--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/matcher/cw1template.sc	Fri Oct 11 19:13:00 2024 +0100
@@ -0,0 +1,80 @@
+// A template of the simple matcher with simplification 
+// of derivatives to be used in CW1
+
+
+abstract class Rexp
+case object ZERO extends Rexp
+case object ONE extends Rexp
+case class CHAR(c: Char) extends Rexp
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp 
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp 
+case class STAR(r: Rexp) extends Rexp 
+
+case class RANGE(cs: Set[Char]) extends Rexp             // set of characters
+case class PLUS(r: Rexp) extends Rexp                    // plus
+case class OPTIONAL(r: Rexp) extends Rexp                // optional
+case class INTER(r1: Rexp, r2: Rexp) extends Rexp        // intersection
+case class NTIMES(r: Rexp, n: Int) extends Rexp          // n-times
+case class UPTO(r: Rexp, n: Int) extends Rexp            // up n-times
+case class FROM(r: Rexp, n: Int) extends Rexp            // from n-times
+case class BETWEEN(r: Rexp, n: Int, m: Int) extends Rexp // between nm-times
+case class NOT(r: Rexp) extends Rexp                     // not
+case class CFUN(f: Char => Boolean) extends Rexp  
+ 
+
+
+// the nullable function: tests whether the regular 
+// expression can recognise the empty string
+def nullable (r: Rexp) : Boolean = r match {
+  case ZERO => false
+  case ONE => true
+  case CHAR(_) => false
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  case NTIMES(r, i) => if (i == 0) true else nullable(r)
+  // ??? other cases
+}
+
+// the derivative of a regular expression w.r.t. a character
+def der(c: Char, r: Rexp) : Rexp = r match {
+  case ZERO => ZERO
+  case ONE => ZERO
+  case CHAR(d) => if (c == d) ONE else ZERO
+  case ALT(r1, r2) => ALT(der(c, r1), der(c, r2))
+  case SEQ(r1, r2) => 
+    if (nullable(r1)) ALT(SEQ(der(c, r1), r2), der(c, r2))
+    else SEQ(der(c, r1), r2)
+  case STAR(r1) => SEQ(der(c, r1), STAR(r1))
+  case NTIMES(r, i) => 
+    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
+  // ??? other cases  
+}
+
+// simplification
+def simp(r: Rexp) : Rexp = r match {
+  case ALT(r1, r2) => (simp(r1), simp(r2)) match {
+    case (ZERO, r2s) => r2s
+    case (r1s, ZERO) => r1s
+    case (r1s, r2s) => if (r1s == r2s) r1s else ALT (r1s, r2s)
+  }
+  case SEQ(r1, r2) =>  (simp(r1), simp(r2)) match {
+    case (ZERO, _) => ZERO
+    case (_, ZERO) => ZERO
+    case (ONE, r2s) => r2s
+    case (r1s, ONE) => r1s
+    case (r1s, r2s) => SEQ(r1s, r2s)
+  }
+  case r => r
+}
+
+// the derivative w.r.t. a string (iterates der and simp)
+def ders(s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, simp(der(c, r)))
+}
+
+// the main matcher function
+def matcher(r: Rexp, s: String) : Boolean = 
+  nullable(ders(s.toList, r))
+