--- a/progs/while1.scala Mon Jul 27 11:02:48 2020 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,221 +0,0 @@
-// 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(_))
-
-
-
-
-
-
-