diff -r 54a483a33763 -r 02ef5c3abc51 solutions/cw4/lexer.sc
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4/lexer.sc	Fri Nov 04 12:07:40 2022 +0000
@@ -0,0 +1,251 @@
+import scala.language.implicitConversions    
+import scala.language.reflectiveCalls
+
+// Rexp
+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 RECD(x: String, r: Rexp) extends Rexp
+
+case class RANGE(s: Set[Char]) extends Rexp
+case class PLUS(r: Rexp) extends Rexp
+case class OPTIONAL(r: Rexp) extends Rexp
+case class NTIMES(r: Rexp, n: Int) extends Rexp 
+
+// Values
+abstract class Val
+case object Empty extends Val
+case class Chr(c: Char) extends Val
+case class Sequ(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
+
+
+// Convenience typing
+def charlist2rexp(s : List[Char]): Rexp = s match {
+  case Nil => ONE
+  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
+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 RECD(_, r1) => nullable(r1)
+  case RANGE(_) => false
+  case PLUS(r1) => nullable(r1)
+  case OPTIONAL(_) => true
+  case NTIMES(r1, i) => if (i == 0) true else nullable(r1)
+}
+
+// der
+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(r) => SEQ(der(c, r), STAR(r))
+
+  case RECD(_, r1) => der(c, r1)
+  case RANGE(s) => if (s.contains(c)) ONE else ZERO 
+  case PLUS(r1) => SEQ(der(c, r1), STAR(r1))
+  case OPTIONAL(r1) => ALT(der(c, r1), ZERO)
+  case NTIMES(r, i) => 
+    if (i == 0) ZERO else SEQ(der(c, r), NTIMES(r, i - 1))
+}
+
+// Flatten
+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 Sequ(v1, v2) => flatten(v1) + flatten(v2)
+  case Stars(vs) => vs.map(flatten).mkString
+  case Rec(_, v) => flatten(v)
+}
+
+// Env
+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 Sequ(v1, v2) => env(v1) ::: env(v2)
+  case Stars(vs) => vs.flatMap(env)
+  case Rec(x, v) => (x, flatten(v))::env(v)
+}
+
+// Mkeps
+def mkeps(r: Rexp) : Val = r match {
+  case ONE => Empty
+  case ALT(r1, r2) => 
+    if (nullable(r1)) Left(mkeps(r1)) else Right(mkeps(r2))
+  case SEQ(r1, r2) => Sequ(mkeps(r1), mkeps(r2))
+  case STAR(r) => Stars(Nil)
+  case RECD(x, r) => Rec(x, mkeps(r))
+
+  case PLUS(r) => Stars(List(mkeps(r)))   // the first copy must match the empty string
+  case OPTIONAL(r) => Right(Empty)
+  case NTIMES(r, i) => Stars(List.fill(i)(mkeps(r)))
+}
+
+// Inj
+def inj(r: Rexp, c: Char, v: Val) : Val = (r, v) match {
+  case (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj(r1, c, v1), v2)
+  case (SEQ(r1, r2), Right(v2)) => Sequ(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(d), Empty) => Chr(c) 
+  case (RECD(x, r1), _) => Rec(x, inj(r1, c, v))
+
+  case (RANGE(_), Empty) => Chr(c)
+  case (PLUS(r), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+  case (OPTIONAL(r), Left(v1)) => Left(inj(r, c, v1))
+  case (NTIMES(r, n), Sequ(v1, Stars(vs))) => Stars(inj(r, c, v1)::vs)
+}
+
+// Rectification functions
+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 Sequ(v1, v2) => Sequ(f1(v1), f2(v2))
+}
+def F_SEQ_Empty1(f1: Val => Val, f2: Val => Val) = 
+  (v:Val) => Sequ(f1(Empty), f2(v))
+def F_SEQ_Empty2(f1: Val => Val, f2: Val => Val) = 
+  (v:Val) => Sequ(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")
+
+// Simp
+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 (ZERO, _) => (r2s, F_RIGHT(f2s))
+      case (_, ZERO) => (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 (ZERO, _) => (ZERO, F_ERROR)
+      case (_, ZERO) => (ZERO, F_ERROR)
+      case (ONE, _) => (r2s, F_SEQ_Empty1(f1s, f2s))
+      case (_, ONE) => (r1s, F_SEQ_Empty2(f1s, f2s))
+      case _ => (SEQ(r1s,r2s), F_SEQ(f1s, f2s))
+    }
+  }
+  case r => (r, F_ID)
+}
+
+// Lex
+def lex_simp(r: Rexp, s: List[Char]) : Val = s match {
+  case Nil => if (nullable(r)) mkeps(r) else 
+    { throw new Exception("lexing error") } 
+  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) = env(lex_simp(r, s.toList))
+
+// Language specific code
+val KEYWORD : Rexp = "while" | "if" | "then" | "else" | "do" | "for" | "to" | "true" | "false" | "read" | "write" | "skip" 
+val OP : Rexp = "+" | "-" | "*" | "%" | "/" | "==" | "!=" | ">" | "<" | ">=" | "<=" | ":=" | "&&" | "||"
+val LET: Rexp = RANGE(('A' to 'Z').toSet ++ ('a' to 'z'))
+val SYM : Rexp = LET | RANGE(Set('.', '_', '>', '<', '=', ';', ',', ':'))
+val PARENS : Rexp = "(" | "{" | ")" | "}"
+val SEMI : Rexp = ";"
+val WHITESPACE : Rexp = PLUS(" ") | "\n" | "\t" | "\r"
+val DIGIT : Rexp = RANGE(('0' to '9').toSet)
+val DIGIT1 : Rexp = RANGE(('1' to '9').toSet)
+val STRING : Rexp = "\"" ~ (SYM | " " | "\\n" | DIGIT).% ~ "\""
+val ID : Rexp = LET ~ (LET | "_" | DIGIT).%
+val NUM : Rexp = "0" | (DIGIT1 ~ DIGIT.%)
+val EOL : Rexp = "\n" | "\r\n"
+val COMMENT : Rexp = "//" ~ (SYM | PARENS | " " | DIGIT).% ~ EOL
+
+val WHILE_REGS = (("k" $ KEYWORD) | 
+                  ("o" $ OP) | 
+                  ("str" $ STRING) |
+                  ("p" $ PARENS) |
+                  ("s" $ SEMI) | 
+                  ("w" $ WHITESPACE) | 
+                  ("i" $ ID) | 
+                  ("n" $ NUM) |
+		  ("c" $ COMMENT)).%
+
+// Token
+abstract class Token extends Serializable 
+case class T_KEYWORD(s: String) extends Token
+case class T_OP(s: String) extends Token
+case class T_STRING(s: String) extends Token
+case class T_PAREN(s: String) extends Token
+case object T_SEMI extends Token
+case class T_ID(s: String) extends Token
+case class T_NUM(n: Int) extends Token
+
+val token : PartialFunction[(String, String), Token] = {
+  case ("k", s) => T_KEYWORD(s)
+  case ("o", s) => T_OP(s)
+  case ("str", s) => T_STRING(s)
+  case ("p", s) => T_PAREN(s)
+  case ("s", _) => T_SEMI
+  case ("i", s) => T_ID(s)
+  case ("n", s) => T_NUM(s.toInt)
+}
+
+// Tokenise
+def tokenise(s: String) : List[Token] = 
+  lexing_simp(WHILE_REGS, s).collect(token)
+
+