 | nonterm = do 112 | label <- upper 113 | return $ stdVar $ Just label 114 | 115 | -- Parse a reserved character 116 | reserved :: Parsec String () Expr 117 | reserved = do 118 | char <- oneOf $ fst <$> reservedChars 119 | let Just expr = lookup char reservedChars 120 | return expr 121 | 122 | -- Parse a character class 123 | charClass :: Parsec String () Expr 124 | charClass = char '[' `between` (skipOrEnd $ char ']') $ do 125 | include <- many $ try classRange <|> try border <|> pure <$> Just <$> classChar 126 | maybeExclude <- optionMaybe $ char ',' >> (many $ try classRange <|> try border <|> pure <$> Just <$> classChar) 127 | return $ case (null include, maybeExclude) of 128 | (True, Nothing) -> mkSomeChar False [] 129 | (False, Nothing) -> mkSomeChar True $ concat include 130 | (True, Just exclude) -> mkSomeChar False $ concat exclude 131 | (False, Just exclude) -> mkSomeChar True $ concat include \\ concat exclude 132 | where needsEscape = "[]-,\\" 133 | classChar = noneOf (needsEscape ++ "\n\r") <|> (char '\\' >> oneOf needsEscape) 134 | border = string "\\b" >> return [Nothing] 135 | classRange = do 136 | a <- classChar 137 | char '-' 138 | b <- classChar 139 | return $ map Just [a..b] 140 | 141 | -- Parse a numeric range with default minimum 142 | numRange :: Int -> Parsec String () Range 143 | numRange m = do 144 | lower <- many digit 145 | maybeDash <- optionMaybe $ char '-' 146 | upper <- many digit 147 | let lowerNum = if null lower then m else read lower 148 | upperNum = if null upper then Nothing else Just $ read upper 149 | return $ case maybeDash of 150 | Nothing -> (lowerNum, if null lower then Nothing else Just lowerNum) 151 | Just _ -> (lowerNum, upperNum) 152 | 153 | -- Parse two numeric ranges with default minima 154 | numRange2D :: Int -> Parsec String () (Range, Range) 155 | numRange2D m = do 156 | xRange <- numRange 0 157 | maybeYRange <- optionMaybe $ char ',' >> numRange 0 158 | return $ case maybeYRange of 159 | Nothing -> (xRange, xRange) 160 | Just yRange -> (xRange, yRange) 161 | 162 | -- Parse a size constraint 163 | sizeConstr :: Parsec String () (Expr -> Expr) 164 | sizeConstr = do 165 | char '{' 166 | (xRange, yRange) <- numRange2D 0 167 | optionMaybe $ char '}' 168 | return $ Sized xRange yRange 169 | 170 | -- Encoding of orientations 171 | charToD4 :: Char -> [D4] 172 | charToD4 '0' = [Rot 0] 173 | charToD4 '1' = [Rot 1] 174 | charToD4 '2' = [Rot 2] 175 | charToD4 '3' = [Rot 3] 176 | charToD4 '4' = [RefRot 0] 177 | charToD4 '5' = [RefRot 1] 178 | charToD4 '6' = [RefRot 2] 179 | charToD4 '7' = [RefRot 3] 180 | charToD4 'O' = [Rot 0, Rot 1, Rot 2, Rot 3, RefRot 0, RefRot 1, RefRot 2, RefRot 3] 181 | charToD4 'X' = [Rot 0, Rot 1, Rot 2, Rot 3] 182 | charToD4 'N' = [Rot 0, Rot 2] 183 | charToD4 'T' = [Rot 0, RefRot 0] 184 | charToD4 'K' = [Rot 0, RefRot 2] 185 | charToD4 'H' = [Rot 0, RefRot 0, RefRot 2, Rot 2] 186 | charToD4 'A' = [Rot 0, RefRot 1] 187 | charToD4 'D' = [Rot 0, RefRot 3] 188 | charToD4 'C' = [Rot 0, RefRot 1, RefRot 3, Rot 2] 189 | charToD4 'F' = [] 190 | 191 | -- Parse a set of orientations 192 | orientationSet :: Parsec String () (Expr -> Expr) 193 | orientationSet = do 194 | char 'o' 195 | choices <- many1 $ oneOf "01234567OXNTKHADCF" 196 | optionMaybe $ char '}' 197 | let transformations = \expr -> 198 | [Fixed expr | 'F' `elem` choices] ++ nub [orient expr rot | ch <- choices, rot <- charToD4 ch] 199 | return $ foldr1 (:|) . transformations 200 | 201 | -- Parse a postfix grid specification 202 | gridSpec :: Parsec String () (Expr -> Expr) 203 | gridSpec = do 204 | char ':' 205 | (xRange, yRange) <- numRange2D 1 206 | optionMaybe $ char '}' 207 | return $ Grid xRange yRange 208 | 209 | -- Parse a counting specification 210 | countSpec :: Parsec String () (Expr -> Expr) 211 | countSpec = do 212 | char '#' 213 | range <- numRange 1 214 | optionMaybe $ char '}' 215 | return $ Count range 216 | 217 | -- Parse a context anchor 218 | anchor :: Parsec String () Expr 219 | anchor = do 220 | label <- oneOf ['0'..'9'] 221 | return $ Anchor $ read [label] 222 | 223 | -- Parse an expression 224 | expression :: Parsec String () Expr 225 | expression = mkPrattParser opTable term "expression" 226 | where term = parenthesized <|> quoted <|> inContext <|> anchor <|> nonterm <|> reserved <|> escapedLit <|> charClass "term" 227 | parenthesized = char '(' `between` (skipOrEnd $ char ')') $ expression 228 | quoted = char '"' `between` char '"' $ expression 229 | inContext = char '<' `between` (skipOrEnd $ char '>') $ InContext <$> expression 230 | basicInfixes = [lookAhead term >> return (:>), 231 | char '/' >> lookAhead term >> return (:^)] ++ 232 | map addPostfix 233 | [char ' ' >> return (:>), 234 | char '&' >> return (:&), 235 | char '-' >> return (\e1 e2 -> e1 :& Not e2), 236 | char '|' >> return (:|), 237 | char '~' >> return (:~)] 238 | opTable = [[Postfix $ try $ char '^' >> postfix]] ++ 239 | map (return . InfixR . try . (char '^' >>)) basicInfixes ++ 240 | [[Postfix $ try $ postfix]] ++ 241 | map (return . InfixR . try) basicInfixes ++ 242 | [[Postfix $ try $ char 'v' >> postfix]] ++ 243 | map (return . InfixR . try . (char 