diff -r 61a936be50c4 -r f345e89895f5 progs/lexer/token2.scala
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/lexer/token2.scala	Mon Jun 29 21:05:34 2020 +0100
@@ -0,0 +1,463 @@
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls
+import scala.annotation.tailrec   
+
+abstract class Rexp 
+case object NULL extends Rexp
+case object EMPTY 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 RECD(x: String, r: Rexp) extends Rexp
+case class CRANGE(cs: String) extends Rexp
+case class PLUS(r: Rexp) extends Rexp
+case class OPT(r: Rexp) extends Rexp
+case class NTIMES(r: Rexp, n: Int) extends Rexp
+
+abstract class Val
+case object Empty extends Val
+case class Chr(c: Char) extends Val
+case class Seq(v1: Val, v2: Val) extends Val
+case class Left(v: Val) extends Val
+case class Right(v: Val) extends Val
+case class Stars(vs: List[Val]) extends Val
+case class Rec(x: String, v: Val) extends Val
+   
+// some convenience for typing in regular expressions
+def charlist2rexp(s : List[Char]): Rexp = s match {
+  case Nil => EMPTY
+  case c::Nil => CHAR(c)
+  case c::s => SEQ(CHAR(c), charlist2rexp(s))
+}
+implicit def string2rexp(s : String) : Rexp = charlist2rexp(s.toList)
+
+implicit def RexpOps(r: Rexp) = new {
+  def | (s: Rexp) = ALT(r, s)
+  def % = STAR(r)
+  def ~ (s: Rexp) = SEQ(r, s)
+}
+
+implicit def stringOps(s: String) = new {
+  def | (r: Rexp) = ALT(s, r)
+  def | (r: String) = ALT(s, r)
+  def % = STAR(s)
+  def ~ (r: Rexp) = SEQ(s, r)
+  def ~ (r: String) = SEQ(s, r)
+  def $ (r: Rexp) = RECD(s, r)
+}
+
+// nullable function: tests whether the regular 
+// expression can recognise the empty string
+def nullable (r: Rexp) : Boolean = r match {
+  case NULL => false
+  case EMPTY => true
+  case CHAR(_) => false
+  case ALT(r1, r2) => nullable(r1) || nullable(r2)
+  case SEQ(r1, r2) => nullable(r1) && nullable(r2)
+  case STAR(_) => true
+  case RECD(_, r) => nullable(r)
+  case CRANGE(_) => false
+  case PLUS(r) => nullable(r)
+  case OPT(_) => true
+  case NTIMES(r, n) => if (n == 0) true else nullable(r)
+}
+
+// derivative of a regular expression w.r.t. a character
+def der (c: Char, r: Rexp) : Rexp = r match {
+  case NULL => NULL
+  case EMPTY => NULL
+  case CHAR(d) => if (c == d) EMPTY else NULL
+  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(r) => SEQ(der(c, r), STAR(r))
+  case RECD(_, r1) => der(c, r1)
+  case CRANGE(cs) => if (cs.contains(c)) EMPTY else NULL
+  case PLUS(r) => SEQ(der(c, r), STAR(r))
+  case OPT(r) => ALT(der(c, r), NULL)
+  case NTIMES(r, n) => if (n == 0) NULL else der(c, SEQ(r, NTIMES(r, n - 1)))
+}
+
+// derivative w.r.t. a string (iterates der)
+def ders (s: List[Char], r: Rexp) : Rexp = s match {
+  case Nil => r
+  case c::s => ders(s, der(c, r))
+}
+
+// extracts a string from value
+def flatten(v: Val) : String = v match {
+  case Empty => ""
+  case Chr(c) => c.toString
+  case Left(v) => flatten(v)
+  case Right(v) => flatten(v)
+  case Seq(v1, v2) => flatten(v1) + flatten(v2)
+  case Stars(vs) => vs.map(flatten).mkString
+  case Rec(_, v) => flatten(v)
+}
+
+// extracts an environment from a value
