--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/comb1-test.scala	Tue Jul 30 23:44:56 2019 +0100
@@ -0,0 +1,200 @@
+import scala.language.implicitConversions
+import scala.language.reflectiveCalls
+
+/* Note, in the lectures I did not show the implicit type consraint
+ * I => Seq[_], which means that the input type 'I' needs to be
+ * a sequence. */
+
+type IsSeq[A] = A => Seq[_]
+
+abstract class Parser[I : IsSeq, T] {
+  def parse(ts: I): Set[(T, I)]
+
+  def parse_all(ts: I) : Set[T] =
+    for ((head, tail) <- parse(ts); 
+        if (tail.isEmpty)) yield head
+}
+
+// convenience for matching later on
+case class ~[+A, +B](_1: A, _2: B)
+
+class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], 
+                                 q: => Parser[I, S]) extends Parser[I, ~[T, S]] {
+  def parse(sb: I) = 
+    for ((head1, tail1) <- p.parse(sb); 
+         (head2, tail2) <- q.parse(tail1)) yield (new ~(head1, head2), tail2)
+}
+
+class AltParser[I : IsSeq, T](p: => Parser[I, T], 
+                              q: => Parser[I, T]) extends Parser[I, T] {
+  def parse(sb: I) = p.parse(sb) ++ q.parse(sb)   
+}
+
+class FunParser[I : IsSeq, T, S](p: => Parser[I, T], 
+                                 f: T => S) extends Parser[I, S] {
+  def parse(sb: I) = 
+    for ((head, tail) <- p.parse(sb)) yield (f(head), tail)
+}
+
+// atomic parsers for characters, numbers and strings
+case class CharParser(c: Char) extends Parser[String, Char] {
+  def parse(sb: String) = 
+    if (sb != "" && sb.head == c) Set((c, sb.tail)) else Set()
+}
+
+import scala.util.matching.Regex
+case class RegexParser(reg: Regex) extends Parser[String, String] {
+  def parse(sb: String) = reg.findPrefixMatchOf(sb) match {
+    case None => Set()
+    case Some(m) => Set((m.matched, m.after.toString))  
+  }
+}
+
+val NumParser = RegexParser("[0-9]+".r)
+def StringParser(s: String) = RegexParser(Regex.quote(s).r)
+
+// NumParserInt2 transforms a "string integer" into an Int;
+// needs new, because FunParser is not a case class
+
+val NumParserInt2 = new FunParser(NumParser, (s: String) => s.toInt)
+
+
+// convenience
+implicit def string2parser(s: String) = StringParser(s)
+implicit def char2parser(c: Char) = CharParser(c)
+
+implicit def ParserOps[I, T](p: Parser[I, T])(implicit ev: I => Seq[_]) = new {
+  def || (q : => Parser[I, T]) = new AltParser[I, T](p, q)
+  def ==>[S] (f: => T => S) = new FunParser[I, T, S](p, f)
+  def ~[S] (q : => Parser[I, S]) = new SeqParser[I, T, S](p, q)
+}
+
+implicit def StringOps(s: String) = new {
+  def || (q : => Parser[String, String]) = new AltParser[String, String](s, q)
+  def || (r: String) = new AltParser[String, String](s, r)
+  def ==>[S] (f: => String => S) = new FunParser[String, String, S](s, f)
+  def ~[S] (q : => Parser[String, S]) = 
+    new SeqParser[String, String, S](s, q)
+  def ~ (r: String) = 
+    new SeqParser[String, String, String](s, r)
+}
+
+// NumParserInt can now be written as
+val NumParserInt = NumParser ==> (s => s.toInt)
+
+
+lazy val Pal : Parser[String, String] = 
+  (("a" ~ Pal ~ "a") ==> { case x ~ y ~ z => x + y + z } ||
+   ("b" ~ Pal ~ "b") ==> { case x ~ y ~ z => x + y + z } || "a" || "b" || "")
+
+Pal.parse_all("abaaaba")
+Pal.parse("abaaaba")
+
+println("Palindrome: " + Pal.parse_all("abaaaba"))
+
+// well-nested parentheses parser (transforms '(' -> '{' , ')' -> '}' )
+lazy val P : Parser[String, String] = 
+  "(" ~ P ~ ")" ~ P ==> { case _ ~ x ~ _ ~ y => "{" + x + "}" + y } || ""
+
+P.parse_all("(((()()))())")
+P.parse_all("(((()()))()))")
+P.parse_all(")(")
+P.parse_all("()")
+
+// Arithmetic Expressions (Terms and Factors)
+
+lazy val E: Parser[String, Int] = 
+  (T ~ "+" ~ E) ==> { case x ~ y ~ z => x + z } ||
+  (T ~ "-" ~ E) ==> { case x ~ y ~ z => x - z } || T 
+lazy val T: Parser[String, Int] = 
+  (F ~ "*" ~ T) ==> { case x ~ y ~ z => x * z } || F
+lazy val F: Parser[String, Int] = 
+  ("(" ~ E ~ ")") ==> { case x ~ y ~ z => y } || NumParserInt
+
+/* same parser but producing a string
+lazy val E: Parser[String, String] = 
+  (T ~ "+" ~ E) ==> { case ((x, y), z) => "(" + x + ")+(" + z + ")"} || T 
+lazy val T: Parser[String, String] = 
+  (F ~ "*" ~ T) ==> { case ((x, y), z) => "(" + x + ")*("+ z + ")"} || F
+lazy val F: Parser[String, String] = 
+  ("(" ~ E ~ ")") ==> { case ((x, y), z) => y } || NumParser
+*/
+
+println(E.parse_all("1+3+4"))
+println(E.parse("1+3+4"))
+println(E.parse_all("4*2+3"))
+println(E.parse_all("4*(2+3)"))
+println(E.parse_all("(4)*((2+3))"))
+println(E.parse_all("4/2+3"))
+println(E.parse("1 + 2 * 3"))
+println(E.parse_all("(1+2)+3"))
+println(E.parse_all("1+2+3"))  
+
+
+
+// no left-recursion allowed, otherwise will loop
+lazy val EL: Parser[String, Int] = 
+  (EL ~ "+" ~ EL ==> { case x ~ y ~ z => x + z} || 
+   EL ~ "*" ~ EL ==> { case x ~ y ~ z => x * z} ||
+   "(" ~ EL ~ ")" ==> { case x ~ y ~ z => y} ||
+   NumParserInt)
+
+//println(EL.parse_all("1+2+3"))
+
+
+
+
+// non-ambiguous vs ambiguous grammars
+
+// ambiguous
+lazy val S : Parser[String, String] =
+  ("1" ~ S ~ S) ==> { case x ~ y ~ z => x + y + z } || ""
+
+S.parse("1" * 10)
+
+// non-ambiguous
+lazy val U : Parser[String, String] =
+  ("1" ~ U) ==> { case x ~ y => x + y  } || ""
+
+U.parse("1" * 25)
+
+U.parse("11")
+U.parse("11111")
+U.parse("11011")
+
+U.parse_all("1" * 100)
+U.parse_all("1" * 100 + "0")
+
+lazy val UCount : Parser[String, Int] =
+  ("1" ~ UCount) ==> { case x ~ y => y + 1 } || "" ==> { x => 0 }
+
+UCount.parse("11111")
+UCount.parse_all("11111")
+
+
+
+// Single Character parser
+lazy val One : Parser[String, String] = "1"
+lazy val Two : Parser[String, String] = "2"
+
+One.parse("1")
+One.parse("111")
+
+(One ~ One).parse("111")
+(One ~ One ~ One).parse("111")
+(One ~ One ~ One ~ One).parse("1111")
+
+(One || Two).parse("111")
+
+
+
+
+
+// a problem with the parser -> gets slow with nestedness
+E.parse("1")
+E.parse("(1)")
+E.parse("((1))")
+E.parse("(((1)))")
+E.parse("((((1))))")
+E.parse("((((((1))))))")
+E.parse("(((((((1)))))))")
\ No newline at end of file