'v' >>)) basicInfixes 244 | postfixes = [sizeConstr, 245 | orientationSet, 246 | gridSpec, 247 | countSpec, 248 | char '\'' >> return Fixed, 249 | char '?' >> return (thin :|), 250 | try (string "/?") >> return (flat :|), 251 | char '+' >> return (Grid (1, Nothing) (1, Just 1)), 252 | try (string "/+") >> return (Grid (1, Just 1) (1, Nothing)), 253 | char '*' >> return (Grid (0, Nothing) (1, Just 1)), 254 | try (string "/*") >> return (Grid (1, Just 1) (0, Nothing)), 255 | char '!' >> return Not] 256 | postfix = do 257 | operations <- many1 $ choice postfixes 258 | return $ foldr1 (flip (.)) operations 259 | addPostfix :: Parsec String () (Expr -> Expr -> Expr) -> Parsec String () (Expr -> Expr -> Expr) 260 | addPostfix parseOp = do 261 | op <- parseOp 262 | pfix <- optionMaybe postfix 263 | return $ case pfix of 264 | Just p -> \e1 e2 -> p $ op e1 e2 265 | Nothing -> op 266 | 267 | -- Parse a line of a grammar file into options, label, and expression 268 | contentLine :: Parsec String () ([Option], (Label, Expr)) 269 | contentLine = do 270 | opts <- try (options <* char '`') <|> return [] 271 | label <- optionMaybe $ try (upper <* char '=') 272 | expr <- expression 273 | return (opts, (label, expr)) 274 | 275 | -- Parse a comment 276 | commentLine :: Parsec String () () 277 | commentLine = do 278 | char '|' 279 | many $ noneOf "\n\r" 280 | return () 281 | 282 | -- Parse either a content line or a comment 283 | grammarLine :: Parsec String () (Maybe ([Option], (Label, Expr))) 284 | grammarLine = try (commentLine >> return Nothing) <|> (Just <$> contentLine) 285 | 286 | -- File parser 287 | parseGrFile :: String -> String -> Either ParseError ([Option], Map Label Expr) 288 | parseGrFile filename grammar = foldToMap <$> contents 289 | where contents :: Either ParseError [([Option], (Label, Expr))] 290 | contents = do 291 | unquoted <- runParser quoted False filename grammar 292 | catMaybes <$> parse (grammarLine `sepEndBy` endOfLine <* eof) ("pre-processed " ++ filename) unquoted 293 | foldToMap triples = (firsts, folded) 294 | where firsts = concat $ fst <$> triples 295 | folded = foldr (\(label, expr) assoc -> insert label expr assoc) empty $ snd <$> triples 296 | 297 | -- Parse a matrix from newline-delimited string 298 | parseMatFile :: String -> (Size, Map Coord Char) 299 | parseMatFile s = ((w, h), fromList pairs) 300 | where rows = lines s 301 | pairs = [((x, y), c) | (y, row) <- zip [0..] rows, (x, c) <- zip [0..] row] 302 | w = maximum $ 0 : map length rows 303 | h = length rows 304 | 305 | -- Parse a chain of options form a string 306 | parseOptions :: String -> [Option] 307 | parseOptions str = case parse options "" str of 308 | Right result -> result 309 | Left _ -> [] 310 | -------------------------------------------------------------------------------- /PrattParser.hs: -------------------------------------------------------------------------------- 1 | -- Simplified Pratt parser for expressions, adapted from http://stackoverflow.com/a/33534426 2 | 3 | module PrattParser where 4 | 5 | import Text.Parsec (Parsec, choice, (<|>)) 6 | import Data.List (tails) 7 | import Control.Applicative (pure, (<*>)) 8 | 9 | data Operator t = Postfix (Parsec String () (t -> t)) 10 | | InfixL (Parsec String () (t -> t -> t)) -- Left associative 11 | | InfixR (Parsec String () (t -> t -> t)) -- Right associative 12 | 13 | -- Make a Pratt parser from a precedence table and a term parser 14 | -- Precedence table is given from highest to lowest precedence 15 | mkPrattParser :: [[Operator t]] -> Parsec String () t -> Parsec String () t 16 | mkPrattParser precTable parseTerm = parseExpr precs 17 | where precs = reverse precTable -- We go from lowest to highest precedence 18 | parseExpr operators = do 19 | term <- parseTerm 20 | parseOper operators term 21 | parseOper operators lhs = choice stepParsers <|> return lhs -- Choose an operator; if fails, return lhs 22 | where stepParsers = do 23 | newPrecs@(precLev : higherPrecs) <- tails operators -- Choose a precedence level and all higher levels 24 | operator <- precLev -- Choose an operator from the level 25 | stepParser <- case operator of -- Make a "next step" parser 26 | Postfix parseOp -> return $ parseOp <*> pure lhs -- For postfix, just grab that 27 | InfixL parseOp -> return $ parseOp <*> pure lhs <*> parseExpr higherPrecs -- For left infix, grab everything with higher precedence 28 | InfixR parseOp -> return $ parseOp <*> pure lhs <*> parseExpr newPrecs -- For right infix, grab everything with same or higher precedence 29 | return $ stepParser >>= parseOper operators -- Parse with "next step", then with all operators 30 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Grime 2 | 3 | ## Introduction 4 | 5 | Grime is a two-dimensional pattern matching language based on Boolean grammars. 6 | The basic idea is to construct rectangular patterns from smaller components, and check whether they are found in the input matrix. 7 | 8 | You can [try Grime online](http://grime.tryitonline.net/), courtesy of [Dennis from PPCG](http://codegolf.stackexchange.com/users/12012/dennis). 