1 import scala.language.implicitConversions  | 
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     2 import scala.language.reflectiveCalls  | 
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     3   | 
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     4 /* Note, in the lectures I did not show the implicit type   | 
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     5  * constraint IsSeq, which means that the input type 'I' needs   | 
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     6  * to be a sequence. */  | 
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     7   | 
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     8 type IsSeq[A] = A => Seq[_]  | 
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     9   | 
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    10 abstract class Parser[I : IsSeq, T] { | 
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    11   def parse(ts: I): Set[(T, I)]  | 
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    12   | 
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    13   def parse_all(ts: I) : Set[T] =  | 
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    14     for ((head, tail) <- parse(ts);   | 
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    15         if tail.isEmpty) yield head  | 
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    16 }  | 
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    17   | 
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    18 class SeqParser[I : IsSeq, T, S](p: => Parser[I, T],   | 
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    19                                  q: => Parser[I, S]) extends Parser[I, (T, S)] { | 
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    20   def parse(sb: I) =   | 
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    21     for ((head1, tail1) <- p.parse(sb);   | 
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    22          (head2, tail2) <- q.parse(tail1)) yield ((head1, head2), tail2)  | 
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    23 }  | 
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    24   | 
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    25 class AltParser[I : IsSeq, T](p: => Parser[I, T],   | 
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    26                               q: => Parser[I, T]) extends Parser[I, T] { | 
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    27   def parse(sb: I) = p.parse(sb) ++ q.parse(sb)     | 
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    28 }  | 
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    29   | 
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    30 class FunParser[I : IsSeq, T, S](p: => Parser[I, T],   | 
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    31                                  f: T => S) extends Parser[I, S] { | 
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    32   def parse(sb: I) =   | 
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    33     for ((head, tail) <- p.parse(sb)) yield (f(head), tail)  | 
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    34 }  | 
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    35   | 
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    36 // atomic parsers for characters, numbers and strings  | 
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    37 case class CharParser(c: Char) extends Parser[String, Char] { | 
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    38   def parse(sb: String) =   | 
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    39     if (sb != "" && sb.head == c) Set((c, sb.tail)) else Set()  | 
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    40 }  | 
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    41   | 
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    42 import scala.util.matching.Regex  | 
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    43 case class RegexParser(reg: Regex) extends Parser[String, String] { | 
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    44   def parse(sb: String) = reg.findPrefixMatchOf(sb) match { | 
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    45     case None => Set()  | 
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    46     case Some(m) => Set((m.matched, m.after.toString))    | 
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    47   }  | 
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    48 }  | 
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    49   | 
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    50 val NumParser = RegexParser("[0-9]+".r) | 
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    51 def StringParser(s: String) = RegexParser(Regex.quote(s).r)  | 
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    52   | 
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    53 // NumParserInt2 transforms a "string integer" into an actual Int;  | 
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    54 // needs new, because FunParser is not a case class  | 
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    55 val NumParserInt2 = new FunParser(NumParser, (s: String) => s.toInt)  | 
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    56   | 
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    57   | 
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    58 // convenience  | 
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    59 implicit def string2parser(s: String) = StringParser(s)  | 
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    60 implicit def char2parser(c: Char) = CharParser(c)  | 
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    61   | 
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    62 implicit def ParserOps[I, T](p: Parser[I, T])(implicit ev: I => Seq[_]) = new { | 
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    63   def ||(q : => Parser[I, T]) = new AltParser[I, T](p, q)  | 
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    64   def ==>[S] (f: => T => S) = new FunParser[I, T, S](p, f)  | 
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    65   def ~[S] (q : => Parser[I, S]) = new SeqParser[I, T, S](p, q)  | 
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    66 }  | 
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    67   | 
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    68 implicit def StringOps(s: String) = new { | 
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    69   def ||(q : => Parser[String, String]) = new AltParser[String, String](s, q)  | 
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    70   def ||(r: String) = new AltParser[String, String](s, r)  | 
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    71   def ==>[S] (f: => String => S) = new FunParser[String, String, S](s, f)  | 