--- a/progs/comb1.scala	Tue Jul 30 20:19:40 2019 +0100
+++ b/progs/comb1.scala	Tue Jul 30 23:44:56 2019 +0100
@@ -1,11 +1,13 @@
 import scala.language.implicitConversions
 import scala.language.reflectiveCalls
 
-/* Note, in the lectures I did not show the implicit type consraint
- * I => Seq[_], which means that the input type 'I' needs to be
- * a sequence. */
+/* Note, in the lectures I did not show the implicit type 
+ * constraint IsSeq, which means that the input type 'I' needs 
+ * to be a sequence. */
 
-abstract class Parser[I, T](implicit ev: I => Seq[_]) {
+ type IsSeq[A] = A => Seq[_]
+
+abstract class Parser[I : IsSeq, T] {
   def parse(ts: I): Set[(T, I)]
 
   def parse_all(ts: I) : Set[T] =
@@ -13,20 +15,20 @@
         if (tail.isEmpty)) yield head
 }
 
-class SeqParser[I, T, S](p: => Parser[I, T], 
-                         q: => Parser[I, S])(implicit ev: I => Seq[_]) extends Parser[I, (T, S)] {
+class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], 
+                                 q: => Parser[I, S]) extends Parser[I, (T, S)] {
   def parse(sb: I) = 
     for ((head1, tail1) <- p.parse(sb); 
          (head2, tail2) <- q.parse(tail1)) yield ((head1, head2), tail2)
 }
 
-class AltParser[I, T](p: => Parser[I, T], 
-                      q: => Parser[I, T])(implicit ev: I => Seq[_]) extends Parser[I, T] {
+class AltParser[I : IsSeq, T](p: => Parser[I, T], 
+                              q: => Parser[I, T]) extends Parser[I, T] {
   def parse(sb: I) = p.parse(sb) ++ q.parse(sb)   
 }
 
-class FunParser[I, T, S](p: => Parser[I, T], 
-                         f: T => S)(implicit ev: I => Seq[_]) extends Parser[I, S] {
+class FunParser[I : IsSeq, T, S](p: => Parser[I, T], 
+                                 f: T => S) extends Parser[I, S] {
   def parse(sb: I) = 
     for ((head, tail) <- p.parse(sb)) yield (f(head), tail)
 }