diff -r 90946a2eb48a -r c7bdd7eac4cb progs/parser-combinators/comb2.sc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/parser-combinators/comb2.sc	Sat Jul 04 16:58:12 2020 +0100
@@ -0,0 +1,263 @@
+// Parser Combinators: Simple Version
+//====================================
+
+
+// more convenience for the map parsers later on
+case class ~[+A, +B](_1: A, _2: B)
+
+/* 
+  Note, in the lectures I did not show the implicit type constraint
+  I : IsSeq, 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(in: I): Set[(T, I)]
+
+  def parse_all(in: I) : Set[T] =
+    for ((hd, tl) <- parse(in); 
+        if tl.isEmpty) yield hd
+}
+
+// parser combinators
+
+// sequence parser
+class SeqParser[I : IsSeq, T, S](p: => Parser[I, T], 
+                                 q: => Parser[I, S]) extends Parser[I, ~[T, S]] {
+  def parse(in: I) = 
+    for ((hd1, tl1) <- p.parse(in); 
+         (hd2, tl2) <- q.parse(tl1)) yield (new ~(hd1, hd2), tl2)
+}
+
+// alternative parser
+class AltParser[I : IsSeq, T](p: => Parser[I, T], 
+                              q: => Parser[I, T]) extends Parser[I, T] {
+  def parse(in: I) = p.parse(in) ++ q.parse(in)   
+}
+
+// map parser
+class MapParser[I : IsSeq, T, S](p: => Parser[I, T], 
+                                 f: T => S) extends Parser[I, S] {
+  def parse(in: I) = for ((hd, tl) <- p.parse(in)) yield (f(hd), tl)
+}
+
+
+
+// atomic parser for (particular) strings
+case class StrParser(s: String) extends Parser[String, String] {
+  def parse(sb: String) = {
+    val (prefix, suffix) = sb.splitAt(s.length)
+    if (prefix == s) Set((prefix, suffix)) else Set()
+  }
+}
+
+// atomic parser for identifiers (variable names)
+case object IdParser extends Parser[String, String] {
+  val reg = "[a-z][a-z,0-9]*".r
+  def parse(sb: String) = reg.findPrefixOf(sb) match {
+    case None => Set()
+    case Some(s) => Set(sb.splitAt(s.length))
+  }
+}
+
+
+// atomic parser for numbers (transformed into ints)
+case object NumParser extends Parser[String, Int] {
+  val reg = "[0-9]+".r
+  def parse(sb: String) = reg.findPrefixOf(sb) match {
+    case None => Set()
+    case Some(s) => {
+      val (hd, tl) = sb.splitAt(s.length)
+      Set((hd.toInt, tl)) 
+    }
+  }
+}
+
+// the following string interpolation allows us to write 
+// StrParser(_some_string_) more conveniently as 
+//
+// p"<_some_string_>" 
+
+implicit def parser_interpolation(sc: StringContext) = new {
+    def p(args: Any*) = StrParser(sc.s(args:_*))
+}    
+
+// more convenient syntax for parser combinators
+implicit def ParserOps[I : IsSeq, T](p: Parser[I, T]) = new {
+  def ||(q : => Parser[I, T]) = new AltParser[I, T](p, q)
+  def ~[S] (q : => Parser[I, S]) = new SeqParser[I, T, S](p, q)
+  def map[S](f: => T => S) = new MapParser[I, T, S](p, f)
+}
+
+
+
+// the abstract syntax trees for the WHILE language
+abstract class Stmt
+abstract class AExp
+abstract class BExp 
+
+type Block = List[Stmt]
+
+case object Skip extends Stmt
+case class If(a: BExp, bl1: Block, bl2: Block) extends Stmt
+case class While(b: BExp, bl: Block) extends Stmt
+case class Assign(s: String, a: AExp) extends Stmt
+case class Write(s: String) extends Stmt
+
+case class Var(s: String) extends AExp
+case class Num(i: Int) extends AExp
+case class Aop(o: String, a1: AExp, a2: AExp) extends AExp
+
+case object True extends BExp
+case object False extends BExp
+case class Bop(o: String, a1: AExp, a2: AExp) extends BExp
+case class And(b1: BExp, b2: BExp) extends BExp
+case class Or(b1: BExp, b2: BExp) extends BExp
+
+
+// arithmetic expressions
+lazy val AExp: Parser[String, AExp] = 
+  (Te ~ p"+" ~ AExp).map[AExp]{ case x ~ _ ~ z => Aop("+", x, z) } ||
+  (Te ~ p"-" ~ AExp).map[AExp]{ case x ~ _ ~ z => Aop("-", x, z) } || Te
+lazy val Te: Parser[String, AExp] = 
+  (Fa ~ p"*" ~ Te).map[AExp]{ case x ~ _ ~ z => Aop("*", x, z) } || 
+  (Fa ~ p"/" ~ Te).map[AExp]{ case x ~ _ ~ z => Aop("/", x, z) } || Fa  
+lazy val Fa: Parser[String, AExp] = 
+   (p"(" ~ AExp ~ p")").map{ case _ ~ y ~ _ => y } || 
+   IdParser.map(Var) || 
+   NumParser.map(Num)
+
+// boolean expressions with some simple nesting
+lazy val BExp: Parser[String, BExp] = 
+   (AExp ~ p"==" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop("==", x, z) } || 
+   (AExp ~ p"!=" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop("!=", x, z) } || 
