--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Attic/while1.scala Thu Jul 30 13:50:54 2020 +0100
@@ -0,0 +1,221 @@
+// A parser and evaluator for the WHILE language
+//
+
+
+
+
+
+// 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", "write")
+val SEMI: Rexp = ";"
+val OP: Rexp = ALTS(":=", "=", "-", "+", "*", "!=", "<", ">")
+val WHITESPACE = PLUS(RANGE(" \n"))
+val RPAREN: Rexp = ")"
+val LPAREN: Rexp = "("
+val BEGIN: Rexp = "{"
+val END: Rexp = "}"
+val COMMENT = SEQS("/*", NOT(SEQS(STAR(ALLC), "*/", STAR(ALLC))), "*/")
+
+// tokens for classifying the strings that have been recognised
+abstract class Token
+case object T_WHITESPACE extends Token
+case object T_COMMENT 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),
+ (COMMENT, (s) => T_COMMENT))
+
+// the tokenizer
+val Tok = Tokenizer(lexing_rules, List(T_WHITESPACE, T_COMMENT))
+
+// 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 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
+
+// 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] =
+ (T_KWD("true") ==> ((_) => True: BExp)) ||
+ (T_KWD("false") ==> ((_) => False: BExp)) ||
+ (T_LPAREN ~> BExp <~ T_RPAREN) ||
+ (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("<", z, x): 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) } ||
+ (T_KWD("write") ~ IdParser) ==> { case (x, y) => Write(y) }
+
+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)))
+
+// 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)
+}
+
+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
+ 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_prog(name: String) : Env = {
+ val tks = Tok.fromFile(name)
+ val ast = Stmts.parse_single(tks)
+ eval_bl(ast, Map.empty)
+}
+
+
+//examples
+
+//eval_prog("loops.while")
+eval_prog("fib.while")
+
+
+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)
+}
+
+
+val test_prog = """
+start := XXX;
+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
+}
+"""
+
+
+
+def eval_test(n: Int) : Unit = {
+ val tks = Tok.fromString(test_prog.replaceAllLiterally("XXX", n.toString))
+ val ast = Stmts.parse_single(tks)
+ println(n + " " + time_needed(2, eval_bl(ast, Map.empty)))
+}
+
+List(1, 200, 400, 600, 800, 1000, 1200, 1400, 1600).map(eval_test(_))
+
+
+
+
+
+
+