--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/parser1.scala	Thu Jul 30 13:50:54 2020 +0100
@@ -0,0 +1,88 @@
+// A naive bottom-up parser with backtracking
+//
+// Needs:
+//   :load matcher.scala
+
+// some regular expressions
+val DIGIT = RANGE("0123456789")
+val NONZERODIGIT = RANGE("123456789")
+
+val NUMBER = ALT(SEQ(NONZERODIGIT, STAR(DIGIT)), "0")
+val LPAREN = CHAR('(')
+val RPAREN = CHAR(')')
+val WHITESPACE = PLUS(RANGE(" \n"))
+val OPS = RANGE("+-*")
+
+// for classifying the strings that have been recognised
+
+abstract class Token
+case object T_WHITESPACE extends Token
+case object T_NUM extends Token
+case class T_OP(s: String) extends Token
+case object T_LPAREN extends Token
+case object T_RPAREN extends Token
+case class NT(s: String) extends Token
+
+// lexing rules for arithmetic expressions
+val lexing_rules: List[Rule[Token]]= 
+  List((NUMBER, (s) => T_NUM),
+       (WHITESPACE, (s) => T_WHITESPACE),
+       (LPAREN, (s) => T_LPAREN),
+       (RPAREN, (s) => T_RPAREN),
+       (OPS, (s) => T_OP(s.mkString)))
+
+// the tokenizer
+val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE))
+
+type Grammar = List[(String, List[Token])]
+
+// grammar for arithmetic expressions
+val grammar = 
+  List ("F" -> List(T_NUM),
+        "E" -> List(T_NUM),
+        "E" -> List(NT("E"), T_OP("+"), NT("E")),
+        "E" -> List(NT("E"), T_OP("-"), NT("E")),
+        "E" -> List(NT("E"), T_OP("*"), NT("E")),    
+        "E" -> List(T_LPAREN, NT("E"), T_RPAREN))
+
+
+def chop[A](ts1: List[A], prefix: List[A], ts2: List[A]) : Option[(List[A], List[A])] = 
+  ts1 match {
+    case Nil => None
+    case t::ts => 
+      if (ts1.startsWith(prefix)) Some(ts2.reverse, ts1.drop(prefix.length))
+      else chop(ts, prefix, t::ts2)
+  }
+
+// examples for chop 
+chop(List(1,2,3,4,5,6,7,8,9), List(4,5), Nil)  
+chop(List(1,2,3,4,5,6,7,8,9), List(3,5), Nil)  
+
+def replace[A](ts: List[A], out: List[A], in: List [A]) = 
+  chop(ts, out, Nil) match {
+    case None => None
+    case Some((before, after)) => Some(before ::: in ::: after)
+  }  
+
+def parse(g: Grammar, ts: List[Token]) : Boolean = {
+  println(ts)
+  if (ts == List(NT("E"))) true
+  else {
+    val tss = for ((lhs, rhs) <- g) yield replace(ts, rhs, List(NT(lhs)))
+    tss.flatten.exists(parse(g, _))
+  }
+}
+ 
+def parser(g: Grammar, s: String) = {
+  println("\n")
+  parse(g, Tok.fromString(s))
+}
+  
+
+
+parser(grammar, "2 + 3 *    4 +       1")
+parser(grammar, "(2 + 3) * (4 + 1)")
+parser(grammar, "(2 + 3) * 4 (4 + 1)")
+
+
+