--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/progs/while.scala	Sat Jun 15 09:23:18 2013 -0400
@@ -0,0 +1,231 @@
+// A parser and evaluator for teh while language
+// 
+import matcher._
+import parser._
+
+
+// some regular expressions
+val SYM = RANGE("ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_")
+val DIGIT = RANGE("0123456789")
+val ID = SEQ(SYM, STAR(ALT(SYM, DIGIT))) 
+val NUM = PLUS(DIGIT)
+val KEYWORD = ALTS("skip", "while", "do", "if", "then", "else", "true", "false") 
+val SEMI: Rexp = ";"
+val OP: Rexp = ALTS(":=", "=", "-", "+", "*", "!=", "<", ">")
+val WHITESPACE = PLUS(RANGE(" \n"))
+val RPAREN: Rexp = ")"
+val LPAREN: Rexp = "("
+val BEGIN: Rexp = "{"
+val END: Rexp = "}"
+
+// tokens for classifying the strings that have been recognised
+abstract class Token
+case object T_WHITESPACE extends Token
+case object T_SEMI extends Token
+case object T_LPAREN extends Token
+case object T_RPAREN extends Token
+case object T_BEGIN extends Token
+case object T_END extends Token
+case class T_ID(s: String) extends Token
+case class T_OP(s: String) extends Token
+case class T_NUM(s: String) extends Token
+case class T_KWD(s: String) extends Token
+
+val lexing_rules: List[(Rexp, List[Char] => Token)] = 
+  List((KEYWORD, (s) => T_KWD(s.mkString)),
+       (ID, (s) => T_ID(s.mkString)),
+       (OP, (s) => T_OP(s.mkString)),
+       (NUM, (s) => T_NUM(s.mkString)),
+       (SEMI, (s) => T_SEMI),
+       (LPAREN, (s) => T_LPAREN),
+       (RPAREN, (s) => T_RPAREN),
+       (BEGIN, (s) => T_BEGIN),
+       (END, (s) => T_END),
+       (WHITESPACE, (s) => T_WHITESPACE))
+
+// the tokenizer
+val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE))
+
+// the abstract syntax trees
+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 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
+
+// atomic parsers
+case class TokParser(tok: Token) extends Parser[List[Token], Token] {
+  def parse(ts: List[Token]) = ts match {
+    case t::ts if (t == tok) => Set((t, ts)) 
+    case _ => Set ()
+  }
+}
+implicit def token2tparser(t: Token) = TokParser(t)
+
+case object NumParser extends Parser[List[Token], Int] {
+  def parse(ts: List[Token]) = ts match {
+    case T_NUM(s)::ts => Set((s.toInt, ts)) 
+    case _ => Set ()
+  }
+}
+
+case object IdParser extends Parser[List[Token], String] {
+  def parse(ts: List[Token]) = ts match {
+    case T_ID(s)::ts => Set((s, ts)) 
+    case _ => Set ()
+  }
+}
+
+
+// arithmetic expressions
+lazy val AExp: Parser[List[Token], AExp] = 
+  (T ~ T_OP("+") ~ AExp) ==> { case ((x, y), z) => Aop("+", x, z): AExp } ||
+  (T ~ T_OP("-") ~ AExp) ==> { case ((x, y), z) => Aop("-", x, z): AExp } || T  
+lazy val T: Parser[List[Token], AExp] = 
+  (F ~ T_OP("*") ~ T) ==> { case ((x, y), z) => Aop("*", x, z): AExp } || F
+lazy val F: Parser[List[Token], AExp] = 
+  (T_LPAREN ~> AExp <~ T_RPAREN) || 
+  IdParser ==> Var || 
+  NumParser ==> Num
+
+// boolean expressions
+lazy val BExp: Parser[List[Token], BExp] = 
+  (AExp ~ T_OP("=") ~ AExp) ==> { case ((x, y), z) => Bop("=", x, z): BExp } || 
