Binary file cws/cw04.pdf has changed

--- a/cws/cw04.tex	Tue May 30 16:58:06 2023 +0100
+++ b/cws/cw04.tex	Fri Jun 02 15:58:57 2023 +0100
@@ -233,6 +233,17 @@
 Explain your decision and indicate what this program would
 print out.
 
+\subsection*{Question 4 (Advanced)}
+
+Extend the lexer and parser in order to add a \texttt{break} keyword.
+Modify the compiler such that when a \texttt{break} is encountered the
+code should jump out of the ``enclosing'' while loop, or in case it
+is not inside a while loop to the end of the
+program.
+
+\bigskip\noindent
+\textcolor{red}{ADD EXAMPLE PROGRAMS}
+
 \subsection*{Further Information}
 
 The Java infrastructure unfortunately does not contain an

--- a/solutions/cw4/compiler.sc	Tue May 30 16:58:06 2023 +0100
+++ b/solutions/cw4/compiler.sc	Fri Jun 02 15:58:57 2023 +0100
@@ -1,4 +1,9 @@
 // Compiler for JVM
+// 
+// call with 
+//
+//     amm2 compiler.sc 
+//
 
 import $file.lexer
 import lexer._
@@ -109,6 +114,13 @@
     compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ compile_op(op)
 }
 
+def compile_bop(op: String) = op match {
+  case "==" => "if_icmpne"
+  case "!=" => "if_icmpeq"
+  case "<" => "if_icmpge"
+  case ">" => "if_icmple"
+}
+
 def compile_bexp(b: BExp, env : Env, jmp: String) : String = b match {
   case True => ""
   case False => i"goto $jmp"
@@ -122,14 +134,8 @@
     compile_bexp(b2, env, jmp) ++
     l"$or_end"
   }
-  case Bop("==", a1, a2) => 
-    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ i"if_icmpne $jmp"
-  case Bop("!=", a1, a2) => 
-    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ i"if_icmpeq $jmp"
-  case Bop("<", a1, a2) => 
-    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ i"if_icmpge $jmp"
-  case Bop(">", a1, a2) => 
-    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ i"if_icmple $jmp"
+  case Bop(op, a1, a2) => 
+    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ i"${compile_bop(op)} $jmp"
 }
 
 def compile_stmt(s: Stmt, env: Env) : (String, Env) = s match {

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4a/collatz2.while	Fri Jun 02 15:58:57 2023 +0100
@@ -0,0 +1,27 @@
+// Collatz series
+//
+// needs writing of strings and numbers; comments
+
+bnd := 1;
+while bnd < 100001 do {
+  write bnd;
+  write ": ";
+  n := bnd;
+  cnt := 0;
+
+  while n > 1 do {
+    write n;
+    write ",";
+    
+    if n % 2 == 0 
+    then n := n / 2 
+    else n := 3 * n+1;
+
+    cnt := cnt + 1
+  };
+
+  write " => ";
+  write cnt;
+  write "\n";
+  bnd := bnd + 1
+}
\ No newline at end of file

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4a/collatz3.while	Fri Jun 02 15:58:57 2023 +0100
@@ -0,0 +1,28 @@
+// Collatz series
+//
+// needs writing of strings and numbers; comments
+
+bnd := 1;
+while bnd < 100001 do {
+  write bnd;
+  write ": ";
+  n := bnd;
+  cnt := 0;
+
+  while n > 1 do {
+    write n;
+    write ",";
+    
+    if n % 2 == 0 
+    then n := n / 2 
+    else n := 3 * n+1;
+
+    cnt := cnt + 1
+  };
+
+  write " => ";
+  write cnt;
+  write "\n";
+  bnd := bnd + 1;
+  if (bnd > 1000) then break else skip
+}
\ No newline at end of file