+def env(v: Val) : List[(String, String)] = v match {
+  case Empty => Nil
+  case Chr(c) => Nil
+  case Left(v) => env(v)
+  case Right(v) => env(v)
+  case Seq(v1, v2) => env(v1) ::: env(v2)
+  case Stars(vs) => vs.flatMap(env)
+  case Rec(x, v) => (x, flatten(v))::env(v)
+}
+
+// injection part
+def mkeps(r: Rexp) : Val = r match {
+  case EMPTY => Empty
+  case ALT(r1, r2) => 
+    if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
+  case SEQ(r1, r2) => Seq(mkeps(r1), mkeps(r2))
+  case STAR(r) => Stars(Nil)
+  case RECD(x, r) => Rec(x, mkeps(r))
+  case PLUS(r) => Stars(List(mkeps(r)))
+  case OPT(_) => Right(Empty)
+  case NTIMES(r, n) => if (n == 0) Stars(Nil) else Stars(Nil.padTo(n, mkeps(r)))
+  case _ => { println ("r : " + r.toString); 
+              throw new Exception("mkeps error")}
+}
+
+
+def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
+  case (STAR(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (SEQ(r1, r2), Seq(v1, v2)) => Seq(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Left(Seq(v1, v2))) => Seq(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Right(v2)) => Seq(mkeps(r1), inj(r2, c, v2))
+  case (ALT(r1, r2), Left(v1)) => Left(inj(r1, c, v1))
+  case (ALT(r1, r2), Right(v2)) => Right(inj(r2, c, v2))
+  case (CHAR(_), Empty) => Chr(c) 
+  case (CRANGE(_), Empty) => Chr(c) 
+  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+  case (PLUS(r), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (OPT(r), Left(v1)) => Left(inj(r, c, v1))
+  case (NTIMES(r, n), Seq(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (NTIMES(r, n), Left(Seq(v1, Stars(vs)))) => Stars(inj(r, c, v1)::vs)
+  case (NTIMES(r, n), Right(Stars(v::vs))) => Stars(mkeps(r)::inj(r, c, v)::vs)
+  case _ => { println ("r : " + r.toString + "  v: " + v.toString); 
+              throw new Exception("inj error")}
+}
+
+// main lexing function (produces a value)
+def lex(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+  case c::cs => inj(r, c, lex(der(c, r), cs))
+}
+
+def lexing(r: Rexp, s: String) : Val = lex(r, s.toList)
+
+lexing(("ab" | "ab") ~ ("b" | EMPTY), "ab")
+
+lexing(OPT("ab"), "ab")
+
+lexing(NTIMES("1", 3), "111")
+lexing(NTIMES("1" | EMPTY, 3), "11")
+
+// some "rectification" functions for simplification
+def F_ID(v: Val): Val = v
+def F_RIGHT(f: Val => Val) = (v:Val) => Right(f(v))
+def F_LEFT(f: Val => Val) = (v:Val) => Left(f(v))
+def F_ALT(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
+  case Right(v) => Right(f2(v))
+  case Left(v) => Left(f1(v))
+}
+def F_SEQ(f1: Val => Val, f2: Val => Val) = (v:Val) => v match {
+  case Seq(v1, v2) => Seq(f1(v1), f2(v2))
+}
+def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
+  (v:Val) => Seq(f1(Empty), f2(v))
+def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
+  (v:Val) => Seq(f1(v), f2(Empty))
+def F_RECD(f: Val => Val) = (v:Val) => v match {
+  case Rec(x, v) => Rec(x, f(v))
+}
+def F_ERROR(v: Val): Val = throw new Exception("error")
+
+// simplification of regular expressions returning also an
+// rectification function; no simplification under STAR 
+def simp(r: Rexp): (Rexp, Val => Val) = r match {