9 | Be sure to check the [tutorial](https://github.com/iatorm/grime/blob/master/tutorial.md) too. 10 | 11 | ## Usage 12 | 13 | A Grime program is called a _grammar_, and the correct file extension for a grammar is `.gr`, although this is not enforced. 14 | The program is called like 15 | 16 | runhaskell grime.hs [options] grammarfile matrixfile 17 | 18 | where `matrixfile` is a file containing the character matrix. 19 | For example, the digits program would be called like 20 | 21 | runhaskell grime.hs digits.gr digit-matrix 22 | 23 | If you want a speed boost, you should compile Grime with the command 24 | 25 | ghc -O2 grime.hs 26 | 27 | and then run the resulting executable: 28 | 29 | grime [options] grammarfile matrixfile 30 | 31 | There's also a bash script `rungrime` that compiles Grime if needed and then calls the executable with the provided arguments. 32 | 33 | By default, the interpreter prints the first match it finds, but this can be controlled using the option flags: 34 | 35 | - `-e`: match only the entire matrix, print `1` for match and `0` for no match. 36 | - `-n`: print the number of matches, or the entire matrix if `-e` is also given. 37 | - `-a`: print all matches. 38 | - `-p`: print also the positions of the matches, in the format `(x,y,w,h)`. 39 | - `-s`: do not print the matches themselves. 40 | - `-b`: include borders of width 1. 41 | - `-d` or `-d0`: print debug information. 42 | - `-d1`: print logs from the matcher. 43 | 44 | These can be inserted from the command line, or in the beginning of any line of a grammar file, separated from the rest of the line by a backtick `` ` ``. 45 | 46 | ## Syntax and Semantics 47 | 48 | A Grime grammar consists of one or more _definitions_, each on a separate line. 49 | Each of them defines the value of a _nonterminal_, and one of them must define the anonymous _toplevel nonterminal_. 50 | The syntax of a definition is either `N=E` or `E`, where `N` is an uppercase letter and `E` is an _expression_. 51 | 52 | Expressions are constructed as follows. 53 | 54 | - Any character escaped with `\` matches any `1x1` rectangle containing that character. 55 | - `.` matches any single character. 56 | - `b` matches a `1x1` rectangle outside the character matrix. It's only relevant if the `-b` option is used, or if the input is not rectangular. 57 | - `e` matches a 0-height or 0-width segment of the input's edge. 58 | - `$` always matches. 59 | - `f` matches any 0-height (flat) rectangle, and `t` matches any 0-width (thin) rectangle. 60 | - The pre-defined character groups are `d`igit, `u`ppercase, `l`owercase, `a`lphabetic, alpha`n`umeric, and `s`ymbol. 61 | - New character classes can be defined by the syntax `[a-prt-w,d-gu]`. The letters on the left are included, and those on the right are excluded, so this matches exactly the letters `abchijklmnoprtvw`. If the left side is empty, it is taken to contain all characters and the border. The comma can be omitted if the right side is empty. The characters `[],-\` must be escaped with `\`. `\b` matches a border. 62 | - An unescaped uppercase letter is a nonterminal, and matches the expression it is assigned. 63 | - `_` is the anonymous toplevel nonterminal. 64 | - If `P` and `Q` are expressions, then `PQ` is just their horizontal concatenation, and `P/Q` is their vertical concatenation, with `P` on top. 65 | - `P Q` is like `PQ`, but with lower precedence than `/`. This sometimes saves parentheses. 66 | - `P+` is one or more `P`s aligned horizontally, and `P/+` is the same aligned vertically. 67 | - The Boolean operations are denoted `P|Q`, `P&Q` and `P!`. Exclusive OR is `P~Q`, and difference is `P-Q`. 68 | - `P?` is shorthand for `t|P`, `P/?` for `f|P`, `P*` for `t|P+`, and `P/*` for `f|P/+`. 69 | - `P{a-b,c-d}`, where `abcd` are nonnegative integers, is a _size constraint_ on `P`. If `P` is a character class, then the expression matches any `mxn` rectangle containing only those characters, provided that `m` is between `a` and `b` inclusive, and `n` is between `c` and `d` inclusive. In other cases, the expression matches any rectangle that has the correct size and that `P` also matches. If `a` or `c` are omitted, they are taken to be `0`, and if `b` or `d` are omitted, they are infinite. If the hyphen between `a` and `b` is omitted, then we use the same number for both ends of the interval. If the entire `c-d` part is omitted, both axes are constrained. To clarify, `{-b}` is equivalent to `{0-b,0-b}`, and `{a-,c}` is equivalent to `{a-infinity,c-c}`. The `}` can be omitted. 70 | - `P:a-b,c-d}` is a _grid specifier_. It matches a rectangle that can be divided into an `mxn` grid of matches of `P`, where `m` is between `a` and `b` inclusive, and `n` is between `c` and `d` inclusive. The ranges and `}` can be omitted, with the same defaulting behavior as in the size constraint, except that the beginning of a range defaults to `1` instead of `0`. 71 | - `P#a-b}` is a _counting specifier_. It matches a rectangle that contains between `a` and `b` possibly overlapping matches of `P`, inclusive. The `}` is optional, `a` defaults to `1` and `b` to infinity. 72 | - `PoS`, where `S` is a (greedily parsed) string of the characters `01234567`, optionally terminated with `}`, is an _orientation modifier_. Each of the characters stands for a rotation (`0123`) or reflection (`4567`), which is applied to the expression `P`. The transformed expressions are combined with Boolean disjunctions. The characters `OXNTKHADC` encode convenient classes of orientations. The character `F` fixes an expression, so that its orientation cannot be modified. 73 | - `