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4a/compiler.sc	Fri Jun 02 15:58:57 2023 +0100
@@ -0,0 +1,288 @@
+// Compiler for JVM
+// 
+// call with 
+//
+//     amm2 compiler.sc 
+//
+
+import $file.lexer
+import lexer._
+
+import $file.parser
+import parser._
+
+
+val beginning = """
+.class public XXX.XXX
+.super java/lang/Object
+
+.method public static write(I)V 
+    .limit locals 1 
+    .limit stack 2 
+    getstatic java/lang/System/out Ljava/io/PrintStream; 
+    iload 0
+    invokevirtual java/io/PrintStream/print(I)V 
+    return 
+.end method
+
+.method public static writes(Ljava/lang/String;)V
+    .limit stack 2
+    .limit locals 1
+    getstatic java/lang/System/out Ljava/io/PrintStream;
+    aload 0
+    invokevirtual java/io/PrintStream/print(Ljava/lang/String;)V
+    return
+.end method
+
+.method public static read()I 
+    .limit locals 10 
+    .limit stack 10
+
+    ldc 0 
+    istore 1  ; this will hold our final integer 
+Label1: 
+    getstatic java/lang/System/in Ljava/io/InputStream; 
+    invokevirtual java/io/InputStream/read()I 
+    istore 2 
+    iload 2 
+    ldc 10   ; the newline delimiter 
+    isub 
+    ifeq Label2 
+    iload 2 
+    ldc 32   ; the space delimiter 
+    isub 
+    ifeq Label2
+
+    iload 2 
+    ldc 48   ; we have our digit in ASCII, have to subtract it from 48 
+    isub 
+    ldc 10 
+    iload 1 
+    imul 
+    iadd 
+    istore 1 
+    goto Label1 
+Label2: 
+    ;when we come here we have our integer computed in local variable 1 
+    iload 1 
+    ireturn 
+.end method
+
+.method public static main([Ljava/lang/String;)V
+   .limit locals 200
+   .limit stack 200
+
+; COMPILED CODE STARTS
+
+"""
+
+val ending = """
+; COMPILED CODE ENDS
+   return
+
+.end method
+"""
+
+// Compiler
+
+var counter = -1
+
+def Fresh(x: String) = {
+  counter += 1
+  x ++ "_" ++ counter.toString()
+}
+
+implicit def string_interpolations(sc: StringContext) = new {
+    def i(args: Any*): String = "   " ++ sc.s(args:_*) ++ "\n"
+    def l(args: Any*): String = sc.s(args:_*) ++ ":\n"
+}
+
+type Env = Map[String, Int]
+
+def compile_op(op: String) = op match {
+  case "+" => i"iadd"
+  case "-" => i"isub"
+  case "*" => i"imul"
+  case "/" => i"idiv"
+  case "%" => i"irem"
+}
+
+def compile_aexp(a: AExp, env : Env) : String = a match {
+  case Num(i) => i"ldc $i"
+  case Var(s) => i"iload ${env(s)} \t\t; $s"
+  case Aop(op, a1, a2) => 
+    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ compile_op(op)
+}
+
+def compile_bop(op: String) = op match {
+  case "==" => "if_icmpne"
+  case "!=" => "if_icmpeq"
+  case "<" => "if_icmpge"
+  case ">" => "if_icmple"
+}
+
+def compile_bexp(b: BExp, env : Env, jmp: String) : String = b match {
+  case True => ""
+  case False => i"goto $jmp"
+  case And(b1, b2) => compile_bexp(b1, env, jmp) ++ compile_bexp(b2, env, jmp)
+  case Or(b1, b2) => {
+    val b1_false = Fresh("Or_second");
+    val or_end = Fresh("Or_end");
+    compile_bexp(b1, env, b1_false) ++
+    i"goto $or_end" ++
+    l"$b1_false" ++
+    compile_bexp(b2, env, jmp) ++
+    l"$or_end"
+  }
+  case Bop(op, a1, a2) => 
+    compile_aexp(a1, env) ++ compile_aexp(a2, env) ++ i"${compile_bop(op)} $jmp"
+}
+
+def compile_stmt(s: Stmt, env: Env, jmp: String) : (String, Env) = s match {
+  case Skip => ("", env)
+  case Break => (i"goto $jmp", env)
+  case Assign(x, a) => {
+    val index = env.getOrElse(x, env.keys.size)
+    (compile_aexp(a, env) ++ i"istore $index \t\t; $x", env + (x -> index))
+  } 
+  case If(b, bl1, bl2) => {
+    val if_else = Fresh("If_else")
+    val if_end = Fresh("If_end")
+    val (instrs1, env1) = compile_block(bl1, env, jmp)