+  case ALT(r1, r2) => {
+    val (r1s, f1s) = simp(r1)
+    val (r2s, f2s) = simp(r2)
+    (r1s, r2s) match {
+      case (NULL, _) => (r2s, F_RIGHT(f2s))
+      case (_, NULL) => (r1s, F_LEFT(f1s))
+      case _ => if (r1s == r2s) (r1s, F_LEFT(f1s))
+                else (ALT (r1s, r2s), F_ALT(f1s, f2s)) 
+    }
+  }
+  case SEQ(r1, r2) => {
+    val (r1s, f1s) = simp(r1)
+    val (r2s, f2s) = simp(r2)
+    (r1s, r2s) match {
+      case (NULL, _) => (NULL, F_ERROR)
+      case (_, NULL) => (NULL, F_ERROR)
+      case (EMPTY, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
+      case (_, EMPTY) => (r1s, F_SEQ_Empty2(f1s, f2s))
+      case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
+    }
+  }
+  case RECD(x, r1) => {
+    val (r1s, f1s) = simp(r1)
+    (RECD(x, r1s), F_RECD(f1s))
+  }
+  case r => (r, F_ID)
+}
+
+def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else throw new Exception("Not matched")
+  case c::cs => {
+    val (r_simp, f_simp) = simp(der(c, r))
+    inj(r, c, f_simp(lex_simp(r_simp, cs)))
+  }
+}
+
+def lexing_simp(r: Rexp, s: String) : Val = lex_simp(r, s.toList)
+
+lexing_simp(("a" | "ab") ~ ("b" | ""), "ab")
+
+lexing_simp(OPT("ab"), "ab")
+
+// Lexing Rules for a Small While Language
+
+val SYM = CRANGE("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ")
+val DIGIT = CRANGE("0123456789")
+val ID = SYM ~ (SYM | DIGIT).% 
+val NUM = PLUS(DIGIT)
+val KEYWORD : Rexp = "skip" | "while" | "do" | "if" | "then" | "else" | "read" | "write" | "true" | "false"
+val SEMI: Rexp = ";"
+val OP: Rexp = ":=" | "==" | "-" | "+" | "*" | "!=" | "<" | ">" | "<=" | ">=" | "%" | "/"
+val WHITESPACE = PLUS(" " | "\n" | "\t")
+val RPAREN: Rexp = ")"
+val LPAREN: Rexp = "("
+val BEGIN: Rexp = "{"
+val END: Rexp = "}"
+val STRING: Rexp = "\"" ~ SYM.% ~ "\""
+
+
+val WHILE_REGS = (("k" $ KEYWORD) | 
+                  ("i" $ ID) | 
+                  ("o" $ OP) | 
+                  ("n" $ NUM) | 
+                  ("s" $ SEMI) | 
+                  ("str" $ STRING) |
+                  ("p" $ (LPAREN | RPAREN)) | 
+                  ("b" $ (BEGIN | END)) | 
+                  ("w" $ WHITESPACE)).%
+
+// filters out all white spaces
+def tokenise(r: Rexp, s: String) = 
+  env(lexing_simp(r, s)).filterNot { (s) => s._1 == "w"}
+
+//   Testing
+//============
+
+def time[T](code: => T) = {
+  val start = System.nanoTime()
+  val result = code
+  val end = System.nanoTime()
+  println((end - start)/1.0e9)
+  result
+}
+
+println(lexing_simp(OPT("1"), "1"))
+println(lexing_simp(OPT("1"), ""))
+println(ders("111".toList, NTIMES("1",3)))
+println(lexing_simp(NTIMES("1",3), "111"))
+
+val r1 = ("a" | "ab") ~ ("bcd" | "c")
+println(lexing(r1, "abcd"))
+
+val r2 = ("" | "a") ~ ("ab" | "b")
+println(lexing(r2, "ab"))
+
+
+// Two Simple While Tests
+//========================
+println("prog0 test")
+
+val prog0 = """read n"""
+println(env(lexing_simp(WHILE_REGS, prog0)))
+
+println("prog1 test")
+
+val prog1 = """read  n; write (n)"""
+println(env(lexing_simp(WHILE_REGS, prog1)))
+
+
+// Big Test
+//==========
+
+def escape(raw: String): String = {
+  import scala.reflect.runtime.universe._