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    72   def ~[S](q : => Parser[String, S]) =   | 
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    73     new SeqParser[String, String, S](s, q)  | 
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    74   def ~(r: String) =   | 
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    75     new SeqParser[String, String, String](s, r)  | 
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    76 }  | 
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    77   | 
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    78 // NumParserInt can now be written as _ ===> _  | 
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    79 // the first part is the parser, and the second the   | 
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    80 // semantic action  | 
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    81 val NumParserInt = NumParser ==> (s => s.toInt)  | 
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    82   | 
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    83   | 
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    84 // palindromes  | 
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    85 lazy val Pal : Parser[String, String] =   | 
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    86   (("a" ~ Pal ~ "a") ==> { case ((x, y), z) => x + y + z } || | 
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    87    ("b" ~ Pal ~ "b") ==> { case ((x, y), z) => x + y + z } || "a" || "b" || "") | 
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    88   | 
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    89 Pal.parse_all("abaaaba") | 
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    90 Pal.parse_all("abacba") | 
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    91 Pal.parse("abaaaba") | 
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    92   | 
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    93 println("Palindrome: " + Pal.parse_all("abaaaba")) | 
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    94   | 
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    95 // parser for well-nested parentheses (transforms '(' -> '{' , ')' -> '}' ) | 
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    96 lazy val P : Parser[String, String] =   | 
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    97   "(" ~ P ~ ")" ~ P ==> { case (((_, x), _), y) => "{" + x + "}" + y } || "" | 
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    98   | 
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    99 P.parse_all("(((()()))())") | 
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   100 P.parse_all("(((()()))()))") | 
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   101 P.parse_all(")(") | 
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   102 P.parse_all("()") | 
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   103   | 
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   104 // just counts parentheses  | 
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   105 lazy val P2 : Parser[String, Int] =   | 
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   106   ("(" ~ P2 ~ ")" ~ P2 ==> { case (((_, x), _), y) => x + y + 2 } ||  | 
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   107    "" ==> { _ => 0 }) | 
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   108   | 
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   109 P2.parse_all("(((()()))())") | 
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   110 P2.parse_all("(((()()))()))") | 
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   111   | 
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   112 // counts opening and closing parentheses  | 
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   113 lazy val P3 : Parser[String, Int] =   | 
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   114   ("(" ~ P3 ==> { case (_, x) => x + 1 } || | 
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   115    ")" ~ P3 ==> { case (_, x) => x - 1 } ||  | 
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   116    "" ==> { _ => 0 }) | 
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   117   | 
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   118 P3.parse_all("(((()()))())") | 
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   119 P3.parse_all("(((()()))()))") | 
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   120 P3.parse_all(")(") | 
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   121   | 
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   122 // Arithmetic Expressions (Terms and Factors)  | 
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   123 // (because it is mutually recursive, you need :paste   | 
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   124 //  for munching this definition in the REPL)  | 
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   125   | 
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   126 lazy val E: Parser[String, Int] =   | 
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   127   (T ~ "+" ~ E) ==> { case ((x, y), z) => x + z } || | 
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   128   (T ~ "-" ~ E) ==> { case ((x, y), z) => x - z } || T  | 
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   129 lazy val T: Parser[String, Int] =   | 
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   130   (F ~ "*" ~ T) ==> { case ((x, y), z) => x * z } || F | 
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   131 lazy val F: Parser[String, Int] =   | 
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   132   ("(" ~ E ~ ")") ==> { case ((x, y), z) => y } || NumParserInt | 
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   133   | 
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   134 println(E.parse_all("1+3+4")) | 
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   135 println(E.parse("1+3+4")) | 
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   136 println(E.parse_all("4*2+3")) | 
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   137 println(E.parse_all("4*(2+3)")) | 
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   138 println(E.parse_all("(4)*((2+3))")) | 
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   139 println(E.parse_all("4/2+3")) | 
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   140 println(E.parse("1 + 2 * 3")) | 
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   141 println(E.parse_all("(1+2)+3")) | 
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   142 println(E.parse_all("1+2+3"))   | 
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   143   | 
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   144 /* same parser but producing a string  | 
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   145 lazy val E: Parser[String, String] =   | 