+  (AExp ~ T_OP("!=") ~ AExp) ==> { case ((x, y), z) => Bop("!=", x, z): BExp } || 
+  (AExp ~ T_OP("<") ~ AExp) ==> { case ((x, y), z) => Bop("<", x, z): BExp } || 
+  (AExp ~ T_OP(">") ~ AExp) ==> { case ((x, y), z) => Bop(">", x, z): BExp } || 
+  (T_KWD("true") ==> ((_) => True)) || 
+  (T_KWD("false") ==> ((_) => False: BExp))
+
+lazy val Stmt: Parser[List[Token], Stmt] =
+  (T_KWD("skip") ==> ((_) => Skip: Stmt)) ||
+  (IdParser ~ T_OP(":=") ~ AExp) ==> { case ((x, y), z) => Assign(x, z): Stmt } ||
+  (T_KWD("if") ~ BExp ~ T_KWD("then") ~ Block ~ T_KWD("else") ~ Block) ==>
+    { case (((((x,y),z),u),v),w) => If(y, u, w): Stmt } ||
+  (T_KWD("while") ~ BExp ~ T_KWD("do") ~ Block) ==> { case (((x, y), z), w) => While(y, w) } 
+ 
+lazy val Stmts: Parser[List[Token], Block] =
+  (Stmt ~ T_SEMI ~ Stmts) ==> { case ((x, y), z) => x :: z : Block } ||
+  (Stmt ==> ((s) => List(s) : Block))
+
+lazy val Block: Parser[List[Token], Block] =
+  (T_BEGIN ~> Stmts <~ T_END) || 
+  (Stmt ==> ((s) => List(s)))
+
+
+// examples
+val p1 = "x := 5"
+val p1_toks = Tok.fromString(p1) 
+val p1_ast = Block.parse_all(p1_toks)
+println(p1_toks)
+println(p1_ast)
+
+val p1a = "{ x := 5; y := 8}"
+val p1a_toks = Tok.fromString(p1a) 
+val p1a_ast = Block.parse_all(p1a_toks)
+println(p1a_ast)
+
+val p2 = "5 = 6"
+val p2_toks = Tok.fromString(p2) 
+val p2_ast = BExp.parse_all(p2_toks)
+println(p2_ast)
+
+val p2a = "true"
+val p2a_toks = Tok.fromString(p2a) 
+val p2a_ast = BExp.parse_all(p2a_toks)
+println(p2a_ast)
+
+val p3 = "if true then skip else skip"
+val p3_toks = Tok.fromString(p3) 
+val p3_ast = Stmt.parse_all(p3_toks)
+println(p3_ast)
+
+val p3a = "if true then x := 5 else x := 10"
+val p3a_toks = Tok.fromString(p3a) 
+val p3a_ast = Stmt.parse_all(p3a_toks)
+println(p3a_ast)
+
+val p3b = "if false then x := 5 else x := 10"
+val p3b_toks = Tok.fromString(p3b) 
+val p3b_ast = Stmt.parse_all(p3b_toks)
+println(p3b_ast)
+
+// multiplication
+val p4 = """{ x := 5;
+              y := 4;
+              r := 0;
+              while y > 0 do {
+                 r := r + x;
+                 y := y - 1
+              } 
+            }"""
+val p4_toks = Tok.fromString(p4) 
+val p4_ast = Block.parse_all(p4_toks)
+println(p4_ast)
+
+val p5 = """
+ n := 9;
+ minus1 := 0;
+ minus2 := 1;
+ temp := 0;
+ while n > 0 do  {
+   temp := minus2;
+   minus2 := minus1 + minus2;
+   minus1 := temp;
+   n := n - 1
+ };
+ fib_res := minus2
+"""
+val p5_toks = Tok.fromString(p5) 
+val p5_ast = Stmts.parse_all(p5_toks)
+
+// interpreter
+type Env = Map[String, Int]
+
+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)
+}
+
+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)
+}
+
+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
+}
+
+def eval_bl(bl: Block, env: Env) : Env = bl match {
+  case Nil => env
+  case s::bl => eval_bl(bl, eval_stmt(s, env))
+}
+
+//examples
+println(eval_stmt(p3a_ast.head, Map.empty))
+println(eval_stmt(p3b_ast.head, Map.empty))
+println(eval_bl(p4_ast.head, Map.empty))
+println(eval_bl(p5_ast.head, Map.empty))