+  Literal(Constant(raw)).toString
+}
+
+val prog2 = """
+write "Fib";
+read n;
+minus1 := 0;
+minus2 := 1;
+while n > 0 do {
+  temp := minus2;
+  minus2 := minus1 + minus2;
+  minus1 := temp;
+  n := n - 1
+};
+write "Result";
+write minus2
+"""
+
+val prog3 = """
+start := 1000;
+x := start;
+y := start;
+z := start;
+while 0 < x do {
+ while 0 < y do {
+  while 0 < z do {
+    z := z - 1
+  };
+  z := start;
+  y := y - 1
+ };     
+ y := start;
+ x := x - 1
+}
+"""
+
+
+println("Tokens")
+println(tokenise(WHILE_REGS, prog2).mkString("\n"))
+
+val fib_tokens = tokenise(WHILE_REGS, prog2)
+fib_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")
+
+
+val test_tokens = tokenise(WHILE_REGS, prog3)
+test_tokens.map{case (s1, s2) => (escape(s1), escape(s2))}.mkString(",\n")
+
+
+/*
+for (i <- 1 to 120 by 10) {
+  print(i.toString + ":  ")
+  time(lexing_simp(WHILE_REGS, prog2 * i))
+}
+*/
+
+val toks_fib = 
+  List(("k","write"),
+       ("str","Fib"),
+       ("s",";"),
+       ("k","read"),
+       ("i","n"),
+       ("s",";"),
+       ("i","minus1"),
+       ("o",":="),
+       ("n","0"),
+       ("s",";"),
+       ("i","minus2"),
+       ("o",":="),
+       ("n","1"),
+       ("s",";"),
+       ("k","while"),
+       ("i","n"),
+       ("o",">"),
+       ("n","0"),
+       ("k","do"),
+       ("b","{"),
+       ("i","temp"),
+       ("o",":="),
+       ("i","minus2"),
+       ("s",";"),
+       ("i","minus2"),
+       ("o",":="),
+       ("i","minus1"),
+       ("o","+"),
+       ("i","minus2"),
+       ("s",";"),
+       ("i","minus1"),
+       ("o",":="),
+       ("i","temp"),
+       ("s",";"),
+       ("i","n"),
+       ("o",":="),
+       ("i","n"),
+       ("o","-"),
+       ("n","1"),
+       ("b","}"),
+       ("s",";"),
+       ("k","write"),
+       ("str","Result"),
+       ("s",";"),
+       ("k","write"),
+       ("i","minus2"))
+
+val toks_test =
+  List(("i","start"),
+       ("o",":="),
+       ("n","1000"),
+       ("s",";"),
+       ("i","x"),
+       ("o",":="),
+       ("i","start"),
+       ("s",";"),
+       ("i","y"),
+       ("o",":="),
+       ("i","start"),
+       ("s",";"),
+       ("i","z"),
+       ("o",":="),
+       ("i","start"),
+       ("s",";"),
+       ("k","while"),
+       ("n","0"),
+       ("o","<"),
+       ("i","x"),
+       ("k","do"),
+       ("b","{"),
+       ("k","while"),
+       ("n","0"),
+       ("o","<"),
+       ("i","y"),
+       ("k","do"),
+       ("b","{"),
+       ("k","while"),
+       ("n","0"),
+       ("o","<"),
+       ("i","z"),
+       ("k","do"),
+       ("b","{"),
+       ("i","z"),
+       ("o",":="),
+       ("i","z"),
+       ("o","-"),
+       ("n","1"),
+       ("b","}"),
+       ("s",";"),
+       ("i","z"),
+       ("o",":="),
+       ("i","start"),
+       ("s",";"),
+       ("i","y"),
+       ("o",":="),
+       ("i","y"),
+       ("o","-"),
+       ("n","1"),
+       ("b","}"),
+       ("s",";"),
+       ("i","y"),
+       ("o",":="),
+       ("i","start"),
+       ("s",";"),
+       ("i","x"),
+       ("o",":="),
+       ("i","x"),
+       ("o","-"),
+       ("n","1"),
+       ("b","}"))