` is a _context bracket_. It matches any rectangle **r** that's contained in a larger rectangle that matches `P`. The rectangle **r** can be matched by a digit in `P`; this is `0` by default, and increases with the nesting depth (`0` matches the anchor of the innermost brackets, `1` the next one etc). 74 | 75 | You can add the prefix `^` to any infix operator or chain of postfix operators to raise its precedence higher than all other operators, or `v` to lower it; for example, `\a\b^|\cv+` is parsed as `(\a(\b|\c))+`. 76 | If `i` is any infix operator apart from concatenation or `/`, and `p` a chain of postfix operators, then `PipQ` is a shorthand for `(PiQ)p`; for example, `\a|+\b` is equivalent to `(\a|\b)+`. 77 | Double quotes `""` are used for swapping the `\`-escaped status of all characters inside them, except for the characters `"\/`. 78 | They allow text grids like `"this/is a/grid"`. 79 | Non-literal syntax elements, like nonterminals, operations and parentheses, can be used in quoted expressions by escaping them. 80 | Note that quotes define syntax elements, so `"ab/cd"+/E` will be parsed as `(\a\b/\c\d)+/E`. 81 | All open parentheses, brackets and quotes are implicitly closed at the end of a line. 82 | Lines beginning with `|` are comments, and the parser ignores them. 83 | 84 | ## Notes 85 | 86 | Grime does allow paradoxical definitions of the form `A=A!`; these will result in no match. 87 | In general, the matching engine can resolve any grammar where no match of a single nonterminal on a single rectangle depends on itself (although for complex grammars, this can take a while). 88 | A nontrivial example of a resolvable grammar is 89 | 90 | A=E?\a 91 | B=[ab]+&A! 92 | E=A|B 93 | a`A 94 | 95 | Given a one-dimensional string of `a`s and `b`s, this grammar will match every substring that ends in `a`. 96 | Note how the nonterminal `A` is self-referential in more than one way (via `E` directly, and via `E` through `B`), but since the `E` in `A` must be a proper substring, the system can always be resolved. 97 | 98 | Grime supports non-rectangular inputs; the rows are simply aligned to the left, and the gaps can be matched using `b`. 99 | -------------------------------------------------------------------------------- /grime.hs: -------------------------------------------------------------------------------- 1 | -- A two-dimensional language based on Boolean grammars 2 | 3 | import Expression 4 | import Matcher (matchAllEmpty) 5 | import Parser (Option(..), parseMatFile, parseGrFile, parseOptions) 6 | import Data.List (nub) 7 | import Data.Map.Strict (toList) 8 | import Control.Monad (forM_, when) 9 | import System.Environment (getArgs) 10 | import System.IO (hPutStrLn, stderr) 11 | 12 | 13 | -- Take a submatrix of a newline-delimited string, possibly with border 14 | submatrix :: Bool -> Rect -> String -> String 15 | submatrix border (x, y, w, h) = unlines . take h . drop y' . map (take w . drop x') . addBorder . lines 16 | where addBorder matrix = if border 17 | then let blankRow = replicate (maximum $ map length matrix) ' ' 18 | in blankRow : map (\row -> ' ' : row ++ " ") matrix ++ [blankRow] 19 | else matrix 20 | (x', y') = if border then (x+1, y+1) else (x, y) 21 | 22 | -- Print a string to STDERR with newline 23 | printErr :: String -> IO () 24 | printErr = hPutStrLn stderr 25 | 26 | main :: IO () 27 | main = do 28 | args <- getArgs 29 | let (cmdOpts, grFile, matFile) = case args of 30 | ['-':a, b, c] -> (parseOptions a, b, c) 31 | [a, b] -> ([], a, b) 32 | _ -> error "Incorrect arguments. Usage: grime [opts] grammarfile patternfile" 33 | parsedGrammar <- fmap (parseGrFile grFile) $ readFile grFile 34 | case parsedGrammar of 35 | Left parseError -> printErr $ show parseError 36 | Right (fileOpts, grammar) -> do 37 | pict <- readFile matFile 38 | let opts = [opt | opt <- nub $ cmdOpts ++ fileOpts, elem opt cmdOpts /= elem opt fileOpts] 39 | (sze@(wMat, hMat), mat) = parseMatFile pict 40 | (minX, minY, numX, numY) = if elem AddBorder opts then (-1, -1, wMat+2, hMat+2) else (0, 0, wMat, hMat) 41 | (matches, logs) = matchAllEmpty sze (elem AddBorder opts) mat grammar $ 42 | if elem Entire opts 43 | then [(minX, minY, numX, numY)] 44 | else [(x, y, w, h) | 45 | w <- [numX,numX-1..0], h <- [numY,numY-1..0], 46 | x <- [minX..numX-w], y <- [minY..numY-h]] 47 | finalMatches = if elem AllMatches opts || elem Number opts then matches else take 1 matches 48 | when (elem Debug0 opts) $ do 49 | printErr $ "Options: " ++ show opts 50 | printErr $ "Input dimensions: " ++ show sze 51 | printErr "Definitions:" 52 | forM_ (toList grammar) $ \(l, e) -> 53 | printErr $ " " ++ (case l of Nothing -> "_ = "; Just a -> a:" = ") ++ show e 54 | when (elem Debug1 opts) $ printErr logs 55 | if (elem Number opts /= elem Entire opts) 56 | then print $ length finalMatches 57 | else forM_ finalMatches $ \rect -> do 58 | when (elem Positions opts) $ print rect 59 | when (not $ elem Patterns opts) . putStrLn $ submatrix (elem AddBorder opts) rect pict 60 | -------------------------------------------------------------------------------- /rungrime: -------------------------------------------------------------------------------- 1 | #!