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   146   (T ~ "+" ~ E) ==> { case ((x, y), z) => "(" + x + ")+(" + z + ")"} || T  | 
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   147 lazy val T: Parser[String, String] =   | 
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   148   (F ~ "*" ~ T) ==> { case ((x, y), z) => "(" + x + ")*("+ z + ")"} || F | 
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   149 lazy val F: Parser[String, String] =   | 
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   150   ("(" ~ E ~ ")") ==> { case ((x, y), z) => y } || NumParser | 
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   151 */  | 
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   152   | 
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   153 // no left-recursion allowed, otherwise will loop  | 
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   154 lazy val EL: Parser[String, Int] =   | 
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   155   (EL ~ "+" ~ EL ==> { case ((x, y), z) => x + z} ||  | 
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   156    EL ~ "*" ~ EL ==> { case ((x, y), z) => x * z} || | 
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   157    "(" ~ EL ~ ")" ==> { case ((x, y), z) => y} || | 
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   158    NumParserInt)  | 
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   159   | 
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   160 //println(EL.parse_all("1+2+3")) | 
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   161   | 
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   162   | 
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   163 // non-ambiguous vs ambiguous grammars  | 
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   164   | 
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   165 // ambiguous  | 
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   166 lazy val S : Parser[String, String] =  | 
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   167   ("1" ~ S ~ S ~ S) ==> { case (((x, y), z), v) => x + y + z } || "" | 
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   168   | 
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   169 S.parse("1" * 10) | 
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   170   | 
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   171 // non-ambiguous  | 
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   172 lazy val U : Parser[String, String] =  | 
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   173   ("1" ~ U) ==> { case (x, y) => x + y  } || "" | 
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   174   | 
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   175 U.parse("1" * 25) | 
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   176   | 
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   177 U.parse("11") | 
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   178 U.parse("11111") | 
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   179 U.parse("11011") | 
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   180   | 
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   181 U.parse_all("1" * 100) | 
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   182 U.parse_all("1" * 100 + "0") | 
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   183   | 
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   184 lazy val UCount : Parser[String, Int] =  | 
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   185   ("1" ~ UCount) ==> { case (x, y) => y + 1 } || "" ==> { x => 0 } | 
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   186   | 
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   187 UCount.parse("11111") | 
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   188 UCount.parse_all("11111") | 
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   189   | 
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   190   | 
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   191   | 
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   192 // Single Character parser  | 
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   193 lazy val One : Parser[String, String] = "1"  | 
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   194 lazy val Two : Parser[String, String] = "2"  | 
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   195   | 
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   196 One.parse("1") | 
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   197 One.parse("111") | 
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   198   | 
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   199 (One ~ One).parse("111") | 
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   200 (One ~ One ~ One).parse("1111") | 
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   201 (One ~ One ~ One ~ One).parse("1111") | 
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   202   | 
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   203 (One || Two).parse("111") | 
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   204   | 
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   205   | 
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   206 // a problem with the arithmetic expression parser -> gets   | 
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   207 // slow with deeply nested parentheses  | 
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   208 E.parse("1") | 
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   209 E.parse("(1)") | 
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   210 E.parse("((1))") | 
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   211 E.parse("(((1)))") | 
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   212 E.parse("((((1))))") | 
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   213 E.parse("((((((1))))))") | 
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   214 E.parse("(((((((1)))))))") | 
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   215   | 
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   216   | 
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   217   | 
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   218   | 
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   219 /*  | 
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   220   | 
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   221 starting symbols  | 
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   222 tokenise/detokenise  | 
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   223 :paste  | 
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   224 pairs in sequences  | 
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   225   | 
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   226 */  | 
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