+    val (instrs2, env2) = compile_block(bl2, env1, jmp)
+    (compile_bexp(b, env, if_else) ++
+     instrs1 ++
+     i"goto $if_end" ++
+     l"$if_else" ++
+     instrs2 ++
+     l"$if_end", env2)
+  }
+  case While(b, bl) => {
+    val loop_begin = Fresh("Loop_begin")
+    val loop_end = Fresh("Loop_end")
+    val (instrs1, env1) = compile_block(bl, env, loop_end)
+    (l"$loop_begin" ++
+     compile_bexp(b, env, loop_end) ++
+     instrs1 ++
+     i"goto $loop_begin" ++
+     l"$loop_end", env1)
+  }
+  case For(id, lower, upper, code) => {
+      val (assignment_code, env1) = compile_stmt(Assign(id, lower), env, jmp)  // id := lower;
+      val while_equivalent = While(
+          Or(Bop("<", Var(id), upper), Bop("==", Var(id), upper)),    // while id <= upper do {
+          code ++                                                     //    code  
+          List(
+            Assign(id, Aop("+", Var(id), Num(1)))                     //    id := id + 1
+          ))                                                          // };
+
+      val (while_code, env2) = compile_stmt(while_equivalent, env1, jmp)
+      (assignment_code ++ while_code, env2)
+  }
+  case WriteId(x) => (i"iload ${env(x)} \t\t; $x" ++ 
+     i"invokestatic XXX/XXX/write(I)V", env)
+  case WriteString(x) => (s"   ldc ${x}\n" ++
+     i"invokestatic XXX/XXX/writes(Ljava/lang/String;)V", env)
+  case Read(x) => {
+    val index = env.getOrElse(x, env.keys.size) 
+    (i"invokestatic XXX/XXX/read()I" ++ 
+     i"istore $index \t\t; $x", env + (x -> index))
+  }
+}
+
+def compile_block(bl: Block, env: Env, jmp: String) : (String, Env) = bl match {
+  case Nil => ("", env)
+  case s::bl => {
+    val (instrs1, env1) = compile_stmt(s, env, jmp)
+    val (instrs2, env2) = compile_block(bl, env1, jmp)
+    (instrs1 ++ instrs2, env2)
+  }
+}
+
+def compile(bl: Block, class_name: String) : String = {
+  val instructions = compile_block(bl, Map.empty, "")._1
+  (beginning ++ instructions ++ ending).replaceAllLiterally("XXX", class_name)
+}
+
+// Compiling and running
+
+import scala.util._
+import scala.sys.process._
+import scala.io
+
+def compile_tofile(bl: Block, class_name: String) = {
+  val output = compile(bl, class_name)
+  val fw = new java.io.FileWriter(class_name + ".j") 
+  fw.write(output) 
+  fw.close()
+}
+
+def compile_all(bl: Block, class_name: String) : Unit = {
+  compile_tofile(bl, class_name)
+  println("compiled ")
+  val test = ("java -jar jasmin.jar " + class_name + ".j").!!
+  println("assembled ")
+}
+
+def time_needed[T](i: Int, code: => T) = {
+  val start = System.nanoTime()
+  for (j <- 1 to i) code
+  val end = System.nanoTime()
+  (end - start)/(i * 1.0e9)
+}
+
+def compile_run(bl: Block, class_name: String) : Unit = {
+  println("Start compilation")
+  compile_all(bl, class_name)
+  println("running")
+  println("Time: " + time_needed(1, ("java " + class_name + "/" + class_name).!))
+}
+
+// ---- Q1
+
+// Fibonacci
+
+val fibonacciProgram = """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"""
+
+compile_all(Stmts.parse_all(tokenise(fibonacciProgram)).head, "fib")
+
+val factorialProgram = """write "Factorial";
+read n;
+fact := 1;
+
+while n > 0 do {
+  fact := n * fact;
+  n := n - 1
+};
+
+write "Result";
+write fact
+"""
+
+compile_all(Stmts.parse_all(tokenise(factorialProgram)).head, "factorial")
+
+// ---- Q3
+
+/* compile_run(Stmts.parse_all(tokenise("""for i := 1 upto 10 do {
+  for i := 1 upto 10 do {
+    write i
+  }
+}""")).head, "nestedloop") */
+
+
+compile_run(Stmts.parse_all(tokenise(os.read(os.pwd / "collatz2.while"))).head, "collatz2")
+
+
+
+compile_run(Stmts.parse_all(tokenise(os.read(os.pwd / "collatz3.while"))).head, "collatz3")