/bin/bash 2 | 3 | if [ ! -f grime ] || 4 | [ Expression.hs -nt grime ] || 5 | [ PrattParser.hs -nt grime ] || 6 | [ Parser.hs -nt grime ] || 7 | [ Matcher.hs -nt grime ] || 8 | [ grime.hs -nt grime ]; then 9 | >&2 echo "Newer source files detected, compiling." 10 | >&2 ghc -O2 grime.hs 11 | fi 12 | 13 | ./grime "$@" 14 | -------------------------------------------------------------------------------- /tutorial.md: -------------------------------------------------------------------------------- 1 | # Tutorial 2 | 3 | _This tutorial is incomplete. 4 | Suggestions are welcome!_ 5 | 6 | ## First Principles 7 | 8 | Grime is a language for matching two-dimensional patterns (grids) of characters. 9 | This is analogous to how regular expressions are used to match strings, which are one-dimensional patterns of characters. 10 | The idea is that a Grime program, called a _grammar_, defines an _expression_ that may or may not match a given rectangular grid. 11 | The executable takes such a grammar and a grid, and either tries to find a match in the grid (the default), enumerates all matches, or just tries to match the entire grid. 12 | 13 | As with regular expressions, Grime expressions are constructed from simple parts using different combinators (infix operations) and modifiers (postfix operations). 14 | For example, take the regular expression `a+ba+`. 15 | The parts `a` and `b` are _atomic expressions_, which match the respective letters. 16 | The modifier `+` transforms the expression `a` into `a+`, which matches one or more adjacent copies of `a`. 17 | The concatenation `a+ba+` can be seen as a combination of `a+`, `b` and `a+`: it matches first `a+`, then `b`, then `a+` again. 18 | 19 | ## A Simple Grammar 20 | 21 | As said, a Grime expression may match a rectangular grid of characters. 22 | The simplest expression is a _literal_, which matches a **1×1** grid containing a fixed character. 23 | All Grime literals are escaped with a backslash; for example, the expression `\a` matches the character `a`. 24 | 25 | The modifier `+` is _horizontal repetition_. 26 | If `E` is an expression, then `E+` matches any rectangle formed by gluing one or more `E`s in a row. 27 | The `E`s may be of different widths, but their heights must match. 28 | Here's an ASCII art picture of the situation: 29 | 30 | +----+---+-------+--+ 31 | | | | | | 32 | | E | E | E |E | 33 | | | | | | 34 | +----+---+-------+--+ 35 | 36 | For example, the expression `\a+` matches any **n×1** grid of `a`s, where **n ≥ 1**. 37 | 38 | The concatenation of two expressions (which is really an "invisible" binary operator) means horizontal gluing: `EF` matches a rectangle whose left side matches `E` and right side matches `F`. 39 | The border between `E` and `F` may go anywhere in the rectangle, and the expressions may even have zero width. 40 | Here's again a picture: 41 | 42 | +----+-------+ 43 | | | | 44 | | E | F | 45 | | | | 46 | +----+-------+ 47 | 48 | Thus, `\a+\b` matches an **n×1** rectangle, where **n ≥ 2**, the rightmost character is a `b`, and the other are `a`s. 49 | The expression `\a+\b\a+` matches one `b` surrounded by one or more `a`s on both sides. 50 | 51 | Let's try out this grammar! 52 | Grime has an [online interpreter](http://grime.tryitonline.net/) hosted by [Dennis from PPCG](http://codegolf.stackexchange.com/users/12012/dennis). 53 | Paste the expression `\a+\b\a+` on the Code box (which corresponds to the grammar file), the string `ababaa` to the Input box (which corresponds to the pattern file), and click Run. 54 | The result in the Output box should be `abaa`, the first matching sub-rectangle that Grime found in the pattern string (it tries large rectangles first, so `abaa` matches before anything else). 55 | 56 | The grammar file may contain _option flags_, which are reparated from the main grammar by a backtick. 57 | If you modify the grammar into `` a`\a\b+ ``, the output will list all matched sub-rectangles instead of just the first. 58 | Also, `` n`\a\b+ `` counts the number of matches, and `` e`\a\b+ `` matches the entire pattern against the expression, producing `0` for "no match" in our case. 59 | 60 | ## Vertical Concatenation 61 | 62 | In addition to gluing rectangles side by side, Grime allows them to be glued on top of each other. 63 | The operator `/` is vertical concatenation: `E/F` matches a rectangle whose top part matches `E` and bottom part matches `F`. 64 | Also, `E/+` matches one or more `E`s stacked vertically on top of each other. 65 | Analogously to the horizontal case, the parts may have different heights, but their widths must match. 66 | 67 | Let's put the vertical concatenation operators into action! 68 | Consider the expression `\a\b+/\d+`. 