# HG changeset patch # User Christian Urban # Date 1353482908 0 # Node ID cc3f7908b9428a5a7e4bc92b8594cc476df8dd48 # Parent a09ecb1e7384f95d05cb06f091df4b62fe7f6474 tuned diff -r a09ecb1e7384 -r cc3f7908b942 slides08.pdf Binary file slides08.pdf has changed diff -r a09ecb1e7384 -r cc3f7908b942 slides08.tex --- a/slides08.tex Wed Nov 21 02:34:37 2012 +0000 +++ b/slides08.tex Wed Nov 21 07:28:28 2012 +0000 @@ -570,8 +570,6 @@ \end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \mode{ \begin{frame}[c] @@ -585,6 +583,54 @@ \end{frame}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}While-Language\end{tabular}} + + +\begin{center} +\bl{\begin{tabular}{lcl} +$Stmt$ & $\rightarrow$ & $\text{skip}$\\ + & $|$ & $Id := AExp$\\ + & $|$ & $\text{if}\; B\!Exp \;\text{then}\; Block \;\text{else}\; Block$\\ + & $|$ & $\text{while}\; B\!Exp \;\text{do}\; Block$\bigskip\\ +$Stmt$ & $\rightarrow$ & $Stmt \;\text{;}\; Stmts$\\ + & $|$ & $Stmt$\bigskip\\ +$Block$ & $\rightarrow$ & $\{ Stmts \}$\\ + & $|$ & $Stmt$\\ +\end{tabular}} +\end{center} + + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\mode{ +\begin{frame}[c] +\frametitle{\begin{tabular}{c}An Interpreter\end{tabular}} + +\begin{center} +\bl{\begin{tabular}{l} +$\{$\\ +\;\;$x := 5 \text{;}$\\ +\;\;$y := x * 3\text{;}$\\ +\;\;$y := x * 4\text{;}$\\ +\;\;$x := u * 3$\\ +$\}$ +\end{tabular}} +\end{center} + +\begin{itemize} +\item the interpreter has to record the value of \bl{$x$} before assigning a value to \bl{$y$}\pause +\item \bl{\text{eval}(stmt, env)} +\end{itemize} + + +\end{frame}} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + \end{document} %%% Local Variables: diff -r a09ecb1e7384 -r cc3f7908b942 while.scala --- a/while.scala Wed Nov 21 02:34:37 2012 +0000 +++ b/while.scala Wed Nov 21 07:28:28 2012 +0000 @@ -4,57 +4,178 @@ // some regular expressions val SYM = RANGE("""ABCDEFGHIJKLMNOPQRSTUVXYZabcdefghijklmnopqrstuvwxyz_""") val DIGIT = RANGE("0123456789") -val ID = SEQ(PLUS(SYM)) ~ STAR(ALT(SYM, DIGIT)) - -val BTAG = SEQS("<", WORD, ">") -val ETAG = SEQS("") - +val ID = SEQ(SYM, STAR(ALT(SYM, DIGIT))) +val NUM = PLUS(DIGIT) +val KEYWORD = ALTS("skip", "while", "do", "if", "then", "else", "begin", "end", "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 = "}" // for classifying the strings that have been recognised abstract class Token case object T_WHITESPACE extends Token -case class T_WORD(s: String) extends Token -case class T_ETAG(s: String) extends Token -case class T_BTAG(s: String) extends Token -case class T_NT(s: String, rhs: List[Token]) 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[Rule[Token]] = - List((BTAG, (s) => T_BTAG(s.mkString)), - (ETAG, (s) => T_ETAG(s.mkString)), - (WORD, (s) => T_WORD(s.mkString)), + 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 T = Tokenizer(lexing_rules) +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 + -// width for printing -val WIDTH = 60 +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 () + } +} -def interpret(ts: List[Token], c: Int, ctr: List[String]) : Unit= ts match { - case Nil => println(Console.RESET) - case T_WHITESPACE::rest => print(Console.RESET + " "); interpret(rest, c + 1, ctr) - case T_WORD(s)::rest => { - val newstr = Console.RESET + ctr.reverse.mkString + s - if (c + s.length < WIDTH) { - print(newstr); - interpret(rest, c + s.length, ctr) - } - else { - print("\n" + newstr) - interpret(rest, s.length, ctr) - } - } - case T_BTAG("

")::rest => print("\n"); interpret(rest, 0, ctr) - case T_ETAG("

")::rest => print("\n"); interpret(rest, 0, ctr) - case T_BTAG("")::rest => interpret(rest, c, Console.BOLD :: ctr) - case T_BTAG("")::rest => interpret(rest, c, Console.UNDERLINED :: ctr) - case T_BTAG("")::rest => interpret(rest, c, Console.CYAN :: ctr) - case T_BTAG("")::rest => interpret(rest, c, Console.RED :: ctr) - case T_BTAG("")::rest => interpret(rest, c, Console.BLINK :: ctr) - case T_ETAG(_)::rest => interpret(rest, c, ctr.tail) - case _::rest => interpret(rest, c, ctr) +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 ==> ((s) => Var(s)) || + NumParser ==> ((i) => Num(i)) + +lazy val BExp: Parser[List[Token], BExp] = + (AExp ~ T_OP("=") ~ AExp) ==> { case ((x, y), z) => Bop("=", x, z): BExp } || + (T_KWD("true") ==> ((_) => True: BExp)) || + (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 } + +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))) + +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 p2 = "5 = 6" +val p2_toks = Tok.fromString(p2) +val p2_ast = BExp.parse_all(p2_toks) +println(p2_toks) +println(p2_ast) + +val p2a = "true" +val p2a_toks = Tok.fromString(p2a) +val p2a_ast = BExp.parse_all(p2a_toks) +println(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_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_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_toks) +println(p3b_ast) + + +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) } - -interpret(T.fromFile("test.html"), 0, Nil) + +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) +} + +def eval_bl(bl: Block, env: Env) : Env = bl match { + case Nil => env + case s::bl => eval_bl(bl, eval_stmt(s, env)) +} + +//println(eval_stmt(p3a_ast.head, Nil.toMap)) +//println(eval_stmt(p3b_ast.head, Nil.toMap))