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4a/fib.while	Fri Jun 02 15:58:57 2023 +0100
@@ -0,0 +1,13 @@
+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 
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4a/lexer.sc	Fri Jun 02 15:58:57 2023 +0100
@@ -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" | "break"
+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)
+
+

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/solutions/cw4a/parser.sc	Fri Jun 02 15:58:57 2023 +0100
@@ -0,0 +1,164 @@
+// CW3
+
+import $file.lexer
+import lexer._ 
+
+
+case class ~[+A, +B](_1: A, _2: B)
+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
+}
+
+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)
+}
+
+// New parser that takes as input a list of tokens
+case class TokenListParser(ts: List[Token]) extends Parser[List[Token], List[Token]] {
+    def parse(tsb: List[Token]) = {
+        val (prefix, suffix) = tsb.splitAt(ts.length)
+        if (prefix == ts) Set((prefix, suffix)) else Set()
+    }
+}
+
+// Implicit definitions to go from a token 
+// or a list of tokens to a TokenListParser
+implicit def token2parser(t: Token) = TokenListParser(List(t))
+implicit def tokenList2parser(ts: List[Token]) = TokenListParser(ts)
+
+implicit def ParserOps[I : IsSeq, T](p: Parser[I, T]) = 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 TokenOps(t: Token) = new {
+    def || (q : => Parser[List[Token], List[Token]]) = new AltParser[List[Token], List[Token]](List(t), q)
+    def || (qs : List[Token]) = new AltParser[List[Token], List[Token]](List(t), qs)
+    def ==>[S] (f: => List[Token] => S) = new FunParser[List[Token], List[Token], S](List(t), f)
+    def ~[S](q : => Parser[List[Token], S]) =
+        new SeqParser[List[Token], List[Token], S](List(t), q)
+    def ~ (qs : List[Token]) =
+        new SeqParser[List[Token], List[Token], List[Token]](List(t), qs)
+}
+
+implicit def TokenListOps(ts: List[Token]) = new {
+    def || (q : => Parser[List[Token], List[Token]]) = new AltParser[List[Token], List[Token]](ts, q)
+    def || (qs : List[Token]) = new AltParser[List[Token], List[Token]](ts, qs)
+    def ==>[S] (f: => List[Token] => S) = new FunParser[List[Token], List[Token], S](ts, f)
+    def ~[S](q : => Parser[List[Token], S]) =
+        new SeqParser[List[Token], List[Token], S](ts, q)
+    def ~ (qs : List[Token]) =
+        new SeqParser[List[Token], List[Token], List[Token]](ts, qs)
+}
+
+// Abstract Syntax Trees
+abstract class Stmt
+abstract class AExp
+abstract class BExp
+
+type Block = List[Stmt]
+
+case object Skip extends Stmt
+case object Break 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 Read(s: String) extends Stmt
+case class WriteId(s: String) extends Stmt  // for printing values of variables
+case class WriteString(s: String) extends Stmt  // for printing words
+case class For(counter: String, lower: AExp, upper: AExp, code: Block) 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
+
+case class IdParser() extends Parser[List[Token], String] {
+    def parse(tsb: List[Token]) = tsb match {
+        case T_ID(id) :: rest => Set((id, rest))