69 | The `/` has lower precedence than horizontal concatenation, so it will be parsed as `(\a\b+)/(\d+)`. 70 | On the left, we have the expression `\a\b+`, which matches an **n×1** rectangle consisting of an `a` and then one or more `b`s. 71 | On the right, we have `\d+`, which matches an **n×1** rectangle consisting of one or more `d`s. 72 | Their vertical concatenation matches an **n×2** rectangle like 73 | 74 | abbb 75 | dddd 76 | 77 | Let's make a vertical repetition of this pattern. 78 | We can use parentheses for grouping, so `(\a\b+/\d+)/+` does the job: it matches patterns like 79 | 80 | abbb 81 | dddd 82 | abbb 83 | dddd 84 | abbb 85 | dddd 86 | 87 | where the above **n×2** pattern is repeated one or more times. 88 | 89 | > ### Excercise 90 | > 91 | > Write an expression that matches any **n×m** rectangle, where **n≥3** and **m≥3**, that consists entirely of `a`s with the exception of one `b` that doesn't touch the borders. 92 | > Like this: 93 | > 94 | > aaaaa 95 | > aaaba 96 | > aaaaa 97 | > aaaaa 98 | 99 | ## Character Classes 100 | 101 | Similarly to regular expressions, Grime supports character classes defined by brackets `[]`. 102 | The expression […] matches any **1×1** pattern whose character occurs inside the brackets. 103 | It is effectively a disjunction of literals, but with a more terse syntax.1 104 | For example `[abcdr]` matches either `a`, `b`, `c`, `d` or `r`. 105 | Hyphens can be used to shorten ranges of characters, so the above is equivalent to `[a-dr]`. 106 | The comma is used to define _negative characters_ that are excluded from the class. 107 | For example, `[a-z,aeiou]` matches all lowercase English consonants, since we excluded the vowels. 108 | If no non-negative characters are listed, as in `[,asdf]`, the resulting class will match all characters except the negative ones. 109 | The characters `[]-,\` have to be escaped with backslashes inside the character class construct. 110 | 111 | > ### Excercise 112 | > 113 | > Write an expression that matches any **n×m** rectangle, where **n≥2** and **m≥2**, that contains only vowels on its left and bottom borders, and only consonants everywhere else. 114 | > Like this: 115 | > 116 | > anrbz 117 | > ejhjp 118 | > egghw 119 | > eaaio 120 | 121 | ## Logical Operators 122 | 123 | Expressions can also be combined using logical conjunction (`E&F`) or disjunction (`E|F`), which behave as expected. 124 | For example, `\a+|\a/+` matches either an **n×1** or **1×n** rectangle of `a`s. 125 | Note that the logical operations only work on expressions, not operators, so you cannot do `\a(+|/+)` or something similar. 126 | Disjunction has higher precedence than conjunction, so `E&F|G` is parsed as `(E&F)|G`. 127 | Logical negation is denoted by the exclamation mark: `E!` matches whenever `E` does not match. 128 | 129 | Logical conjunction is already a quite powerful tool. 130 | For example, we can match a rectangle that's divided into four parts by two lines, where the upper-left and lower-right parts consist of `a`s and the others of `b`s, like this: 131 | 132 | aaabbbb 133 | aaabbbb 134 | bbbaaaa 135 | bbbaaaa 136 | bbbaaaa 137 | 138 | Namely, we can get the unbroken horizontal line with the expression `(\a+/+\b+/+)/(\b+/+\a+/+)`, and the unbroken vertical line with the expression `(\a+/+/\b+/+)(\b+/+/\a+/+)`. 139 | Their conjunction 140 | 141 | (\a+/+\b+/+)/(\b+/+\a+/+)&(\a+/+/\b+/+)(\b+/+/\a+/+) 142 | 143 | has both an unbroken horizontal line and unbroken vertical line. 144 | 145 | > ### Excercise 146 | > 147 | > Write an expression that matches any rectangle of `a`s and `b`s where every horizontal row and vertical column contains at least one `b`, like this: 148 | > 149 | > aaabb 150 | > baaab 151 | > aabab 152 | > abaab 153 | 154 | ## Built-in Expressions 155 | 156 | Grime contains several atomic expressions that are built into the language. 157 | We list some of them here. 158 | 159 | - The dot `.` is equivalent to `[]`; it matches any single character.2 160 | - The dollar `$` is a "wildcard" that matches all rectangles, regardless of size or content. 161 | - The letter `f` (called "flat") matches all rectangles of height 0, and `t` (called "thin") matches all rectangles of width 0. 162 | - The letter `e` matches any flat or thin rectangle on the border of the input. 163 | - There are six built-in character classes: `d`igit, `u`ppercase, `l`owercase, `a`lphabetic, alpha`n`umeric, and `s`ymbol. They all work in the ASCII range only. 164 | 165 | Some operators are defined in terms of these expressions. 166 | The option operator `E?` is syntactic sugar for `t|E`, and the vertical choice `E/?` is equivalent to `f|E`. 167 | We also have the zero-or-more-repetitions operators `E*` (equivalent to `t|E+`) and `E/*` (equivalent to `f|E/+`). 168 | 169 | ## Containment 170 | 171 | The operator `#` denotes _containment_: `E#` matches any pattern that contains a match of `E` as a sub-pattern. 172 | For example, `(\a\b/\b\a)#` matches a pattern that contains a copy of 173 | 174 | ab 175 | ba 176 | 177 | The idiom `E#!` denotes _forbidden patterns_ (it's a combination of containment and logical negation), and it is surprisingly powerful. 