+   (AExp ~ p"<" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop("<", x, z) } || 
+   (AExp ~ p">" ~ AExp).map[BExp]{ case x ~ _ ~ z => Bop(">", x, z) } ||
+   (p"(" ~ BExp ~ p")" ~ p"&&" ~ BExp).map[BExp]{ case _ ~ y ~ _ ~ _ ~ v => And(y, v) } ||
+   (p"(" ~ BExp ~ p")" ~ p"||" ~ BExp).map[BExp]{ case _ ~ y ~ _ ~ _ ~ v => Or(y, v) } ||
+   (p"true".map[BExp]{ _ => True }) || 
+   (p"false".map[BExp]{ _ => False }) ||
+   (p"(" ~ BExp ~ p")").map[BExp]{ case _ ~ x ~ _ => x }
+
+// statement 
+lazy val Stmt: Parser[String, Stmt] =
+  ((p"skip".map[Stmt]{_ => Skip }) ||
+   (IdParser ~ p":=" ~ AExp).map[Stmt]{ case x ~ _ ~ z => Assign(x, z) } ||
+   (p"write(" ~ IdParser ~ p")").map[Stmt]{ case _ ~ y ~ _ => Write(y) } ||
+   (p"if" ~ BExp ~ p"then" ~ Block ~ p"else" ~ Block)
+     .map[Stmt]{ case _ ~ y ~ _ ~ u ~ _ ~ w => If(y, u, w) } ||
+   (p"while" ~ BExp ~ p"do" ~ Block).map[Stmt]{ case _ ~ y ~ _ ~ w => While(y, w) }) 
+ 
+// statements
+lazy val Stmts: Parser[String, Block] =
+  (Stmt ~ p";" ~ Stmts).map[Block]{ case x ~ _ ~ z => x :: z } ||
+  (Stmt.map[Block]{ s => List(s) })
+
+// blocks (enclosed in curly braces)
+lazy val Block: Parser[String, Block] =
+  ((p"{" ~ Stmts ~ p"}").map{ case _ ~ y ~ _ => y } || 
+   (Stmt.map(s => List(s))))
+
+
+// Examples
+Stmts.parse_all("x2:=5+3;")
+Block.parse_all("{x:=5;y:=8}")
+Block.parse_all("if(false)then{x:=5}else{x:=10}")
+
+
+val fib = """n := 10;
+             minus1 := 0;
+             minus2 := 1;
+             temp := 0;
+             while (n > 0) do {
+                 temp := minus2;
+                 minus2 := minus1 + minus2;
+                 minus1 := temp;
+                 n := n - 1
+             };
+             result := minus2""".replaceAll("\\s+", "")
+
+Stmts.parse_all(fib)
+
+
+// an interpreter for the WHILE language
+type Env = Map[String, Int]
+
+def eval_aexp(a: AExp, env: Env) : Int = a match {
+  case Num(i) => i
+  case Var(s) => env(s)
+  case Aop("+", a1, a2) => eval_aexp(a1, env) + eval_aexp(a2, env)
+  case Aop("-", a1, a2) => eval_aexp(a1, env) - eval_aexp(a2, env)
+  case Aop("*", a1, a2) => eval_aexp(a1, env) * eval_aexp(a2, env)
+  case Aop("/", a1, a2) => eval_aexp(a1, env) / eval_aexp(a2, env)
+}
+
+def eval_bexp(b: BExp, env: Env) : Boolean = b match {
+  case True => true
+  case False => false
+  case Bop("==", a1, a2) => eval_aexp(a1, env) == eval_aexp(a2, env)
+  case Bop("!=", a1, a2) => !(eval_aexp(a1, env) == eval_aexp(a2, env))
+  case Bop(">", a1, a2) => eval_aexp(a1, env) > eval_aexp(a2, env)
+  case Bop("<", a1, a2) => eval_aexp(a1, env) < eval_aexp(a2, env)
+  case And(b1, b2) => eval_bexp(b1, env) && eval_bexp(b2, env)
+  case Or(b1, b2) => eval_bexp(b1, env) || eval_bexp(b2, env)
+}
+
+def eval_stmt(s: Stmt, env: Env) : Env = s match {
+  case Skip => env
+  case Assign(x, a) => env + (x -> eval_aexp(a, env))
+  case If(b, bl1, bl2) => if (eval_bexp(b, env)) eval_bl(bl1, env) else eval_bl(bl2, env) 
+  case While(b, bl) => 
+    if (eval_bexp(b, env)) eval_stmt(While(b, bl), eval_bl(bl, env))
+    else env
+  case Write(x) => { println(env(x)) ; env }  
+}
+
+def eval_bl(bl: Block, env: Env) : Env = bl match {
+  case Nil => env
+  case s::bl => eval_bl(bl, eval_stmt(s, env))
+}
+
+def eval(bl: Block) : Env = eval_bl(bl, Map())
+
+// parse + evaluate fib program; then lookup what is
+// stored under the variable result 
+println(eval(Stmts.parse_all(fib).head)("result"))
+
+
+// more examles
+
+// calculate and print all factors bigger 
+// than 1 and smaller than n
+println("Factors")
+
+val factors =  
+   """n := 12;
+      f := 2;
+      while (f < n / 2 + 1) do {
+        if ((n / f) * f == n) then  { write(f) } else { skip };
+        f := f + 1
+      }""".replaceAll("\\s+", "")
+
+println(eval(Stmts.parse_all(factors).head))
+
+// calculate all prime numbers up to a number 
+println("Primes")
+
+val primes =  
+   """end := 100;
+      n := 2;
+      while (n < end) do {
+        f := 2;
+        tmp := 0;
+        while ((f < n / 2 + 1) && (tmp == 0)) do {
+          if ((n / f) * f == n) then  { tmp := 1 } else { skip };
+          f := f + 1
+        };
+        if (tmp == 0) then { write(n) } else { skip };
+        n  := n + 1
+      }""".replaceAll("\\s+", "")
+
+println(eval(Stmts.parse_all(primes).head))