+        case _ => Set()
+    }
+}
+
+case class NumParser() extends Parser[List[Token], Int] {
+    def parse(tsb: List[Token]) = tsb match {
+        case T_NUM(n) :: rest => Set((n, rest))
+        case _ => Set()
+    }
+}
+
+case class StringParser() extends Parser[List[Token], String] {
+    def parse(tsb: List[Token]) = tsb match {
+        case T_STRING(s) :: rest => Set((s, rest))
+        case _ => Set()
+    }
+}
+
+// WHILE Language Parsing
+lazy val AExp: Parser[List[Token], AExp] = 
+  (Te ~ T_OP("+") ~ AExp) ==> { case x ~ _ ~ z => Aop("+", x, z): AExp } ||
+  (Te ~ T_OP("-") ~ AExp) ==> { case x ~ _ ~ z => Aop("-", x, z): AExp } || Te
+lazy val Te: Parser[List[Token], AExp] = 
+  (Fa ~ T_OP("*") ~ Te) ==> { case x ~ _ ~ z => Aop("*", x, z): AExp } || 
+  (Fa ~ T_OP("/") ~ Te) ==> { case x ~ _ ~ z => Aop("/", x, z): AExp } || 
+  (Fa ~ T_OP("%") ~ Te) ==> { case x ~ _ ~ z => Aop("%", x, z): AExp } || Fa  
+lazy val Fa: Parser[List[Token], AExp] = 
+   (T_PAREN("(") ~ AExp ~ T_PAREN(")")) ==> { case _ ~ y ~ _ => y } || 
+   IdParser() ==> Var  || 
+   NumParser() ==> Num
+
+lazy val BExp: Parser[List[Token], BExp] = 
+   (AExp ~ T_OP("==") ~ AExp) ==> { case x ~ _ ~ z => Bop("==", x, z): BExp } || 
+   (AExp ~ T_OP("!=") ~ AExp) ==> { case x ~ _ ~ z => Bop("!=", x, z): BExp } || 
+   (AExp ~ T_OP("<") ~ AExp) ==> { case x ~ _ ~ z => Bop("<", x, z): BExp } || 
+   (AExp ~ T_OP(">") ~ AExp) ==> { case x ~ _ ~ z => Bop(">", x, z): BExp } ||
+   (T_PAREN("(") ~ BExp ~ List(T_PAREN(")"), T_OP("&&")) ~ BExp) ==> { case _ ~ y ~ _ ~ v => And(y, v): BExp } ||
+   (T_PAREN("(") ~ BExp ~ List(T_PAREN(")"), T_OP("||")) ~ BExp) ==> { case _ ~ y ~ _ ~ v => Or(y, v): BExp } ||
+   (T_KEYWORD("true") ==> (_ => True: BExp )) || 
+   (T_KEYWORD("false") ==> (_ => False: BExp )) ||
+   (T_PAREN("(") ~ BExp ~ T_PAREN(")")) ==> { case _ ~ x ~ _ => x }
+
+lazy val Stmt: Parser[List[Token], Stmt] =
+    T_KEYWORD("skip") ==> (_ => Skip: Stmt) ||
+    T_KEYWORD("break") ==> (_ => Break: Stmt) ||
+    (IdParser() ~ T_OP(":=") ~ AExp) ==> { case id ~ _ ~ z => Assign(id, z): Stmt } ||
+    (T_KEYWORD("if") ~ BExp ~ T_KEYWORD("then") ~ Block ~ T_KEYWORD("else") ~ Block) ==> { case _ ~ y ~ _ ~ u ~ _ ~ w => If(y, u, w): Stmt } ||
+    (T_KEYWORD("while") ~ BExp ~ T_KEYWORD("do") ~ Block) ==> { case _ ~ y ~ _ ~ w => While(y, w) : Stmt } ||
+    (T_KEYWORD("read") ~ IdParser()) ==> { case _ ~ id => Read(id): Stmt} ||
+    (T_KEYWORD("write") ~ IdParser()) ==> { case _ ~ id => WriteId(id): Stmt} ||
+    (T_KEYWORD("write") ~ StringParser()) ==> { case _ ~ s => WriteString(s): Stmt} ||
+    (T_KEYWORD("for") ~ IdParser() ~ T_OP(":=") ~ AExp ~ T_KEYWORD("upto") ~ AExp ~ T_KEYWORD("do") ~ Block) ==> {
+      case _ ~ id ~ _ ~ lower ~ _ ~ upper ~ _ ~ blck => For(id, lower, upper, blck): Stmt
+    }
+
+lazy val Stmts: Parser[List[Token], Block] =
+    (Stmt ~ T_SEMI ~ Stmts) ==> { case x ~ _ ~ z => x :: z : Block } ||
+    (Stmt ==> (s => List(s) : Block))
+
+lazy val Block: Parser[List[Token], Block] =
+    (T_PAREN("{") ~ Stmts ~ T_PAREN("}")) ==> { case x ~ y ~ z => y} ||
+    (Stmt ==> (s => List(s)))
+