178 | For example, consider the task of matching an arbitrary-sized "chessboard" of `a`s and `b`s, like this: 179 | 180 | abababa 181 | bababab 182 | abababa 183 | bababab 184 | 185 | The top left corner may also be a `b`. 186 | We could construct an expression by repeating the pattern `\a\b/\b\a` and taking care of the borders in some way, but this quickly becomes complicated. 187 | A much simpler approach is to match a rectangle of `a`s and `b`s that contains no adjacent characters: 188 | 189 | [ab]+/+&(\a\a|\a/\a|\b\b|\b/\b)#! 190 | 191 | As another example, if `P` is an arbitrary expression, then `P&e#` matches any rectangle that touches an edge of the input and is a match of `P`. 192 | 193 | ## Size Constraints 194 | 195 | In Grime, there is a simple way for constraining the size of a expression: _size constraints_. 196 | A size constraint is a postfix operator defined with braces `{}`, and it contains one or two numerical ranges. 197 | The most complete form of a size constraint is `E{a-b,c-d}`, and it matches a pattern that matches `E`, and is also of size **n×m**, where **a≤n≤b** and **c≤m≤d**. 198 | For example, a **3×3** chessboard can be matched with 199 | 200 | ([ab]+/+&(\a\a|\a/\a|\b\b|\b/\b)#!){3-3,3-3} 201 | 202 | However, if `E` is a literal, a dot, or a character class, then `E{a-b,c-d}` matches a rectangle of the given sizes that only contains characters from that class or literal. 203 | For example, `[aeiou]{2-2,2-4}` matches a rectangle of vowels of width 2 and height 2, 3 or 4. 204 | If you leave out some of the numbers, reasonable defaults will be used instead. 205 | If the second range is missing, the first one is simply dupicated. 206 | A missing lower bound is replaced by `0`, and a missing upper bound by infinity. 207 | A missing dash gives equal upper and lower bounds, so `{2,4}` means `{2-2,4-4}`. 208 | Thus, a more compact way of matching **3×3** chessboards is 209 | 210 | [ab]{3}&(\a\a|\a/\a|\b\b|\b/\b)#! 211 | 212 | In particular, for character literals `\a*/*` is equivalent to `\a{}`. 213 | 214 | ## Nonterminals 215 | 216 | _Nonterminals_ in Grime are used for two purposes: as shorthands for long expressions, and to implement recursion. 217 | A nonterminal is denoted by an uppercase letter, and it must be defined on a separate line in the grammar file. 218 | The syntax for defining a nonterminal, in this case `A`, is this: 219 | 220 | A=\a\b\c 221 | 222 | This line defines `A` as the expression `\a\b\c`, and it can then be used anywhere in the grammar file. 223 | For example, you could define the main expression `A/A/A`, which would match the pattern 224 | 225 | abc 226 | abc 227 | abc 228 | 229 | However, the main strength of nonterminals is that they can refer to themselves. 230 | As an example, suppose we want to match all rectangles of size **n×n** where **n≥1** (also known as squares). 231 | We can build a square recursively: it is either a **1×1** rectangle, or it is a smaller rectangle plus a border of width 1 below and to its right. 232 | Let's turn this into a definition: 233 | 234 | S=.|S./+/.+ 235 | 236 | As stated above, this defines `S` as either a single character (`.`), or a smaller `S` with a vertical border (`./+`) to its right, and a horizontal border (`.+`) below that. 237 | As a picture, where `A` stands for `./+` and `B` for `.+`: 238 | 239 | +---+-+ 240 | | | | 241 | | S |A| 242 | | | | 243 | +---+-+ 244 | | B | 245 | +-----+ 246 | 247 | Note how the concatenations force the borders to have the correct lengths. 248 | Now, a grammar file must contain exactly one anonymous "toplevel expression" that's not bound to any nonterminal. 249 | Thus a complete grammar file for matching square-shaped inputs is this: 250 | 251 | S=.|S./+/.+ 252 | e`S 253 | 254 | As a shorthand, the character `_` refers to the toplevel nonterminal, and can be used in its own definition. 255 | This shortens the above grammar file to the following: 256 | 257 | e`.|_./+/.+ 258 | 259 | You can define very complex grammars using nonterminals whose definitions refer to each other. 260 | 261 | > ### Excercise 262 | > 263 | > Write a grammar that matches an odd-sized square of `a`s whose center point is a `b`, like this: 264 | > 265 | > aaaaa 266 | > aaaaa 267 | > aabaa 268 | > aaaaa 269 | > aaaaa 270 | 271 | > ### Excercise 272 | > 273 | > Write a grammar that matches correctly nested parentheses `()` and `[]`, like this: 274 | > 275 | > (())[()([])] 276 | 277 | ## Orientation modifiers 278 | 279 | Suppose you want to match a rectangle of `0`s with a single `1` in any corner. 280 | The expression `\1\0+/\0+/+` of course matches such a rectangle with `1` in the upper left corner, but to get them all, you'd need to repeat the pattern four times with slight modifications, which is really cumbersome: 281 | 282 | \1\0+/\0+/+|\0+\1/\0+/+|\0+/+/\1\0+|\0+/+/\0+\1 283 | 284 | _Orientation modifiers_, which are postfix operators, allow you to more easily rotate and reflect Grime patterns. 285 | For example, the modifier `oX` means "rotated by any multiple of 90 degrees", so the above expression can be shortened to `(\1\0+/\0+/+)oX`. 