--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/automata/der.sc	Mon Oct 19 17:50:11 2020 +0100
@@ -0,0 +1,50 @@
+// Another automaton construction
+//================================
+
+import $file.dfa, dfa._ 
+
+// regular expressions
+abstract class Rexp
+case object ZERO extends Rexp                    // matches nothing
+case object ONE extends Rexp                     // matches the empty string
+case class CHAR(c: Char) extends Rexp            // matches a character c
+case class ALT(r1: Rexp, r2: Rexp) extends Rexp  // alternative
+case class SEQ(r1: Rexp, r2: Rexp) extends Rexp  // sequence
+case class STAR(r: Rexp) extends Rexp            // star
+
+// 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
+}
+
+// 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))
+}
+
+
+def flaw(r: Rexp) : DFA[Rexp, Char] = {
+  DFA(r, 
+      { case (r, c) => der(c, r) }, 
+      nullable(_))
+}
+
+val r = STAR(CHAR('a'))
+val pseudo = flaw(r)
+println(pseudo.accepts("".toList))    // true
+println(pseudo.accepts("a".toList))   // true
+println(pseudo.accepts("aa".toList))  // true
+println(pseudo.accepts("bb".toList))  // false