286 | 287 | The full syntax of an orientation modifier is `oS}`, where `S` is a nonempty string of the characters `01234567OXNTKHADCF`, and the final `}` is optional. 288 | Each digit `0123` denotes counterclockwise rotation by the corresponding multiple of 90 degrees, and `4567` are the same followed by reflection around the vertical axis. 289 | Each of the letters (except `F`) corresponds to a subgroup of rotations and reflections, usually the symmetry group of the glyph itself. 290 | For example, `O` stands for all rotations and reflections, `X` for all rotations, and `N` for rotation by 0 or 180 degrees. 291 | The exceptions are `D` (nothing or reflection around diagonal), `A` (nothing or reflection around anti-diagonal) and `C` (nothing or reflection around diagonal and/or anti-diagonal). 292 | If `S` contains several characters, they are combined with disjunctions (logical OR). 293 | For example, `oN4` would mean no change, rotation by 180 degrees or reflection around vertical axis. 294 | Using the `A` option for reflecting around the andi-diagonal, the chessboard example above can be shortened to 295 | 296 | [ab]+/+&(\a\a|\b\b)oA#! 297 | 298 | The `F` option is special, and stands for _fixed orientation_. 299 | Sometimes you want to rotate a pattern as a whole, but keep some things unchanged. 300 | For example, you might want to match the patterns `()` and `[]` side by side or on top of one another, in any orientation. 301 | However, the pattern `(\(\)\[\])oX` is not what we want, since it matches the following rectanges: 302 | 303 | ()[] 304 | 305 | ] 306 | [ 307 | ) 308 | ( 309 | 310 | ][)( 311 | 312 | ( 313 | ) 314 | [ 315 | ] 316 | 317 | What we can do is to fix the patterns `()` and `[]` with the `F` option, and rotate the rest of the expression around them: `((\(\))oF(\[\])oF)oX`. 318 | This correctly matches the following rectangles: 319 | 320 | ()[] 321 | 322 | [] 323 | () 324 | 325 | []() 326 | 327 | () 328 | [] 329 | 330 | > ### Excercise 331 | > 332 | > Write a grammar that matches a rectangular "track" lined by `#`-characters with one "runner" represented by `@` at any point of the track, on a background or `.`-characters, like this: 333 | > 334 | > ########## 335 | > #........# 336 | > #.######.# 337 | > #@#....#.# 338 | > #.#....#.# 339 | > #.######.# 340 | > #........# 341 | > ########## 342 | 343 | 344 | ## Context Brackets 345 | 346 | _Context brackets_ provide a method for matching a rectangle depending on its surroundings. 347 | The syntax consists of the angle brackets `<>`: the expression `` is read as "in context `E`", and it matches any rectangle **r** that's contained in a larger rectangle that matches `E`. 348 | For example, consider the definition `A=<\a\b+\a>`. 349 | In the one-dimensional string `abbcabba`, the first `b` does not match `A`, since it's not contained in a run of `b`s surrounded by `a`s. 350 | However, the third `b` is, and so it does match `A`. 351 | 352 | Inside a context bracket, the currently-matched rectangle **r** can be explicitly matched by an _anchor_, which by default is the digit `0`. 353 | For example, the expression `<0\a>` matches any rectangle that has a single `a` as its right neighbor (and thus has height 1). 354 | With nested context brackets, the anchor of the `n`th surrounding bracket is the digit `n`, up to `9`. 355 | This means that the anchor of the innermost bracket is always matched with `0`. 356 | 357 | Context brackets can be used for many things, but an very useful application is path-finding. 358 | Consider the following problem: we have a grid consisting of the characters `SE#.`, and we want to count the number of `S`s that are connected to an `E` by a path of `.`s. 359 | In the grid 360 | 361 | ..#.#..E# 362 | S.#...### 363 | ....#.... 364 | ###.#.##. 365 | .S##..#S. 366 | ....###.# 367 | 368 | the bottom left `S` should not be counted, while the other two should. 369 | We can achieve this with the following grammar: 370 | 371 | R=\E|[S.]&<(0RoF)oX> 372 | n`R&\S 373 | 374 | The nonterminal `R` matches any non-`#` character that contains a path to an `E`: it is either an `E` itself, or one of `S` or `.` that has a match of `R` as a neighbor in any direction (which we achieve with an orientation modifier; the `oF` fixes the orientation of `R`, which doesn't change the semantics, but speeds up the matching). 375 | It should be noted that anchors have lexical scope, so you cannot match an anchor "through" a nonterminal. 376 | 377 | > ### Excercise 378 | > 379 | > Write a grammar that counts the number of `a`s that have occurrences of `b`s in all four cardinal directions (not necessarily as nearest neighbors). 380 | > The left `a` here is an example, but the right one is not, so the correct result is `1`: 381 | > 382 | > xxbxxxx 383 | > bxaxxbx 384 | > bxxxxax 385 | > xbbxxbx 386 | 387 | 1 This is not entirely true, as character classes are given special treatement by the size constraint operator. We'll return to that later. 388 | 389 | 2 This is not entirely true either, since `[]` can also match special _border characters_. 390 | --------------------------------------------------------------------------------